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How to Solve Percent Problems
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Solve simple percent problems.
Finding 100% of a number: Remember that 100% means the whole thing, so 100% of any number is simply the number itself:
100% of 5 is 5
100% of 91 is 91
100% of 732 is 732
Finding 50% of a number: Remember that 50% means half, so to find 50% of a number, just divide it by 2:
50% of 20 is 10
50% of 88 is 44

Finding 25% of a number: Remember that 25% equals 1/4, so to find 25% of a number, divide it by 4:
25% of 40 is 10
25% of 88 is 22

Finding 20% of a number: Finding 20% of a number is handy if you like the service you’ve received in a restaurant, because a good tip is 20% of the check. Because 20% equals 1/5, you can find 20% of a number by dividing it by 5. But you can use an easier way:
To find 20% of a number, move the decimal point one place to the left and double the result:
20% of 80 = 8 2 = 16
20% of 300 = 30 2 = 60
20% of 41 = 4.1 2 = 8.2
Finding 10% of a number: Finding 10% of any number is the same as finding 1/10 of that number. To do this, just move the decimal point one place to the left:
10% of 30 is 3
10% of 41 is 4.1
10% of 7 is 0.7
Finding 200%, 300%, and so on of a number: Working with percents that are multiples of 100 is easy. Just drop the two 0s and multiply by the number that’s left:
200% of 7 = 2 7 = 14
300% of 10 = 3 10 = 30
1,000% of 45 = 10 45 = 450
Make tough-looking percent problems easy
Suppose someone wants you to figure out the following:
Finding 88% of anything isn’t an activity that anybody looks forward to. But an easy way of solving the problem is to switch it around:
88% of 50 = 50% of 88
This move is perfectly valid, and it makes the problem a lot easier. As you learned above, 50% of 88 is simply half of 88:
88% of 50 = 50% of 88 = 44
As another example, suppose you want to find
Again, finding 7% is tricky, but finding 200% is simple, so switch the problem around:
7% of 200 = 200% of 7
Above, you learned that to find 200% of any number, you just multiply that number by 2:
7% of 200 = 200% of 7 = 2 7 = 14
Solve more-difficult percent problems
35% of 80 = ?
Ouch — this time, the numbers you’re working with aren’t so friendly. When the numbers in a percent problem become a little more difficult, the tricks no longer work, so you want to know how to solve all percent problems.
Here’s how to find any percent of any number:
Change the word of to a multiplication sign and the percent to a decimal.
Changing the word of to a multiplication sign is a simple example of turning words into numbers. This change turns something unfamiliar into a form that you know how to work with.
So, to find 35% of 80, you would rewrite it as:
35% of 80 = 0.35 80
Solve the problem using decimal multiplication.
Here’s what the example looks like:

So 35% of 80 is 28.
12% of 31 = 0.12 31
Now you can solve the problem with decimal multiplication:

So 12% of 31 is 3.72.
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How to Solve Percent Problems? (+FREE Worksheet!)
Learn how to calculate and solve percent problems using the percent formula.

Related Topics
- How to Find Percent of Increase and Decrease
- How to Find Discount, Tax, and Tip
- How to Do Percentage Calculations
- How to Solve Simple Interest Problems
Step by step guide to solve percent problems
- In each percent problem, we are looking for the base, or part or the percent.
- Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base
Percent Problems – Example 1:
\(2.5\) is what percent of \(20\)?
In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)
Percent Problems – Example 2:
\(40\) is \(10\%\) of what number?
Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).
Percent Problems – Example 3:
\(1.2\) is what percent of \(24\)?
In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)
Percent Problems – Example 4:
\(20\) is \(5\%\) of what number?
Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).
Exercises for Calculating Percent Problems
Solve each problem..
- \(51\) is \(340\%\) of what?
- \(93\%\) of what number is \(97\)?
- \(27\%\) of \(142\) is what number?
- What percent of \(125\) is \(29.3\)?
- \(60\) is what percent of \(126\)?
- \(67\) is \(67\%\) of what?
Download Percent Problems Worksheet
- \(\color{blue}{15}\)
- \(\color{blue}{104.3}\)
- \(\color{blue}{38.34}\)
- \(\color{blue}{23.44\%}\)
- \(\color{blue}{47.6\%}\)
- \(\color{blue}{100}\)
by: Reza about 3 years ago (category: Articles )
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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Calcworkshop
How to Solve Percent Problems? 13 Amazing Examples!
// Last Updated: January 20, 2020 - Watch Video //
Ratios and proportions help us in solving problems with percents .
Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)
Because a percent is the ratio (fraction) of one number to another.
In other words, its a number divided by 100.
What is most important to note is that our overall goal is to translate each problem into an algebraic expression by looking for keywords such as “of” and “is,” and then solve for the unknown variable.
First, we will look at how a percent is created by understanding it is simply a proportion:
Percents as a Proportion
And we will quickly see that most problems will follow a very simple Percents Formula, as Khan Academy so accurately states.
Together will look at how to change percents to fractions, percents to decimals, and decimals to percents for various problems.
Additionally, we will look at real-world examples, such as finding the percent of commission, the price of an item with a percent discount, change in population, as well as mixture problems.
Solving Percents (How-To) – Video
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Calculator Soup ®
Online Calculators

Percentage Calculator

Calculator Use
Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations.
How to Calculate Percentages
There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.
Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:
- Find P percent of X
- Find what percent of X is Y
- Find X if P percent of it is Y
Read on to learn more about how to figure percentages.
1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y
Example: What is 10% of 150?
- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 10%, X is 150, so the equation is 10% * 150 = Y
- Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y
- Do the math: 0.10 * 150 = 15
- So 10% of 150 is 15
- Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15
2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%
Example: What percent of 60 is 12?
- Convert the problem to an equation using the percentage formula: Y/X = P%
- X is 60, Y is 12, so the equation is 12/60 = P%
- Do the math: 12/60 = 0.20
- Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
- Converting 0.20 to a percent: 0.20 * 100 = 20%
- So 20% of 60 is 12.
- Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%
3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X
Example: 25 is 20% of what number?
- Convert the problem to an equation using the percentage formula: Y/P% = X
- Y is 25, P% is 20, so the equation is 25/20% = X
- Convert the percentage to a decimal by dividing by 100.
- Converting 20% to a decimal: 20/100 = 0.20
- Substitute 0.20 for 20% in the equation: 25/0.20 = X
- Do the math: 25/0.20 = X
- So 25 is 20% of 125
- Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125
Remember: How to convert a percentage to a decimal
- Remove the percentage sign and divide by 100
- 15.6% = 15.6/100 = 0.156
Remember: How to convert a decimal to a percentage
- Multiply by 100 and add a percentage sign
- 0.876 = 0.876 * 100 = 87.6%
Percentage Problems
There are nine variations on the three basic problems involving percentages. See if you can match your problem to one of the samples below. The problem formats match the input fields in the calculator above. Formulas and examples are included.
What is P percent of X?
- Written as an equation: Y = P% * X
- The 'what' is Y that we want to solve for
- Remember to first convert percentage to decimal, dividing by 100
- Solution: Solve for Y using the percentage formula Y = P% * X
Example: What is 10% of 25?
- Written using the percentage formula: Y = 10% * 25
- First convert percentage to a decimal 10/100 = 0.1
- Y = 0.1 * 25 = 2.5
- So 10% of 25 is 2.5
Y is what percent of X?
- Written as an equation: Y = P% ? X
- The 'what' is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
- Solution: Solve for P% using the percentage formula P% = Y ÷ X
Example: 12 is what percent of 40?
- Written using the formula: P% = 12 ÷ 40
- P% = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- So 12 is 30% of 40
Y is P percent of what?
- The 'what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
- Solution: Solve for X using the percentage formula X = Y ÷ P%
Example: 9 is 60% of what?
- Writen using the formula: X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- So 9 is 60% of 15
What percent of X is Y?
- Written as an equation: P% * X = Y
- (P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X
Example: What percent of 27 is 6?
- Written using the formula: P% = 6 ÷ 27
- 6 ÷ 27 = 0.2222
- Convert decimal to percent
- P% = 0.2222 × 100
- P% = 22.22%
- So 22.22% of 27 is 6
P percent of what is Y?
- Written as an equation: P% × X = Y
- (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
Example: 20% of what is 7?
- Written using the formula: X = 7 ÷ 20%
- Convert the percent to a decimal
- 20% ÷ 100 = 0.2
- X = 7 ÷ 0.2
- So 20% of 35 is 7.
P percent of X is what?
Example: 5% of 29 is what.
- Written using the formula: 5% * 29 = Y
- 5% ÷ 100 = 0.05
- Y = 0.05 * 29
- So 5% of 29 is 1.45
Y of what is P percent?
- Written as an equation: Y / X = P%
- Multiply both sides by X to get X out of the denominator
- (Y / X) * X = P% * X becomes Y = P% * X
- Divide both sides by P% so that X is on one side of the equation
- Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X
Example: 4 of what is 12%?
- Written using the formula: X = 4 ÷ 12%
- Solve for X: X = Y ÷ P%
- 12% ÷ 100 = 0.12
- X = 4 ÷ 0.12
- X = 33.3333
- 4 of 33.3333 is 12%
What of X is P percent?
- Multiply both sides by X to get Y on one side of the equation
- (Y ÷ X) * X = P% * X becomes Y = P% * X
Example: What of 25 is 11%?
- Written using the formula: Y = 11% * 25
- 11% ÷ 100 = 0.11
- Y = 0.11 * 25
- So 2.75 of 25 is 11%
Y of X is what percent?
- Solution: Solve for P% using the percentage formula P% = Y / X
Example: 9 of 13 is what percent?
- Written using the formula: P% = Y / X
- 9 ÷ 13 = P%
- 9 ÷ 13 = 0.6923
- Convert decimal to percent by multiplying by 100
- 0.6923 * 100 = 69.23%
- 9 ÷ 13 = 69.23%
- So 9 of 13 is 69.23%
Related Calculators
Find the change in percentage as an increase or decrease using the Percentage Change Calculator .
Solve decimal to percentage conversions with our Decimal to Percent Calculator .
Convert from percentage to decimals with the Percent to Decimal Calculator .
If you need to convert between fractions and percents see our Fraction to Percent Calculator , or our Percent to Fraction Calculator .
Weisstein, Eric W. " Percent ." From MathWorld -- A Wolfram Web Resource.
Cite this content, page or calculator as:
Furey, Edward " Percentage Calculator " at https://www.calculatorsoup.com/calculators/math/percentage.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
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Unit 3: Lesson 6
- Percent word problem: recycling cans
- Rates and percentages FAQ
Percent word problems
- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text
How do we calculate percentage?

- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
- All solvers
- Arithmetics
- Determinant
- Percentages
- Scientific Notation
- Inequalities

Enter the value(s) for the required question and click the adjacent Go button.
PERCENTAGES
This section will explain how to apply algebra to percentage problems.
In algebra problems, percentages are usually written as decimals.
Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?
The number of questions correct is indicated by:

Ethan got 44 questions correct.
Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.
Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

Darrel’s grade for the course is an 89.6, or a B+.
b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?
The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.
So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.
Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.
a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).
Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

b. Simplify the equation.

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.
c. Solve the equation when the sale price is $97.

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)
The following diagram is meant as a visualization of problem 3.

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount
Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.
Study Tip: Remember to use descriptive letters to describe the variables.
CHAPTER 1 REVIEW
This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.
Signed Numbers:
Informal Rules:
Adding or subtracting like signs: Add the two numbers and use the common sign.

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

Study Tip: All of these informal rules should be written on note cards.
Introduction to Variables:
Generate a table to find an equation that relates two variables.
Example 6. A car company charges $14.95 plus 35 cents per mile.


Simplifying Algebraic Equations:

Combine like terms:

Solving Equations:
1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

Applications of Linear Equations:
This section summarizes the major skills taught in this chapter.
Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.
a. Create a table to find the equation that relates cost and minutes.

c. If the call costs $23.50, how long were you on the phone?

If the call costs $23.50, then you were on the phone for approximately 79 minutes.
Literal Equations:
A literal equation involves solving an equation for one of two variables.

Percentages:
Write percentages as decimals.
Example 11. An English teacher computes his grades as follows:

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

Sue has to get a 78.36 in the final exam to get an 80 for the course.
Study Tips:
1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.
Math Topics
More solvers.
- Add Fractions
- Simplify Fractions

How to Solve Percentage Problems Like A Math Expert in 2023
You might have noticed two different sale labels on two different shops on the same item. Like one offers a 50% discount, and the other offers a 60% discount with a minor difference in MRP. Let’s take an example of it:
Shop A offers a 50% discount on Rs 500 items, and shop B offers a 60% discount on Rs 600 items. You might be attracted to the Shop A offer because it has less MRP and a nice % discount.
Wait, do you know that Shop B offers a much better offer. How? Let’s know it with understanding about how to solve percentage problems?

Calculation of MRP of shop A
Table of Contents
You can see that Shop A sells the item at a 50% discount on MRP of 500 Rs that means 500 x (50/100) = 250. Now, subtract 250 from the original MRP, that is, 500 – 250 = 250. It means Shop A offers the item at 250 Rs.
Calculation of MRP of shop B
You can see that Shop B sells the item at a 60% discount on MRP of 600 Rs that means 600 x (60/100) = 360. Now, subtract 360 from the original MRP, that is, 600 – 360 = 240. It means Shop B offers the item at 240 Rs.
This implies that shop B offers the item on the less MRP. Now, you can understand how important it is to know the percentage concept. Don’t know how to solve percentage problems?
Do not worry; we have mentioned all the necessary details about how to solve percentage problems. Let’s check all the details and save more money.
What is the percentage?
In mathematics, the percent or percentage is the ratio or the number expression that is denoted as a fraction of 100. In Latin, it means ” by a hundred. ”
It is denoted using the symbol “%.” But the abbreviations used to denote percentage are “pct,” “pct.” and “pc”. Moreover, the percentage is the pure number that does not have any dimension and unit of measurement.
The basic percentage formula is:

Is it important to learn about percentage?
Yes, it is! There are several applications where the concept of percentage is used, such as:
Sports: It is used to determine how many percentages of a sports person’s performance have improved. Like, we say, there is an 80% improvement of a batman’s shots. It means that batman hit 8 balls out of 10 balls.

Shopping: Sale is the major factor of shopping where the percentage’s concept is used. Like there is a 25% discount on the 100 Rs item. It means the item will be sold at the MRP of 75.

Packed food nutrients: You have noticed that the packed food items have a % table at the packet’s backside. It denotes how many percent the particular nutrient has in the food with respect to the 100 like a pickle has 20% sodium. This denotes that if you take 1 teaspoon of pickle, it has 1/5 of sodium of overall nutrient elements.

Cell phone battery usage: Suppose you have to visit out of the station and you check your cell phone battery that shows only 10% battery value. It means that you need to charge it before living from home. Otherwise, it will not last long, even upto 1 hour.
The interest rate offered by the bank: When you deposit or borrow money from the bank, it always declares a certain interest rate on the money. If you deposit $ 5,000/ year and the bank offers a 7% interest rate per year. It means that you will get the $350 interest at the end of the year, and your amount will be $5,350.

Apart from this, there are several applications where the concept of percentage is used. Therefore, it is always worthy of learning the concept of percentage. So, now let’s understand the method to solve percentage problems.
How to solve percentage problems?
Key points:.
The percentage is always 100. So we find out the percentage of any number from 100 percent. Always know that 100% is absolute, so 100 percent of any number is always the whole number. For example, 100% of 10 numbers is 10; similarly, 100 % of 20 numbers is 20.
The next point to learn on how to solve percentage problems is that if you have to find the 50 % of any number, you just have to divide it by 2 only if you find 50 % (that is 50/100 is always 1/2). Let’s understand it through an example-
Suppose students have to find out the 50% of the 70 is 70/2 = 35
Another example can be 50 % of 60 = 60 /2 = 30.
As the 50 percent of any number is half similarly, the 25% of any number shall be 1/4. So you have to divide by 4 to find the one-fourth of any number.
Let’s take another point, suppose you have to find out the 20% of any number then it will always be one-fifth of the number. So if you have to find the 20 % of 80 thus, it will be as follows –
80 x 1/5 = 16.
Follow the following steps to solve the percentage problems:
- Determine the whole or the total amount.
- Divide the amount to express it as a percent . In maximum cases, you need to divide the smaller amount by the higher amount.
- Multiply the result with 100.
Let’s take an example of it:
Suppose you have 60 marbles. 15 of those marbles are red; what percent of all marbles are red?
- The obtained value is 15, and the maximum value is 60.
- As per the given formula:

The number of red marble = (15/60) x 100
(1/4) x 100 = 25%
It means that you have 25% red marbles.
Let’s take one more example of it:
Suppose you bought an item of price $6.00, and you paid $7.00. Calculate the sales tax rate of the city?
We know that the sales tax might be a certain percentage of the original price, so let’s figure out the actual tax. The actual tax was:
7.00 – 6.00 = 1.00
Now, the sales tax would be a percentage of the cost:
1.00 = (x)(6.00)
Solving the value of x , you will get:
1.00 ÷ 6.00 = x = 0.1666666 = 16.666%
The sales tax rate was 16.66%.
Let’s understand percentages with more practice questions!
Suppose we have a question in which you need to find out the 60 percent of 200. Let’s understand it through examples –
So firstly you must learn that percentage is written as % and it means per one hundred.
Thus we write 60 percent of 200 as follows –
60 % of 200
= (60 /100) x 200
Now let’s take another example. Suppose students have a question that you have got 40 marks out of 80, so now you have to find out what is the percentage of 40 marks out of 80 marks.
Let’s learn how to solve percentage problems by the x method.
So let’s take the answer is X.
So we will have the equation –
X% of 80 = 40
(X / 100) x 80 = 40
40/80 = X/100
X = 100 x 40/ 80
X = 4000/80
X = 50
Thus the answer is 50%.
Let’s take another high-level example
Suppose students have to compute your grades for your course as follows –
Suppose you have scored the following –
This is a more tough situation in how to solve percentage problems. Follow the following steps-
Firstly you have to write all the percentages in decimals, so we all know that we need to divide the number of percentage by 100 as the percent means 100 thus, you will do the following
So the next step is to add all these decimals, and if you add these decimals, you will get 100 as the answer because the percentage is always 100.
The next step in how to solve percentage problems is to multiply the score with respective decimals. Follow the given equation –
Let’s take the answer as Z.
Z = 0.05 x 80 + 0.1 x 70 + 0.85 x 95
= 4 + 8 + 80.75
= 92.75
Thus the total marks in the percentage you have got is 92.75.
Percentage problems are the easiest mathematical problem . But still, many students face difficulty in solving percentage problems because they fail to understand the concept.
But if you follow the above-mentioned steps and ways, and you easily solve the problems. We hope this blog would have helped you solve all kinds of percentage problems.
If you are still struggling with percentages homework queries or any other math problems, you can contact our expert panel anytime and resolve all your queries. Get the best math homework help from the experts.
Frequently Asked Questions
How do you calculate percentages quickly?
To find the given percent decimal form, you need to move the decimal to the two places right. For instance, you can write a decimal form of 10% as 0.1. If you calculate what 10% of is, say, 300 seniors, you can multiply the seniors’ number by 0.1.
What is percentage of a number?
In math, a percentage is a ratio or number, which describes a fraction of 100. The symbol “%” denotes percent. For example, 45% is equivalent to the decimal point 0.45, or 45/100.
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How to solve the percentage problems
1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y Convert the problem to an equation using the percentage formula: P% * X = Y
Solving problems with percentages
Word Problems on Percentage 1. In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks. 2. An alloy contains 26 % of copper. 3
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To solve problems with percent we use the percent proportion shown in Proportions and percent.
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Percentage (How to Calculate, Formula and Tricks)
To solve percent problems, you can use the equation, Percent Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.
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Solve simple percent problems Finding 100% of a number: Remember that 100% means the whole thing, so 100% of any number is simply the number
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Tutorial of The Best Methods on How to Solve Percentage

Mathematics plays an important role in our daily life as we all use math on a daily basis either while buying any goods or for some other thing etc. Despite its leading role, many students just don’t want to study math because they consider it tricky and complex. But if you know the concepts then you will understand how easy math is. So what we need to do is to understand the rationale of mathematical concepts instead of cramming it.
As there are n number of concepts and questions and it is not possible to cram each and every question. Thus one should always understand the concept. Many students face difficulty in solving percentages as they don’t know what a percentage is and how it is solved. So follow this tutorial on how to solve percentage problems steps wise and excel in math and improve your grades. Master the math by following our given instructions on solving percentage problems.
What is a Percentage?
Table of Contents
Before leading how to solve percentage problems learn what is a percentage. Suppose you have 10 chocolates and you have 4 chocolates to your friend and now you want to learn what is the relation of 4 chocolates with the total 10 chocolates and you can write such relation in percentage basis. So here we use the percentages in mathematics. Thus, a percentage is basically a method used for computing how much of something is there in relation to that entire something. Don’t think that usage of percentages is restricted to mathematics as an education rather it is used on a daily basis in everyday situations.
Understand about percentages
Percentage is written as ‘%’ in mathematics.
Percentage in numeric value is always 100 this is why we take the number as 100 and the number with which we want to find out the relation must be less than 100.
Next point to know in percentages is that it is absolute that is 100 %.
For example 100% of 20 is 20.
Learn following percentages – How To solve percentage
100 percent of any number will always be the exact number. It shall be the absolute number.
When you have to find out the 50% of any number then you just have to divide the actual number by 2 then you will get the percentage.
For example, if you need to find out the 50% of the number 50 then divide the 50 by 2 and then you will get the answer that is 50/2 = 25.
75% is ⅔ of any number. So if you have to find out the 75% of any number then you just have to multiply the number by ⅔.
10% of any number shall be 1/10th of the number so if you have to find out the 10% of any number then divide the number with 10. For example if you need to find the 10% of 50 then the answer shall be 50/10 that is 5.
Steps : How To solve percentage problems
Let’s learn the steps for solving percentage through examples –
Example 1 – how to solve percentage problems
So the first step is to write down the number of which you want to find out the percentage. Suppose you need to find the 70 % of 200 then the number is 200 and percent is 70 so you have to write down the percentage 70 / 100.
Thus the next thing to learn in how to solve percentage is that you will write the equation in following manner –
70% of 200
Of means the multiply which is written as ‘x’.
70/100 x 200
= 140
Hence, the answer is 140.
Example 2 – how to solve percentage problems
Now let’s learn how to solve the percentage through x method whereby we will take the result as x and then we will find the value of x accordingly.
So let’s assume the answer is X and you need to find the x% of 200 and the answer is 50 this we will have the following equation –
X% of 300 = 50
Now write the % as 1/100 and of as x thus we will have the following result –
X x 1/100 x 200 = 50
X x 2 = 50
X = 50/2
Thus 50 is the 25 percent of 200.
Example 3 – how to solve percentage problems
Suppose you have to find the marks percentage on the basis of following information –
Math – 75 out of 100
Science – 90 out of 100
English – 65 out of 100
Social science – 80 out of 100
In order to solve this percentage problem, you first have to add all the marks then we will get the following answer
X = 75 + 90 + 65 + 80
= 310
Thus total marks you have got is 310 and the total number of marks shall be 400 as one subject is of 100 marks and there are 4 subjects. Thus the person has got 310 out of 400.
So let’s take the percentage as x%. Thus, we will have the following equation –
X% of 400 is 310
It can be written as –
X x (1/100) x 400 = 310
X x 4 = 310
X = 310/4
= 77.5
Thus the person has got 77.5%.
Percentage seems tough initially but it becomes a mind game with the practice and if you know how to solve percentage problems. if you know how to solve the percentage. So if you are struggling with percentages then follow the given steps and excel in percentages. If you still face difficulty in solving percentages then you can contact our expert team 24 by 7 for providing you immediate math homework answers . Get the best help with me my homework math .
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How to Equip Your Team to Problem Solve Without You
- Luis Velasquez
- Kristin Gleitsman

Stop shielding your team from challenges and responsibilities.
In trying to “protect” their teams, many managers become what the authors refer to as “umbrella managers”: well-intentioned leaders who want to protect their teams from all inclement organizational weather. But this type of leadership comes with a heavy price for the manager, the team, and the organization. Many individuals leading highly sophisticated teams for the first time need help to figure out the balance between supporting their teams and delegating effectively. The authors present several key mental shifts umbrella managers should make to move from protecting their employees to supporting them.
Susan,* a client of Luis’ and a mentee of Kristin’s, managed her team with a fundamental belief that it was her job to “protect” them. Her belief was grounded in good intentions. She wanted her team to be happy and successful in a highly demanding and fast-moving organization. However, her approach constantly put her in the position of intercepting challenges, wanting to become a shield for her team .
Perhaps this behavior endeared Susan to her team initially, but it had other unintended consequences, especially as the team’s scope of responsibilities grew. Her peers and cross-functional colleagues didn’t see her as collaborative, partly because she was often perceived as a blocker. Her behavior led her team to adopt a disempowered stance, and they became dependent on her to fight their battles. Worse, it put a lot of pressure on her to be present in all major decisions. As her overwhelm mounted, her performance slipped, both in terms of her ability to stay on top of key projects and to show up at meetings with a calm, clear perspective. Ultimately, the behavior caused senior leadership to view her as volatile and not in control.
We call leaders who engage in this kind of behavior “umbrella managers”: well-intentioned leaders who want to protect their teams from all inclement organizational weather. But this type of leadership comes with a heavy price for the manager, the team, and the organization:
- The umbrella manager feels personally responsible for every decision. Their ability to stay on top of all details is unrealistic; managers can’t do it all . And their sense of overwhelm rapidly increases. As a result, the team becomes passive and complacent in their decision making. The manager becomes a bottleneck, slowing decisions and frustrating would-be collaborators.
- Team members don’t benefit from learning to navigate the storm themselves, resulting in reduced employee development. They’re not positioned to form strong cross-functional relationships and therefore miss out on having higher organizational visibility and impact.
- With team members’ inability to navigate independently, the organization experiences reduced productivity and innovation capability from the team. The capacity to be nimble and adapt to changing circumstances in these organizations becomes almost impossible, resulting in the team rigidly holding onto outdated plans, wasting precious time and resources.
In our experience, this behavior is not uncommon in emerging leaders. Many individuals leading highly sophisticated teams for the first time need help to figure out the balance between supporting their teams and delegating effectively.
Shift your thinking
We recently caught up with Susan and asked about the “lightbulb” moment that led her to stop protecting her employees and start supporting them:
As I progressed in my career and began to manage more senior staff, it became increasingly clear that I needed to put away my umbrella and look for more effective and scalable ways of helping the managers on my team navigate challenges. I let go of the need to protect my employees and adopted a different mental model that more closely resembles handing out rain ponchos than opening an umbrella. Instead of putting myself between my reports and difficulty, I now support them by providing the tools they need to navigate these challenges independently.
To move from protecting your employees to supporting them, you need to make a few key mental shifts:
Face your fears directly.
The first step is understanding what beliefs underpin your current behavior. Where does your instinct to “protect” come from? Do you worry your employees will crumble under pressure and, as a result, make you look bad? Do you believe that their wrong decisions will compromise project outcomes and jeopardize their own success? Are you concerned that your value to your team depends on your ability to represent all aspects of their work fully? Ask yourself if other leaders in the organization are operating under the same assumptions. Challenge yourself to figure out what would need to be true in order for you to let go of this underlying belief. Additionally, ask yourself how your current approach might be harming your team.
Assume your employee can solve the problem.
By empowering your employees to solve their own problems, you can demonstrate your trust and confidence in the team’s abilities. For example, when people raise a challenge, they often don’t need help finding the solution — they either have one already or can come up with one by talking the challenge through with a trusted partner. You can turn yourself into that partner to improve your leadership effectiveness and avoid offering solutions too quickly. Doing so also encourages team members to think independently and come up with creative solutions to issues. To help them identify workable solutions and pick the right course of action, consider asking, “What options do you have?”
Embrace short-term stumbles for long-term gains.
Short-term stumbles provide learning experiences and opportunities; they can uncover weaknesses, areas of opportunity, and improvement. Allowing your team to “fail” (and learn) independently is a faster path to growth and long-term success than ensuring the short-term outcomes are well controlled.
For Susan, this realization was central to her realization that she was stifling her team. As she put it:
Early in my career, I thought the objective as a manager was to ensure a good outcome for every situation, large or small. However, when I moved to manage a larger organization, I had to get clear on what the truly high-stakes decisions were and help myself and the team build capabilities around recovering from small setbacks or missteps. This perspective allowed me to let go of many of the decisions I had been making, which gave me more time to coach emerging leaders on the team and for higher-level strategic thinking.
Lean more on your leadership strengths.
As leaders grow and their scope of responsibilities expands, their functional knowledge becomes less relevant as leadership skills take priority. Many managers struggle with this identity shift. They worry that if they’re not personally on top of all the details, they’ll be perceived as ineffective when in fact the opposite is true.
Stop chasing down every detail and free up time for activities like figuring out which decisions are critical, clarifying “what good looks like,” and getting alignment with your peers and other parts of the organization.
Empower your team
Once you’ve adjusted your mindset about how you support your employees, you can start to take action:
Provide your team support and tools for navigating challenges.
Whether the issue is technical or interpersonal, your job is to help your team develop options for handling the situation now and in the future. When an employee brings up a challenge, ask what kind of support would be helpful, but avoid putting yourself at the center of the challenge. Sometimes information and context gaps need to be closed, and the solution can be as simple as directing your team member to the right person to talk to.
Other times, you might find yourself carrying around a huge amount of company- or domain-specific knowledge that needs to be transferred. In these cases, there’s no way around spending the time it takes to bring your team member up to speed. However, when you couple this time investment with the additional expectation that your team member will create reference documentation for future members, you reinforce learning and build a stronger knowledge base for your team.
That’s not to say that you should never play a role in navigating challenges; in fact, managers are often better positioned to see the systematic forces creating the challenge. If a systems-level challenge is best addressed at a higher level in the organization, you must work with your leadership and/or peers to find solutions at a systems level. For example, a lack of clarity on roles and responsibilities can cause persistent friction between teams, and misaligned goals can unnecessarily bring different parts of the organization into conflict and create power struggles. In these cases, the leader has an essential role to play in removing ambiguity, finding alignment, and prioritizing solutions.
Help your team embrace discomfort and maintain perspective.
It’s never comfortable to navigate new challenges — even the most emotionally resilient among us still have moments of insecurity when stepping outside our comfort zone. However, you can provide a few mental models to support your team and encourage them to tackle difficult situations. For example:
- Create a “safe-to-try” team environment and embrace a growth mindset
- Model approaching situations with curiosity instead of fear
- Reduce guesswork by clearly communicating assumptions and needs
When things go wrong, model a solutions-oriented, optimistic mindset.
Leaders who model optimism set a positive tone in the workplace, empowering team members to recover from setbacks. If you want your team to navigate challenges independently, the worst thing you can do in the face of a setback is look for who to blame. Developing the organizational muscle to pull together to overcome setbacks is crucial. And while blame is not helpful, team retrospectives can help the team collectively get better at anticipating and avoiding similar setbacks in the future, creating a sense of shared accountability.
For Susan, transitioning from protecting to supporting her team was transformational. Reframing the value you bring to the organization, shifting from doing to coaching, and focusing on creating the right team environment and processes instead of concentrating solely on individual outcomes are all foundational to this transition. Getting out of the middle makes space for the perspective needed to see organizational context more clearly and spend the requisite energy on addressing systems-level challenges. Putting away the managerial umbrella and fitting your organization with ponchos is not easy, but the payoff is worth it.

- Luis Velasquez , MBA, Ph.D. is an executive coach who works with senior leaders and their teams to become more cohesive, effective, and resilient. He is the founder and managing partner of Velas Coaching LLC , a leadership facilitator at the Stanford University Graduate School of Business, a former University professor, and research scientist. Connect with him on LinkedIn.
- KG Kristin Gleitsman , PhD, is the Vice President of Discovery Research at Veracyte, a pioneering global diagnostics company. She has spent nearly a decade building and leading teams in the biotechnology sector.
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How To Begin Solving Our Higher Education Problem | Opinion
Society's expectation for students is to go to college for four years, apply for an internship, get a job, and work. And if life was was that simple, all would be well. But the reality is that everyone has his/her own issues, and unforeseen circumstances routinely arise. College is a lengthy, expensive process that everyone experiences differently.
For myself, I always knew where I wanted to go and wanted to be. And for the most part, I had an execution plan.
During my time at Hofstra University, I stumbled upon a media opportunity with Siruis XM for the recent Los Angeles-hosted Super Bowl. I told my sports reporting professor that I would be missing class due to work, and I offered to make up the work in advance.
He curtly responded: "If you go to L.A., you will fail my course."
I was thus forced to decide if this particular class or the hands-on experience at the Super Bowl was more worthwhile to my goals and my career.
I decided to go to the Super Bowl.
The entire time I was gone, my classmates told me I was mocked, and made fun of, by my professor.
The extra hard work I had to put in to leave that course with a decent grade was beyond frustrating. The entire semester, I had also been ghost-writing for a friend who had been published in high-profile outlets with my writing, but apparently that writing wasn't good enough for a decent grade in class. For instance, a profile piece for which I got a "67%" grade in class brought New England Patriots owner Robert Kraft and many others to tears.
Simply put, the treatment I got for being a working student was sad. The whole ordeal was an eye-opener for me.
Another concern was when I had to take a mandatory LBTQ+ class. I didn't mind taking the course, but I did mind the mandatory assignments that came with it. The homework assignments of reading manga lesbian pornography were unbearable. I simply did not feel like watching or reading pornography, so I failed the class.
But I have to ask: Since when did it become acceptable to force pornography onto students? Does any semblance of ethics and morality exist anymore on campus? Related, clubs and fairs attempting to persuade students to come out surely must have some boundaries and restrictions. I support being proud of one's identity, but there is no need to persuade anyone to reconsider her sexuality on the way to Starbucks . Schools need to set boundaries on campus.

I also took a final exam with this essay prompt: "Prove in ___ amount of words or less why [former President Donald] Trump is a dictator." Like many 19-year-olds studying communications, I did not have a strong political opinion at the time. Despite this, I could not come close to proving that for the very simple reason that I do not believe America comes close to resembling a dictatorship. The fact that we have the freedom to even suggest a prompt like that proves that we do not live under a dictator.
And, surprise! The students who were not able to "prove" that wildly tendentious statement received a bad final grade—or even ended up failing.
So I have realized we have many serious issues now plaguing college campuses. Here are just a few that stand out, based on my own experience.
The first issue is professors who look down upon working students. The skills that students acquire by working directly with professionals allow them to achieve more success after graduation. Colleges spend so much effort ensuring that their students have work after graduation, but when a current student is working it seems to be an issue. How many people have had to balance work and school? What about students who have bills to pay and aren't fortunate enough to sacrifice everything to receive an education? Many graduate school programs offer courses fully online; why can't undergraduate programs offer the same? My dean and multiple professors told me it was more worthwhile to simply transfer or take a year off, instead of making classes more accessible while I was working. This is unacceptable.
The second issue is that far too many professors try to brainwash impressionable students. Students choose a major and sign up for courses with the intention to master a certain craft and skillset. It is very uncomfortable to get into political discussions with one's professor, knowing that he or she necessarily determines grades. Teaching is a profession, and students pay for their university education. Professors should separate their business and personal matters. The same way students do not project their personal issues during class time, professors should not do so either.
Finally, college is not easy, fun, or cheap. The stigma that college is a waste of time is likely due to the fact that it indeed has become a huge waste of time for many students. For far too many, it lives up to its poor reputation. College is, at its core, an educational institution that should be predicated upon unbiased teaching.
In short, the higher education needs to become rational again.
Emily Austin is a sports reporter and activist. Twitter: @emilyraustin .
The views expressed in this article are the writer's own.

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Simply move the percent sign from one number to the other and flip the order of the numbers. Suppose someone wants you to figure out the following: 88% of 50 Finding 88% of anything isn't an activity that anybody looks forward to. But an easy way of solving the problem is to switch it around: 88% of 50 = 50% of 88
Solution: Use the following formula: Base = Part ÷ Percent = P a r t ÷ P e r c e n t → → Base = 40 ÷ 0.10 = 400 = 40 ÷ 0.10 = 400 40 40 is 10% 10 % of 400 400. Percent Problems - Example 3: 1.2 1.2 is what percent of 24 24? Solution: In this problem, we are looking for the percent. Use the following equation:
The word "of" means multiply. The word "is" means "=". Translate: 92% of a number is 56 You get: (92/100)x = 56 or as decimals 0.92x = 56 Then solve for x. 2) Proportion method. You will often see this described as "is" over "of" = "percent" over 100. The number associated with "is" in your problem is the 56.
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Using the percentage formula, it is easy to figure out how to solve percentage problems quickly. Remember the general algebraic formula for percentage is: {eq}\% \times W = P {/eq}....
Percents as a Proportion And we will quickly see that most problems will follow a very simple Percents Formula, as Khan Academy so accurately states. Together will look at how to change percents to fractions, percents to decimals, and decimals to percents for various problems.
Convert the problem to an equation using the percentage formula: Y/X = P% X is 60, Y is 12, so the equation is 12/60 = P% Do the math: 12/60 = 0.20 Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage. Converting 0.20 to a percent: 0.20 * 100 = 20%
Percent word problems. CCSS.Math: 6.RP.A.3, 6.RP.A.3c. Google Classroom. Problem. 2 % 2\% 2 % 2, percent of the students at Hamilton Middle School have red hair. There are 700 700 7 0 0 700 students at Hamilton Middle School. How many students at Hamilton Middle School have red hair?
Content Problems are below Percent Problems from Actual SAT's: Question Number 1 CONTENT PROBLEM . 25% of 100 is how much? 25% = . 25 .25 *100=25: Question Number 2 CONTENT PROBLEM . 3% of 10 is how much? 3% = .30.30 *10=3. Question Number 3 CONTENT PROBLEM . 150% of 10 is how much? 150% = 1.50
c. Solve the equation when the sale price is $97. The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.) The following diagram is meant as a visualization of problem 3. The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So
Follow the following steps to solve the percentage problems: Determine the whole or the total amount. Divide the amount to express it as a percent. In maximum cases, you need to divide the smaller amount by the higher amount. Multiply the result with 100. Let's take an example of it:
algebratesthelper 11.8K subscribers John Zimmerman, http://www.algebratesthelper.com explains how to solve percent problems using an equation; In this lesson, students learn to find a percent...
STEP 1: Change the percentage to a decimal. Remove the % sign from the 20% and drop a period in front of the 20 so we have .20. We are allowed to do this because when we are finding percents, we are really multiplying a decimal number against another number.
Word Problems on Percentage. 1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y Convert the problem to an equation using the percentage formula: P% * X = Y
How to solve percentage math problems - Solved Examples on Percentage 1. In an election, candidate A got 75% of the total valid votes. 2. A shopkeeper bought. ... Solving Percent Problems (Sections 2. When you are doing actual math, you need to use actual numbers. Percents, being the values with a percent sign tacked on, are not technically ...
The following percentage calculator will make it very easy to solve all your percentage word problems. Read your problem carefully and just enter the order now. Calculate percentages with Step. In this lesson, we will work through two percentage word problems to give you more experience solving multi-step problems with percentages.
To solve percent problems, you can use the equation, Percent Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = Percentage (How to Calculate, Formula and Tricks) Find the percentage of the original or real number. In this case, it's 500.
Percentage Increase and Decrease Word Problems To find 40%, first find 10% and then multiply it by 4. 10% is found by dividing the number by Explain math questions If you're ever stuck on a math question, remember that you can always ask for help.
Social science - 80 out of 100. In order to solve this percentage problem, you first have to add all the marks then we will get the following answer. X = 75 + 90 + 65 + 80. = 310. Thus total marks you have got is 310 and the total number of marks shall be 400 as one subject is of 100 marks and there are 4 subjects.
However, you can provide a few mental models to support your team and encourage them to tackle difficult situations. For example: Create a "safe-to-try" team environment and embrace a growth ...
And if life was was that simple, all would be well. But the reality is that everyone has his/her own issues, and unforeseen circumstances routinely arise. College is a lengthy, expensive process ...
Expert Answer. From the given data,p = 85% or 0.85q = 1 - p = 1 - 0.85 = 0.15Number of students randomly selected (n) = 6a) The probability that all of these six stud …. Problem 5: Use Mega-Stat to solve this problem A report on high school graduation stated that 85 percent of high school students graduate. Suppose 6 high school students are ...
In Summary. •The 22-year-old had struggled with an ankle injury after coming back from Qatar and then found it tough to get game time. •Foden's return to form is timely for City, after a ...