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VLD [36.1K]
3 years ago
5

William has 19 tiles. Elizabeth has 3 fewer tiles than William. Write the expression that can be used to find the total number o

f tiles they have altogether.
Mathematics
1 answer:
iVinArrow [24]3 years ago
8 0
William had 19 tiles and Elizabeth has 16 so you could do 19+16=35
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Tia made a scale drawing of the White House for her history project. The actual length of the building is 168 feet, and its widt
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3 years ago
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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
What is the volume of a right circular cone that has a height of 14.9 cm and a base with the circumference of 2.9 cm rounded to
xxMikexx [17]

Answer:

The answer to your question is  Volume = 3.30 cm³

Step-by-step explanation:

Data

Volume = ?

height = 14.9 cm

circumference = 2.9 cm

Process

1.- Calculate the radius

   circumference = 2πr

-Substitution

   2.9 = 2πr

-Solve for r

   r = 2.9/2π

   r = 1.45/π cm

2) Calculate the volume of the cone

   Volume = 1/3πr²h

-Substitution

   Volume = 1/3π(1.45/π)²(14.9)

-Simplify

   Volume = (1.04)(0.213)(14.9)

   Volume = 3.30 cm³

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3 years ago
Suppose the total area is represented by the equation x^2+14x+24. If the area 1 is x^2 square units and area IV is 24 units, wha
Nutka1998 [239]

Answer:

See Explanation

Step-by-step explanation:

Given

Total = x^2 + 14x + 24

Area\ I = x^2

Area\ IV = 24

Required

True about area II and III

The question is incomplete; so, I will answer using general knowledge.

If the total area is:

Total = x^2 + 14x + 24

And there are 4 areas, then;

Total = Area\ I + Area\ II + Area\ III + Area\ IV

Rewrite as:

Total = Area\ I + Area\ IV+ Area\ II + Area\ III

This gives:

x^2 + 14x + 24 = x^2 + 24+ Area\ II + Area\ III

Collect like terms

x^2 -x^2 + 14x + 24 -24=  Area\ II + Area\ III

14x =  Area\ II + Area\ III

Rewrite as:

Area\ II + Area\ III  = 14x

<em>So, the sum of areas III and IV must be 14x</em>

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3 years ago
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