Answer:
1716 ;
700 ;
1715 ;
658 ;
1254 ;
792
Step-by-step explanation:
Given that :
Number of members (n) = 13
a. How many ways can a group of seven be chosen to work on a project?
13C7:
Recall :
nCr = n! ÷ (n-r)! r!
13C7 = 13! ÷ (13 - 7)!7!
= 13! ÷ 6! 7!
(13*12*11*10*9*8*7!) ÷ 7! (6*5*4*3*2*1)
1235520 / 720
= 1716
b. Suppose seven team members are women and six are men.
Men = 6 ; women = 7
(i) How many groups of seven can be chosen that contain four women and three men?
(7C4) * (6C3)
Using calculator :
7C4 = 35
6C3 = 20
(35 * 20) = 700
(ii) How many groups of seven can be chosen that contain at least one man?
13C7 - 7C7
7C7 = only women
13C7 = 1716
7C7 = 1
1716 - 1 = 1715
(iii) How many groups of seven can be chosen that contain at most three women?
(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)
Using calculator :
(15 * 35) + (6 * 21) + (1 * 7)
525 + 126 + 7
= 658
c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?
(First in second out) + (second in first out) + (both out)
13 - 2 = 11
11C6 + 11C6 + 11C7
Using calculator :
462 + 462 + 330
= 1254
d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?
Number of ways with both in the group = 11C5
Number of ways with both out of the group = 11C7
11C5 + 11C7
462 + 330
= 792
Answer:
<em>The input when the output is 17 is x=6.</em>
Step-by-step explanation:
<u>Functions</u>
Assume the input is called x and the output is the function f(x). Two times the input is 2x. 5 more than that is 2x+5.
Knowing the output of the function is 5 more than 2 times the input, we can write the function as:
f(x)=2x+5
Now find the input x when the output is 17:
17=2x+5
Swap sides of the equation:
2x+5=17
Subtract 5:
2x=17-5=12
Divide by 2:
x=12/6=6
The input when the output is 17 is x=6.
Info given :
vehicles : (colors)red car, green car, yellow car, blue car, white car
types : sedan, minivan, SUV, convertible, pick-up truck
people : Diego, Ingrid, Rachel, Anton, Yuna
Diego -- red car -- minivan -- 3rd car
Ingrid -- white car -- sedan -- 4th car
Yuna -- green car -- truck -- 5th car
Rachel -- yellow car -- SUV -- 1st car
Anton -- blue car -- convertible -- 2nd car
I am thinking the truck, it is green, is driven by Yuna