Find the ratio of the perimeters and the ratio of the areas of the larger rectangle to the smaller rectangle.

Find the critical value needed to construct a 95% CI of a population mean with an unknown standard deviation and a sample size o

kaheart [24]

Answer:

$t_{\alpha/2}=-2.02, t_{1-\alpha/2}=2.02$

Step-by-step explanation:

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".

In order to find the critical value we need to take in count that we are finding the critical value for the population mean and without the standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . We need to calculate the degrees of freedom are given by:

$df=n-1=39-1=38$

We can find the critical value using the following excel codes:

"=T.INV(0.025;38)" or "T.INV(1-0.025;38)"

And the critical values would be given by:

$t_{\alpha/2}=-2.02, t_{1-\alpha/2}=2.02$

7 0

3 years ago

The half-life is a substance is 375 years. If 70 grams is present now, how much will be present in 500 years?

Lynna [10]

Answer:

27.76 grams will be present in 500 years

Step-by-step explanation:

The given formula is $A=A_{o}e^{kt}$ , where A is the value of the substance in t years, and $A_{o}$ is the initial value

∵ The half-life is a substance is 375 years

- Substitute A by $\frac{1}{2}A_{o}$ and t by 375 to find the value of k

∴ $\frac{1}{2}A_{o}=A_{o}e^{375k}$

- Divide both sides by $A_{o}$

∴ $\frac{1}{2}=e^{375k}$

- Insert ㏑ in both sides

∴ ㏑( $\frac{1}{2}$ ) = ㏑ ( $e^{375k}$ )

- Remember ㏑ ( $e^{n}$ ) = n

∵ ㏑ ( $e^{375k}$ ) = 375 k

∴ ㏑( $\frac{1}{2}$ ) = 375 k

- Divide both sides by 375

∴ k ≈ -0.00185

∴ $A=A_{o}e^{-0.00185t}$

∵ 70 grams is present now

- That means the initial value is 70 grams

∴ $A_{o}$ = 70

∵ The time is 500 years

∴ t = 500

- Substitute the values of $A_{o}$ and t in the formula

∵ $A=70e^{-0.00185(500)}$

∴ A = 27.76

∴ 27.76 grams will be present in 500 years

3 0

3 years ago

The function f(x) models the average cost per unit, f(x), for Electrostuff to manufacture x units of Electrogadget IV. How man

andrey2020 [161]

Complete question is;

The function f(x) = (25000 + 280x)/x models the average cost per unit, f(x), for Electrostuff to manufacture x units of Electrogadget IV. How many units must the company produce to have an average cost per unit of $390?

Answer:

227 units

Step-by-step explanation:

We are given the function;

f(x) = (25000 + 280x)/x

Where;

f(x) is the average cost per unit

x is the number of units

Now, we want to find out how many units the company must produce to have an average cost per unit of $390.

Thus, plugging $390 for f(x), we have;

390 = (25000 + 280x)/x

When we cross multiply, we get;

390x = 25000 + 280x

390x - 280x = 25000

110x = 25000

x = 25000/110

x ≈ 227

6 0

3 years ago

Which point lies on the graph of the function shown below y=-x^2+5x-3

Andrei [34K]

Answer:

C: (2,3)

Step-by-step explanation:

to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you

4 0

3 years ago

Which congruence theorem can be used to prove △ABC ≅ △DEF? AAS ASA HL SAS

Delicious77 [7]

Answer:

HL

Step-by-step explanation:

Use the HL Congruence Theorem to prove that the triangles are congruent.

8 0

3 years ago