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3 years ago

Which transformations take f(x)=3x+1 to g(x)=−3x-5 ?

1 answer:

8 0

reflection over the x-axis and a translation 4 units down Refelcting f(x) over the x axis gives -f(x)=-3x-1 Subtracting a constant from -f(x) moves the graph of -f(x) that many units down. -f(x)-4=-3x-5=g(x) This shows that g(x) is obtained by reflecting f(x) over the x-axis and then translating 4 units down.

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15. Bradley has a goal to work 28 hours each week at the pizza shop. So far he has

Lina20 [59]

16

28-12=16

He needs 16 more hours of work to complete

7 0

3 years ago

Multiply. (х4 + 1)(3х2 + 9x + 2)

lakkis [162]

Answer:

3x^6+9x^5+2x^4+3x^2+9x+2

5 0

3 years ago

A manufacturer reported a sample mean = 22.0 g and a sample standard deviation = 2.5 g based on a sample of 20 of their products

tester [92]

Answer:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

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".

$\bar X=22$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.5 represent the sample standard deviation

n represent the sample size

ME = 2 represent the margin of error accepted

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =2 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (3)

We can use as estimator for the population deviation the sample deviation $\hat \sigma = s$

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got $z_{\alpha/2}=1.640$ , replacing into formula (3) we got:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

6 0

3 years ago

The incomes in a certain large population of college teachers have a Normal distribution, with mean $75,000 and standard deviati

Natali [406]

Answer:

probability that their average salary is more than $77,500 is 0.1587

Step-by-step explanation:

standard error

= 10,000/sqrt(16)

=10,000/4

= 2500

(77,500 - 75000)/2500

2,500/2500

= 1

p (z > 1) = .1587

So, the probability that their average salary is more than $77,500 is 0.1587

8 0

3 years ago

Read 2 more answers

The city of Raleigh has 11700 registered voters. There are two candidates for city council in an upcoming election: Brown and Fe

Vesnalui [34]

Answer:

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.308.

The expected numbers of voters who would vote for Brown is 3604.

Step-by-step explanation:

The sample statistic is a numerical quantity used to represent a characteristic of a sample. For example, sample mean is a sample statistic representing the average of the sample. Or, sample proportion is a sample statistic representing the proportion of a particular variable in the sample. Or sample variance is a sample statistic representing the variance of the sample.

The sample statistic can be used to estimate the population parameter.

They are known as the point estimate of the parameter.

The sample proportion of a variable X is given by:

$\hat p=\frac{X}{n}$

It is provided that of the n = 250 registered voters selected, the number of voters who said they would vote for Brown is X = 77.

Compute the sample statistic for the proportion of voters surveyed who said they'd vote for Brown as follows:

$\hat p=\frac{X}{n}$

$=\frac{77}{250}\\$

$=0.308$

Thus, the sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.308.

Compute the expected number of people of the 11700 registered voters who would vote for Brown as follows:

$E(X)=N\times \hat p$

$=11700\times 0.308\\=3603.6\\\approx 3604$

Thus, the expected numbers of voters who would vote for Brown is 3604.

6 0

3 years ago