Why does the following system of linear equations have no solution? x + 4y = 20 x + 4y = 16

A common factor is a factor that is shared by two or more numbers (or, in this case, polynomials). The highest common factor (HCF) is found by finding all common factors of the two expressions and selecting the largest one.

Find HCF of $2x^5-4x^4-6x \ \ \textsf{and} \ \ x^5+x^4-3x^3-3x^2$

Factor $2x^5-4x^4-6x$

Factor out common term: $2x(x^4-2x^3-3)$

Factor $x^4-2x^3-3$ : $2x(x+1)(x^3-3x^2+3x-3)$

Factor $x^5+x^4-3x^3-3x^2$

Factor out common term: $x^2(x^3+x^2-3x-3)$

Factor $x^3+x^2-3x-3$ : $x^2(x+1)(x+\sqrt{3} )(x-\sqrt{3} )$

Therefore, from inspection the HCF = $(x + 1)$

5 0

2 years ago

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

kondaur [170]

Answer:

Due to the higher z-score, Norma should be offered the job

Step-by-step explanation:

Z-score:

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.

In this question:

Whoever has the higher z-score should get the job.

Norma:

Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.

This means that $X = 84.2 \mu = 67.4, \sigma = 14$