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Elina [12.6K]
2 years ago
12

Complete the square for x2 - 4x + Then write the resulting expression as a binomial squared.

Mathematics
1 answer:
alekssr [168]2 years ago
4 0

Answer:

x(x-4)

Step-by-step explanation:

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Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length
Paladinen [302]

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

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 normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, 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(also called standard error) 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.

In this problem, we have that:

\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44

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

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

s = \frac{2}{\sqrt{21}} = 0.44

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

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

By the Central Limit Theorem

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

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

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

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

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

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

X = 25.05

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

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

8 0
3 years ago
Triangle ABC has measures a equals 2 b equals 2 and angle a equals 30 degrees what is the measure of angle B
Stella [2.4K]
<h2>Hello!</h2>

The answer is: Angle B is 30°

<h2>Why?</h2>

Since we know that both sides, a and b are equal to 2, and angle A is equal to 30°, we can conclude that angle B is also equal to 30°. Also, we can know that the other angle (C) will be equal to 120° since the sum of all the angles in a triangle will be always equal to 180°.

Have a nice day!

4 0
3 years ago
You and a friend of your choice are driving to the island of chincoteague in Virginia in two different cars.You are traveling 65
shutvik [7]

Answer:

  2.5 hours after you start

Step-by-step explanation:

You are driving 14 mph faster than your friend, so will make up the 35 mile head start in 35/14 = 2.5 hours. You will meet 162.5 miles from your starting location. If that is Philadelphia, you will have 37.5 miles to go.

You will catch up after 2.5 hours of driving.

_____

You will arrive about 9 1/2 minutes ahead of your friend.

3 0
3 years ago
GEOMETRY HELP!! (Image here)
Deffense [45]

Step-by-step explanation:

option B is the correct answer of this question .

5 0
2 years ago
Write any algebraic expression with at least two operations and the word phrase it represents.
alina1380 [7]
Algebraic Expression: 5x + 3y ÷ 2 = z

Word Phrase: 5 times x plus 3 times y divided by 2 equals z
______________________________________________________________
I am 99.9% sure that this is correct, if not, I am truly sorry, and please forgive me. Thank You!
7 0
3 years ago
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