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Lynna [10]
2 years ago
8

To estimate μ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sam

ple of 400 full professors. The sample mean is ¯x = $73,220 and the sample standard deviation is s = $4400. A 99% confidence interval for μ is:A.) 73220 ± 11440B.) 73220 ± 577C.) 73220 ± 431D.) 73220 ± 28.6
Mathematics
1 answer:
GenaCL600 [577]2 years ago
5 0

Answer:

<h3>73220±566.72</h3>

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as;

CI = xbar ± z*s/√n

xbar is the sample mean =  $73,220

z is the z score at 99% CI = 2.576

s is the standard deviation = $4400

n is the sample size = 400

Substitute the given values into the formula;

CI = 73,220 ± 2.576*4400/√400

CI = 73,220 ± 2.576*4400/20

CI = 73,220± (2.576*220)

CI = 73220±566.72

Hence a 99% confidence interval for μ is 73220±566.72

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Dennis_Churaev [7]
If u were to add 5x+20=9x you’d get x=5
3 0
2 years ago
Penelope determined the solutions of the quadratic function by completing the square. F(x) = 4x2 8x 1 –1 = 4x2 8x –1 = 4(x2 2x)
Ymorist [56]

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

<h3>What is quadratic equation ?</h3>

Any equation of the form ax^2+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Given work of Penelope is

$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$$

Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following

$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$$

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

To learn more about quadratic equations visit : brainly.com/question/1214333

8 0
2 years ago
phil has 3 times as many rocks as peter. togethe they have 48 rocks. how many mire rocks does phil have than phil
pav-90 [236]
Phil has 144 more rocks
8 0
3 years ago
Read 2 more answers
WILL MARK BRAINLIEST!!! HELP!​
Virty [35]

Answer:

d) x=4

Step-by-step explanation:

\sqrt{x} +5 = \sqrt{x + 45}

(\sqrt{x} +5)^{2}   = (\sqrt{x + 45})^{2}

x + 10\sqrt{x} +25 = x + 45

10\sqrt{x}  = 20

divide 10 in both sides

(\sqrt{x}){2}  = (2){2}

x=4

8 0
3 years ago
1.the ratio if the weight of an object on mars to its weight in earth is 9 to 25.If a person weighs 120pouns on earth,how much w
Ilya [14]
Question #1
\frac{9}{25}=\frac{x}{120}\\\\120(9) = 25x\\\\1080 = 25x\\\\x= 43.2

For #1, the answer is 43.2

Question #2
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For #2, the answer is 2150
8 0
3 years ago
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