Question

1. jeanine keeps careful records on the performance of her automobile. the table shows the amount of fuel she recorded for trips of different lengths: table with distance (miles) 72, 144, 192, 288, 336, 360 and fuel (gallons) 3, 6, 8, 12, 14, 15 which equation relates the trip distance (d) to the amount of fuel used (f)? a. $d = 24f$ b. $d = 72f$ c. $d = 24 + f$ d. $d = \frac{72}{f}$ 49. the speed of light is roughly 186,000 miles per second. how many minutes does it take for light to arrive from the sun, which is 93,000,000 miles away? write your answer in the blank. 50. bulk flour costs $1.79 per pound. how many pounds of flour can be purchased for $17.37? write your answer in the blank.

Explanation:

Question 48

Step1: Check Option A

For the first pair (Distance = 72, Fuel = 3), substitute \( f = 3 \) into \( D = 24f \): \( D = 24\times3 = 72 \), which matches. For the second pair (144, 6): \( 24\times6 = 144 \), matches. Third (192, 8): \( 24\times8 = 192 \), matches. Let's check others to be sure.

Step2: Check Option B

Substitute \( f = 3 \) into \( D = 72f \): \( 72\times3 = 216
eq 72 \), so B is wrong.

Step3: Check Option C

Substitute \( f = 3 \) into \( D = 24 + f \): \( 24 + 3 = 27
eq 72 \), wrong.

Step4: Check Option D

Substitute \( f = 3 \) into \( D=\frac{72}{f} \): \( \frac{72}{3}=24
eq 72 \), wrong.

Step1: Recall the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \)

We know distance \( d = 93000000 \) miles, speed \( s = 186000 \) miles per second. First, find time in seconds: \( t=\frac{93000000}{186000} \).

Step2: Calculate time in seconds

\( \frac{93000000}{186000}=500 \) seconds.

Step3: Convert seconds to minutes

Since 1 minute = 60 seconds, \( \text{minutes}=\frac{500}{60}=\frac{25}{3}\approx8.33 \) (or keep as fraction, but likely decimal is okay). Wait, let's recalculate: \( 93000000\div186000 = 500 \) seconds. \( 500\div60=\frac{25}{3}\approx8.33 \)? Wait, no: 186000500 = 93,000,000. Then 500 seconds is 500/60 = 8.333... minutes? Wait, no, 608 = 480, 500 - 480 = 20, so 8 minutes and 20 seconds, which is \( 8\frac{1}{3} \) minutes or approximately 8.33 minutes. Wait, but let's do it properly: \( t=\frac{93000000}{186000}=500 \) seconds. \( 500\div60=\frac{25}{3}\approx8.33 \) (or \( 8\frac{1}{3} \)).

Step1: Recall the formula \( \text{quantity} = \frac{\text{total cost}}{\text{cost per unit}} \)

Total cost \( C = 17.37 \) dollars, cost per pound \( c = 1.79 \) dollars per pound.

Step2: Calculate the quantity

\( \text{pounds} = \frac{17.37}{1.79} \). Let's divide: 1.799 = 16.11, 17.37 - 16.11 = 1.26, 1.26/1.79 ≈ 0.703, no, wait 1.799.7 =? Wait, 1.7910 = 17.9, which is more than 17.37. So 17.37/1.79: 17.37 ÷ 1.79. Let's do long division: 1.799 = 16.11, 17.37 - 16.11 = 1.26. 1.26/1.79 = 0.703, so total is 9.7? Wait, no, 1.799.7 = 1.79(9 + 0.7) = 16.11 + 1.253 = 17.363 ≈ 17.37. So it's 9.7? Wait, no, 17.37 ÷ 1.79: let's multiply numerator and denominator by 100: 1737 ÷ 179. 1799 = 1611, 1737 - 1611 = 126. 1790.7 = 125.3, so 9.7. Wait, 1799.7 = 179(10 - 0.3) = 1790 - 53.7 = 1736.3, which is close to 1737. So approximately 9.7, but actually 17.37 ÷ 1.79 = 9.7 (exactly? Let's check 1.799.7 = 17.363, which is 0.007 less, so maybe 9.7 is correct. Wait, 17.37 / 1.79 = 9.7 (since 1.799.7 = 17.363, which is very close, maybe a typo, but actually 17.37 ÷ 1.79 = 9.7 (rounded to one decimal) or exactly 9.7 (since 1737 ÷ 179 = 9.7 (as 17997 = 17363, so 17370 ÷ 1790 = 9.7). So the answer is 9.7? Wait, no, 1.799 = 16.11, 17.37 - 16.11 = 1.26. 1.26/1.79 = 0.703, so 9.703, so 9.7 or 9.70. But let's do it precisely: 17.37 ÷ 1.79 = (17.37 × 100) ÷ (1.79 × 100) = 1737 ÷ 179. 179 × 9 = 1611, 1737 - 1611 = 126. 126 ÷ 179 = 0.703, so total is 9.703, so 9.7 (or 9.70).

Answer:

A. \( D = 24f \)

Question 49