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Bingel [31]
3 years ago
13

Two squares overlap. The area of the overlapped region is 1/4 of the small square's area and is 2/9 of the large square's area.

What is the ratio of the area of the small square to the large square?
Mathematics
1 answer:
guajiro [1.7K]3 years ago
7 0

Answer:

Step-by-step explanation:

.25+.24+2^=1.8-25/2=12

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A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 ​respon
Komok [63]

Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14​% chose chocolate​ pie, and the margin of error was given as plus or minus ±3 percentage points. 

The pivotal quantity for the confidence interval for the population proportion is given by;

                            P.Q.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of adults who chose chocolate​ pie = 14%

            n = sample of adults = 500

            p = true proportion

Now, the 99% confidence interval for p =  \hat p \pm Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }

Here, \alpha = 1% so  (\frac{\alpha}{2}) = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }  = 0.03 for 99% interval.

<u>So, 99% confidence interval for p</u>  =  0.14 \pm2.5758  \times \sqrt{\frac{0.14(1-0.14)}{500} }

                                                        = [0.14 - 0.03 , 0.14 + 0.03]

                                                        = [0.11 , 0.17]

Similarly, <u>80% confidence interval for p</u>  =  0.14 \pm 1.2816  \times \sqrt{\frac{0.14(1-0.14)}{500} }

Here, \alpha = 20% so  (\frac{\alpha}{2}) = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }  = 0.02 for 80% interval.

So, <u>80% confidence interval for p</u>  =  [0.14 - 0.02 , 0.14 + 0.02]

                                                           =  [0.12 , 0.16]

Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

5 0
3 years ago
If the length of AC equals 30, what is the length of the midsegment DE? A) 10 B) 15 C) 20 D) 25
Serhud [2]

Answer:

Step-by-step explanation:

10

3 0
3 years ago
How to write g(x)=2x+3/x+1 in the form of:g(x)=a/x+p +q
aliya0001 [1]
Hello,

Please write correctly.

g(x)= (2x+3)/(x+1) to be written like a/(x+p) + q

It is very simple!

(2x+3)/(x+1)= [(2x+2)+1]/(x+1)= (2(x+1)+1)/(x+1)= 2+1/(x+1)


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3 years ago
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olga2289 [7]
307.85
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+23.75
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3 years ago
Which equation has infinitely many solutions?
mestny [16]
The correct answer is the letter B
4 0
3 years ago
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