Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee at local fast food restaurants. Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg. If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result

Answer:

2.75 miles, 14520 feet

Step-by-step explanation:

11 miles/4=2.75

1 mile=5280 feet

2.75 miles=14520 feet

The question is incomplete. The complete question is :

The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.

b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.

a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)

b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)

Solution :

Given :

The volume of the right circular cone with a radius r and height h is

[tex]$V=\frac{1}{3} \pi r^2 h$[/tex]

[tex]$dV = d\left(\frac{1}{3} \pi r^2 h\right)$[/tex]

[tex]$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96

So, r = 5.9  and dr = 6.8 - 5.9 = 0.9

     h = 4  and dh = 3.96 - 4 = -0.04

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$[/tex]

[tex]$dV=44.484951 - 1.458117$[/tex]

[tex]$dV=43.03$[/tex]

Therefore, the approximate change in volume is dV = 43.03 cubic units.

b).  The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92

So, r = 6.47  and dr = 6.45 - 6.47 = -0.02

     h = 10  and dh = 9.92 - 10 = -0.08

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$[/tex]

[tex]$dV=-2.710147-3.506930$[/tex]

[tex]$dV= -6.22$[/tex]

Hence, the approximate change in volume is dV = -6.22 cubic units

Answer:

Assuming that this data is used to conduct a hypothesis test to test the manufacturers' claim, the test statistic we an use is:

the paired sample t-test.

Step-by-step explanation:

a) Data and Analysis:

Subject   Before   After

1                 225      215

2                245     240

3                 188      188

4                210       212

5               282       175

6               275      260

7               230      225

8               195      200

9               190       185

b) The paired sample t-test is used to compare the means from the same dataset but at different times (say, one month apart).  It supports the comparison of sample data before and after the data subjects have taken the dietary supplement.  When the t-value is high, it is an evidence that the null hypothesis should be rejected.  The higher value of the t-test, therefore, indicates that there is a large difference between the two sample sets.  On the other hand, a small t-value shows similarity between the two sample sets.

Answer:

Positive value of correlation Coefficient

Step-by-step explanation:

The correlation Coefficient value, R is a correlation measure which gives information about both the strength of association between two variables and also the type of association between them (negative or positive). R has a standardized value which ranges from - 1 to +1

Negative relationship between variables are depicted with negative (where one variable decreases as the other increases) R value while positive association (increase in one variable means leads to increase in the other variable) are depicted with positive R values.

Therefore, for the relationship described above, the correlation Coefficient will be positive.

Answer:

37.6 dollars

Step-by-step explanation:

4 pounds = 32 dollars

0.2 pound = 1.6 dollars

0.5 = 4 dollars

0.1 = 0.8 dollars

Answer:

10.3

Step-by-step explanation:

6²+b²=9²

36+b²=81

b²=81-36

b²=45

b=√45

b=6.7

So CE is 6.7.

6²+b²=7²

36+b²=49

b²=49-36

b²=13

b=√13

b=3.6

so EA is 3.6

AC = CE+EA = 6.7+3.6 = 10.3

Please put how many pizzas there are and how much money he has (please put the full question)

Answer:

4

Step-by-step explanation:

the third side = x

Pythagorean theorem: a² + b² = c²

3² + x² = 5²

=> x² = 5² - 3²

=> x = √5² - 3²

=> x = √25 - 9

=> x = √16

=> x = 4

bro i will do it but just tell me the answer to question 1 cuz thats what it is referring too

Answer:

5 units.

Step-by-step explanation:

Since the distance is straight up.

You have two options:

Graph those two points and count the spaces separating them

or

Since they have the same x, you would only need to subtract 7-2.

Answer:

The answer is 40

Step-by-step explanation:

The cost of 50 pounds of beans is 40 dollars.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We can use a ratio to solve the problem;

5 pounds/ 4 dollars  = 50 pounds/ x dollars

Using cross products;

5x = 4 x 50

5x = 200

Divide by 5;

5x/5 = 200/5

x = 40

The cost of 50 pounds of beans is 40 dollars.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

32 yd²

Step-by-step explanation:

because 8 • 4 is 32 so it's 32 yd²

Answer:

A = 32 yds^2

Step-by-step explanation:

We know the formula for the area of a rectangle is

A = lw  where l is the length and w is the width

A = 4 yds * 8 yds

A = 32 yds^2

Answer:

the no elephant or bear car precedes the first car with lions is 0.60

Step-by-step explanation:

The computation of the probability is shown below:

= 1 - (no depend or acrobat car precedes)

=  1 - (4 ÷ 20  + 4 ÷ 20)

= 1 - 8 ÷ 20

= 20 - 8 ÷ 20

= 12 ÷ 20

= 0.60

Hence, the no elephant or bear car precedes the first car with lions is 0.60

The same would be considered and relevant too

Answer:

10^20

Step-by-step explanation:

So in this word problem, we have to multiply 10^13 bacteria cells on a single person by the 10^7 of people.

Always remember this, when you have exponenets with the same bases, and the question asks for multiplying and dividing exponents, you just need to add and subtract the exponent.

So in this case, we will just add since it calls for multipactation.

So we need to solve:

10^13+7

This will just equal:

10^20 power

Hope this helps ;)

Answer:

So 4 ÷ 1/5 = 4 × 5. So your answer is 5.

Answer:

F'=(1,-5)

Step-by-step explanation:

First off, F is moved 4 units right and 2 units down: add 4 to the x component of the coordinate and take 2 from the y component:

-3+4=1

7-2=5

So our point is (1.5) before it is reflected over the y-axis.

When a point (a,b) is reflected over the y-axis, it's coordinates change to (a,-b). Therefore (1,5) changes to (1,-5)

Answer:

answer a

Step-by-step explanation:

Answer:

an arithmetic sequence

Step-by-step explanation:

I think it's because it adds 5 each time and in arithmetic sequences there's a common difference, so it'd be an arithmetic sequence :)

Answer:

D I'm not sure if it is correct but I'm sorry if wrong Good luck!

Answer:

48

Step-by-step explanation:

Answer:

140 cm²

Step-by-step explanation:

The height of the parallelogram is 10cm . And its base is 14cm .We know that the area of parallelogram is product of base and height .

⇒ Area = base × Height

⇒ Area = 14cm × 10cm

⇒ Area = 140 cm² .

Answer:

x = 30°

y = 70°

z = 80°

Step-by-step explanation:

[tex]x = 180 \degree - 150 \degree = 30 \degree \\ \\ z = 180 \degree - 100 \degree = 80 \degree \\ \\ y = 180 \degree - (30 \degree + 80 \degree ) \\ \\ y = 180 \degree -110 \degree \\ \\ y = 70 \degree[/tex]

Answer:

5π/12

Step-by-step explanation:

5 pie / 12

(hope this helps can i plz have brainlist :D hehe)

Answer:

4/10, 6/15, 8/20

Step-by-step explanation:

Answer:

(2,067 + 49) x 21

Step-by-step explanation:

I did the math for each answer