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V125BC [204]
3 years ago
7

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at miles 90 per

hour. The westbound train travels at miles 80 per hour. How long will it take for the two trains to be 204 miles apart?
Mathematics
1 answer:
algol [13]3 years ago
8 0
So the eastbound train travels at 90 miles per hour in the complete opposite direction to the westbound equivalent, which travels at 80 miles per hour. Therefore, per hour, they get 170 miles away from each other. Since we are working out how long it would take for them to be 204 miles apart:

204 / 170 = 1.2 Hours, or 1 hour and 12 minutes.

Hope I helped!
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The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning ca
Fed [463]

Answer:

Sam had a finish time with a z-score of -2.93.

Karen had a finish time with a z-score -1.91.

Sam had the more convincing victory.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

Sam:

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning car, driven by Sam, finished in 185.85 minutes.

So \mu = 186.94, \mu = 0.372, X = 185.85

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

Z = \frac{185.85 - 186.94}{0.372}

Z = -2.93

Sam finishing time was 2.93 standard deviations below the mean.

Sam had a finish time with a z-score of -2.93.

Karen:

The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

So \mu = 110.7, \sigma = 0.115, X = 110.48

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

Z = \frac{110.48 - 110.7}{0.115}

Z = -1.91

Karen finishing time was 1.91 standard deviations below the mean.

Karen had a finish time with a z-score -1.91.

Who had the more convincing victory?

Sam finishing time was 2.93 standard deviations below the mean.

Karen finishing time was 1.91 standard deviations below the mean.

Sam finished more standard deviations below the mean than Karen, that is, he was faster relative to his competition than Karen.

So Sam had the more convincing victory.

8 0
4 years ago
Ok last problem of the day
tatuchka [14]
Answer: 36/25
Steps: Evaluate the power & reduce
(3•2/5)^2 • (1/5^-3) ^3 • 5^-9
Rewrite
9•4/25 • 5^9 • 5^-9
Write in exponential form
9•4/5^2 • 5^9 • 5^-9
Reduce expression
9•4•5^7 •5^-9
Calculate
36•5^-2
Express with a positive exponent
36• 1/5^2
Evaluate & Calculate
36•1/25 → 36/25

Hope this helps ʕ•ᴥ•ʔ
3 0
4 years ago
Jeremy explained to Samantha that the factor (x 3 – 8) can be factored further as a __ of cubes
mote1985 [20]

Answer:

x ^3 cubed is  x  and -8 cubed is 2

Step-by-step explanation:

7 0
3 years ago
Rjfkdmfmfmfmfmggmgm​
Sever21 [200]

Answer:

same

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What figure has a greater perimeter and why
Yuki888 [10]
The second one because it has more sides exposed? im not sure about the explanation but i know its the second one
4 0
3 years ago
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