Use the distributive property to expand 5(-2t+3)

a 12 foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. find th

aleksandr82 [10.1K]

Use the equation
12= 3+2x

8 0

4 years ago

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

monitta

Answer:

a) n =1623

b) $ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken

$\hat p=0.19$ estimated proportion of customers are not satisfied with the service provided by the local dealer

Confidence =0.96 or 96%

Me= 0.02 represent the margin of error

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 96% of confidence, our significance level would be given by $\alpha=1-0.96=0.04$ and $\alpha/2 =0.02$ . And the critical value would be given by:

$z_{\alpha/2}=-2.0538, z_{1-\alpha/2}=2.0538$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.19(1-0.19)}{(\frac{0.02}{2.0538})^2}=1622.912$

And rounded up we have that n=1623

Part b

The margin of error is given by:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

So then if w replace the value of n obtained from part a we got:

$ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

3 0

3 years ago

You have to find the domain and range

Dahasolnce [82]

Answer:

First off, we look for which circles are open or closed.

We start with an open interval since the circle on the left is open and end with a closed interval since the circle on the right is closed.

Domain is all x values, Range is all y values

The graph shows the continous function going from -3 to 1 on the x axis.

According to the circles, this means our domain will be (-3,1].

Now, the range doesn't care about if its closed or not. So we can say the graph is on the y axis from -4 and 0. This means the range is -4<y<0

I used different notations for both just incase you need to represent your answer differently :)

-3<x<1 & (-3,1] . Range is [-4,0]. 0>y>-4 looks correct as-well.

3 0

3 years ago

X2 – 11x + 5 = -2x Solve equation to the nearest tenth

Nataly [62]

Answer:

x = 5/7 -> 0.714285 which to the nearest tenth would be 0.7

Step-by-step explanation:

is it x*2 or x^2?

If it were x to the power of two, then the answer would be about x1 = 0.594875 and x2 = 8.40512

7 0

3 years ago

Hi guys, I need help to solve this. I can’t understand how the percentage is calculated in (a) and (b) and how the rent is calcu

lana [24]

Answers :

(A) 18.33%
(B) 21.65%
(C) about 173.33
(D) i really have no way of finding the angles for you, you could try to find them yourself; or maybe just leave it blank?

<h3>OK, so judging from the bar shown : </h3>

It looks like Rent takes up 1/3 of the space so 33.33..%

It also looks like Loan Repayment + Savings is another 33.33..% but Savings is slightly larger than Loan Repayment so you could just estimate Savings to be 55% and LR to be 45% of the 1/3 space.

55% of 33.33.. = 18.33%

45% of 33.33.. = 14.99%

LR looks equal to Entertainment making it another 14.99.

It also looks like Entertainment + Electricity + Groceries = the last 33.33..%

And since we know Entertainment = 14.99 / 45% of 33.33..

Making Electricity and Water ABOUT 35% of 33.33... which is 11.66

And Groceries is somehow 20% of 33.33 = 6.66

Rent = 33.33..%
Savings = 18.33%
Loan Repayment 14.99%
Entertainment 14.99%
Electricity and Water 11.66%
Groceries = 6.66%

<h3>All of these added together equal ABOUT 100%</h3>

4 0

3 years ago