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3 years ago

Find the Missing side length for #8

Mathematics

1 answer:

tia_tia [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

$\frac{LM}{QR}$ = $\frac{KL}{PQ}$ , substitute values

$\frac{x}{15}$ = $\frac{28}{21}$ ( cross- multiply )

21x = 420 ( divide both sides by 21 )

x = 20 → A

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The surface area of 2 spheres are in ration of 1:16 what is the ratio of their volume

crimeas [40]

S1/S2 = 1/16
Thus R1/R2 = 1/4
So V1/V2 = 1/64
Answer: 1/64

4 0

3 years ago

The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6.

Wittaler [7]

Answer:

a) There is a 10.75% probability of observing less than 60 hits in an hour.

b) The 99th percentile of the distribution of the number of hits is 95.21 hits.

c) There is a 24% probability of observing between 80 and 90 hits an hour

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

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

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. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.

In this problem, we have that

The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6, so $\mu = 75, \sigma = 8.6$ .

a) What’s the probability of observing less than 60 hits in an hour? Use the normal approximation

This is the pvalue of Z when X = 60. So

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

$Z = \frac{60 - 75}{8.6}$

$Z = -1.74$

$Z = -1.74$ has a pvalue of 0.1075. This means that there is a 10.75% probability of observing less than 60 hits in an hour.

b) What’s the 99th percentile of the distribution of the number of hits?

What is the value of X when Z has a pvalue of 0.99.

Z = 2.35 has a pvalue of 0.99

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

$2.35 = \frac{X - 75}{8.6}$

$X - 75 = 20.21$

$X = 95.21$

The 99th percentile of the distribution of the number of hits is 95.21 hits.

c) What’s the probability of observing between 80 and 90 hits an hour?

This is the pvalue of the zscore of X = 90 subtracted by the pvalue of the zscore of X = 80.

For X = 90

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

$Z = \frac{90 - 75}{8.6}$

$Z = 1.74$

$Z = 1.74$ has a pvalue of 0.95907

For X = 80

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

$Z = \frac{80 - 75}{8.6}$

$Z = 0.58$

$Z = 0.58$ has a pvalue of 0.71904

There is a 0.95907 - 0.71904 = 0.24003 = 24% probability of observing between 80 and 90 hits an hour

6 0

3 years ago

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection ac

7nadin3 [17]

Answer:

the answe is d

Step-by-step explanation:

3 0

3 years ago

20% of megans number is 64 what is 50% of megans number

Rzqust [24]

160 is the answer.

You know that 20%, or 1/5 equals 64 so you multiple 64 by 5 to get the full 100% number. In this question 320. You then divide 320 by 100 to get the value per 1%. Then multiple this by 50 to get 160. 

To check that you have the right answer, you divide 320 by 100 then multiple by 20 and if you get 64, you have the right answer.

8 0

3 years ago

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Your friend really wants to buy the newest coolest cell phone which will cost him $310 he gets a job detailing cars and suvs and

RoseWind [281]

Answer:

$60c + 85s \geqslant 310$

Step-by-step explanation:

He needs to earn at least $310 so $60 per car is 60c and $85 per SUV is 85s. So the answer is the third option.

5 0

3 years ago

Read 2 more answers