Find the value of the variable.

Mathematics

1 answer:

Archy [21]3 years ago

3 0

Answer:

x = 10, y = 10

Step-by-step explanation:

This is a 45° 45° 90° triangle. In this triangle, the legs of said shape will be equal and the hypotenuse will be the leg length multiplied by √2. Therefore, we can simply divide 10√2 by √2 to get the leg length.

10√2/√2 = 10

Therefore, x = 10 and y = 10.

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The 99% confidence interval for the difference between the mean fill volumes at the two locations is;

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Step-by-step explanation:

The number of bottles in the sample at the first location, n₁ = 18 bottles

The mean fill volume, $\bar{x}_{1}$ = 2.007 L

The standard deviation, σ₁ = 0.010 L

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The standard deviation, σ₂ = 0.012 L

The nature of the variance of the two samples = Equal variance

The confidence interval of the statistics, C = 99%

The difference between the mean

$\mu_1 - \mu_2 = \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times \sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}+\dfrac{\sigma _{2}^{2}}{n_{2}}}$