We can express an equation to find the fraction of the catering order that is sandwiches or salads by summing up the fractions of the sandwiches and the salads, in this case, the fraction of the sandwiches is 5/12 and the fraction of the salads is 2/12, then the equation looks like this:
c = 5/12 + 2/12, option B is the correct answer
Answer:
(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0
(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0
Step-by-step explanation:
(a) when i = 2, the expected number of played games will be:
E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.
If p = 1/2, then:
d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.
(b) when i = 3;
E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]
Simplification and rearrangement lead to:
E(X) = 6p⁴-12p³+3p²+3p+3
if p = 1/2, then:
d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10
Therefore, E(X) is maximized.
Take a common point ( C in this case)
1. Take the difference of the y coordinates from the point vertical to C.
C from D in this case.
2.Take the diff of the x coordinates from the points horizontal to the first.
C from B in this case.
3. Now add the diff to the common point. X to x Y to y.
You just have to plug your coordinates into the distance formula.
(1, 6) (8, 1)
(X1, Y1) (X2, Y2)
do the work and you get 8.6
They will each have 2.5 fruit bars
