A corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also appoint a planning committee with three different members. There are 14 qualified​ candidates, and officers can also serve on the committee. Complete parts​ (a) through​ (c) below.

Answers

Answer 1

Using the permutation formula and the combination formula, it is found that:

a) There are 24,024 ways to appoint the officers.

b) There are 1,001 ways to appoint the committee members.

c) [tex]p = \frac{1}{1001}[/tex] probability that the four youngest members are appointed to the committee.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

What is the combination formula?

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Item a:

For the officers, the order is important, as there are different roles, and 4 officers will be appointed from a set of 14 qualified candidates, hence we use the permutation formula to find the number of ways they can be appointed.

[tex]P_{14,4} = \frac{14!}{10!} = 24024[/tex]

Item b:

For the committee, the order is not important, as there are no different roles, and 4 members will be appointed from a set of the 10 remaining candidates, hence we use the combination formula to find the number of ways they can be appointed.

[tex]C_{14,4} = \frac{14!}{4!10!} = 1001[/tex]

Item c:

The four youngest is only one possible outcome, hence the probability they are appointed to the committee is given by:

[tex]p = \frac{1}{1001}[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1


Related Questions

1. What is the surface area of this rectangular prism?

A. 16 square units

B. 32 square units

C. 48 square units

D. 64 square units

Answers

Hi! :)

Answer:

B) 32 Square Units

Step-by-step explanation:

I counted the squares. <3

Which is the greatest?



5/100 5/10 24/1000

Answers

Answer:

5/10

Step-by-step explanation:

To solve this problem we find equivalent fractions with the same denominator:

The LCM of 10,100 and 1000 is 1000. So we make all the denominators 1000:

5/100 = 50/1000

5/10 = 500/1000

24/1000 = 24/1000

Now we compare the numerators and see which is the largest number.

24 < 50 < 500

So 5/10 must be the greatest.

Hope this helped and brainliest please

Which statement is true?


7.11>−7.1

7.11≤−7.1

7.11<−7.1

Answers

Step-by-step explanation:

I think 1 is correct..

all positive numbers are greater than negative. 7.11 is greater that -7.1

Answer:

7.11 > -7.1

Step-by-step explanation:

» Concept

Negative numbers will always be less than positive numbers. Negative numbers will always have the (-) sign to indicate its value.

» Solution

The only correct inequality is A. 7.11 > -7.1 because it displays that the positive number, 7.11, is greater than the negative number, -7.1.

What is the formula for standard error of the mean?

Answers

Write the formula σM =σ/√N to determine the standard error of the mean.

The population of a small town was 10,800 in 2002. Since then the population has decreased at a rate of 2.5% each year. Write an exponential function to model the situation then find the population of 2020

Answers

Answer:

See below

Step-by-step explanation:

A 2.5 % decrease means  97.5 % remains (.975)

population =  10800 ( .975) ^n     where n = years past 2002

  in 2020    n = 18

    10800 (.975)^18 = 6847  people

There are 12 turkey sandwiches and 8 ham sandwiches. There are 6 bags of chips and 10 bags of pretzels. What is the probability of selecting a turkey sandwich and a bag of pretzels?
a) 1/5
b) 3/8
c) 3/5
d) 5/8

Answers

The probability of selecting a turkey sandwich and a bag of pretzels is 3/8.

What is the probability?

Probability determines the likelihood that an event would happen. The odds the event occurs is 1 and the odds that the event does not occur is 0.

The probability of selecting a turkey sandwich and a bag of pretzels = number of turkey sandwiches / total number of sandwiches x number of pretziel bags / total number of bags

12/20 x 10/16 = 3/8

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

Examine the system of equations.

t = 5c + 35,

t = 10c

How many solutions will the system have?


What is the reason you determined that number of solutions?

Answers

Answer:

One solution

Step-by-step explanation:

Analyzing both equations

Simplify both to simplest formy = 5c + 35 = c + 7y = 10c

Slope is different

As the slopes are different, then it can be concluded that the system has only one solution.

Answer:

How many solutions will the system have?

one solution

What is the reason you determined that number of solutions?

The equations graph intersecting lines.

Solve for x in the inequality 11|x + 1| < 44

Answers

[tex]~~~~~~11|x+1| < 44\\\\\implies |x+1| < \dfrac{44}{11}\\\\\implies |x+1| < 4\\\\\implies x +1 > -4~~~ \text{and}~~~ x+1 < 4\\\\\implies x > -4-1~~~ \text{and}~~~~ x < 4-1\\\\\implies x > -5~~~~~~~~ \text{and}~~~~~ x < 3\\\\\text{Hence,}~~ -5 < x < 3[/tex]

What is the volumen , in cube centimeters, if a cube with a side length, s, of 0.2cm?

Answers

Answer:

[tex]\frac{1}{125}[/tex]cm³

Step-by-step explanation:

volume of cube= (side)³

0.2³ = [tex]\frac{1}{125}[/tex]

3. If I give you £90 because I want to give you
90% of my prize, what did I win?

Answers

Answer:

81

Step-by-step explanation:

Multiply 90/100 with 90 = (90/100)*90 = (90*90)/100 = 81.

i got 100. not sure how the other guy got 81, but what i did is compare it to a test score or a discount. if you have a total of 100 possible points on the test with every question worth 10 points and i got 9 questions right, i got a 90 percent.

let's say a shopping discount. If you got a 90% discount for a item with original price of $100, it costs $10 with "90" being the amount you took off

if 100 isn't right, i honestly have no clue lol. good luck though

I need help with the last two !!!

Answers

Step-by-step explanation:

G(x) = - x^2 + 10x

a + G(a) = a - a^2 + 10a = - a^2 + 11a or 11a - a^2 or a(11 - a)

1/G(a) = 1/(10a - a^2) = 1/a(10 - a)

14÷2+3²×(7-2) pemdas order

Answers

Answer:

Step-by-step explanation:

14÷2+3²×(7-2) pemdas order

14 : 2 + 3^2 * (7 - 2) =

14 : 2 + 3^2 * 5 =

14 : 2 + 9 * 5 =

7 + 9 * 5 =

7 + 45 =

52

In the following exercises, identify whether each number is rational or irrational.

. (a) √25 (b) √30

Answers

Answer:

(a) √25 rational

(b) √30 irrational

Step-by-step explanation:

Note : only perfect squares have rational roots

25 = 5² then 25 is a perfect square

            therefore √25 = 5 is a rational number

30 cannot be written in the form a² where ‘a’ I start a natural number then 30 is not a perfect square

           Therefore √30 is irrational.

Rewrite 5 2/3 using radical notation.

Answers

The radical form of   [tex]5^{\frac{2}{3}}[/tex] is   [tex]\sqrt[3]{25}[/tex].

What is Radical Notation?

If n is a positive integer that is greater than 1 and a is a real number then, n√a = [tex]a^{1/n}[/tex]. where n is called the index, a is called the radicand, and the symbol √ is called the radical.

Here, given value =  [tex]5^{\frac{2}{3}}[/tex]

                              =   [tex](5^2)^{1/3}[/tex]

                             = [tex](25)^{1/3}[/tex]

                             = [tex]\sqrt[3]{25}[/tex]

Thus, the radical form of [tex]5^{\frac{2}{3}}[/tex] is [tex]\sqrt[3]{25}[/tex].

Learn more about Radical Notation from:

https://brainly.com/question/1810591

#SPJ1



Find the first four terms of:
a) An arithmetic series with first term of 3 and sum to five terms is 75

Answers

[tex]\textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\[-0.5em] \hrulefill\\ a_1=3\\ n=5\\ S_5=75 \end{cases} \implies \begin{array}{llll} S_5=\cfrac{5(a_1+a_5)}{2} \\\\\\ 75=\cfrac{5(3+a_5)}{2} \end{array} \\\\\\ 150=5(3+a_5)\implies \cfrac{150}{5}=3+a_5\implies 30=3+a_5\implies \boxed{27=a_5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ n=5\\ a_5=27\\ a_1=3 \end{cases}\implies 27=3+(5-1)d \\\\\\ 24=(5-1)d\implies 24=4d\implies \cfrac{24}{4}=d\implies \boxed{6=d} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\LARGE Terms}}{3~~,~~\stackrel{3+6}{9}~~,~~\stackrel{9+6}{15}~~,~~\stackrel{15+6}{21}}~\hfill[/tex]

The lengths of the 2 legs of right triangle AABC shown
below are given in inches. The midpoint of AB is how
many inches from A?

A. 16
B. 20
C. 21
D. 28
E. 40

Answers

Answer:

E. 40

Step-by-step explanation:

First, we can start out by stating that this is a right triangle, since it has a right angle, shown by the marker square in the corner of the triangle. The x part, is called the hypotenuse. When finding the value of the hypotenuse, we use a thing called the Pythagorean Theorem. This theorem is :

a^2 + b^2 = c^2

a is one side length, and b is the other. c is the hypotenuse. To find x, the hypotenuse, we simply plug in the values, and solve.

24^2+32^2 = c^2

576 + 1024 = c^2

1600 = c^2

40 = c

The answer is E. 40.

Need help with this problem, doesn't make sense to me.

Answers

Answer:

A = x² - 5x - 8

Step-by-step explanation:

Finding x

Area (deck) = Area (Rectangle) - [Area (bench) + Area (planter)]A = x(x - 4) - [ 2(6) + 1/2(2)(x - 4) ]A = x(x - 4) - [12 + x - 4]A = x² - 4x - 8 - xA = x² - 5x - 8

How to calculate minimization of cost when given the marginal revenue

Answers

Answer: Cost is minimized at the levels of capital and labor such that the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r)

Step-by-step explanation:

Find the distance (A) for the bend of electrical conduit that is passing under the girder shown in the figure.?​

Answers

Answer:

15 1/8"

Step-by-step explanation:

Adding the values

⇒ 9 3/4" + 2 1/8" + 3 1/4"

⇒ 13 + 2 1/8"

15 1/8"

PLEASE HELP WILL MAEK YOU THE BRAINLIEST

Answers

Answer:

1

Step-by-step explanation:

[tex]F =\cos 0^{\circ} = 1[/tex]

A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a triangle. Which of the following solids could have resulted in that cross section?

Answers

Solids or three-dimensional forms are shapes or figures that have three (or more) dimensions. The solid could be a Triangular prism or a pyramid.

What is a solid?

Solids or three-dimensional forms are shapes or figures that have three (or more) dimensions. Solid Geometry is the study of the characteristics, volume, and surface area of three-dimensional forms.

Given a solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross-section in the shape of a triangle. Therefore, the solid could be a Triangular prism or a pyramid.

Learn more about Solid:

https://brainly.com/question/14424882

#SPJ1

Answer: right cone because if you use a right cone and cut it perpendicular to the base you get a triangle making cone triangle the answer.

PLEASE HELP!

Correct answers will be mark as BRAINLIEST and get 50 points

If wrong answers will be reported ​

Answers

Mean=Sum of data/No of data

#a

17,19,25

Mean

17+19+25/361/3

#b

38,36,34,32

Mean:-

38+36+34+32/4140/435

#c

8.3,2.6,7.4,1.8,9.5

Mean

8.3+2.6+7.4+1.8+9.5/529.6/55.92

#d

-5,-2,-1,0,-9,4

Mean

-5+2-1+0-9+4/6-9/6

Answer:

See below ~

Step-by-step explanation:

a)

Mean = 17 + 19 + 25 / 3Mean = 61/3Mean = 20.3

b)

Mean = 38 + 36 + 34 + 32 / 4Mean = 140/4Mean = 35

c)

Mean = 8.3 + 2.6 + 7.4 + 1.8 + 9.5 / 5Mean = 29.6/5Mean = 5.92

d)

Mean = -5 + 2 - 1 + 0 - 9 + 4 / 6Mean = -9/6Mean = -1.5

❗100points❗
y is directly proportional to √x .
y is 24 when x is 36. Find a formula linking x and y
thanks.​

Answers

Answer:

y = 4√x

Step-by-step explanation:

Finding the constant of proportionality, k

y = k√x24 = k√36k = 24/6 = 4

Equation

y = k√xy = 4√x

Answer:

Y will equal

4√x as the answer

A total of 840 people ate at lunch.Which statement is true

Answers

what kinda question is this

2.48 times 3.25 equals

Answers

The answer is 8.06.

does the formula matter in area?

Answers

Answer:

Yes

Step-by-step explanation:

You need the formula to solve area.

You must plug in / subsitute numbers in order to find the area.

Yes you need the formula

A case of 24 cans of soup costs $38.16. What is the cost of 7 cans of soup?

Answers

Answer:

$11.13

Step-by-step explanation:

24 cans = $38.16

divide both sides by 24 to find the cost per can, as this leaves us with 1 can on one side

24 cans / 24 = $38.16 / 24

1 can = $1.59

multiply both sides by 7 to get 7 cans of soup on one side, which is what we want

1 can * 7 = $1.59 * 7

7 cans = $11.13

Solve the logarithmic equation. Show steps

Answers

[tex]\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \underset{\stackrel{\uparrow }{\textit{let's use this one}}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\log_4(x+10)-\log_4(x-2)=\log_4(x)\implies \log_4\left( \cfrac{x+10}{x-2} \right)=\log_4(x) \\\\\\ \stackrel{\textit{exponentializing both sides}}{4^{\log_4\left( \frac{x+10}{x-2} \right)}=4^{\log_4(x)}}\implies \cfrac{x+10}{x-2}=x\implies x+10=x^2-2x \\\\\\ 10=x^2-3x\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5~~\checkmark\\ -2 \end{cases}[/tex]

notice, -2 is a valid value for the quadratic, however, the argument value for a logarithm can never 0 or less, it has to be always greater than 0, so for the logarithmic expression with (x-2), using x = -2 will give us a negative value, so -2 is no dice.

Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=3x+5
s(x)=4x
Write the expressions for (r-s)(x) and (r*s)(x) and evaluate (r+s)(-2).

Answers

A function assigns the values. The value of (r+s)(-2) is equal to 9.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the function r(x)=3x+5, while s(x)=4x, therefore, the expressions can be written as,

(r-s)(x) =r(x)-s(x) = 3x+5 - 4x = -x+5

(r*s)(x) = r(x)·s(x) = (3x+5)·(4x) = 12x² + 20x

The expression for (r+s)(x) can be written as,

(r+s)(x) = r(x)+s(x) = 3x+5+4x = 7x+5

(r+s)(-2) = 7(-2)+5 = -14+5 = 9

Hence, the value of (r+s)(-2) is equal to 9.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

Jeremy wants to visit the Duck Pond. Which is a correct description of how to find the ordered pair for the Duck Pond? ​

Answers

Answer: 2,4

Step-by-step explanation:

Other Questions
Find two numbers whose difference is 30 and whose product is a minimum. PLE HELPWhat is the best description of temperature?Temperature is the same thing as heat.Temperature measures the number of Kelvins in a substance.Temperature is the measurement of kinetic energy (movement of molecules).Temperature only measures an increase in heat energy. Before complex development of a fetus can begin, implantation into the uterine wall must occur. What gets implanted in the uterine wall? Nazis murdered millions of Jews because of their religion and ethnicity. True or False PLEASE ANSWER FAST I NEED HELP Describe the relationship between a thermal inversion and pollution. Find the surface area of the rectangular prism True or false. A solvent is the part of a solution that dissolves the solute Why is knowing agricultural statistics, background information, and soil characteristics about the territory in which your farm is located important? Find the domain and range of the relation graphed below. Please help with this health question ) Angelique lands on the trampoline.She bends her knees and pushes hard against the trampoline.Complete the sentence.Choose the best word from the list.force friction mass weightAngelique exerts more .............................................................. so she jumps higherplease help asap choose answer from the list Which of the following has more than one kind of monomer in its repeating unit? homodimer copolymer codimer homopolymer Which sentence best explains the meaning of the bolded line in this excerpt from act v, scene i, of twelfth night? clown: why, 'some are born great, some achieve greatness, and some have greatness thrown upon them.' i was one, sir, in this interlude;one sir topas, sir; but that's all one:'by the lord, fool, i am not mad;'but do you remember? 'madam, why laugh you at such a barren rascal? an you smile not, he's gagged'? and thus the whirligig of time brings in his revenges. a. the clown suggests that the complications in the play have been amicably resolved. b. the clown is commenting on the cyclic nature of time and saying that malvolio has received the treatment he deserved. c. the clown believes that malvolio will not be rewarded for his good deeds before the time is right. d. the clown emphasizes that time always teaches people to patiently perform good deeds and not expect rewards. Instead of calming people down, smoking cigarettes can make them more Please help me with this math problem!! Will give brainliest!! :) What is a type of government where elected officials run the country? a oligarchy b republic c monarchy d direct democracy Write cos 32 in terms of sine.cos 32 = sin Please help me math 24) A technician is load testing a fully charged battery rated at 600 cold-cranking amps (CCA). The ambient temperature is 70 F Which of these curent draw and the pericts should be used for the t AC 150 years for 30 seconds C200 amps for 15 seconds 600 amps for 30 seconds CO 1200 amps for 15 seconds