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3 years ago

Use synthetic division and the remainder theorem to find p(a) = 2x3 -x2 + 10x; = a = 1/2

Mathematics

1 answer:

sergey [27]3 years ago

8 0

Answer:

p(1/2) = 5

Step-by-step explanation:

Find the value of p(1/2) if p(x) = 2x^3 -x^2 + 10x

Set up synthetic div.:

1/2 ) 2 -1 10 0

1 0 5

------------------------

2 0 10 5

The remainder is 5, so we conclude that p(x) = 2x^3 -x^2 + 10x = 5 when x = 1/2.

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3 years ago

A study of peach trees found that the average number of peaches per tree was 725. The standard deviation of the population is 70

TEA [102]

Answer:

She needs to sample 189 trees.

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:

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

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.

The standard deviation of the population is 70 peaches per tree.

This means that $\sigma = 70$

How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree?

She needs to sample n trees.

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

$10 = 1.96\frac{70}{\sqrt{n}}$

$10\sqrt{n} = 1.96*70$

Dividing both sides by 10:

$\sqrt{n} = 1.96*7$

$(\sqrt{n})^2 = (1.96*7)^2$

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Rounding up:

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I need help on finding an equation!?

Sedbober [7]

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Subtract [62 mph]t from both sides of this equation, obtaining:

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