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2 years ago

A. Solve for y. B. What is the measure of the missing angles?

Mathematics

1 answer:

Alik [6]2 years ago

5 0

Answer: A.) y = 15 B.) (5y + 3)° = 78° (4y + 8)° = 68° and 34°

Steps:
180° - 146° = 34°

180 = 34 + (5y + 3) + (4y + 8)
180 - 34 = (5y + 3) + (4y + 8)
146 = (5y + 3) + (4y + 8)
146 = 5y + 3 + 4y + 8
146 = 9y + 11
146 - 11 = 9y
135 = 9y
135/ 9 = y
15 = y

(5y + 3)
5(15) + 3
75 + 3
78
(5y + 3) = 78

(4y + 8)
4(15) + 8
60 + 8
68
68 = (4y + 8)

Check:
68 + 78 + 34 = 180
180 = 180 ✅

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3 years ago

The proportion of defective computers built by Byte Computer Corporation is 0.15. In an attempt to lower the defective rate, the

FinnZ [79.3K]

Answer:

a) Null hypothesis : H₀: the proportion of defective item of computer has been lowered. That is P < 0.15

Alternative hypothesis: H₁: The proportion of defective item of computer

has been higher. That is P> 0.15 (Right tailed test)

b) Test statistic $Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

c) Calculate the value of the test statistic = 0.991

d) The critical value at 0.01 level of significance = Z₀.₀₁ = 2.57

e) Null hypothesis accepted at 0.01 level of significance

f) we accepted null hypothesis.

Hence the proportion of defective item of computer has been lowered.

Step-by-step explanation:

Step(i):-

Given the sample size 'n' = 42

Given random sample of 42 computers were tested revealing a total of 4 defective computers.

The defective computers 'x' = 4

The sample proportion of defective computers

$p = \frac{x}{n} = \frac{4}{42} = 0.095$

Given The Population proportion 'P' = 0.15

The level of significance ∝=0.01

Step(ii):-

a) Null hypothesis : H₀: the proportion of defective item of computer has been lowered. That is P < 0.15

Alternative hypothesis: H₁: The proportion of defective item of computer

has been higher. That is P> 0.15 (Right tailed test)

Test statistic $Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.095-0.15}{\sqrt{\frac{0.15(0.85)}{42} } }$

$z = \frac{-0.055}{\sqrt{0.00303} } = - 0.9991$

Calculate the value of the test statistic Z = - 0.9991

|Z| = |- 0.9991| = 0.991

Step(iii):-

The critical value at 0.01 level of significance = Z₀.₀₁ = 2.57

e) Calculate the value of the test statistic Z = 0.991 < 2.57 at 0.01 level of significance.

Conclusion:-

Hence the null hypothesis is accepted at 0.01 level of significance.

The proportion of defective item of computer has been lowered.

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