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Andrew [12]
3 years ago
10

Membership selection. A town council has 10 ​members, 5 Democrats and 5 Republicans. ​(A) If the president and​ vice-president a

re selected at​ random, what is the probability that they are both​ Democrats? ​(B) If a​ 3-person committee is selected at​ random, what is the probability that Republicans make up the​ majority?
Mathematics
1 answer:
SOVA2 [1]3 years ago
7 0

Answer:

(A) P=0.22 or 22% (B) P=50%

Step-by-step explanation:

(A) We have a tree of probabilities, with two steps: president and vice-president.

If the president is elected first, there is a 5/10 chances it will be Democrat.

If this happened, in the election of vice-president, there is 4/9 chances it will be a Democrat chosen again, because there is one Democrat member already selected for President.

So the chances of having a Democrat president and vice president are:

(5/10) x (4/9) = 20/90 = 0.22 = 22%.

(B) We have another tree, with tree steps. The Republicans have majority whenever there are 2 or 3 members in the 3-person comitee.

It can be calculated as the sum of the probability of having 3 republican members (RRR) and the probability of having 2 republican members (RRD, RDR and DRR).

P(RRR) = (5/10) x (4/9) x (3/8) = 1/9

P(RRD) = (5/10) x (4/9) x (5/8) = 1/7

P(RDR) = (5/10) x (5/9) x (4/8) = 1/7

P(DRR) = (5/10) x (5/9) x (4/8) = 1/7

P(RRR) + P(RRD) + P(RDR) + P(DRR) = 1/9 + 1/7 + 1/7 + 1/7 = 1/2 = 50%

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Step-by-step explanation:

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3 years ago
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Answer:

D .points (2,2) (4,4) (0,9)

Step-by-step explanation:

5 0
3 years ago
ANSWER ASAP ITS FOR FINALS
Roman55 [17]

Answer:

9. 66°

10. 44°

11. 2\sqrt{7}

12. 2\sqrt{3}

13. 27.3

14. 33.9

15. 22°

16. 24°

Step-by-step explanation:

9. Add 120 + 80 (equals 200) and subtract that from 360 (Because all angles in a quadrilteral add to 360°), this equals 160. Plug the same number in for both variables in the two other angle equations until the two angles add to 160. For shown work on #9, write:

120 + 80 = 200

360 - 200 = 160

12(5) + 6 = 66°

19(5) - 1 = 94°

94 + 66 = 160

10. Because the two sides are marked as congruent, the two angles are as well. This means the unlabeled angle is also 68°. The interior angles of a triangle always add to 180°, so add 68+68 (equals 136) and subtract that from 180, this equals 44. For shown work on #10, write:

68 x 2 = 136

180 - 136 = 44

11. Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #10, write:

a² + b² = c²

a² + 6² = 8²

a² + 36 = 64

a² = 28

a = \sqrt{28}

a = 2\sqrt{7}

12. (Same steps as #11) Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #11, write:

a² + b² = c²

a² + 2² = 4²

a² + 4 = 16

a² = 12

a = \sqrt{12}

a = 2\sqrt{3}

13. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #13, write:

Sin(47°) = \frac{20}{x}

x = 27.3

14. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #14, write:

Tan(62°) = \frac{x}{18}

x = 33.9

15. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #15, write:

cos(θ) = 52/56

θ = cos^-1 (0.93)

θ = 22°

16. (Same steps as #15) Use SOH CAH TOA and solve with a scientific calculator. For shown work on #16, write:

sin(θ) = 4/10

θ = sin^-1 (0.4)

θ = 24°

Good luck!!

8 0
3 years ago
Please help me I need help
dsp73

Answer:

i think it would be 87% i have been working on ths for a mnet and it got confusing for a sec i may be rong but i am pretty shure that this is the answer

btw i cant spell

Step-by-step explanation:

8 0
3 years ago
Solve the unknown variable
dsp73
Set measurements equal to each other.
7X + 20 = 8X + 8
-7X           -7X

20 = X + 8
-8          -8

ANSWER: X=12
5 0
3 years ago
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