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Varvara68 [4.7K]
3 years ago
11

Suppose that a random sample of size 64 is to be selected from a population with mean 50 and standard deviation 5. (a) What are

the mean and standard deviation of the sampling distribution of x
Mathematics
1 answer:
grin007 [14]3 years ago
6 0

Answer:

Mean of sampling distribution = 50

Standard deviation of sampling distribution, = 0.625

Step-by-step explanation:

Given :

Mean, μ = 50

Standard deviation, σ = 5

Sample size, n = 64

The mean of sampling distribution, μxbar = population mean, μ

μxbar = μ

According to the central limit theorem, the sampling distribution converges to the population mean as the sample size increases, hence, , μxbar = μ = 50

Standard deviation of sampling distribution, σxbar = σ/√n

σxbar = 5/√64 = 5 / 8 = 0.625

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Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Us
Eva8 [605]

The area of the base would be found using the area of a triangle formula which is 1/2 x base x height.

The base and height are the two sides perpendicular to each other, which are both 5 inches.

The area of the base = 1/2 x 5 x 5 = 12.5 square inches.

The volume of the triangular prism is the area of the base times the height, which is 4 inches.

Volume of the triangular prism is 12.5 x 4 = 50 cubic inches.

Volume of the triangular prism is 1/3 x area of base x height, which is 7:

Volume of the triangular prism = 1/3 x 12.5 x 7 = 29.17 cubic inches.

Total volume = 29.17 + 50 = 79.17 cubic inches.

3 0
3 years ago
The variables a, b, and c represent polynomials where a = x 1, b = x2 2x − 1, and c = 2x. what is ab c in simplest form?
inna [77]
If you would like to write a * b + c in simplest form, you can do this using the following steps:

a = x + 1
b = x^2 + 2x - 1
c = 2x
a * b + c = (x + 1) * (x^2 + 2x - 1) + 2x = x^3 + 2x^2 - x + x^2 + 2x - 1 + 2x = x^3 + 3x^2 + 3x - 1

The correct result would be x^3 + 3x^2 + 3x - 1.




7 0
3 years ago
Read 2 more answers
An angle measures 40° less than the measure of its supplementary angle. What is the measure of each angle?
Vilka [71]

Step-by-step explanation:

(180-x)-40=X

140 -x=X

140= 2x

x=140/2

x=70

the answer is 70 degree

4 0
2 years ago
A company produces x units of a product per month, where c(x) represents the total cost and r(x) represents the total revenue fo
Nat2105 [25]

Answer:

The total profit P(x) or the month is P(x)=-0.5x^2+500x-350.

Step-by-step explanation:

A company produces x units of a product per month.

The total cost represents by the function C(x).

C(x)=300x+250

The total revenue represents by the function R(x).

R(x)=-0.5x^2+800x-100

The profit is the difference between revenue and cost.

P(x)=R(x)-C(x)

P(x)=-0.5x^2+800x-100-(300x+250)

P(x)=-0.5x^2+800x-100-300x-250

Combine like terms.

P(x)=-0.5x^2+(800x-300x)+(-100-250)

P(x)=-0.5x^2+500x-350

Therefore, the total profit P(x) or the month is P(x)=-0.5x^2+500x-350.

5 0
3 years ago
A U.S. dime has a thickness of 1 7/20 millimeters. Gary has a stack of dimes 78 3/10 millimeters tall. How many dimes does he ha
Dahasolnce [82]

Answer:

58 number of dimes.

A. $5.8

B. 131.602 grams.

Step-by-step explanation:

A U.S. dime has a thickness of 1\frac{7}{20} = 1.35 mm.

Now, Gary has a stack of dimes that is 78\frac{3}{10} = 78.3 mm in height.

Therefore, Gary has \frac{78.3}{1.35} = 58 dimes in total.

A. Now, each dime is equivalent to $0.1.

Therefore, the total value of the dimes that Gary has is $(0.1 × 58) = $5.8.

B. If each dime weighs 2.269 grams, then the mass of the entire stack of dimes will be (2.269 × 58) = 131.602 grams. (Answer)

8 0
3 years ago
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