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2 years ago

%20-%20%20%7Bb%7D%5E%7B2%7D%20%29" id="TexFormula1" title="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" alt="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Zigmanuir [339]2 years ago

5 0

Answer:

$\frac{1}{2}$ (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² ← factor out $\frac{1}{2}$ from each term

= $\frac{1}{2}$ (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² = $\frac{1}{2}$ (a + 2b)(a - b)

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A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

yawa3891 [41]

Answer:

The probability is 0.003

Step-by-step explanation:

We know that the average $\mu$ is:

$\mu=500$

The standard deviation $\sigma$ is:

$\sigma=100$

The Z-score is:

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

We seek to find

$P(x800)$

For P(x>800) The Z-score is:

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

$Z=\frac{800-500}{100}$

$Z=3$

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

$P(x>800)=0.15\%$

For P(x<200) The Z-score is:

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

$Z=\frac{200-500}{100}$

$Z=-3$

The score of Z = -3 means that 200 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

$P(x$