X | Y
--|--
1 | 1
2 | 4
3 | 9
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.
19 answers
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?
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.
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.
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?
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.
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.
Compare 2a to a squared if a is a whole number.
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.
- 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.
Simplify 8 and 1/3 over 100
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.
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.
Write the prime factorization of 17,640 using exponents
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.
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.
The radius of a circle is 4 meters. Use 3.14 for Pi to find the circumference if the circle.
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.
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.
The radius of a circle is 4 meters. Use 3.14 for Pi to find the area of the circle.
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.
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.
Use a unit multiplier to convert 0.98 L to milliliters
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.
0.98 L x 1000 mL/L = 980 mL
Therefore, 0.98 L is equivalent to 980 mL.
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?
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.
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.