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3 years ago

What is the equation of the line, in slope-intercept form, that passes through (4.2) and (-2, -3)?

Mathematics

1 answer:

Keith_Richards [23]3 years ago

3 0

Answer:

y = 5/6x + -8

Step-by-step explanation:

you first need to find the gradient using the formula m = (y2 - y1)/(x2 - x1)

the gradient would be 5/6.

the slope intercept form equation is y = mx + c. so by taking one of the points, 2 = 5/6(4) + c

12 = 5(4) + c

12 = 20 + c

c = 12 - 20

c = -8

hence, y = 5/4x + -8

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Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive wit

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Answer:

0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive

Step-by-step explanation:

For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Assume that there is a 8% rate of disk drive failure in a year.

So 100 - 8 = 92% probability of working, which means that $p = 0.92$

Two disks are used:

This means that $n = 2$

What is the probability that during a year, you can avoid catastrophe with at least one working drive?

This is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064$

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0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive

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3 years ago

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2 years ago

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sveticcg [70]

Answer: The multiplication factor of increase should be inverse of the multiplication factor of decrease.

e.g. Say you have a number 100. You increase it by 25%. The multiplication factor is 5/4 i.e. when you multiply 100 by 5/4, you get 100*5/4 = 125. This is 25% more than 100. Now you want to decrease it by a certain % such that you get 100 back. Basically, 100*5/4 * x = 100 So x = 4/5 (inverse of 5/4) Hence, you decrease by 20% (the multiplication factor of 20% is 4/5) or Use this formula: cumulative % change = a + b + ab/100 You want the cumulative change to be 0. a + b + ab/100 = 0 If you know that you are increasing by 25% and want to find the % by which you should decrease to get the same number, 25 + b + 25b/100 = 0 5b/4 = -25 b = -20 So you need to decrease (hence you get the -ve sign) by 20%.

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3 years ago