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Afina-wow [57]
3 years ago
10

The price of an item has been reduced by 30%. The original price was $61.

Mathematics
2 answers:
UNO [17]3 years ago
8 0

Answer:

Step-by-step explanation:

ser-zykov [4K]3 years ago
3 0

Answer:

$42.70

Step-by-step explanation:

61 x 31% is 18.3.  so $61 - 18.3 =$42.70

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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
HELP ME I NEED TO FIND THE SLOPEEE!!
N76 [4]

Answer:

y=3/4 x+1

Step-by-step explanation:

first you start with y=mx+b find the y intercept first which is 1 next you just count down the block which is 3 then count to the right till you find a spot where it lands which would get you y=3/4+1

5 0
2 years ago
Read 2 more answers
Four years ago Ravi was 8 years older than Priya. If he is now 3times as old as she is, find their present ages?
GenaCL600 [577]

Answer:

24

Step-by-step explanation:

Hope this helps and please mark me brainliest :D

4 0
3 years ago
Find the area of the unshaded reason for these two problems​
Taya2010 [7]

9514 1404 393

Answer:

  a) 96 m²

  b) 26,000 ft²

Step-by-step explanation:

The area of the unshaded region is the difference between the overall area of the rectangle and the area of the shaded region. It can also be found directly using the dimensions of the unshaded region.

a) We have the height of the right triangle, but need to know its base. The Pythagorean theorem can help with that. Let the base of the triangle be represented by x. Then ...

  x² +16² = 20²

  x² = 400 -256 = 144

  x = √144 = 12

The area of the unshaded triangle is given by the formula ...

  A = (1/2)bh

  A = (1/2)(12)(16) = 96 . . . . square meters

__

b) The shaded area at upper left is a square 100 ft on a side. Its area is ...

  A = s² = (100 ft)² = 10,000 ft²

The shaded area at upper right is a triangle with base and height 120 ft and 150 ft. Its area is ...

  A = (1/2)bh = (1/2)(120 ft)(150 ft) = 9,000 ft²

The area of the overall rectangle is ...

  A = LW = (300 ft)(150 ft) = 45,000 ft²

So, the unshaded area is ...

  unshaded area = overall area - left shaded area - right shaded area

  unshaded area = 45,000 ft² -10,000 ft² -9,000 ft² = 26,000 ft²

7 0
3 years ago
What are the solutions of 4x+8<img src="https://tex.z-dn.net/?f=%5Cleq%20%5C%5C" id="TexFormula1" title="\leq \\" alt="\leq \\"
Fynjy0 [20]

Answer: x≤−7

Step-by-step explanation:

hope that helps

4 0
2 years ago
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