Explanation

Given:

- Percentage of students who wore glasses: 20%

- Percentage of students who wore contact lenses: 30%

- Percentage of students who wore both glasses and contact lenses: 10%

Let's denote:

-A : Set of students who wore glasses

-B : Set of students who wore contact lenses

The formula for the union of two sets is given by:

Substitute the given values:

Explanation

To determine the fraction of the pizza that remains after 4 slices are eaten from a pizza divided into 10 equal slices, we can follow these steps:

1. Total slices in the pizza:

10 equal slices

2. Slices eaten:

4 slices

3. Slices remaining:

Subtract the slices eaten from the total slices to find the slices that remain:

10 - 4 = 6

4. Fraction of the pizza remaining:

The fraction of the pizza that remains after 4 slices are eaten out of 10 slices can be calculated as:

slices remaining / total slices = 6/10 = 3/5

Explanation

The range of a data set is defined as the difference between the maximum and minimum values in the data set.

It provides a measure of the spread or variability of the data.

Explanation

Given the information that the sum of two numbers is 35 and one number is 8 more than the other, we can set up a system of equations to solve for the numbers.

Let's denote the two numbers as  and , where:

 = one of the numbers

 = the other number

Given:

1. The sum of the two numbers is 35: 

x + y = 35

2. One number is 8 more than the other: 

x = y + 8

Substitute the value of  from the second equation into the first equation:

y + y + 8 = 35

2y + 8 = 35 

2y + 8 = 35 

2y = 27 

y = 13.5

Now, substitute the value of y back into:

x = y +8 

x = 13.5 + 8 

x = 21.5

Explanation

Given:

Total pages in the book = 300

Total days to finish the book = 10

Calculate the number of pages the student should read per day:

 300 pages / 10 days = 30 pages per day

Explanation

To solve the equation, we need to simplify both sides of the equation by expanding and combining like terms.

Then, we can isolate the variable.

1. Expand the expressions on both sides of the equation:

3x + 12 - 2 = 4x - 6 + 5

3x + 10 = 4x -1

2. Move all terms involving  to one side of the equation:

3x - 4x = -1 -10

-x = -11

3. Solve by dividing both sides by -1:

 x = -11/-1

x = 11

Explanation

To find the solution set for the inequality, we need to isolate by solving the inequality step by step.

1. Subtract 5 from both sides to isolate the term with :

4x + 5 - 5 < 9 - 5

4x < 4

2. Divide by 4 to solve for :

 x < 4/4 

x< 1

Therefore, the solution set for the inequality is.

This means that any value of less than 1 will satisfy the given inequality.

Explanation

Explanation

To find the range of a data set, we need to determine the difference between the maximum and minimum values in the set.

Given data set of student ages: 16, 17, 18, 16, 19, 20

1. The minimum age in the data set is 16.

2. The maximum age in the data set is 20.

3. To calculate the range, we subtract the minimum age from the maximum age:

Range = 20 = 16 = 4

Explanation

The fruit seller initially had 35 mangoes.

He sells 12 mangoes to one customer and 8 mangoes to another customer.

To find out how many mangoes he has left, we subtract the total number of mangoes sold from the initial number of mangoes.