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2 years ago

In 2000 Michele paid $3.980.40 in Social Security (6.2%) tax. What was Michele's taxable income in 2000?

Mathematics

1 answer:

Mademuasel [1]2 years ago

6 0

$39840.40 *0.062 = 246.78$

The portion of his income that was taxable was equal to $246.78

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A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

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".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$

The standard error is given by the following formula:

$SE=\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$

And replacing we have:

$SE=\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=1.118$

Confidence interval

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

$5-1.88\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=2.898$

$5+1.8\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=7.102$

So on this case the 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

7 0

3 years ago

There are (4^9)5 ⋅ 4^0 books at the library. What is the total number of books at the library? 4^9 - 4^45 - 4^46 - 1

maria [59]

Exponent rules : (a^m)^n = a^(mn) and a^0 = 1

(4^9)^5 * 4^0 =
4^45 * 1 =
4^45 <==

7 0

3 years ago

Is a parallelogram an equilateral?

Vladimir [108]

"A quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram."

4 0

3 years ago

Find the approximate value of the circumference of a circle with the given radius. UseT 3.14. Round your results to one more dec

Temka [501]

Answer:

25.1 inches

Step-by-step explanation:

Radius of the circle = 4 inches

We have to calculate the value of Circumference of the circle.

The formula to calculate the circumference is:

Circumference = 2πr

We have to use π = 3.14, as said in the question:

So using the values, we get:

Circumference = 2 x 3.14 x 4 = 25.12 inches

Number of decimals in radius is zero, so we have to round the answer to one decimal place as said in the question.

Therefore, the circumference of the circle rounded to one decimal place will be 25.1 inches

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3 years ago

What is the solution, vertex, and y-intercept of the graph? Please answer ASAP.

inna [77]

Graph is accurate enuf so that you can determine immed that the vertex / minimum is at (3,-4) and that the y-intercept is at (0,5).

If by "solutions" you mean "roots," the roots are {1, 5} (where y=0).

4 0

3 years ago

In 2000 Michele paid $3.980.40 in Social Security (6.2%) tax. What was Michele's taxable income in 2000? ​

In 2000 Michele paid $3.980.40 in Social Security (6.2%) tax. What was Michele's taxable income in 2000?