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AURORKA [14]
3 years ago
11

Danielle has her finals coming up and she's worried she'll fail her class. Her past 3 test grades were a 72. an 85, and a 68. Sh

e needs a 70 to pass the class. What grade does she need to make on the final to get a 70?
Mathematics
1 answer:
natka813 [3]3 years ago
7 0

Answer:

55

Step-by-step explanation:

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Matt is playing a game. He gains 7 points, loses 10 points, and then loses 8 points. What is his final score? *​
Juli2301 [7.4K]

Answer:

-11

Step-by-step explanation:

7-10-8 = -11

8 0
2 years ago
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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

4 0
3 years ago
14. 3/64 + 2/32 + 5/16 = <br>what is the answer ​
Anit [1.1K]

Answer:

27/64

Step-by-step explanation:

(7×16)+(5×64)64×16

=112+3201/024

=432/1024

Simplifying 432/1024, the answer is

=27/64

3 0
2 years ago
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Find x so that l || m.
fredd [130]

Answer:

x = 17

Step-by-step explanation:

Line l and m are two parallel lines cut across by the transversal line, therefore, the angle measuring 53° and (8x - 9)° are interior angles on the same side. Interior angles on the same side are supplementary.

Therefore:

53° + (8x - 9)° = 180°

Solve for x

53 + 8x - 9 = 180

Collect like terms

53 - 9 + 8x = 180

44 + 8x = 180

Subtract 44 from both sides

44 + 8x - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

3 0
3 years ago
Which equation represents a parabola that has a focus of (0 0) and a directrix of y = 2
Ilya [14]
The answer is 3 because z to the y a-1
3 0
3 years ago
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