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ohaa [14]
3 years ago
9

Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same poi

nt. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes. What are their rates, in meters per minute?
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
6 0

Answer:

  • Alan: 200 m/min
  • Brian: 150 m/min

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

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sp2606 [1]

Step-by-step explanation:

(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:

g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)

g = 8 − 2.5t

(b) If d is the distance traveled:

d = 60 mi/hr × t hr

d = 60t

(c) When George runs out of gas, g = 0.

0 = 8 − 2.5t

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d = 60(3.2)

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(1 point) The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with a mean of 12
garik1379 [7]

Answer:

a) Z = -2.7

b) Z = 2.3

c) Kyle's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.

d) X = 144.5

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 127, \sigma = 10

(a) 100 millimeters z-score =

Z = \frac{X - \mu}{\sigma}

Z = \frac{100 - 127}{10}

Z = -2.7

(b) 150 millimeters z-score =

Z = \frac{X - \mu}{\sigma}

Z = \frac{150 - 127}{10}

Z = 2.3

(c) Kyle's doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of his score?

1.75 standard deviations above the mean systolic blood pressure of males.

The problem does not talk about age.

So the answer is:

Kyle's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.

d) Calculate Kyle's blood pressure

This is X when Z = 1.75. So

Z = \frac{X - \mu}{\sigma}

1.75 = \frac{X - 127}{10}

X - 127 = 1.75*10

X = 144.5

7 0
4 years ago
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