Cavalries principles states that two solids with equal heights and base areas have equal volumes true or false?

A researcher is interested in looking at a new type of insulin that can treat diabetics with high fasting glucose levels. Suppos

Makovka662 [10]

Answer:

The sample size should be at least 79.

Step-by-step explanation:

Let Y be be the resting glocose level of a member of the population chosen randomly, then Y is a random variable with unkown mean λ and Standard deviation σ = 27.

Let X be the sample mean of a sample of lenght n. X has the same mean as Y and the standard deviation is $\sigma = \frac{27}{\sqrt{n}} .$

If n is reasonable high, the Central Limit Theorem states that X has distribution approximately Normal, with mean λ and Standard deviation $sigma = \frac{27}{\sqrt{n}} .$

If we standarize X, we get a random variable W

$W = \frac{X-\lambda}{\frac{27}{\sqrt{n}}} \simeq N(0,1)$

The values of W are tabulated and can be found on the attached file. We want a 95% confidence interval, so we want Z such that

P(-Z < w < Z) = 0.95

Using the symmetry of the normal density function, we get that

P(W < Z) = 0.975

If we look at the table, we will find that Z = 1.96, therefore we have

$P(-1.64 < \frac{X-\lambda}{\frac{27}{\sqrt{n}}} < 1.64) = 0.95$

Equivalently,

$0.95 = P(-1.64*\frac{27}{\sqrt{n}} < X- \lambda < 1.64*\frac{27}{\sqrt{n}})$

Taking out the X and the sign, after reverting the inequalities, we obtain

$P(X -1.64*\frac{27}{\sqrt{n}} < \lambda < X +1.64*\frac{27}{\sqrt{n}}) = 0.95$

Thus, a confidence interval with 95% confidence is

$CI = [ X-1.64*\frac{27}{\sqrt{n}}, X+1.64*\frac{27}{\sqrt{n}}]$

The (absolute) margin of error of this interval is $1.64*\frac{27}{\sqrt{n}} ,$ we want that number to be at most 5, so we take n such that

$1.64*\frac{27}{\sqrt{n}} = 5 \, \rightarrow \frac{1}{\sqrt{n}} = \frac{5}{1.64*27} \, \rightarrow \sqrt{n} = 8.85 \, \rightarrow n = 78.42$

We take n = 79. I hope that works for you!

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4 0

3 years ago

Please help me

swat32

Answer: C

Step-by-step explanation:

Use Desmos | Graphing Calculator <33 This app/website works wonders fro math

4 0

3 years ago

Read 2 more answers

Please all answers I'm in a hurry

givi [52]

#2 is 35°C (just plug in 95 to the formula)

#3:
in the left column are:
(8x-(6+y))
(3/4)w+x^2

in the right column are:
y^2-0.5w
w/4+3(x+y)

to solve you just plug in to the formula

6 0

4 years ago

Help with these questions plzz 21,22,23 PLZZZ

vivado [14]

Let x represent the original number of books (the value we're asked for by the problem question). Then after this number was doubled, its was 2x. After 4028 was added, it was 2x+4028. That value is given by the problem statement as being 51,514, so the equation can be ...

... 2x + 4,028 = 51,514

... 2x = 47,486 . . . . . . . . . . . subtract 4028

... x = 23,743 . . . . . . . . . . . . divide by 2

The library had 23,743 books before the transactions described.

Let t represent the number of minutes required for you to finish. Then in t minutes, you have prepared 2t carrots. The number of carrots you need can be described by ...

... 2t + 18 = 60

... t + 9 = 30 . . . . . . divide by the coefficient of t

... t = 21 . . . . . . . . . . subtract 9

It will take you 21 minutes to finish.

<h2>23.</h2><h3>Given</h3>

cost is $39.95 plus $0.35 for each minute over 500

cost as a function of the number of minutes usage over 500
the number of minutes over 500 for a bill of $69.70

<h3>Solution</h3>

Let m represent the number of minutes usage over 500. Let c(m) represent the cost as a function of m. The given relation can be expressed as

... c(m) = 39.95 + 0.35m

We can substitute the bill information to find m:

... 69.70 = 39.95 + 0.35m

... 29.75 = 0.35m . . . . . . . . . subtract 39.95

... 85 = m . . . . . . . . . . . . . . . . divide by 0.35

The number of minutes over 500 for a bill of $69.70 is 85 minutes.

5 0

3 years ago

Help with this question, please ASAP!! I need help!!

SashulF [63]

i did this before the answer is choice B

I hope this helps :D

6 0

3 years ago