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3 years ago

Please help!! 30 points

Mathematics

1 answer:

Stels [109]3 years ago

8 0

Answer:

x = 4

31x + 6 = 130

12x + 2 = 50

Step-by-step explanation:

two angles side by side are equal to 180.

(31x + 6) + (12x + 2) = 180

43x + 8 = 180

43x = 172

x = 4

31x + 6 = 124 + 4 = 130

12x + 2 = 48 + 2 = 50

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The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A

Aloiza [94]

Answer:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

$\mu=37$ and $\sigma=28$ and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

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

And we want to find this probability:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

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3 years ago

A simple random sample of the sitting heights of 36 male students has a mean of 92.8cm. The population of males has sitting heig

Naily [24]

Answer:

there is sufficient evidence to support the claim that male student have a sitting height different of 91.4 cm.

Step-by-step explanation:

p value = 0.0198

level of significance = 0.05

hypothesis:-

$H_{0}:\mu=91.4$

$H_{1}:\mu\neq91.4$

decision:-

p value = 0.0198 <0.05

so, we reject the null hypothesis.]

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if the area of a rectangle is expressed as x^4 - 9y^2, then the product of the length and the width of the rectangle could be ex

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Answer:the product of the length and the width of the rectangle could be expressed as

(x^2 - 3y)(x^2 + 3y)

Step-by-step explanation:

If the area of a rectangle is expressed as x^4 - 9y^2, we would determine the dimensions by simplifying the given expression. The simplified expression becomes

(x^2 - 3y)(x^2 + 3y)

Let us check by multiplying each term in one parenthesis by each term in the other parenthesis to get the given expression. It becomes

(x^2 - 3y)(x^2 + 3y) = x^4 + 3x^2y - 3x^2y - 9y^2 = x^4 - 9y^2

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Vikentia [17]

Answer:

I think it's 39 I'm wrong but that's what I think sorry

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