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Musya8 [376]
3 years ago
9

Which equation shows the correct use of the Distributive Property? −4(3/2x−1/2)=−15

Mathematics
1 answer:
hjlf3 years ago
5 0

Answer:

x=2.833

Step-by-step explanation:

−4(3/2x−1/2)=−15

-4(3/2x)-4(-1/2)= -15

-2(3x)+2=-15

-6x=-15-2

-6x = -17

x= -17/-6

x=2.833

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Step-by-step explanation:

a. To construct a 95% confidence interval for the mean:

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mean = 21.9

s = 7.7

n = 12

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The formula for interval:

mean ± t.\frac{s}{\sqrt{n} }

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21.9 ± 2.200.\frac{7.7}{\sqrt{12} }

21.9 ± 4.573

The interval is: 17.327 < μ < 26.473

b. A 95% confidence interval for the variance:

The given values are:

s^{2} = 7.7^{2}

s^{2} = 59.29

α = 0.05

\frac{\alpha}{2} = 0.025

1-\frac{\alpha}{2} = 0.975

\chi^{2}_{0.025,11} = 21.92

\chi^{2}_{0.975,11} = 3.816

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The formula to calculate interval:

(\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}})

are the lower and upper limits, respectively.

Substituing values:

(\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816})

(29.7532, 170.9093)

The interval for variance is: 29.7532 ≤ \sigma^{2} ≤ 170.9093

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