Find the sum of 2/3 and it’s additive inverse

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

Develop an estimate for each of the following situations.(at) The cost of a 500-mile automobile trip, if gaso-line is $4 per gal

Olin [163]

Answer:

The answer is below

Step-by-step explanation:

develop an estimate for each of the following situations.

(a) The cost of a 500- mile automobile trip, if gasoline is $4.00 per gallon, vehicle wear and tear is $0.65 per mile, and our vehicle gets 25 miles per gallon.

(b) The total number of hours in the average human life, if the average life is 75 years.

(c) The number of days it takes to travel around the equator using a hot air balloon, if the balloon averages 100 miles per day, the diameter of the earth is ~4,000 miles.

Solution:

a) The total trip = 500 mile

Cost of wear and tear = $0.65 per mile = $0.65 * 500 mile = $325

25 miles takes 1 gallon of gasoline at a cost of $4 per gallon

Cost of gasoline = $4 per gallon * 500 miles / 25 miles per gallon = $80

cost of a 500-mile automobile trip = Cost of wear and tear + Cost of gasoline = $325 + $80 = $405

b) Average life of human = 75 years.

1 year = 365 days, 1 day = 24 hours

Average life of human in hours = 75 years * 365 days * 24 hours =657000 hours

c) Diameter of earth = 4000 miles

Distance of equator = diameter of earth = 4000 miles

100 mile per day

number of days for the balloon to travel round the earth = 4000 miles / (100 mile per day) = 40 days

5 0

2 years ago

The table below shows the cube roots of different numbers:

Mila [183]

part A)

$\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}$

part B)

f(x) = 10 + 20x

so if you rent the bike for a few hours that is

1 hr.............................10 + 20(1)

2 hrs..........................10 + 20(2)

3 hrs..........................10 + 20(3)

so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.

f(100) = 10 + 20(100) => f(100) = 2010.

f(100), the cost of renting the bike for 100 hours.

4 0

3 years ago

*80 POINTS!!!! PLEASE HELP ME I HAVE BEEN WAITING FOR MORE THAN AN HOUR!!!!!!!!!! MARKING AS BRAINLIEST!! PLEASE SHOW WORK AND E

ruslelena [56]

Answer:

D. tan(-π/6)

Step-by-step explanation:

The tangent function is periodic with a period of π, so ...

tan(5π/6) = tan(5π/6 ± kπ) . . . for any integer k

For k = -1, we have ...

tan(5π/6) = tan(5π/6 -π) = tan(-π/6)

7 0

3 years ago

What is the slope of the line that passes through the points (1,1) and(-1,-5)

bija089 [108]

$\frac{2}{ - 6}$

5 0

3 years ago