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3 years ago

Find the value of each missing variable?

Mathematics

1 answer:

LenKa [72]3 years ago

6 0

Step-by-step explanation:

9x - 2 = 5x + 54 because these angles are corresponding

9x - 5x = 54 + 2 add/subtract like terms

4x = 56 and this divided by 4

x = 14

9x - 2 + 10y + 6 = 180° because these two angles makes a straight line

9×14 - 2 + 10y + 6 = 180°

126 - 2 + 10y + 6 = 180° add like terms

130 + 10y = 180° subtract 130 from both sides

10y = 50 divide by 10

y = 10

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The 95% confidence interval for the population mean rating is (5.73, 6.95).

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$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$