1. John earns $500 in a work week. A regular work week for John consists of 5 work days with 8 hours a day. How much does John earn each hour?

Question

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1 point
$10.50 an hour
$11.00 an hour
$12.50 an hour
$13.00 an hour

2. A proportional relationship has a unit rate of 4 to 1. Which situation below represents this relationship?
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1 point
A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles
Hikers travel 48 miles in 6 hours
A DJ is required to play 60 songs over a 4-hour shift
A cookie recipe uses 1 3/4 cups of brown sugar for 2 batches

3. An Alien is 5 feet tall. His shadow is 8 feet long. At the same time of the day, a tree's shadow is 32 feet long. What is the height of the tree?
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1 point
20 feet
24 feet
29 feet
51 feet

4. Polygon KLMN is similar to polygon PQRS. What is the length of QR?
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1 point

16m
9m
8m
6m

Answer 1

Let's go through each question one by one.

1. John's weekly earnings:
   John earns $500 for a 40-hour work week (8 hours per day for 5 days). To find out how much he earns per hour, we divide his weekly earnings by the total hours worked in a week: \[ \text{Hourly Rate} = \frac{\text{Total Earnings}}{\text{Total Hours}} = \frac{500}{40} = 12.50 \text{ an hour} \] So, John earns $12.50 an hour.

2. Proportional relationship with a unit rate of 4 to 1:
   A unit rate of 4 to 1 means for every 4 of one quantity, there is 1 of another. We will analyze each option:

   • Tire warehouse: 12,800 tires for 3,200 automobiles → \( \frac{12800}{3200} = 4 \) (This is a 4 to 1 ratio)
   • Hikers: 48 miles in 6 hours → \( \frac{48}{6} = 8 \) (Not a 4 to 1 ratio)
   • DJ: 60 songs over 4 hours → \( \frac{60}{4} = 15 \) (Not a 4 to 1 ratio)
   • Cookie recipe: 1.75 cups for 2 batches → \( \frac{1.75}{2} = 0.875 \) (Not a 4 to 1 ratio) The situation that represents the relationship of 4 to 1 is the tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles.

3. Height of the tree:
   We can use the concept of similar triangles. The ratio of the height of the alien to the length of its shadow is \( \frac{5 \text{ feet}}{8 \text{ feet}} \) = \( \frac{h}{32 \text{ feet}} \), where \( h \) is the height of the tree. Setting up the proportion: \[ \frac{5}{8} = \frac{h}{32} \] Cross-multiplying gives: \[ 5 \times 32 = 8h \implies 160 = 8h \implies h = \frac{160}{8} = 20 \text{ feet} \] So, the height of the tree is 20 feet.

4. Length of QR in similar polygons:
   Without more context, we typically need information on the ratio of the sides of the similar polygons. However, assuming the lengths are provided from KLMN to PQRS and QR correlates directly based on a proportionality factor we can derive. Let’s assume the ratio of lengths in the two polygons is known and direct options are given. If it is not provided, we cannot determine the length of QR. However, among the options given, I cannot choose without additional information such as the scaling ratio. If the ratio was known, then the length of QR would stem from the ratio provided.

To summarize the answers:

1. $12.50 an hour
2. A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles
3. 20 feet
4. Insufficient information provided (Cannot determine QR without scaling information).

If you have specifics for the last portion, please provide them to calculate QR accurately!