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2 years ago

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Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average n

umber of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.

1 answer:

Kobotan [32]2 years ago

7 0

Answer:

The test statistic value is 15.3.

Step-by-step explanation:

The hypothesis for this test is:

<em>H</em>₀: The average number of homeless people is not increasing, i.e. <em>μ</em> = 42.3.

<em>H</em>ₐ: The average number of homeless people is increasing, i.e. <em>μ</em> > 42.3.

Given:

$\bar x=45.3\\\sigma=6.2\\n=1000$

As the population standard deviation is provided use a single mean <em>z</em>-test for the hypothesis testing.

The test statistic is:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3$

Thus, the test statistic value is 15.3.

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<em><u>Question:</u></em>

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total. Write a system of linear inequalities

<em><u>Answer:</u></em>

The system of linear inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$

<em><u>Solution:</u></em>

Let "x" be the pounds of finishing nails

Let "y" be the pounds of common nails

Given that,

He would like to purchase at least 30 pounds of nails total.

"at least" means that he can purchase 30 pounds or more than 30 pounds also

So, we have to use "greater than or equal to" symbol

$x + y\geq 30$

From given,

Cost of 1 pound of finishing nail = $ 0.45

Cost of 1 pound of common nail = $ 0.60

A contractor has at most $42 to spend on nails for a project

"at most" means he can spend 42 or less than 42

So we have to use " less than or equal to" symbol

Thus we frame a inequality as:

$x \times 0.45 + y \times 0.60\leq 42\\\\0.45x + 0.60y\leq 42$

Thus the system of inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$

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You have $10 in your coin bank. Nickels (n) are worth $0.05, dimes (d) are worth $0.10, and quarters (q) are worth $0.25, each.

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Given:

At the store a cell phone cost 1.1 times as much as it sells online.

The cost of it is $888.98 online.

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Cost of a cell phone online = $888.98

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The cost of cell phone at store is $977.878 .

The difference between the cost of cell phone at store and online is

$\$977.878
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Therefore, the cell phone cost is $88.898 much more at the store.

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Answer:

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Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

$h(t)=-16t^2+80t+64$

where

h(t) is the height of a potato in feet

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we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

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$-16t^2+80t+64=0$

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The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+80t+64=0$

so

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

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therefore

The potato hit the ground at t=5.70 seconds

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substitute in the quadratic equation

$-16t^2+80t+64=40$

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Answer:

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Step-by-step explanation:

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