Cos 0=9/15 find tan 0

Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

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.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

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?

We would need a sample of n.

n is found when $M = 0.5$ . So

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

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

3 years ago

A book sold 41,900 copies in its first month of release. Suppose this represents 8.1% of copies sold to date. How many copies ha

babymother [125]

517284 books have been sold to date.

Step-by-step explanation:

Given,

Copies sold in first month = 41900

This represents 8.1% of copies sold to date.

Let,

x be the number of copies that have been sold to date.

8.1% of x = 41900

$\frac{8.1}{100}*x=41900\\0.081x=41900\\$

Dividing both sides by 0.081

$\frac{0.081x}{0.081}=\frac{41900}{0.081}\\x=517283.95$

Rounding off to nearest whole number

x = 517284

517284 books have been sold to date.

Keywords: percentage, division

Learn more about division at:

#LearnwithBrainly

3 0

3 years ago

Pls help with n.b : 10,11,12 U GET 13 COINS BC ITS ALL I HAVE PLS HELP!!

Nat2105 [25]

Fresh Harbour
Netherton
Old Town Harbour

Please mark as brainliest

8 0

2 years ago

Write the equivalent fractions of 11/12

skelet666 [1.2K]

Answer:

11/2, 22/4, 33/6, 44/8, 55/10, 66/12, 77/14, 88/16, 99/18, 110/20, 121/22, 132/24, 143/26, 154/28, 165/30, 176/32, 187/34, 198/36, 209/38, 220/40, and so on ...

8 0

3 years ago

Normal Distribution. Cherry trees in a certain orchard have heights that are normally distributed with mu = 112 inches and sigma

Lubov Fominskaja [6]

Answer:

The probability that a randomly chosen tree is greater than 140 inches is 0.0228.

Step-by-step explanation:

Given : Cherry trees in a certain orchard have heights that are normally distributed with $\mu = 112$ inches and $\sigma = 14$ inches.