There are 500 employees in a firm, 45% are female. a sample of 60 employees is selected randomly. the probability that the sample proportion of females is between 0.40 and 0.55 is

Answers

Answer 1

Answer:

Let X be the number of female employee. Let n be the sample size, p be the probability that selected employee is female.

It is given that 45% employee are female it mean p=0.45

Sample size n=60

From given information X follows Binomial distribution with n=50 and p=0.45

For large value of n the Binomial distribution approximates to Normal distribution.

Let p be the proportion of female employee in the given sample.

Then distribution of proportion P is normal with parameters

mean =p and standard deviation = $\sqrt{(p(1-p))/(n)}$

Here we have p=0.45

So mean = p = 0.45 and

standard deviation = $\sqrt{(0.45(1-0.45))/(60)}$

standard deviation = 0.0642

Now probability that sample proportions of female lies between 0.40 and 0.55 is

P(0.40 < P < 0.45) = $P((0.40 - 0.45)/(0.0642) < (P-mean)/(standard deviation) < (0.55- 0.45)/(0.0642) )$

= P(-0.7788 < Z < 1.5576)

= P(Z < 1.5576) - P(Z < -0.7788)

= P(Z < 1.56) - P(Z < -0.78)

= 0.9406 - 0.2177

= 0.7229

The probability that the sample proportion of females is between 0.40 and 0.55 is 0.7229

Answer 2

Answer:

Final answer:

To find the probability that the sample proportion of females is between 0.40 and 0.55, convert the sample proportions to z-scores and use the z-table to find the probabilities.

Explanation:

To find the probability that the sample proportion of females is between 0.40 and 0.55, we need to find the z-scores associated with these proportions and use the z-table to find the probabilities.

First, we need to convert the sample proportions to z-scores using the formula: z = (p - P) / √(P(1-P) / n), where p is the sample proportion, P is the population proportion, and n is the sample size.

Once we have the z-scores, we can use the z-table to find the probabilities. The probability that the sample proportion of females is between 0.40 and 0.55 is the difference between the probabilities associated with the z-scores for 0.40 and 0.55.

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A man buys a horse for $60. He sells the horse for $70. He then buys the horse back for $80. And he sells the horse again for $90. In the end, how much money did the man make or lose? Or did he break even?
Will give extra points and brainliest !! /:
Draw a bar diagram for the equation and then solve 2,400/6=m
Answer the questions in the picture please

Carol drew an isosceles triangle that has an angle that measures 62°. Which could be the measures of the other two angles in Carol’s triangle?A. 62° and 62°
B. 56° and 56°
C. 28° and 90°
D. 56° and 62°

Answers

Answer: the answer is B

Step-by-step explanation:

Answer:

56 and 62

Step-by-step explanation:

HELP ME I WILL GIVE BRAINLIEST California has a population of approximately 4 × 10^7 people and South Dakota has a population of approximately 8 × 10^5 people.

Answers

The population in California is 50 times greater than the population in South Dakota.

The number of times the population in California is higher than that in South Dakota

To find out how many times greater the population in California is than in South Dakota, you can divide the population of California by the population of South Dakota:

Population of California = 4 * 10⁷

Population of South Dakota = 8 * 10⁵

Population ratio = (Population of California) / (Population of South Dakota)

Population ratio = (4 * 10⁷) / (8 * 10⁵)

Population ratio = 50

Therefore the population in California is 50 times greater than the population in South Dakota.

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Question

California Has A Populatio Of Approximately 4*10^(7)People And South Dakota Has Populatio Of Approximately 8*10^(5) People. How Many Times Greater Is The Population In California Than In South Dakota

california has a populatio of approximately 4*10^(7)people and south dakota has populatio of approximately 8*10^(5) people. how many times greater is the population in california than in south dakota

Answer:

40000000 800000

Step-by-step explanation:

whats the question here?

Convert the measurements below:
a. 8 millimeters = ____meters

Answers

Answer:

0.008 meters

Step-by-step explanation:

Answer:

0.008 meters

Step-by-step explanation:

Hope this helps! :3

plz mark as brainliest!

4y-x=2x-4=x+y
solve for x

Answers

X=12

Explanation: in the photo

Answer:

a system of equations , as below

Step-by-step explanation:

4y-x

2x-4

x+y

use any two of the above to find a formula for one of the variables since they are all equal to each other.. btw.. it makes it much easier .. that they are all equal. :)

2x-4=x+y ⇒ x-4=y use this to plug into the y in the top formula

4(x-4)-x=2x-4 ⇒ 4x-16-x=2x-4 ⇒ 3x-16=2x-4 ⇒ x=12 yay! ;) now plug in 12 for x

2(12)-4=(12)+y ⇒ 24-4 = 12 +y ⇒ 8=y yay ! now we have both x and y

x=12

y= 8

this checks by plugging in the two number found for x & y (btw I had to try this about 4 times ) :P I kept messing up the algebra which is soooo easy to mess up.

Evaluate the indefinite integral as a power series f(x) = 1 tan-1(x7) dx n=0 What is the radius of convergence R? R= -/0.77 points
Evaluate the indefinite integral as a power series x7 In(1 x) dx f(x) = C + n=0
What is the radius of convergence R?

Answers

Answer:

$\mathbf{f(x)=C + \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}$

For convergence since |x| > 1

The radius of convergence R = 1

$\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0) \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}$

For convergence since |x| < 1

The radius of convergence R = 1

Step-by-step explanation:

Given that:

$f(x) = \int tan^(-1) (x^7) \ dx$

Let recall that for Power series of tan⁻¹ (x)

$tan^(-1) (x) = \sum \limits ^(\infty)_(n=0) ((-1)^n x^(2n+1))/((2n+1))$

Then $tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n (x^7)^(2n+1))/((2n+1))$

$tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n+7))/((2n+1))$

Thus;

$f(x) =\int tan^(-1) (x^7) \ dx = \int \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n+7))/((2n+1))$

$\implies \sum \limits ^(\infty)_(n=0) ((-1)^n )/((2n+1)) \int x^(14n+7) \ dx$

$\mathbf{f(x)=C + \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}$

For convergence since |x| > 1

The radius of convergence R = 1

$\int x^7 \ In (1 + x) \ dx$

Recall that for power series of,

$In(1+x) = \sum \limits ^(\infty)_(n = 0) ((-1)^n \ x^(n+1))/(n +1)$

Thus;

$x^7 \ In (1+x) = x^7 \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+1) )/(n+1)$

$\implies \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+8) )/(n+1)$

$f(x) = \int x^7 \ In (1+x) \ dx = \int \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+8) )/(n+1) \ dx$

$=\sum \limits ^(\infty)_(n =0) ((-1)^n)/(n+1) \int \ x^(n+8) \ dx$

$\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0) \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}$

For convergence since |x| < 1

The radius of convergence R = 1

Final answer:

To evaluate the indefinite integral as a power series for the given equations, we use the power series expansions of the functions involved. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

Explanation:

To evaluate the indefinite integral f(x) = 1/tan-1(x7) dx as a power series, we can use the power series expansion of tan-1(x). The power series expansion of tan-1(x) is x - (x3/3) + (x5/5) - (x7/7) + .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

To evaluate the indefinite integral f(x) = x7ln(1-x) dx as a power series, we can use the power series expansion of ln(1-x). The power series expansion of ln(1-x) is -x - (x2/2) - (x3/3) - (x4/4) - .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

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These triangles are similar. What is the value for it?

Answers

Answer:

The vault of h is 10

Step-by-step explanation:

Since the whole triangle is 27 and the one side is 9 we know the other side must be 18. You multiply by 2 to get get from 9. That means they are similar and you just multiply 5 by 2 to get h=10.

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