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>
multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.
and so, we see
110P = 110010
P = 010
FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.
<span>Find the equation of the line parallel to the line y = 4x – 2 that passes through the point (–1, 5).
</span>y = 4x – 2 has slope = 4 <span>parallel lines have same slope so slope = 4
</span><span>passes through the point (–1, 5). </span><span>y = mx+b 5 = 4(-1) + b b =9
equation y = 4x + 9
answer
The slope of y = 4x – 2 is 4 The slope of a line parallel to y = 4x – 2 is 4 The equation of the line parallel to y = 4x – 2 that passes through the point (–1, 5) is y = 4x + 9</span>
