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3 years ago

Please help me ASAP

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

7 0

Answer:

∠ 1 = 123°

Step-by-step explanation:

One way

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 1 is an external angle of the triangle, thus

∠ 1 = 90° + 33° = 123°

Second way

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle in Δ

third angle = 180° - (90 + 33)° = 180° - 123° = 57°

The third angle and ∠ 1 form a straight angle and are supplementary, thus

∠ 1 = 180° - 57° = 123°

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Step-by-step explanation:

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The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

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And for the margin of error we have the following estimation:

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

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