Question

1. apply math models the winning team in a 400-meter relay race had a time of 198.608 seconds. suppose all 4 of the split times were the same. write and solve an equation to find the split times. 18. represent and connect teresa placed parentheses in the expression below so that its value was greater than 80. write the expression to show where teresa might have placed the parentheses. 10.5 + 9.5 × 3 - 1 × 2.5 19. there are 6 people seated, equally spaced, along a counter. if each person has 1\frac{7}{8} feet of counter space, how long is the counter? tell how you can check that your answer is reasonable. 20. higher order thinking a bus left new york city and arrived in philadelphia after 2\frac{1}{3} hours. from there, it took 1\frac{3}{4} hours to travel to baltimore. it took another \frac{5}{6} hour to go from baltimore to washington. if the bus arrived in washington at 10:05 p.m., at what time did it leave new york city? explain. 21. which value for y makes the equation y ÷ 2.5 = 1.95 true? ⓐ y = 0.78 ⓒ y = 48.75 ⓑ y = 4.875 ⓓ y = 4,875 22. which value for x makes the equation x - 4.21 = 6.047 true? ⓐ x = 10.68 ⓒ x = 10.247 ⓑ x = 10.257 ⓓ x = 1.837 write and solve equations with rational numbers

Explanation:

Problem 17

Step1: Define variable, set equation

Let $x$ = split time. Total time: $4x = 198.608$

Step2: Solve for x

$x = \frac{198.608}{4}$

Step1: Test parenthesis placement

Place parentheses around $10.5 + 9.5$: $(10.5 + 9.5) \times 3 - 1 \times 2.5$

Step2: Calculate the value

$20 \times 3 - 2.5 = 60 - 2.5 = 57.5$ (too low). Place parentheses around $3 - 1$: $10.5 + 9.5 \times (3 - 1) \times 2.5$

Step3: Calculate new value

$10.5 + 9.5 \times 2 \times 2.5 = 10.5 + 47.5 = 58$ (too low). Place parentheses around $10.5 + 9.5 \times 3$: $(10.5 + 9.5 \times 3) - 1 \times 2.5$

Step4: Calculate final valid value

$(10.5 + 28.5) - 2.5 = 39 - 2.5 = 36.5$ (too low). Correct placement: $(10.5 + 9.5) \times (3 - 1) \times 2.5$

Step5: Verify the result

$20 \times 2 \times 2.5 = 100$, which is $>80$

Step1: Convert mixed number to fraction

$1\frac{7}{8} = \frac{15}{8}$

Step2: Calculate total counter length

Total length: $6 \times \frac{15}{8} = \frac{90}{8} = \frac{45}{4} = 11.25$

Step3: Check reasonableness

Round $1\frac{7}{8}$ to 2. $6 \times 2 = 12$, which is close to 11.25.

Answer:

The split time is 49.652 seconds.

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Problem 18