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3 years ago

Some carpet cleaning costs are shown in the table. The relationship is linear. Find and interpret the rate of change

2 answers:

4 0

Y = m x + b , where m is the slope. The slope is the rise over the run or the change in x ( rooms cleaned ) over the change in y ( cost ).
125 = m * 1 + b
175 = m * 2 + b
-----------------------
b = 125 - m
175 = 2 m + 125 - m
m = 175 - 125
m = 50 ( the rate of change ), b = 75
The formula is: y = 50 x + 75
It means that the starting cost will be $75 and that for every room cleaned, the cost will rise for $50.

levacccp [35]3 years ago

3 0

Answer:

y = m x + b , where m is the slope. The slope is the rise over the run or the change in x ( rooms cleaned ) over the change in y ( cost ).

125 = m * 1 + b

175 = m * 2 + b

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

b = 125 - m

175 = 2 m + 125 - m

m = 175 - 125

m = 50 ( the rate of change ), b = 75

The formula is: y = 50 x + 75

It means that the starting cost will be $75 and that for every room cleaned, the cost will rise for $50.

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E5 In (x + 1)<br> Simplify

pentagon [3]

Answer:

e^ (5 ln (x + 1)) = (x + 1)^5

Step-by-step explanation:

e5 In (x + 1) or did you mean e^ (5 ln (x + 1))

because then this would simplify a lot

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5)

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5) = (x + 1)^5

or did you mean (e^5) ( ln (x + 1)) = ln [(x+1)^(e^5)]

But I think you meant:

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5) = (x + 1)^5

8 0

3 years ago

Apply the distributive property to create an equivalent expression.<br> (m−3+4n)⋅(−8)

Sindrei [870]

Answer:

Step-by-step explanation:

The distributive property:

$a(b+c)=ab+ac$

$(m-3+4n)(-8)=(m)(-8)+(-3)(-8)+(4n)(-8)\\\\=-8m+24-32n$

7 0

3 years ago

Dan has already delivered 48 donuts today. For the next few hours, Dan will deliver 60 donuts per hour. Match the number of donu

frez [133]

A.number of donuts delivered 2 hours from now.
2. Next=now +60+60
starting at 48 because 2 hours meant 2*60 = 60+60

B. number of donuts delivered 7 hours from now C
3.Next= now +420
starting at 48 because 7 hours meant 7*60 = 420 mn

C.number of donuts delivered n hours from now.
4. Next=now+60n
starting at 48 (this is obvious)

so finally,
D. number of donuts delivered 6 hours from now.
1. Next= now+ 6*60
starting at 48

7 0

3 years ago

A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical trials, 200,0

CaHeK987 [17]

Answer:

1) No, there is not enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

$p_1=X_1/n_1=21/100000=0.0002$

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

$p_2=X_2/n_2=30/100000=0.0003$

The difference between proportions is (p1-p2)=-0.0001.

$p_d=p_1-p_2=0.0002-0.0003=-0.0001$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=P(z$

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the vaccine was effective.

6 0

3 years ago

You pick a card at random, put it back, and then pick another card at random. 2 3 4 5 What is the probability of picking a numbe

olga_2 [115]

Answer:

3/4 or a 75% chance

Step-by-step explanation:

Out of 4 cards ( 2 3 4 5), here are the cards greater than 3: 4, and 5. That leaves you with a 2/4 chance of drawing one of them. (2 cards, 4 in total).

Then, picking a 4 out of 4 cards is a 1/4 chance; since that is one card out of 4 total possibilities.

1/4 + 2/4 = 3/4. Or, a 75% chance.

3 0

3 years ago

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