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Gemiola [76]
3 years ago
10

Harlem is redecorating his room. A new desk costs (d) dollars. A bookshelf costs $114 less than the desk. A new lamp costs twice

as much as the bookshelf. Write an expression showing how much all of Harlem s new furniture will cost.
​
Mathematics
1 answer:
Alexxx [7]3 years ago
5 0

Answer:

Harlem is redecorating his room. A new desk costs (d) dollars. A bookshelf costs $114 less than the desk. A new lamp costs twice as much as the bookshelf. Write an expression showing how much all of Harlem s new furniture will cost.

Harlem is redecorating his room. A new desk costs (d) dollars. A bookshelf costs $114 less than the desk. A new lamp costs twice as much as the bookshelf. Write an expression showing how much all of Harlem s new furniture will cost.

Harlem is redecorating his room. A new desk costs (d) dollars. A bookshelf costs $114 less than the desk. A new lamp costs twice as much as the bookshelf. Write an expression showing how much all of Harlem s new furniture will cost.

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What is the formula for a confidence interval?
ikadub [295]

Answer:

a) The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) \bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Part a

The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

5 0
3 years ago
Solve the problem. Use the Central Limit Theorem.The annual precipitation amounts in a certain mountain range are normally distr
bazaltina [42]

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use 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 establishes 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 109.0 inches, and a standard deviation of 12 inches.

This means that \mu = 109, \sigma = 12

Sample of 25.

This means that n = 25, s = \frac{12}{\sqrt{25}} = 2.4

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

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

By the Central Limit Theorem

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

Z = \frac{112 - 109}{2.4}

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

7 0
3 years ago
Solve 8(x+2)=36.......
brilliants [131]
We have to use the Distributive Property in this equation.
By the Distributive Property,
8(x+2)=36

becomes
8x+16=36.
Now we need to isolate x. Remember PEMDAS?
8x=20
x=20/8
Simplify the right side.
x=10/4
x=5/2
3 0
3 years ago
Read 2 more answers
I don't know what it means
xz_007 [3.2K]

Answer:   x + 1 = 15

Step-by-step explanation:

solve -

x= 15 - 1

x = 14

x is a variable so it's not fix value in math

7 0
3 years ago
Which monomials are perfect cubes? Check all that apply.
lozanna [386]
A perfect cube is a number that resulted from multiplying a number three times by itself. A perfect cube is also a number that has an exact cube root.

8x^12 ⇒ 2x^4 * 2x^4 * 2x^4
27x^9 ⇒ 3x³ * 3x³ * 3x³

Only two monomials are perfect cubes.


6 0
3 years ago
Read 2 more answers
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