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Nadusha1986 [10]
3 years ago
7

9. What is the slope of the line that goes through the points (−3, 8) and (0, 23)?

Mathematics
2 answers:
emmasim [6.3K]3 years ago
6 0

Answer:

It would be 5.

LuckyWell [14K]3 years ago
6 0

Answer:

The slope is 5

Step-by-step explanation:

Hope this helped:)

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Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the cu
Diano4ka-milaya [45]

Answer:

At a .05 level of significance, it can be concluded that the mean of the population is significantly more than 3 minutes.

Step-by-step explanation:

We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.

At the null hypothesis, we test if the mean is of at most 3 minutes, that is:

H_0: \mu \leq 3

At the alternative hypothesis, we test if the mean is of more than 3 minutes, that is:

H_1: \mu > 3

The test statistic is:

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

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

3 is tested at the null hypothesis:

This means that \mu = 3

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute.

This means that n = 100, X = 3.1, \sigma = 0.5

Value of the test statistic:

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

z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}

z = 2

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 3.1, which is 1 subtracted by the p-value of z = 2.

Looking at the z-table, z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228

The p-value of the test is of 0.0228 < 0.05, meaning that the is significant evidence to conclude that the mean of the population is significantly more than 3 minutes.

6 0
3 years ago
Rob and Amy each improved their yards by planting rose bushes and shrubs. They bought their supplies from the same store. Rob sp
Lemur [1.5K]

Answer:

The correct answer is that a rose bush costs $10 and a shrub costs $4

Step-by-step explanation:

To solve this, start by writing equations for what each spent. Use x for the cost of a rose bush and y for the cost of a shrub. Below would be the equations for each.

Rob: 8x + 5y = 100

Amy: 8x + 8y = 112

Now to find the cost, we multiply Rob's equation by -1 and add them together. This will get x to cancel and allow us to solve for y.

-8x - 5y = -100

8x + 8y = 112

------------------

3y = 12

y = 4

So we know the cost of a shrub is $4. Now we can plug that in to either of the original equations and solve for the rose bush cost.

8x + 5y = 100

8x + 5(4) = 100

8x + 20 = 100

8x = 80

x = 10

Which means that a rose bush costs $10.

3 0
3 years ago
Assume that r varies directly as p. What is the constant of proportionality if r = 3 when p = 15.
nataly862011 [7]
The answer for this question would be K= 1/5
6 0
3 years ago
Read 2 more answers
Solve the initial-value problem using the method of undetermined coefficients.
andrey2020 [161]

First check the characteristic solution. The characteristic equation to this DE is

<em>r</em> ² - <em>r</em> = <em>r</em> (<em>r</em> - 1) = 0

with roots <em>r</em> = 0 and <em>r</em> = 1, so the characteristic solution is

<em>y</em> (char.) = <em>C₁ </em>exp(0<em>x</em>) + <em>C₂</em> exp(1<em>x</em>)

<em>y</em> (char.) = <em>C₁</em> + <em>C₂</em> exp(<em>x</em>)

For the particular solution, we try the <em>ansatz</em>

<em>y</em> (part.) = (<em>ax</em> + <em>b</em>) exp(<em>x</em>)

but exp(<em>x</em>) is already accounted for in the second term of <em>y</em> (char.), so we multiply each term here by <em>x</em> :

<em>y</em> (part.) = (<em>ax</em> ² + <em>bx</em>) exp(<em>x</em>)

Differentiate this twice and substitute the derivatives into the DE.

<em>y'</em> (part.) = (2<em>ax</em> + <em>b</em>) exp(<em>x</em>) + (<em>ax</em> ² + <em>bx</em>) exp(<em>x</em>)

… = (<em>ax</em> ² + (2<em>a</em> + <em>b</em>)<em>x</em> + <em>b</em>) exp(<em>x</em>)

<em>y''</em> (part.) = (2<em>ax</em> + 2<em>a</em> + <em>b</em>) exp(<em>x</em>) + (<em>ax</em> ² + (2<em>a</em> + <em>b</em>)<em>x</em> + <em>b</em>) exp(<em>x</em>)

… = (<em>ax</em> ² + (4<em>a</em> + <em>b</em>)<em>x</em> + 2<em>a</em> + 2<em>b</em>) exp(<em>x</em>)

(<em>ax</em> ² + (4<em>a</em> + <em>b</em>)<em>x</em> + 2<em>a</em> + 2<em>b</em>) exp(<em>x</em>) - (<em>ax</em> ² + (2<em>a</em> + <em>b</em>)<em>x</em> + <em>b</em>) exp(<em>x</em>)

= <em>x</em> exp(<em>x</em>)

The factor of exp(<em>x</em>) on both sides is never zero, so we can cancel them:

(<em>ax</em> ² + (4<em>a</em> + <em>b</em>)<em>x</em> + 2<em>a</em> + 2<em>b</em>) - (<em>ax</em> ² + (2<em>a</em> + <em>b</em>)<em>x</em> + <em>b</em>) = <em>x</em>

Collect all the terms on the left side to reduce it to

2<em>ax</em> + 2<em>a</em> + <em>b</em> = <em>x</em>

Matching coefficients gives the system

2<em>a</em> = 1

2<em>a</em> + <em>b</em> = 0

and solving this yields

<em>a</em> = 1/2, <em>b</em> = -1

Then the general solution to this DE is

<em>y(x)</em> = <em>C₁</em> + <em>C₂</em> exp(<em>x</em>) + (1/2 <em>x</em> ² - <em>x</em>) exp(<em>x</em>)

For the given initial conditions, we have

<em>y</em> (0) = <em>C₁</em> + <em>C₂</em> = 6

<em>y'</em> (0) = <em>C₂</em> - 1 = 5

and solving for the constants here gives

<em>C₁</em> = 0, <em>C₂</em> = 6

so that the particular solution to the IVP is

<em>y(x)</em> = 6 exp(<em>x</em>) + (1/2 <em>x</em> ² - <em>x</em>) exp(<em>x</em>)

3 0
3 years ago
For what values of r will the area of
Effectus [21]
28828281919mc square
5 0
3 years ago
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