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3 years ago

∠R and ∠S are complementary. If m∠R = (2x+7) and m∠S = (4x - 13), find m∠R

Mathematics

2 answers:

BlackZzzverrR [31]3 years ago

4 0

Answer:

39°

Step-by-step explanation:

Complementary angles add up to 90

2x + 7 + 4x - 13 = 90

6x - 6 = 90

6x = 96

x = 16

Angle R = 2(16) + 7

32 + 7

39°

____ [38]3 years ago

3 0

Answer:

m∠R = 39 degrees

Step-by-step explanation:

As complementary angles add up to 90 degrees, we can set up an equation to get x then find the measure of ∠R:

m∠R + m∠S = 90

2x+7+4x-13=90

6x+7-13=90

6x-6=90

6x=96

x=16

Since m∠R = (2x+7), 2x+7 would be 2(16)+7 or 39 degrees. So in conclusion, m∠R = 39 degrees

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Dafna11 [192]

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Step-by-step explanation:

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The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard devia

torisob [31]

Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 2.5, \sigma = 0.5$

The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is <u>one subtracted by the p-value of Z when X = 2.45</u>, hence:

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

$Z = \frac{2.45 - 2.5}{0.5}$

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

1 - 0.4602 = 0.5398.

0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

More can be learned about the normal distribution at brainly.com/question/4079902

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2 years ago