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Natali [406]
2 years ago
15

LabTech is a company that manufactures microscopes and other laboratory instruments. On (Ipoint) occasion, one of the microscope

s is defective when it comes off of the production line. The probability that a microscope is defective is 0.17% Find the probability that the first defective microscope comes after the first 100 microscopes off of the production line.
a. 0.156
b. 0.181
c. 0.742
d. 0.844
Mathematics
1 answer:
Virty [35]2 years ago
6 0

Answer:

probability of 1st defective = 0.844

correct option is d. 0.844

Step-by-step explanation:

given data

probability defective = 0.17%

undefective microscopes = 100

to find out

the probability that the first defective microscope

solution

we know defective probability P = 0.17% = 0.0017

so non defective probability (1-P)   = 1 - 0.0017

non defective probability (1-P)  = 0.9983

and

1st defective come after 100 it mean 1st 100 are non defective so

probability of 1st defective = (1-P)^{100}

probability of 1st defective = (0.9983)^{100}

probability of 1st defective = 0.844

so correct option is d. 0.844

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I have a good record of guessing the right one so I would say #1.
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3 years ago
For which value of b can the expression x2 + bx + 18 be factored?
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Answers:

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  • b = -11
  • b = -9
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====================================================

Explanation:

Here are all the ways to multiply to 18 when using integers only:

  • -1*(-18) = 18
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Sum each pair of factors to find out a possible value of b.

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Therefore, the possible values of b are

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----------------------

An example:

Let's say b = 11. This would mean x^2+bx+18 becomes x^2+11x+18

It would factor to (x+2)(x+9) since it was stated earlier that:

2+9 = 11

2 * 9 = 18

You can use the FOIL rule, distributive property, or the box method to confirm that x^2+11x+18 = (x+2)(x+9) is a true equation for all real numbers x.

This same idea applies for the other values of b.

----------------------

If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)

Use the FOIL rule to get (x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq

The middle term (p+q)x has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).

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