Write f(x) in the form (x-k)q(x)+r, given that k=-2. f(x)=3x^4+4x^3-10x^2+15

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

3 0

You may perform the division using either long division or synthetic division. Any preference?

I used synthetic div. with -2 as the divisor:

________________
-2 / 3 4 -10 0 15
-6 4 12 -24
-------------------------
3 -2 -6 12 -9

In factored form, with remainder, we then have:

(x+2)(3x^3 - 2x^2 - 6x + 12) remainder -9

If you need clarification of any part of this solution, let me know.

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A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30 What score is necessary to reach

nlexa [21]

Answer:

A score of 150.25 is necessary to reach the 75th percentile.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.

This means that $\mu = 130, \sigma = 30$