A group of students wants to sell T-shirts as a fundraiser. To manufacture the T-shirts, it will cost the students a one-time fee of $150, plus $5 for each T-shirt sold. They plan to sell the T-shirts for $12 each.

Which of the following equations correctly describes Y, the number of dollars raised by students in terms of x, the number of t-shirts sold?

Let's analyze the table to determine the relationship between slices of cake and calories.

We’ll use two points to find the calories per slice:

From the table:

• At 2 slices → 960 calories
• At 5 slices → 2,400 calories

Step 1: Find the difference

2,400−960=1,440caloriesincreasefor5−2=3slices

1,4403=480caloriesperslice

We can verify this with another pair:

• At 11 slices: 11×480=5,280
• At 19 slices: 19×480=9,120

Everything checks out.

Correct answer: C. Each slice of cake is 480 calories.

Let's rule out the others:

• A. Says 960 calories per slice — wrong.
• B. Says it's a negative relationship — incorrect, it’s positive.
• D. Claims no direct relationship — incorrect, it’s a linear relationship.

Let's break it down:

• There are 4 friends.
• One friend eats half of the pizza → 1/2 is gone.
• The remaining half (1/2) is shared equally among the 3 remaining friends.

So, each of the 3 remaining friends gets:

1/2÷3=1/2×1/3=1/6

Correct answer: B. 1/6

An inverse relationship means that as one variable increases, the other decreases.

Let’s evaluate the options:

• A. As the number of credit hours increases, the cost per credit hour decreases.
  → This is an inverse relationship.
• B. As the number of credit hours decreases, the cost per credit hour decreases.
  → This is a direct relationship, not inverse.
• C. Cost remains the same regardless of credit hours.
  → This shows no relationship.
• D. Both increase together.
  → This is a direct relationship.

Correct answer: A.

We are given:

• 1 teaspoon ≈ 4.93 mL
• The recipe calls for 2.5 teaspoons

Step 1: Multiply

2.5×4.93=12.325 mL

Correct answer: B. 12.325 mL

The dependent variable is the one that depends on or is determined by other variables.

In this case:

• Price is determined by the model, mileage, and age

Correct answer: A. Price

Because it depends on the other factors listed.

To display how often students get up after 8 a.m. on each day of the week, we are dealing with categorical data (days) and their frequencies.

Best option:

• A. Scatterplot – Not suitable for categorical data
• B. Pie graph – Good for showing parts of a whole, but not ideal for comparing frequencies across categories
• C. Histogram – Used for continuous numerical data, not categories like days
• D. Bar graph – Best choice for showing frequencies across distinct categories (like days of the week)

Correct answer: D. Bar graph

We are asked to find the probability that a PN or an RN is a female.

Let’s break it down using the table:

Total staff:

• Male PN: 30
• Male RN: 50
• Female PN: 50
• Female RN: 70

Total staff = 30 + 50 + 50 + 70 = 200

Total female PNs and RNs:

• Female PN: 50
• Female RN: 70

Total females = 50 + 70 = 120

Now calculate the probability:

P(female)=1202/00=3/5P

Correct answer: A. 3/5

We’re given the equation:

=10

Step 1: Multiply both sides by 5

−x+36=50

Step 2: Subtract 36 from both sides

−x=14

Step 3: Multiply both sides by -1

x=−14

Correct answer: D. -14

In this scenario, we're told that as the number of hours worked increases, several other quantities also increase. That means:

• The number of hours worked is causing the changes in other variables.
• The other values (taxes, savings, sick leave) depend on it.

So, the independent variable is the one that doesn't depend on other variables — it's the input or cause.

Correct answer: D. Number of hours worked

We are asked to find an equation for Y, the profit (or dollars raised), based on:

• Selling price per T-shirt: $12
• Cost per T-shirt: $5
• One-time fixed cost: $150
• Number of shirts sold: x

Step-by-step breakdown:

• Total Revenue:

Revenue=12x

• Total Cost:

Cost=150+5x

• Profit (Y) = Revenue – Cost:

Y=12x−(150+5x)

Correct answer: D. Y = 12x – (5x + 150)