Compare Proportions from Descriptions & Tables Quick Check

Question

1 of 51 of 5 Items
Question
A bean plant grows 2 inches in 2 days. A strawberry plant grows 4 inches in 5 days. Compare the two proportional relationships. Assume each plant is growing at a constant rate.(1 point)
Responses

The bean plant grows at a slower rate because it grows 2 inches while the strawberry plant grows 4 inches.
The bean plant grows at a slower rate because it grows 2 inches while the strawberry plant grows 4 inches.

The strawberry plant grows at a slower rate because it grows 0.8 inches per day while the bean plant grows 1 inch per day.
The strawberry plant grows at a slower rate because it grows 0.8 inches per day while the bean plant grows 1 inch per day.

The strawberry plant has grown 2 inches more than the bean plant.
The strawberry plant has grown 2 inches more than the bean plant.

Both plants are growing every day.
Both plants are growing every day.
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page 13 of 13

Answer 1

To compare the growth rates of the bean plant and the strawberry plant, we can calculate the growth per day for each plant.

1. Bean plant growth: It grows 2 inches in 2 days.

   • Growth rate = \( \frac{2 \text{ inches}}{2 \text{ days}} = 1 \text{ inch per day} \)

2. Strawberry plant growth: It grows 4 inches in 5 days.

   • Growth rate = \( \frac{4 \text{ inches}}{5 \text{ days}} = 0.8 \text{ inches per day} \)

Now we can compare the growth rates:

• The bean plant grows at a rate of 1 inch per day.
• The strawberry plant grows at a rate of 0.8 inches per day.

From this comparison, we can conclude that:

• The bean plant grows at a faster rate than the strawberry plant.

Among the response options provided, the correct comparison is:

The strawberry plant grows at a slower rate because it grows 0.8 inches per day while the bean plant grows 1 inch per day.

Answer 2

Compare Proportions from Descriptions & Tables Quick Check
2 of 52 of 5 Items
Question
Last week, Malika’s cat slept 18 hours each day. Her baby slept 91 hours total for the week. Compare the proportional relationship of the number of hours the cat and baby sleep each day.(1 point)
Responses

The baby slept fewer hours per day than the cat.
The baby slept fewer hours per day than the cat.

The cat and the baby slept the same amount of hours total for the week.
The cat and the baby slept the same amount of hours total for the week.

The cat slept fewer hours per day than the baby.
The cat slept fewer hours per day than the baby.

Both the cat and the baby spend less than half the hours of the day sleeping.
Both the cat and the baby spend less than half the hours of the day sleeping.
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page 13 of 13

Answer 3

To compare the sleeping hours of Malika’s cat and her baby, we need to determine how many hours each sleeps per day.

1. Cat's sleep: The cat sleeps 18 hours each day.
2. Baby's sleep: The baby slept a total of 91 hours over the week (7 days).
   • To find the average sleep per day for the baby: \[ \text{Baby's sleep per day} = \frac{91 \text{ hours}}{7 \text{ days}} = 13 \text{ hours per day} \]

Now we can compare the daily sleep:

• Cat: 18 hours per day
• Baby: 13 hours per day

From this comparison, we can conclude that:

• The baby slept fewer hours per day than the cat.

Thus, the correct response is:

The baby slept fewer hours per day than the cat.

Answer 4

Compare Proportions from Descriptions & Tables Quick Check
3 of 53 of 5 Items
Question
Use the tables to answer the question.

Company A
Hours of Work Pay ($)
5.5 140.25
22.0 561.00
35.0 892.50
40.0 1,020.00

Company B
Hours of Work Pay ($)
4.0 114.00
10.6 302.10
20.5 584.25
35.0 997.50
Based on the tables showing what two leading gas brands pay employees, compare which company pays the higher rate. Which answer provides the correct company and hourly rate?

(1 point)
Responses

Company B has the best hourly rate of $28.50/hour.
Company B has the best hourly rate of $28.50/hour.

Company A has the best hourly rate of $1,020/40 hours.
Company A has the best hourly rate of $1,020/40 hours.

Company B has the best hourly rate of $997.50/40 hours.
Company B has the best hourly rate of $997.50/40 hours.

Company A has the best hourly rate of $25.50/hour.
Company A has the best hourly rate of $25.50/hour.
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Answer 5

To determine which company pays the higher hourly rate, we can calculate the hourly pay rate for each entry in the tables for Company A and Company B.

Company A:

1. 5.5 hours: \[ \frac{140.25}{5.5} \approx 25.50 \text{ per hour} \]
2. 22.0 hours: \[ \frac{561.00}{22.0} \approx 25.50 \text{ per hour} \]
3. 35.0 hours: \[ \frac{892.50}{35.0} \approx 25.50 \text{ per hour} \]
4. 40.0 hours: \[ \frac{1020.00}{40.0} = 25.50 \text{ per hour} \]

From Company A, the hourly rate is consistently $25.50/hour.

Company B:

1. 4.0 hours: \[ \frac{114.00}{4.0} = 28.50 \text{ per hour} \]
2. 10.6 hours: \[ \frac{302.10}{10.6} \approx 28.50 \text{ per hour} \]
3. 20.5 hours: \[ \frac{584.25}{20.5} \approx 28.50 \text{ per hour} \]
4. 35.0 hours: \[ \frac{997.50}{35.0} = 28.50 \text{ per hour} \]

From Company B, the hourly rate is consistently $28.50/hour.

Conclusion:

• Company A pays $25.50/hour.
• Company B pays $28.50/hour.

Thus, the correct response is:

Company B has the best hourly rate of $28.50/hour.

Answer 6

Compare Proportions from Descriptions & Tables Quick Check
4 of 54 of 5 Items

Question
Use the tables to answer the question.

Marco’s Homework
Number of Days Number of Hours
3 3.25
9 9.75
12 13.0
30 32.5

Maribella’s Homework
Number of Days Number of Hours
4 4.2
8 8.4
20 21.0
28 29.4
Based on the tables showing the hours of homework done by Marco and Maribella for different periods of time, which statement is correct?

(1 point)
Responses

There is not enough information to tell who spends less time doing their homework.
There is not enough information to tell who spends less time doing their homework.

Marco and Maribella spend equal time doing their homework.
Marco and Maribella spend equal time doing their homework.

Maribella spends less time on homework per night.
Maribella spends less time on homework per night.

Marco spends less time on homework per night.
Marco spends less time on homework per night.
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page 13 of 13

Answer 7

To compare the amount of time Marco and Maribella spend on homework per day, we need to calculate the average number of hours spent per day for each of them.

Marco's Homework:

• For 3 days: 3.25 hours \[ \text{Average per day} = \frac{3.25}{3} \approx 1.08 \text{ hours} \]

• For 9 days: 9.75 hours \[ \text{Average per day} = \frac{9.75}{9} \approx 1.08 \text{ hours} \]

• For 12 days: 13.0 hours \[ \text{Average per day} = \frac{13.0}{12} \approx 1.08 \text{ hours} \]

• For 30 days: 32.5 hours \[ \text{Average per day} = \frac{32.5}{30} \approx 1.08 \text{ hours} \]

Maribella's Homework:

• For 4 days: 4.2 hours \[ \text{Average per day} = \frac{4.2}{4} = 1.05 \text{ hours} \]

• For 8 days: 8.4 hours \[ \text{Average per day} = \frac{8.4}{8} = 1.05 \text{ hours} \]

• For 20 days: 21.0 hours \[ \text{Average per day} = \frac{21.0}{20} = 1.05 \text{ hours} \]

• For 28 days: 29.4 hours \[ \text{Average per day} = \frac{29.4}{28} \approx 1.05 \text{ hours} \]

Summary of Averages:

• Marco: Approximately 1.08 hours per day
• Maribella: Approximately 1.05 hours per day

Conclusion:

From the calculations, we see that Marco spends more time doing homework per day (1.08 hours) compared to Maribella (1.05 hours). Therefore:

• Maribella spends less time on homework per night.

Thus, the correct response is:

Maribella spends less time on homework per night.

Answer 8

Compare Proportions from Descriptions & Tables Quick Check
5 of 55 of 5 Items

Question
Use the tables to answer the question.

Community A
Number of Households Total Number of Children
10 26
20 52
40 104
75 195

Community B
Number of Households Total Number of Children
12 30
24 60
50 125
85 212.5
Based on the tables showing the average number of children per household for two different communities, which community has the most children if both neighborhoods have the same number of households? How many children live in this community if 1,000 households?

(1 point)
Responses

Community A has the most children. There are 260 children in this community if there are 1,000 households.
Community A has the most children. There are 260 children in this community if there are 1,000 households.

Community A has the most children. There are 2,600 children in this community if there are 1,000 households.
Community A has the most children. There are 2,600 children in this community if there are 1,000 households.

Community B has the most children. There are 2,500 children in this community if there are 1,000 households.
Community B has the most children. There are 2,500 children in this community if there are 1,000 households.

Community B has the most children. There are 212.5 children which is greater than the 195 in Community A.
Community B has the most children. There are 212.5 children which is greater than the 195 in Community A.
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page 13 of 13

Answer 9

To determine which community has the most children per household and calculate how many children would be in that community if there were 1,000 households, we first need to calculate the average number of children per household for both Community A and Community B.

Community A:

• 10 households: 26 children
  \[ \text{Average} = \frac{26}{10} = 2.6 \text{ children per household} \]

• 20 households: 52 children
  \[ \text{Average} = \frac{52}{20} = 2.6 \text{ children per household} \]

• 40 households: 104 children
  \[ \text{Average} = \frac{104}{40} = 2.6 \text{ children per household} \]

• 75 households: 195 children
  \[ \text{Average} = \frac{195}{75} = 2.6 \text{ children per household} \]

Community B:

• 12 households: 30 children
  \[ \text{Average} = \frac{30}{12} = 2.5 \text{ children per household} \]

• 24 households: 60 children
  \[ \text{Average} = \frac{60}{24} = 2.5 \text{ children per household} \]

• 50 households: 125 children
  \[ \text{Average} = \frac{125}{50} = 2.5 \text{ children per household} \]

• 85 households: 212.5 children
  \[ \text{Average} = \frac{212.5}{85} \approx 2.5 \text{ children per household} \]

Summary of Averages:

• Community A: 2.6 children per household
• Community B: 2.5 children per household

Conclusion:

Community A has a higher average number of children per household.

If there are 1,000 households in Community A, the total number of children would be: \[ \text{Total children} = 2.6 \text{ children/household} \times 1,000 \text{ households} = 2,600 \text{ children} \]

Thus, the correct response is:

Community A has the most children. There are 2,600 children in this community if there are 1,000 households.