The table represents the men’s winning track times at each distance at the 2016 Summer Olympic Games. Based on this information, which of the following statements best describes the relationship between run distance and winning time?

Distance (m)	Winning time (seconds)
100	9.8
200	19.8
400	43.0
800	102.2
1,500	230.0
5,000	783.3
10,000	1,625.2

We're told the relationship is proportional and that the point (7, 157.5) lies on the line, meaning:

7 hours → $157.50

To find the hourly rate, divide total earnings by hours:

157.5/7=22.5

So, the employee earns $22.50 per hour.

Correct answer: D. Manaf earns $22.50 per hour

Let's briefly rule out the others:

• A. 22.5 hours is not mentioned in the original data.
• B. $7/hour is incorrect.
• C. $157.50/hour is incorrect (it's the total, not the rate).

We’re given:

• Ratio of chocolate to vanilla cones = 9:4
• 72 vanilla cones were sold
• We need to find the number of chocolate cones

Step 1: Set up a proportion

=

Let x be the number of chocolate cones:

=

Step 2: Solve for xxx

x=×72==162

Correct answer: C. 162 cones

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

Let's convert all the values to decimals for easy comparison:

• A. 4.4 → already in decimal
• B. 4.25 → already in decimal
• C. 10/3 = 3.33...
• D. 9/2 = 4.5

Compare all values:

• A: 4.4
• B: 4.25
• C: 3.33
• D: 4.5

Correct answer: D. 9/2 (which equals 4.5, the greatest value)

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

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.

Let's evaluate each expression to determine their numerical values:

1. 1.8 - 0.5 = 1.3
2. 1.8 + 0.5 = 2.3
3. 1.8 + (2)(0.5) = 1.8 + 1 = 2.8
4. (1.8)(0.5) = 0.9
5. 1.8 + 0.5 (repeated) = 2.3

Now arrange in ascending order:

• (1.8)(0.5) = 0.9
• 1.8 - 0.5 = 1.3
• 1.8 + 0.5 = 2.3
• 1.8 + 0.5 = 2.3 (duplicate)
• 1.8 + (2)(0.5) = 2.8

Answer (in ascending order):

1. (1.8)(0.5)
2. 1.8 - 0.5
3. 1.8 + 0.5
4. 1.8 + 0.5
5. 1.8 + (2)(0.5)

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.

To find the percent decrease, use the formula:

PercentDecrease =)×100

Step-by-step:

• Original Price = $200,000
• New Price = $180,000
• Difference = $200,000 − $180,000 = $20,000

PercentDecrease=×100=0.1×100=10%

Correct answer: D. 10%

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