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ValentinkaMS [17]
1 year ago
12

As concert goers enter a stadium, a security guard randomly inspects their backpacks for alcoholic beverages. Of 130 backpacks c

hecked so far, 17 contained alcoholic beverages of some kind. The guards want to estimate the percentage of all backpacks of concert goers at this concert that contain alcoholic beverages.a. Identify the population
b. Identify the Sample
c. Identify p
d. Identify
e. Would you trust a confidence interval for the true proportion based on these data? Explain

Mathematics
1 answer:
lisov135 [29]1 year ago
4 0

Answer:

a. The population refers to targeted area under study which is all the backpacks of concertgoers

b. The sample refers to that part of the population inspected for study which is the number of backpacks checked in this case

c. P is the percentage or proportion of all backpacks of concertgoers that contained alcoholic beverages

e Using a confidence interval of 95%, I will.

This is because the true proportion lies between 7.3% and 18.9% and the data given in the question has an estimate of 13.1% which lies within the range of values

Step-by-step explanation:

PLEASE CHECK ATTACHMENT FOR EXPLANATION AND STEP BY STEP SOLUTION

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se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y
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Answer:

It is proved that f_x, f_y exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)

  • To show exixtance of f_x(0,0), f_y(0,0) we take,

f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

And,

f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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2 years ago
Mathew rolls a number cube labeled with the numbers 1−6. He then flips a fair coin. What is the probability that he rolls a 4 an
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Answer: 0.083


Step-by-step explanation:

Numbers on cube=6

faces on coin=2

Therefore, the total outcomes=6\times2=12

Now, the favorable outcome that he rolls a 4 and flips a head=1

The probability that he rolls a 4 and flips a head=\frac{\text{favorable outcome}}{\text{total outcome}}

⇒The probability that he rolls a 4 and flips a head=\frac{1}{12}=0.083333\approx0.83.

Therefore, The probability that he rolls a 4 and flips a head=0.083

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