Mathematics, 06.08.2019 18:20 AdoNice

According to the most recent data, 12.3% of engineers (electrical, mechanical, civil, and industrial) were women. suppose a random sample of 80 engineers is selected. a. how likely is it that a random sample of 80 people will contain 12 or more women in these positions? b. how likely is it that the random sample will contain fewer than 5 women in these positions? c. if the random sample included 160 engineers, how would this change your answer to part b?

Answers: 2

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Answers

Answer from: dekarouh

Step-by-step explanation:

Given that according to the most recent data, 12.3% of engineers (electrical, mechanical, civil, and industrial) were women.

n =80

p is normal with p = 12.3% and std error = $\sqrt{\frac{0.123(0.877}{80} } =0.03672$

Prob 12 or more women = P(p>0.15)

=P(Z> $\frac{0.15-0.123}{0.03672} =0.74)$

=0.5-0.2704=0.2296

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1