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:
About 29
Step-by-step explanation:
575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.
Yes, this is correct. The tenths place is the first number to the right of the decimal. There is a 3 in that spot
To find if it rounds up or down, follow this rule.
Less than 5 round down and greater than 5 round up.
For this you look to the number next to it which is 7.
It rounds up so it is 9.4
In a parallelogram opposite angles are congruent, that means:
Angle L = Angle N, replace L & N by they respective value, then
3x-25 = 2x-10 ==> x=15 , Now plug the value of x in any of the 2 sides
3(15) -25 =20°
hence Angle L =- Angle N = 20°
Now let's calculate Angle M. In a parallelogram the adjacent angle are supplementary, that means their sum = 180°, then
Angle N + Angle N = 180°==> Angle M = 180°-20° = 160°
Answer:
75% of the data will reside in the range 23000 to 28400.
Step-by-step explanation :
To find the range of values :
We need to find the values that deviate from the mean. Since we want at least 75% of the data to reside between the range therefore we have,
Solving this, we would get k = 2 which shows the value one needs to find lies outside the range.
Range is given by : mean +/- (z score) × (value of a standard deviation)
⇒ Range : 25700 +/- 2 × 1350
⇒ Range : (25700 - 2700) to (25700 + 2700)
Hence, 75% of the data will reside in the range 23000 to 28400.
