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mart [117]
3 years ago
8

In a certain Algebra 2 class of 22 students, 5 of them play basketball and 11 of them play baseball. There are 3 students who pl

ay both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball
Mathematics
1 answer:
Alex787 [66]3 years ago
7 0
The answer would be six 6
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Suppose that two teams play a series of games that ends when one of them has won ???? games. Also suppose that each game played
Musya8 [376]

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.

6 0
3 years ago
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.
irakobra [83]
The angular velocity is the linear speed divided by the radius.
  ω = d/(t*r) = (14.13 ft)/((3 s)*(6 ft))
  ω = 0.785 radians/second
There are 180/π degrees per radian, so the angular velocity can also be written as ...
  ω = 45 degrees/second
5 0
3 years ago
What is 45% of 90 ?
Liula [17]

Answer:

40.5

Step-by-step explanation:

This answer makes sense because we know that 50% of 90 is 45.

Since 45% of 90 is 40.5, we can self-check our answer.

Hope I helped!

~PumpkinSpice1♥

4 0
3 years ago
Read 2 more answers
Which expression shows the distance on the number line between 2 and −7?
kumpel [21]

Answer:

d

i did the test

Step-by-step explanation:

8 0
3 years ago
WHAT IS -(-2z+5y) HELP MY HOMEWORK IS DUE IN 50 MINUTES PLEASE
vampirchik [111]

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{2z - 5y}}}}}

Step-by-step explanation:

\sf{ - ( - 2z + 5y)}

Distribute negative ( - ) sign through the parentheses

\sf{( - ) \times ( - 2z)  + ( - ) \times (5y)}

\dashrightarrow{ \sf{2z   + ( - 5y)}}

\dashrightarrow{ \sf{2z - 5y}}

Hope I helped!

Best regards! :D

7 0
4 years ago
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