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: Let's solve your equation step-by-step.
2h−3=3
Step 1: Add 3 to both sides.
2h−3+3=3+3
2h=6
Step 2: Divide both sides by 2.
2h/2 = 6/2
h = 3.
The options aren't given, however, the range of amount spent could be calculated
Answer:
Kindly check explanation
Step-by-step explanation:
Paula purchase 3 dvd and 7 cds and spent between 90 and 100. Each dvd costs the same amount the price of cd is 10 select all amounts that could be the price of the dvd
Given that :
DVD costs the same amount
Number of DVD's = 3
Cost of cds = 10
Number of cds = 7
Total cost of cd's = 10 * 7 = 70
Let the price of DVD = x
Total amount spent = 90 - 100
Lowest price of DVD :
(amount spent - price of cd) / number of dvd
(90 - 70) / 3 = 20 /3 = 6.667
Highest price :
(100 - 70) / 3 = 30 / 3 = 10
Hence the pice of each DVD will range between /
6.6666 and 10.
Hence, prices listed within the range above are possible.
Answer:
Once an expression has been factored, use the Distributive Property to expand the expression. The expanded expression should be the original expression.
Step-by-step explanation:
The distributive property for any binary operation Ф under * in the given set S where a, b, c ∈ S
The binary operation a * (b Ф c) = (a * b) Ф (a * c) .
The operation * distributes over the operation Ф.
Now, when factoring, suppose we have an expression ab + ac. To factor this, we have a(b + c).
To check that our answer is correct, since the expression has been factored, we then distribute the multiplication over the addition to check if the factorization is correct.
So, a(b + c) = ab + ac which is our initial expression.
So, to use the distributive property to check work when factoring, once an expression has been factored, use the Distributive Property to expand the expression. The expanded expression should be the original expression.
12 more boys than girls
ratio of boys to girls = 7:5
thus 2/12 is difference between boys and girls = 12
total students = 12 ÷ 2/12 = 72
