Answer:
pi times 4
Step-by-step explanation:
Circumference: pi times diameter (pi)(d) or pi times 2 times the radius (pi)(2r)
Answer:
Carla has been running 7 miles each day for 13 days.
Step-by-step explanation:
Carla ran 3 miles on her first day, 5 miles on her second day and then 7 miles each day onward.
Let the number of days she ran 7 miles each day = x
Total distance run by Carla = 3 + 5 + 7(x)
= 8 + 7x
If her log book shows that she has run total distance = 99 miles
Equation representing her total run will be,
8 + 7x = 99
7x = 99 - 8
7x = 91
x = 
x = 13 days
Therefore, Carla has been running 7 miles each day for 13 days.
The root

can be converted into the power

. Therefore we can rewrite the problem as

and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.
Thus the problem becomes

, which then can be turned into
![\sqrt[8]{10} ^{3x}](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B10%7D%20%5E%7B3x%7D)
, making the last option our 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.