Which of the following statements describes an inverse relationship?

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 determine the best description of the relationship between run distance and winning time, let’s analyze the data:

As distance increases, the winning time also increases. This indicates a positive relationship.

Let's evaluate each choice:

• A. There is a negative covariance between the two variables
  Incorrect — Covariance is positive because both variables increase together.
• B. On a graph, the slope of the line segment between two points would be positive
  Correct — A graph plotting distance (x-axis) vs. time (y-axis) would show an upward trend with a positive slope.
• C. Distance of run is the dependent variable, while winning time is the independent variable
  Incorrect — Time depends on the distance, so time is the dependent variable.
• D. There is an inverse relationship between the two variables
  Incorrect — An inverse relationship would mean as one increases, the other decreases, which is not the case here.

Correct answer:B. On a graph, the slope of the line segment between two points would be positive.

Let's convert all values to decimals to compare them:

1. 3/4 = 0.75
2. 70% = 0.70
3. 5/7 ≈ 0.714
4. 0.79 = 0.79

Now, arrange from least to greatest:

• 70% (0.70)
• 5/7 (≈0.714)
• 3/4 (0.75)
• 0.79

Final Answer (in order from least to greatest):

70%, 5/7, 3/4, 0.79

Let’s define the total cost for each restaurant:

• Restaurant A: Charges $100 + $20 per person

CostA=100+20x

• Restaurant B: Charges $25 + $25 per person

CostB=25+25x

We want to find the number of people x where the costs are equal:

Step 1: Set the costs equal

100+20x=25+25x

Step 2: Solve for x

Subtract 20x from both sides:

100=25+5x

Subtract 25 from both sides:

75=5x

Divide by 5:

x=15

We are given the expression:

Length=2x+5

Let’s break it down:

• 2x means twice the width
• Then + 5 means five more

So, the phrase should be:

“Five more than twice the width”

Let’s match it with the choices:

• A. Two times the sum of five and the width
  Incorrect — that would be written as 2(5+x)2(5 + x)2(5+x)
• B. Two more than five times the width
  Incorrect — that would be 5x+25x + 25x+2
• C. Five times the sum of two and the width
  Incorrect — that would be 5(2+x)5(2 + x)5(2+x)
• D. Five more than twice the width
  Correct — matches 2x+5

Correct answer: D. Five more than twice the width

To find the average rate of change per year in the child’s height from birth to age 4, we use the formula:

AverageRateofChange =

=

= 22/4=5.5inchesperyear

Correct answer: A. 5.5 inches per year

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're told the ordered pair (3, 24) lies on the line representing the relationship between:

• x = number of lunches,
• y = total cost in dollars.

So, (3, 24) means:

When 3 lunches are ordered, the total cost is $24.

Correct answer: C. 3 lunches cost a total of $24

Let’s quickly rule out the others:

• A. Says each lunch is $24 — wrong.
• B. Reverses the values.
• D. Says 24 lunches cost $3 each — not related to (3, 24).

We are given:

• Monthly income: $2,586.00
• Deductions:
  • Insurance: $517.20
  • Federal taxes: $299.33
  • Social security: $156.69
  • State taxes: $99.77

Step 1: Add all deductions

517.20+299.33+156.69+99.77=1,072.99

Step 2: Subtract from gross income

2,586.00−1,072.99=1,513.01

Correct answer: C. $1,513.01

We are given:

• Bill = $43.20
• Gratuity = 15%

Step 1: Calculate 15% of $43.20

0.15×43.20=6.48

Step 2: Add the gratuity to the bill

43.20+6.48=49.68

Correct answer: D. $49.68