Explanation

Step 1: Calculate the total marks needed for an average of 85 over 5 exams.

Total marks needed=Average×Number of exams

Total marks needed=85×5

Total marks needed=425

Step 2: Calculate the sum of the marks from the first four exams.

78+85+90+92=345

Step 3: Subtract the sum of the first four exam marks from the total marks needed.

Marks needed in the fifth exam=425−345

Marks needed in the fifth exam=80

Explanation

Subtract 7 from both sides:

3x+7−7<22−7

3x<15

Divide both sides by 3:

x< 15/3

​x<5

Explanation

Deserts have little vegetation and moisture to retain the heat absorbed during the day.

This lack of heat retention causes temperatures to drop rapidly at night.

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

Number of pizzas = 4 pizzas

The number of slices in each pizza = 8 slices

Total number of slices =  slices

4 x 8 = 32 slices

Next, we need to divide the total number of slices by the number of people to find out how many slices each person will get:

Number of people = 6 persons

Number of slices per person = Total number of slices / Number of people

Number of slices per person = 32/6 = 5 slices

Explanation

To find the cost of one pen, divide the total cost by the number of pens:

Cost of one pen = Total cost /Number of pens

Given:

Total cost for 5 pens = 125 rupees

Number of pens = 5

Cost of one pen= 125rupees / 5

Cost of one pen=25rupees

So, the cost of one pen is 25 rupees.

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 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 numbers between 20 and 30 are: 21, 22, 23, 24, 25, 26, 27, 28, 29.

Let's check each number to see if it is prime:

- 21 is not prime (divisible by 3 and 7).

- 22 is not prime (divisible by 2 and 11).

- 23 is prime (not divisible by any number other than 1 and 23).

- 24 is not prime (divisible by 2, 3, 4, 6, 8, and 12).

- 25 is not prime (divisible by 5).

- 26 is not prime (divisible by 2 and 13).

- 27 is not prime (divisible by 3 and 9).

- 28 is not prime (divisible by 2, 4, 7, and 14).

- 29 is prime (not divisible by any number other than 1 and 29).

The prime numbers between 20 and 30 are 23 and 29.

Now, we sum these prime numbers:

 23 + 29 = 52

Explanation

Given that two numbers are in the ratio of 6:7 and their sum is -52, we can determine the numbers as follows:

 let the two numbers be 6x and 7x.

The sum of these numbers should be -52:

6x + 7x = -52

13x = -52

Solving for x:

x = -52/13

x = -4

Therefore, the two numbers are 6x and 7x:

6 (-4) = -24

7 (-4) = -28

The numbers in the ratio 6:-7 that sum up to -52 are -24 and -28.