(16-x²)+(4-x) or (-x²+16)+(-x+4)
Combine like terms
(-x²+20-x) or (-x²-x+20)
Answer:
(1 , -2)
Step-by-step explanation:
The intersecting point of two lines is the solution
Answer:
Less than
Step-by-step explanation:
Its less than because the angle of LS is 98 while MS is 95, so LS is longer
Answer:
Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.
Step-by-step explanation:
The table that can be formed by the rate at which they study the number of pages of a book is:
Fred Lonnie total
5 4 9
10 8 18
15 12 27
20 16 36
That means when they read a combined of 36 pages.
Then the number of pages read by Fred is 20 pages.
and the number of pages read by Lonnie is 16 pages.
(
Also it could be done as :
Let Fred reads 'x' pages.
so, the number of pages read by Lonnie is: (4/5)x
Hence,
x+(4/5)x=36
on solving this linear equation we have:
x=20
and (4/5)x=16
)
Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.
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.
