The answer is 285 miles
x = 3.8×150/2
x = 570/2
x = 285 miles
Answer: The graph of h(x) passes the horizontal line test
Step-by-step explanation:
Answer:
3 − m = −2 (m + 6); m = −15 Yes
5 (p + 3) = −35; p = −4 No
8q = 3 (10 + q); q = 6 Yes
Step-by-step explanation:
3 − m = −2 (m + 6)
3 - m = -2m - 12
m = -15
Answer is Yes
5 (p + 3) = −35
5p + 15 = -35
5p = - 50
p = -10
Answer is No
8q = 3 (10 + q)
8q = 30 + 3q
5q = 30
q = 6
Answer is Yes
The answer is infinitely many solutions
If you divide the 2nd equation by 3, you get the first equation, meaning they are identical. That means that any value of x will be true, which means there are infinite solutions
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
