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3 years ago

PLS HELP ME ITS DUE AT 12 AM I WILL GIVE THAT BRAINLY THING

Mathematics

1 answer:

Eduardwww [97]3 years ago

4 0

9514 1404 393

Answer:

1. HA is equivalent to AAS when the triangle is a right triangle.

2. AM = BM, so the triangles are congruent by HL. CPCTC

3. The triangles are congruent by HL. CPCTC

Step-by-step explanation:

1. The acute angle of the triangle together with the right angle comprise two angles of the triangle. When two corresponding angles and a corresponding side (the side opposite the right angle) are congruent, the right triangles are congruent by the AAS theorem. (This can be referred to as the HA theorem.)

2. CM = DM; MA = MB; ∠A = ∠C = 90°, so all of the requirements for the HL theorem are met. ΔCMA ≅ ΔDMB, so AC ≅ BD by CPCTC.

3. TS = TV, TR = TR, ∠S = ∠V = 90°, so all requirements for the HL theorem are met. ΔTSR ≅ ΔTVR, so RS ≅ RV by CPCTC.

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A simple random sample of 32 men from a normally distributed population results in a standard deviation of 12.9 beats per minute

krok68 [10]

Answer:

Null Hypothesis, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

Alternate Hypothesis, H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

Step-by-step explanation:

The null hypothesis is basically the problem statement i.e

Pulse rates of men have a standard deviation equal to 10 beats per minute

Hence, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

The alternate hypothesis will contradict or negate the null hypothesis i.e

H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

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3 years ago

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The es

Mrrafil [7]

Answer:

The minimum sample size required to construct a 95% confidence interval for the population mean is 65.

Step-by-step explanation:

We are given the following in the question:

Population standard deviation,

$\sigma = 3.10\text{ milligrams}$

We need to construct a 95% confidence interval such that the estimate is within 0.75 milligrams of the population mean.

Thus, the margin of error must me 0.75

Formula for margin of error:

$z_{critical}\times \dfrac{\sigma}{\sqrt{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$0.75 = 1.86\times \dfrac{3.10}{\sqrt{n}}\\\\\sqrt{n} = \dfrac{1.96\times 3.10}{0.75}\\\\\sqrt{n} = 8.101\\\Rightarrow n = 65.63\approx 65$

Thus, the minimum sample size required to construct a 95% confidence interval for the population mean is 65.

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3 years ago

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob

Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that $\mu = 36, \sigma = 5.5$

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that $n = 9$ . So

$s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333$

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{38 - 36}{1.8333}$

$Z = 1.09$

$Z = 1.09$ has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{34.5 - 36}{1.8333}$

$Z = -0.82$

$Z = -0.82$ has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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3 years ago

Determine the equation of the line shown in the graph: x = 3 y = 3 y = 0 x = 0

Leona [35]

X = 3, since the 3 on the X-Axis is marked and not 3 on the Y-Axis

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