Question

Jacinta studied a function and found that when X was 1, why was one; when X was 2, y was 4; and when X was 3, y was 9. Make a table of x, Y pairs for this function.

Answer 1

Before the clowns arrived, only 35% of the children had happy faces. If 91 children did not have happy faces, how many children were there in all?

Answer 2

Max was delighted when he found that he had correctly answered 38 of the 40 questions. What percent of the questions had he answered correctly?

Answer 3

Compare 2a to a squared if a is a whole number.

Answer 4

Simplify 8 and 1/3 over 100

Answer 5

Write the prime factorization of 17,640 using exponents

Answer 6

The radius of a circle is 4 meters. Use 3.14 for Pi to find the circumference if the circle.

Answer 7

The radius of a circle is 4 meters. Use 3.14 for Pi to find the area of the circle.

Answer 8

Use a unit multiplier to convert 0.98 L to milliliters

Answer 9

The team's ratio of games won to games played was three to four. If the game played 24 games, how many games did the team fail to win?

Answer 10

X | Y
--|--
1 | 1
2 | 4
3 | 9

Answer 11

Let's call the total number of children "x".

We know that 35% of the children had happy faces, which means that 65% did not have happy faces.

If 91 children did not have happy faces, we can set up an equation to solve for x:

65% of x = 91

To solve for x, we can divide both sides by 65% (or 0.65 as a decimal):

x = 91 ÷ 0.65

x ≈ 140

Therefore, there were approximately 140 children in all.

Answer 12

We can start by using the formula:

percent = (part/whole) x 100%

In this case, the "part" is the number of questions Max answered correctly, which is 38. The "whole" is the total number of questions, which is 40.

So, we can plug those values into the formula:

percent = (38/40) x 100%

Simplifying the fraction, we get:

percent = (19/20) x 100%

To express this as a percentage, we can multiply by 100%:

percent = 95%

Therefore, Max answered 95% of the questions correctly.

Answer 13

If a is a whole number, then we can look at a few examples to compare 2a and a squared:

- If a = 1, then 2a = 2 and a squared = 1. In this case, 2a is greater than a squared.
- If a = 2, then 2a = 4 and a squared = 4. In this case, 2a is equal to a squared.
- If a = 3, then 2a = 6 and a squared = 9. In this case, a squared is greater than 2a.

So, it depends on the value of a. If a is a small whole number, then 2a will be less than a squared. If a is a larger whole number, then a squared will be greater than 2a.

Answer 14

To simplify 8 and 1/3 over 100, we should first convert the mixed number to an improper fraction:

8 and 1/3 = 25/3

Then we can write the expression as a fraction over 100:

25/3 ÷ 100

To divide by 100, we can simply move the decimal point two places to the left:

25/3 ÷ 100 = 25/300

To simplify this fraction, we can divide both the numerator and denominator by 25:

25/300 = 1/12

Therefore, 8 and 1/3 over 100 simplifies to 1/12.

Answer 15

To find the prime factorization of 17,640, we can start by dividing by the smallest prime number, which is 2:

17,640 ÷ 2 = 8,820

So 2 is a factor of 17,640. We can continue to divide by 2 until we get an odd number:

8,820 ÷ 2 = 4,410
4,410 ÷ 2 = 2,205
2,205 ÷ 3 = 735
735 ÷ 3 = 245
245 ÷ 5 = 49

We can see that 2 x 2 x 3 x 5 x 7 x 7 = 17,640.

Using exponents, we can write this as:

2^2 x 3^1 x 5^1 x 7^2

So the prime factorization of 17,640 using exponents is 2^2 x 3 x 5 x 7^2.

Answer 16

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π is Pi, and r is the radius.

Using the given radius of 4 meters and Pi ≈ 3.14, we can plug these values into the formula:

C = 2 x 3.14 x 4
C = 25.12

Therefore, the circumference of the circle with a radius of 4 meters is approximately 25.12 meters.

Answer 17

The formula for the area of a circle is:

A = πr^2

where A is the area, π is Pi, and r is the radius.

Using the given radius of 4 meters and Pi ≈ 3.14, we can plug these values into the formula:

A = 3.14 x 4^2
A = 3.14 x 16
A = 50.24

Therefore, the area of the circle with a radius of 4 meters is approximately 50.24 square meters.

Answer 18

To convert 0.98 L to milliliters, we can use a unit multiplier and the fact that 1 L = 1000 mL:

0.98 L x 1000 mL/L = 980 mL

Therefore, 0.98 L is equivalent to 980 mL.

Answer 19

If the team's ratio of games won to games played was 3 to 4, it means that out of every 3 + 4 = 7 games, they won 3.

To find out how many games they won, we can set up a proportion:

3/7 = x/24

where x is the number of games they won. We can solve for x by cross-multiplying:

3 x 24 = 7x

72 = 7x

x ≈ 10.3

So the team won about 10.3 games out of 24.

To find out how many games they failed to win, we can subtract the number of games they won from the total number of games:

24 - 10.3 ≈ 13.7

Therefore, the team failed to win about 13.7 games out of 24. We can also say that they lost about 13.7 games or had 13.7 games that resulted in a tie.