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leva [86]
3 years ago
12

Write each function in standard form g(x) = 2(x + 6)2 – 11

Mathematics
1 answer:
tia_tia [17]3 years ago
8 0
Have you used a calculator or ask the teacher for help?
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What is 1023x102+112-5=
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Answer:

The answer is 104,453.

Step-by-step explanation:

Multiply 1,023 and 102 first because you always have to do your problems left to right in math. Your equation should now look like 104,346 + 112 - 5. Calculate the sum of the positive numbers by adding 104, 346 + 112. Your equation should now be 104,458 - 5. Then lastly, you subtract the numbers 104,458 and 5, and you should get 104, 453 as your answer.

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Step-by-step explanation:

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3 years ago
A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale,
Lyrx [107]

Answer:

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

\bar X_1 -\bar X_2 =85.82-81.90=3.92  

b) SE=\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=0.975  

And the Margin of error is given by:

Me= z_{\alpha/2} * SE=1.96*0.975=1.910

c) The 95% confidence interval would be given by 2.009 \leq \mu_1 -\mu_2 \leq 5.83.

Step-by-step explanation:

Notation and previous concepts

n_1 =35 represent the sample of ships that carry fewer than 500 passengers

n_2 =44 represent the sample of ships that carry 500 or more passengers

\bar x_1 =85.82 represent the mean sample of of ships that carry fewer than 500 passengers

\bar x_2 =81.90 represent the mean sample of of ships that carry 500 or more passengers

\sigma_1 =4.55 represent the population deviation of ships that carry fewer than 500 passengers

\sigma_2 =3.97 represent the sample deviation of ships that carry 500 or more passengers

\alpha=0.05 represent the significance level

Confidence =95% or 0.95

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)  

Part a

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

\bar X_1 -\bar X_2 =85.82-81.90=3.92  

Part b: At 95% confidence, what is the margin of error?

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96  

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{4.55^2}{35}+\frac{3.97^2}{44})}=0.975  

And the Margin of error is given by:

Me= z_{\alpha/2} * SE=1.96*0.975=1.910

Part c: What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

Confidence interval  

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

3.92-1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=2.009  

3.92+1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=5.830  

So on this case the 95% confidence interval would be given by 2.009 \leq \mu_1 -\mu_2 \leq 5.83.

7 0
3 years ago
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