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Determine whether the following pairs of rates form a proportion:

1. 55 miles in 1 hour; 450 miles in 8 hours

2. [tex]$3.00[/tex] for 32 ounces of strawberries; [tex]$1.75[/tex] for 24 ounces of strawberries

3. 45 baskets in 85 shots; 54 baskets in 102 shots

4. 18 push-ups in 60 seconds; 27 push-ups in 90 seconds

5. One type of cereal has 2 grams of protein per 1-cup serving. Another cereal has 1 gram of protein per half-cup serving.

6. A 50-fluid-ounce bottle of laundry detergent washes 32 loads of laundry. A 100-fluid-ounce bottle washes 60 loads of laundry.

Answer :

Sure! Let's go through each problem one by one to see if the two rates form a proportion.

5. 55 miles in 1 hour; 450 miles in 8 hours

- Calculate the rate for each condition:
- First rate: 55 miles in 1 hour is 55 miles/hour.
- Second rate: 450 miles in 8 hours is 450 ÷ 8 = 56.25 miles/hour.

Since 55 does not equal 56.25, these rates do not form a proportion.

6. [tex]$3.00 for 32 ounces of strawberries; $[/tex]1.75 for 24 ounces of strawberries

- Calculate the rate for each condition:
- First rate: [tex]$3.00 for 32 ounces is 3.00 ÷ 32 = $[/tex]0.09375 per ounce.
- Second rate: [tex]$1.75 for 24 ounces is 1.75 ÷ 24 = $[/tex]0.072916...

Since [tex]$0.09375 does not equal $[/tex]0.072916..., these rates do not form a proportion.

7. 45 baskets in 85 shots; 54 baskets in 102 shots

- Calculate the rate for each condition:
- First rate: 45 baskets in 85 shots is 45 ÷ 85 = 0.5294...
- Second rate: 54 baskets in 102 shots is 54 ÷ 102 = 0.5294...

Since the rates are equal, these rates form a proportion.

8. 18 push-ups in 60 seconds; 27 push-ups in 90 seconds

- Calculate the rate for each condition:
- First rate: 18 push-ups in 60 seconds is 18 ÷ 60 = 0.3 push-ups per second.
- Second rate: 27 push-ups in 90 seconds is 27 ÷ 90 = 0.3 push-ups per second.

Since the rates are equal, these rates form a proportion.

9. 2 grams of protein per 1-cup serving; 1 gram of protein per half-cup serving

- Calculate the rate for each condition:
- First rate: 2 grams per 1 cup is 2 grams/cup.
- Second rate: 1 gram per half-cup is 1 ÷ 0.5 = 2 grams/cup.

Since the rates are equal, these rates form a proportion.

10. A 50-fluid-ounce bottle of laundry detergent washes 32 loads; a 100-fluid-ounce bottle washes 60 loads

- Calculate the rate for each condition:
- First rate: 50 fluid ounces for 32 loads is 50 ÷ 32 ≈ 1.5625 fluid ounces per load.
- Second rate: 100 fluid ounces for 60 loads is 100 ÷ 60 ≈ 1.6667 fluid ounces per load.

Since 1.5625 does not equal 1.6667, these rates do not form a proportion.

In summary:
- Proportions are formed in problems 7, 8, and 9.
- No proportions in problems 5, 6, and 10.

Thanks for taking the time to read Determine whether the following pairs of rates form a proportion 1 55 miles in 1 hour 450 miles in 8 hours 2 tex 3 00. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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