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3 years ago

-1/3x<48 solve this inequality

1 answer:

4 0

-1/3x < 48

Divide each side by -1/3. When you divide by a negative the sign flips...

x > 48 ÷ -1/3

divide fractions by multiplying the reciprocal of the divisor

x > 48 × -3
x > -144

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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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3 years ago

Create an array for 4x3

lana [24]

Just draw a rectangle, cut it into 3 horizontal lines, and cut it into 4 vertical lines.

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3 years ago

In Euclidean geometric terms, which of the below would be the best description of any ANGLE?

Ede4ka [16]

The answer would be option C.

Hope this helps!

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3 years ago

Read 2 more answers

The income from the spanish clubs bake sale was $260. expenses for the sale totaled $60.use integer addition to find the total p

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The total profit was $200

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4 years ago

Write an equation for the parabola whose vertex is at (4, 12) and which passes through (5, 21)

laiz [17]

Answer:

y - 12 = 9(x - 4)

Step-by-step explanation:

The vertex (h, k) is (4, 12) and the point (5, 21) is on the graph. Assuming that this is a vertical parabola, opening up (because the coordinate 21 is greater than the coordinate 12), we insert the knowns into y - k = a(x - h)^2, obtaining

21 - 12 = a(5 - 4), or 9 = a. With a known, we can write the desired equation:

y - 12 = 9(x - 4)

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3 years ago