Item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?

Mathematics

1 answer:

Readme [11.4K]4 years ago

8 0

Let's rewrite the expression as

$8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a)$

So, if $a \neq 4$ , you may divide both sides by $4-a$ , the equation becomes $2x=2$ , and the only solution is $x=1$ , which means that this is not an identity (an indentity is tautologically true, no matter the value of x).

If instead $a = 4$ , you are multiplying both sides by zero, so the equation becomes

$2x \cdot 0 = 2 \cdot 0 \iff 0=0$

So, it doesn't matter which value for x you choose, because you will always end up with $0=0$ , which is obviously always true.

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The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. There

tankabanditka [31]

Answer:

The lifetime value needed is 11.8225 hours.

Step-by-step explanation:

Problems of normally distributed samples 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

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

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 This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. This means that $\mu = 11, \sigma = 1$ .