Generate an image symbolizing a math questionnaire. Include a representation of a math expression from algebra around simplifying an expression, solving an equation. Also include a statistical problem related to consumer preferences for different movie genres. Evoke a learning atmosphere with scholarly imagery such as an abacus, some graph paper, a pencil, and a compass. Please ensure the image contains no text.

1.Simplify the expression (3/7)^2

A.3/7
B.6/14
C.9/49
D.5/9

2.Which is a solution of the equation y=5x+3?
A.(5,28)
B.(28,5)
C.(4,20)
D.(3,19)

3.Solve the equation.
-15=a/5
A.a=-3
B.a=-20
C.a=-10
D.a=-75

4.Of 158 consumers polled, some like only action movies, some prefer just horror movies, and some like both. If 43 people like only action, and 62 like both, how many people prefer only horror movies?
A.58
B.55
C.53
D.43

I think #1 is C, #2 is A, #3 is C, and #4 is C. Please check my work and correct me if im wrong.

1C

2A
3D (multiply by 5, not add)
4C

Not too bad.

Sure, let's go through each question and see if your answers are correct.

1. Simplify the expression (3/7)^2.

To simplify this expression, we need to square the numerator and denominator separately.

(3/7)^2 = (3^2)/(7^2) = 9/49

So, the correct answer is C. 9/49. You are correct!

2. Which is a solution of the equation y=5x+3?

To find the solution to this equation, we need to substitute the values of x and y given in each option and check if the equation holds true.

Let's check each option:
A. (5,28): 28 = 5(5) + 3 -> 28 = 25 + 3 -> 28 = 28 (not true)
B. (28,5): 5 = 5(28) + 3 -> 5 = 140 + 3 -> 5 = 143 (not true)
C. (4,20): 20 = 5(4) + 3 -> 20 = 20 + 3 -> 20 = 23 (not true)
D. (3,19): 19 = 5(3) + 3 -> 19 = 15 + 3 -> 19 = 18 (not true)

None of the options satisfy the equation y = 5x + 3, so there is no correct solution option. You are incorrect on this one.

3. Solve the equation -15 = a/5.

To solve for a, we can multiply both sides of the equation by 5 to eliminate the fraction.

-15 * 5 = a/5 * 5
-75 = a

So, the correct answer is D. a = -75. You are correct!

4. Of 158 consumers polled, some like only action movies, some prefer just horror movies, and some like both. If 43 people like only action, and 62 like both, how many people prefer only horror movies?

To find the number of people who prefer only horror movies, we need to subtract the number of people who like both from the total number of people who prefer horror movies.

Total number of people who like horror movies = Total - People who like only action - People who like both
Total number of people who like horror movies = 158 - 43 - 62 = 53

So, the correct answer is C. 53. You are correct!

Great job on questions 1, 3, and 4! For question 2, there is no correct solution option. Keep up the good work!

You are correct!

1. Simplify the expression (3/7)^2:
To simplify a fraction raised to a power, you raise the numerator and denominator of the fraction to that power. So, (3/7)^2 = 3^2 / 7^2 = 9/49. Therefore, the answer is C. 9/49.

2. Which is a solution of the equation y = 5x + 3:
To find a solution of the equation, substitute the given x and y values into the equation and check if the equation is satisfied. Let's check each option:
A. (5, 28): 28 ≠ 5(5) + 3 (28 ≠ 28 + 3). Incorrect.
B. (28, 5): 5 ≠ 5(28) + 3 (5 ≠ 140 + 3). Incorrect.
C. (4, 20): 20 ≠ 5(4) + 3 (20 ≠ 20 + 3). Incorrect.
D. (3, 19): 19 = 5(3) + 3 (19 = 15 + 3). Correct.
Therefore, the answer is D. (3, 19).

3. Solve the equation -15 = a/5:
To solve for a, multiply both sides of the equation by 5 to isolate a.
-15 * 5 = a/5 * 5
-75 = a
Therefore, a = -75. The answer is D. a = -75.

4. Of 158 consumers polled, some like only action movies, some prefer just horror movies, and some like both. If 43 people like only action, and 62 like both, how many people prefer only horror movies?
To find the number of people who prefer only horror movies, we need to subtract the number of people who like both action and horror movies from the number of people who like only action movies.
Number of people who like only horror movies = Total number of people who prefer horror movies - Number of people who like both action and horror movies.
In this case, the total number of people who prefer horror movies is 158 - (43 + 62) = 158 - 105 = 53.
Therefore, the answer is C. 53 people prefer only horror movies.

Your answers are correct! Well done!

1. To simplify the expression (3/7)^2, you need to square both the numerator and denominator.

(3/7)^2 = (3^2) / (7^2) = 9/49

So, the correct answer is C. 9/49

2. To find the solution of the equation y = 5x + 3, you need to substitute the given options into the equation and check which one satisfies it.

Let's check option A: (5,28)

Plug in the values of x=5 and y=28 into the equation:
28 = 5(5) + 3
28 = 25 + 3
28 = 28

The equation is true, so option A is a solution.

So, the correct answer is A. (5,28)

3. To solve the equation -15 = a/5, you need to isolate the variable "a" by multiplying both sides of the equation by 5.

-15 * 5 = a/5 * 5
-75 = a

So, the correct answer is D. a = -75

4. To find the number of people who prefer only horror movies, you need to subtract the people who like both movies from the total number of people who like action movies.

Total number of people who like action movies (only + both) = 43 + 62 = 105

Total number of people who like horror movies (only + both) = Total number of consumers polled - Total number of people who like action movies (only + both)
= 158 - 105 = 53

So, the correct answer is C. 53