Answer:
digit in the unit's place originally = 5
Step-by-step explanation:
x + y = 14
xy - yx = 36
Now, the only single digits that sum up to 14 are;
9 + 5 = 14
8 + 6 = 14
We can't use 7 + 7 because they said there is a difference when the numbers are reversed.
Now, let's assume 95 is the original number since we are told when it is reversed it is lesser.
Thus, when reversed we have 59.
Difference = 95 - 59 = 36
Thus,unit number of original number = 5
This is just simple subtraction, 59.99 - 47.50
The answer is C: 12.49
Answer:
x = 34.9 to the nearest tenth.
Step-by-step explanation:
tan 64 = opposite side / adjacent side = x / 17.
x = 17 * tan 64
= 34.855
Answer:
4 minutes and 32 seconds
Step-by-step explanation:
card $20.00-money left over $15.68 $20.00-$15.68 4.32
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.
