The table below shows a child’s height, in inches, on their birthday from birth to age 5. What was the average rate of change per year in the child’s height from birth to age 4?

Age (Years)	Height (Inches)
Birth	20
1	26
2	33
3	39
4	42
5	50

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.

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).

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

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

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 find the difference between the mean and the median number of tickets sold, let's follow these steps:

Step 1: List the number of tickets sold

• Lincoln: 200
• Jefferson: 250
• Washington: 300
• Adams: 150
• Jackson: 275

Step 2: Find the mean

Mean =(200+250+300+150+275)/5

=1175/5

=235

Step 3: Find the median

Sort the numbers: 150, 200, 250, 275, 300
The median is the middle value → 250

Step 4: Find the difference

Difference=∣235−250∣=15

Correct answer: C. 15

We can solve this using a proportion, since the dose is directly proportional to the child's weight.

Step 1: Set up the proportion

20 mg/50 lb=x/ mg35 lb

Step 2: Solve for xxx

x =

=700/50

=14 mg

Correct answer: C. 14 mg

To find the digit in the tens place of 12.34, let's break down the number:

• 12 is the whole number part
  • 1 is in the tens place
  • 2 is in the ones place
• .34 is the decimal part
  • 3 is in the tenths place
  • 4 is in the hundredths place

Correct answer: B. 1

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.

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