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mote1985 [20]
2 years ago
5

Find the absolute and local maximum and minimum values of f . (Enter your answers as a comma-separated list. If an answer does

not exist, enter DNE.)
f(t)=4cos(t), â3Ï/2â¤tâ¤3Ï/2
Mathematics
1 answer:
larisa86 [58]2 years ago
6 0

Answer:

f(t)=4cos(t), â3Ï/2â¤tâ¤3Ï/2

Step-by-step explanation:

You might be interested in
Help!!! The one marked red is wrong
kakasveta [241]

Answer:

4x+5

Step-by-step explanation:

5 0
3 years ago
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t
skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that \mu = 273, \sigma = 100

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 30, s = \frac{100}{\sqrt{30}}

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 50, s = \frac{100}{\sqrt{50}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 100, s = \frac{100}{\sqrt{100}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0
2 years ago
Alan is comparing the cost of a fresh lobster dinner at two different restaurants. The first
Pepsi [2]

Good evening ,

Answer:

The weight : 29 pound

Alan would pay for his dinner : $130

Step-by-step explanation:

Let x represent the weight of the lobster

the cost of the dinner at restaurant 1 is 4x + 14  

the cost of the dinner at restaurant 2 is 3x + 43

Now ,we have to solve the equation :  4x + 14 = 3x + 43

4x + 14 = 3x + 43

⇔ x = 43 - 14

⇔ x = 29

In this case Alan would pay the same amount for his dinner at any restaurant:

the price = 4×(29)+14 = 130

               = 3×(29)+43 = 130.

:)

4 0
3 years ago
Write an equation in slope-intercept form for the following line:<br><br> (-14,1) and (13,-2)
alex41 [277]

Answer:

\large \boxed{y =  -  \frac{1}{9} x -  \frac{5}{9} }

Step-by-step explanation:

In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.

\large \boxed{m =  \frac{y_2 - y_1}{x_2 - x_1} }

m-term is defined as slope in y = mx+b form which is slope-intercept form.

Now we substitute these ordered pairs (x, y) in the formula.

\large{m =  \frac{1 - ( - 2)}{ -14 - 13} } \\  \large{m =  \frac{1 + 2}{ - 27} } \\  \large{m =  \frac{3}{ - 27}  =  -  \frac{1}{9} }

After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is

\large \boxed{y = mx + b}

We already know m-value as we substitute it.

\large{y =  -  \frac{1}{9} x  + b}

We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)

We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.

\large{y = -  \frac{1}{9} x + b} \\  \large{ - 2 =  -  \frac{1}{9} (13) + b} \\  \large{ - 2 =  -  \frac{13}{9}  + b} \\  \large{ - 2 +  \frac{13}{9}  = b} \\  \large{ -  \frac{5}{9}  = b}

Finally, we know b-value. Then we substitute it in our equation.

\large{y =  -  \frac{1}{9} x + b} \\  \large{y =  -  \frac{1}{9} x -  \frac{5}{9} }

4 0
2 years ago
PLS help ASAP I DONT have time to answer this, it also detects if it’s right or wrong.
lbvjy [14]

Answer:

I think it's B

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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