How many different 5-person subcommittees can be formed from a club having 12 members

Answers

Answer 1

Answer: Given that there are 12 persons, the first choice may be in 12 different ways, the second choice may be in 11 different ways, ther third in 10 different ways, the fourth in 9 different ways and the fith in 8 different ways, for a total of:

12x11x10x9x8 different combinations.

Now you have to take in account that 5x4x3x2 are repetitions. So you have to divide the previos counting by 5x4x3x2.

(12x11x10x9x8)/(5x4x3x2) = 792 different subcommittees.

Also, you can use the formula for combinations: C(m,n) = m! / (n! (m-n)!)

C (12, 5) = 12! / (5!) (12-5)! = [12x11x10x9x8x7!] / [5! 7!] = [12x11x10x9x8]/[5x4x3x2] = 792

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The expression 3 radical 18 is equivalent to a) 9 radical 2 b) 3 radical 2 c) 3 radical 6 d) 9 radical 3
A store manager timed Janette to see how long it would take her to fold and put away a sweater, a shirt, a pair of pants, and a scarf. It took her 26.1 seconds for the shirt, 24.3 seconds for the sweater, 32.8 seconds for the pants, and 18.2 seconds for the scarf. What was the average time it took Janette to fold and put away all four items

The diameter of a soccer ball is 8.65 inches what is the volume of the ball rounded to nearest hundredth

Answers

A soccer ball is an icosahedron with curved faces that is why it can be regarded as spherical. The volume of a sphere is calculated through,

Vs = 4πr^3/3

where Vs is the volume and r is radius. From the given, 8.65 in is the diameter which is 4.325 in in radius.

Vs = 4π(4.325^3)/3 = 338.88 in cubed.

Thus, the volume of the ball is 338. 88 in cubed.

The average annual salary of the employees of a company in the year 2005 was $70,000. It increased by the same factor each year and in 2006, the average annual salary was $82,000. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?

Answers

f(x) = 70(1.17)^x Hope this helps! :)

If j, k, and n are consecutive integers such that 0 < j < k < n and the units (ones) digits of the product jn is 9, what is the units digits of k?

Answers

All of those numbers have nothing but ones digits, that is, they're all single digits. j=4, k=5, and n=6.

Solve the system of equations using substitution.
3x + 2y = 7
y = –3x + 11

Answers

3x + 2y = 7
y = -3x + 11

Solve the system of equation using substitution.

Substitute the y in the first equation by its value presented in the 2nd equation.

3x + 2y = 7
3x + 2(-3x + 11) = 7
3x - 6x + 22 = 7
-3x + 22 = 7
-3x = 7 - 22
-3x = -15
-3x/-3 = -15/-3
x = 5

Substitute x in the 2nd equation by its computed value. x = 5
y = -3x + 11
y = -3(5) + 11
y = -15 + 11
y = -4

x = 5 ; y = -4

Substitute x and y in the 1st equation with its corresponding values

3x + 2y = 7
3(5) + 2(-4) = 7
15 - 8 = 7
7 = 7

Solve each equation for the indicated variable. u = -3a - 3 , for a

Answers

Answer:

$a = (u + 3)/(-3)$

Step-by-step explanation:

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 3 to both sides of the equation:

u = -3a - 3

u (+3) = -3a - 3 (+3)

u + 3 = -3a

Next, divide -3 from both sides of the equation:

(u + 3)/-3 = (-3a)/-3

a = (u + 3)/-3

$a = (u + 3)/(-3)$ is your answer.

What is the y-value of the solution to the system of equations? 3x + 5y = 1 7x + 4y = −13

Answers

3x + 5y = 1 . . . . . . . . (1)
7x + 4y = -13 . . . . . . .(2)
(1) x 7: 21x + 35y = 7 . . (3)
(2) x 3: 21x + 12y = -39 .(4)
(3) - (4) = 23y = 46
y = 46/23 = 2

Answer:

Step-by-step explanation:

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