Answer:
x = 11
Step-by-step explanation:
Given the expression;
5x+2y=67 ...1
x=3y−7 ....2
Substitute 2 into 1
5(3y-7)+2y = 67
15y - 35 + 2y = 67
17y = 67+35
17y = 102
y = 102/17
y =6
Recall that x = 3y - 7
x = 3(6) - 7
x = 18 - 7
x = 11
Hence the value of x is 11
Answer:
m∠1 = 25° (opposite angles are congruent)
m∠2 = 87° ⇒ 180 - (25 + 68)
m∠3 = 68° ⇒ 180 - (87 + 25)
Hope this helps!
Answer:
9 DIVIDED BY 20 THAT IS BASICALLY AN EXPRESSION!
Step-by-step explanation:
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.
X+x+54=180
2x+54=180
2x=126
x=63
63+54=117
one angle is 63, the other is 117
