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3 years ago

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Karina rode her bike up a mountain trail at an average of 4 mph. Then she rode it back down the trail at an average of 20 mph. T

he entire trip took 3 hours. How far up the mountain did karina go?

1 answer:

earnstyle [38]3 years ago

4 0

Answer:

36 miles.

Step-by-step explanation:

We have been given that Karina rode her bike up a mountain trail at an average of 4 mph. Then she rode it back down the trail at an average of 20 mph. The entire trip took 3 hours.

$\text{Distance}=\text{Speed}\times \text{Time}$

Substitute the given values:

$\text{Distance}=(\frac{4\text{ miles}}{\text{Hour}}+\frac{20\text{ miles}}{\text{Hour}})\times 3\text{ Hours}$

$\text{Distance}=(\frac{24\text{ miles}}{\text{Hour}})\times 3\text{ Hours}$

$\text{Distance}=24\text{ miles}\times 3$

$\text{Distance}=72\text{ miles}$

The total distance is 72 miles, so the distance going up would be half of 72.

$\frac{72}{2}=36$

Therefore, Karina went 36 miles up the mountain.

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Solve the equation. 8x2 – 4 = 28

Flura [38]

Hello,

Your answer would be 2, -2.

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$8x^2 = 32$

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3 years ago

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the unit digitsof a two numberis 1 less than twice the ten digit. if the sum of tje digits is 9, find the number.

Amiraneli [1.4K]

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3 years ago

Among freshman at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 10

lina2011 [118]

Answer:

a) 6.68th percentile

b) 617.5 points

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:

$\mu = 550, \sigma = 100$

a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.

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

$Z = \frac{400 - 550}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

So this student is in the 6.68th percentile.

b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.

He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.

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

$0.675 = \frac{X - 550}{100}$

$X - 550 = 0.675*100$

$X = 617.5$

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3 years ago

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FrozenT [24]

#7
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Stolb23 [73]

Step-by-step explanation:

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