What is the value of 8m + 5n when m = 4 and n = 10?

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer

AlladinOne [14]

Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

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".

$\bar X=4$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=100 represent the sample size

Solution to the problem

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

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

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$

Now we have everything in order to replace into formula (1):

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

4 0

3 years ago

Find the equation of the line.<br> Use exact numbers.

Virty [35]

Answer: https://api-project-1022638073839.appspot.com/questions/how-do-you-use-the-sum-or-difference-identity-to-find-the-exact-value-of-sin-255#582997

Step-by-step explanation:

this will help you.

4 0

3 years ago

A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a

mezya [45]

Answer:

See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

$y=sin(x)$

That function has:

Midline, also known as rest or equilibrium position: y = 0
Minimum: - 1
Maximum: 1
Amplitude: the distance between a minimum or a maximum and the midline = 1
period: the interval of repetition of the function = 2π

The more general sine function is:

$y=Asin(Bx+C)+D$

That function has:

Midline: y = D (it is a vertical shift from the parent function)
Minimum: - A + D
Maximum: A + D
Amplitude: A
period: 2π/B
phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2

Amplitude, A = 3

midline y = - 1 ⇒ D = - 1

y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

$y=3sin(2x/\pi+C)-1$

Substitute (0, -1)

$-1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0$

Hence, the function to graph is:

$y=3sin(\pi x/2)-1$

To draw that function use this:

Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
Minima: 3(-1) - 1 = - 3 - 1 = -4
y-intercept: (0, - 1)
x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

4 0

3 years ago

Between 2005 and 2008, the average rate of inflation was about3.4 per year. If a cart of groceries cost $140 in 2005, what did i

Elan Coil [88]

The formula is
A=p (1+r)^t
A future value?
P current value 140
R rate of inflation 0.034
T time 2008-2005=3 years
A=140×(1+0.034)^(3)
A=154.77 round your answer to get
A=155

3 0

3 years ago

The perimeter of this figure is 70 feet. How long are the unknown sides?

Damm [24]

5+10+10+12+14+7= 58
x= 70-58
x=12 ft

4 0

3 years ago

Read 2 more answers