Team A) 45 people
Team B) 55 people
A)There are two ways to solve this problem, finding the number of combinations possible for Team B, or the number of combinations possible for Team A.
Team A
It's a given that 20 mathematicians are on team A, which leavs the other 25 people for team A to be chosen from a pool of 80 (100- 20 mathletes)
80-C-25 = 80! / (25!/(80-25)!) =<span>363,413,731,121,503,794,368
</span>or 3.63 x 10^20
Solving using Team B
Same concept, but choosing 55 from a pool of 80 (mathletes excluded)
80-C-25 = 80! / (55!(80-55!) = 363,413,731,121,503,794,368
or 3.63 x 10^20
As you can, we get the same answer for both.
B)
If none of the mathematicians are on team A, then we exclude the 20 and choose 45:
80-C-45 = 80! / (45!(80-45)!) = <span>5,790,061,984,745,3606,481,440
or 5.79 x 10^22
Note that, if you solve from the perspective of Team B (80-C-35), you get the same answer</span>
The remaining area that the grass will cover will be given by:
Area=[area of rectangle]-[area of the triangle]
area of rectangle will be:
A1=length*width
=20*8
=160 square feet
The area of the triangle will be:
A2=1/2absin theta
since the triangle is equilateral, all the angles are equal and the size of each angle is 60°. Thus the area will be:
A2=1/2*5*5sin 60
=18.3
thus the remaining area of the grass will be:
Area=160-18.3
=149.7 square feet
Answer:
C. 10.5 pounds
Step-by-step explanation:
The worth of 3 loaves of bread is 3 times that of one loaf:
3 × 1.75 = 5.25
You want the number of pounds of oranges (p) at 0.50 per pound that has this same worth:
0.50p = 5.25
p = 5.25/0.50 = 10.50
10.5 pounds of oranges have an equivalent cost to 3 loaves of bread.
Answer:
x = 5
Step-by-step explanation:
Given
f(x) = - 3x + 21 and f(x) = 6, then equating gives
- 3x + 21 = 6 ( subtract 21 from both sides )
- 3x = - 15 ( divide both sides by - 3 )
x = 5
