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leva [86]
3 years ago
14

A search committee is formed to find a new software engineer.

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0

Answer:

(a) 1,902,231,808,400

(b) 84

(c) 20

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!\cdot(n-k)!}

(a)

Compute the number of ways to select 9 applicants from 100 as follows:

{100\choose 9}=\frac{100!}{9!\cdot(100-9)!}

        =\frac{100!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92}{9!}\\\\=1902231808400

(b)

Compute the number of ways to select 6 people from 9 as follows:

{9\choose 6}=\frac{9!}{6!\cdot(9-6)!}

        =\frac{9!}{6!\times 3!}\\\\=\frac{9\times 8\times 7\times 6!}{6!\times 3!}\\\\=\frac{9\times 8\times 7}{3!}\\\\=84

(c)

Compute the number of ways to select top 3 candidates from 6 as follows:

{6\choose 3}=\frac{6!}{3!\cdot(6-3)!}

        =\frac{6!}{3!\times 3!}\\\\=\frac{6\times 5\times 4\times 3!}{3!\times 3!}\\\\=\frac{6\times 5\times 4}{3!}\\\\=20

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Step-by-step explanation:

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With a height of 68 ​in, Nelson was the shortest president of a particular club in the past century. The club presidents of the
Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: \\ z = -1.1739 \approx -1.174 (Nelson's height is <em>below</em> the population's mean 1.174 standard deviations units).

d. Nelson's height is <em>usual</em> since \\ -2 < -1.174 < 2.

Step-by-step explanation:

The key concept to answer this question is the z-score. A <em>z-score</em> "tells us" the distance from the population's mean of a raw score in <em>standard deviation</em> units. A <em>positive value</em> for a z-score indicates that the raw score is <em>above</em> the population mean, whereas a <em>negative value</em> tells us that the raw score is <em>below</em> the population mean. The formula to obtain this <em>z-score</em> is as follows:

\\ z = \frac{x - \mu}{\sigma} [1]

Where

\\ z is the <em>z-score</em>.

\\ \mu is the <em>population mean</em>.

\\ \sigma is the <em>population standard deviation</em>.

From the question, we have that:

  • Nelson's height is 68 in. In this case, the raw score is 68 in \\ x = 68 in.
  • \\ \mu = 70.7in.
  • \\ \sigma = 2.3in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

That is, <em>the positive difference is 2.7 in</em>.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many <em>standard deviations</em> is that, we need to divide that difference by the <em>population standard deviation</em>. That is:

\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174

In words, the difference found in part (a) is 1.174 <em>standard deviations</em> from the mean. Notice that we are not taking into account here if the raw score, <em>x,</em> is <em>below</em> or <em>above</em> the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

\\ z = \frac{x - \mu}{\sigma}

\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}

\\ z = \frac{-2.7\;in}{2.3\;in}

\\ z = -1.1739 \approx -1.174

This z-score "tells us" that Nelson's height is <em>1.174 standard deviations</em> <em>below</em> the population mean (notice the negative symbol in the above result), i.e., Nelson's height is <em>below</em> the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

\\ -2 < z_{Nelson} < 2

\\ -2 < -1.174 < 2

Then, Nelson's height is <em>usual</em> according to that statement.  

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3 years ago
(fg)-1(5)=g-1f-1(5)​
larisa86 [58]

Answer:

<em>f = g/ g+1</em>

Step-by-step explanation:

Remove Parenthesis.

<em>fg - 1  x 5  = g  - 1  x f  - 1 x 5</em>

Cancel <em>-1 x 5</em> on both sides.

<em>fg =  g - 1  x f</em>

Simplify <em>1 x f</em>  to f.

<em>fg =  g - f</em>

Add <em>f </em>to both sides.

<em>fg + f = g</em>

Factor out the common term <em>f.</em>

<em>f (g + 1)  = g</em>

Divide both sides by <em>g + 1</em>

<em>f =  g/ g + 1</em>

6 0
3 years ago
A new experimental tank is in the shape of a cone, cylinder and sphere. All of the tanks have a volume of 10,000 cm3 . One condi
Vika [28.1K]

Answer:

100/π cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Volume = 10,000cm³

Radius = 10cm

The formula for the height of a cylinder is obtained as:

V = πr²h

h = V/ πr²

h = 10000 /π × 10²

h = 10000 /π × 100

h = 100/π cm

The height of the cylinder in terms of π = 100/π cm

8 0
3 years ago
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