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
Good morning,
Answer:
<h2>5+(-4) > -4 + (-7)</h2>
Step-by-step explanation:
5+(-4) = 5 - 4 = 1
-4 + (-7) = -(4+7) = -11
since 1 > -11 then 5+(-4) > -4 + (-7)
:)
Answer:
y = -4
Step-by-step explanation:
First, let's find the slope. Since the line is horizontal, it's slope has to be 0 (this is because slope = rise/run, there is no "rise" in a horizontal line therefore the slope is 0)
Now, we need to find the y-intercept. This is where the line intercepts the y-axis. Looking at the graph, the line intercepts the axis at (0,-4), therefore the y-intercept is -4.
The equation would be:
y=0x-4
y=-4
The answer equals 6.
Since 3 3/4 equals 15/4, when you divide you have to switch the numbers in the divisor and then you turn the equation into multiplication.
So then it will be 15/4 x 4/3.
15 x 4 = 60
4 x 3 = 12 so the answer is 60/12. But you have to simplify so half of 60/12 is 30/6 and then half of 30/6 is 15/3 then you have to pick the gcf of 3 and 15 which is 3.
15 divided by 3 equals 5.
3 divided by 3 equals 1 so 5/1 equals 5
Hope this helps! ;)
Answer:
d
Step-by-step explanation:
formula for area of a triangle is base * width * 1/2
