Answer: 17 years
Step-by-step explanation:
City A is currently 2,425 people in number and growing at 27 per year.
An expression to find the population in a given year assuming the year is x would be:
= 2,425 + 27 * x
= 2,425 + 27x
Applying the same logic to City B would give an expression of:
= 1,813 + 63x
Equating these together will give the year they will be the same:
2,425 + 27x = 1,813 + 63x
2,425 - 1,813 = 63x - 27x
612 = 36x
x = 612/36
x = 17 years
Wouldn't you have to multiply 12 time 1,000 then that by 84.50? Hope this helps
Answer:
4000
Step-by-step explanation:
A=P(2)^(t/d)
A=future amount
P=starting amount
t=time elapsed
h=doubling time
given
P=10^3
t=6
d=2
A=10^3(2)^(6/2)
A=10^3(2)^2
A=10^3(4)
A=4*10^3
A=4000
4000 bacteria
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
