I can’t solve this. Please explain!

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% c

siniylev [52]

Answer:

19 beers must be sampled.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that $\sigma = 0.26$

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.645\frac{0.26}{\sqrt{n}}$

$0.1\sqrt{n} = 1.645*0.26$

$\sqrt{n} = \frac{1.645*0.26}{0.1}$

$(\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2$

$n = 18.3$

Rounding up:

19 beers must be sampled.

7 0

3 years ago

Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body

PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

(c) The amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

(a)

Compute the 5-hour decay factor as follows:

$5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042$

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

$A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112$

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

4 0

3 years ago

How do you find the arctan 4/3 ? (Without a calculator)

Soloha48 [4]

If arctan 4/3 = the tangent of that angle will be 4/3 , opposite 4 over adjacent 3

Now, you only have to take the sin of that angle it's opposite 4 over hypotenuse 5.

You will get that the answer is 4/5

hope this helps

7 0

3 years ago

Latika reads half as many fiction books as she reads nonfiction.She reads three times as many nonfiction books as mystery novels

telo118 [61]

Answer:

She read 15 fiction books

Step-by-step explanation:

Multiply 10 x 3 = 30

so she reads 30 non fiction books and she reads half as many fiction books as she reads nonfiction.

Divide 30/2=15

4 0

3 years ago

Amanda and her group of friends spent a total of $35.50 on 7 hot dogs and 6 cheese burgers. Greg and his group of friends spent

Alexeev081 [22]

7h + 6b = 35.50
5h + 6b = 30.50

The difference between the 2 totals spent is $5, and there were the same number of burgers, but 2 fewer hotdogs. So $5/2 = $2.50, the cost of a hot dog. Substitute that into the equations to solve for burgers (b)

5(2.50) + 6b = 30.50
12.50 + 6b = 30.50
6b = 18
b = 3

Check the work:
7(2.50) + 6(3) =
17.50 + 18 = 35.50

8 0

3 years ago