The interior angles of a triangle have measures (2x - 5), (4– 1), and 30°

Mathematics

1 answer:

const2013 [10]2 years ago

8 0

Answer: x=26

Step-by-step explanation:

1. Write the equation 2x-5+4x-1+30=180 because all triangle angles add up to 180°

2. Simplify the equation by combining like terms. Write the equation as 6x+24=180

3. Subtract 24 from both sides. Write the equation as 6x=156.

4. Divide 156/6 and get 26. That is your answer (x=26).

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A radio station claims that the amount of advertising per hour of broadcast time has an average of 13 minutes and a standard dev

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Answer:

$Z = 3.33$

Step-by-step explanation:

Z-score:

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 question:

$\mu = 13, \sigma = 1.2$

You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the z-score for this amount of advertising time.

We have to find Z when X = 17. So

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

$Z = \frac{17 - 13}{1.2}$