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boyakko [2]
3 years ago
12

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

the measure of the first angle. The third angle is 10 more than the second.
Mathematics
1 answer:
erastova [34]3 years ago
6 0

Answer:

first angle be 30°

second angle be 70°

third angle be 80°

Step-by-step explanation:

first angle be x

second angle be y

third angle be z

x+y+z=180

given, y+z = 5x; z=5x-y

also, z=y+10

5x-y = y+10

5x= 10+y+y = 10+2y

x= (10+2y)/5

x+y+z=180

(10+2y)/5 + y + y+10 = 180

(10+2y)/5 = 180 -2y -10

(10+2y)/5 = 170-2y

multiply both sides by 5

10+2y = 5(170-2y)

10+2y= 850-10y

2y+10y = 850-10

12y= 840

y= 840/12 = 70°

z=y+10 =70+10= 80°

5x= (10+2y) = 10+2(70) = 10+140= 150

x = 150/5 = 30°

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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It measures how many standard deviations the measure is from the mean.  
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In this problem:

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The mean and the standard error are given by:

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The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:

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You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

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