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Irina18 [472]
3 years ago
6

Solve the equation. -2(x + 3) + 5x = -39​

Mathematics
1 answer:
Brut [27]3 years ago
7 0

Answer:

-11

Step-by-step explanation:

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A room has eight switches, each of which controls a different light. Initially, exactly five of the lights are on. Three people
aivan3 [116]

Answer:

The probability that 3 lights are on after the third person exited the room is 39/128

Step-by-step explanation:

In order for 6 switches to be on at the end, we need exactly 2 people turning on a switch and the other one turning one off. There are 3 possibilities:

  • The first two persons turn the switch in and the last one turns it off
  • The first and last person turn the switch in and the middle one tunrns it off
  • The first person turns the switch off and the 2 remaining turn the switch in

Note that after turning off one switch one more switch will be available to be switched in and one less will be available to be switch off. The contrary happens when someone turns in a switch.

Lets calculate the probability for the first scenario. The probability for the first person to turn the switch in is 3/8, because there are 3 lights off. For the second person, there will be only 2 lights off, thus, the probability for him or her to turn the switch in is only 2/8, leaving only 1 light off and 7 on. The third person will have, as a consecuence, a probability of 7/8 to turn off one of the 7 switches. This gives us a probability of 3/8 * 2/8 * 7/8 = 21/256 for the first scenario.

For the second scenario we will have a probability of 3/8 for the first person, a probability of 6/8 for the second one (he has to turn a switch off this time), and a probability, again, of 3/8 for the third one, giving us a probability of 3/8*6/8*3/8 = 27/256 for the second scenario.

For the third scenario, the first person has to turn off the switch, and it has a probability of 5/8 of doing so. The second person will have 4 switches to turn on, so it has a probability of 4/8 = 1/2, and the third person will have one switch less, thus, a probability of 3/8 of turning a switch on. Therefore, the probability of the third scenario is 5/8*1/2*3/8 = 15/128 = 30/256

By summing all the three disjoint scenarios, the probability that six lights are on is 21/256+27/256+30/256 = 78/256 = 39/128.

8 0
2 years ago
Find the lateral surface area of this
Yakvenalex [24]

lateral surface area of this cylinder is 1584/7 or 226.28...cm square.

5 0
3 years ago
Read 2 more answers
If the lines are parallel with angle a measuring 5x + 8 and angle b measuring 8x - 7, the measure of angle a would be ___ degree
Mandarinka [93]

The value of angle a will be 33°.

It should be noted that when we've parallel lines, then the angles will be equal. In this case, the value of angle a will be equal to that of angle b and this will be:

5x + 8 = 8x - 7.

Collect like terms .

8x - 5x = 8 + 7

3x = 15

Divide both side by 3

3x/3 = 15/3

x = 5

Therefore, the value of angle a will be:

= 5x + 8

= 5(5) + 8

= 25° + 8°

= 33°

The measure of angle a is 33°.

Read related link on:

brainly.com/question/24576134

7 0
3 years ago
100 POINTS! PLEASE HELP!
Semmy [17]

Apply angle bisector theorem

\\ \sf\longmapsto \dfrac{9}{15}=\dfrac{3}{5}=\dfrac{2x-1}{3x}

\\ \sf\longmapsto 9x=5(2x-1)

\\ \sf\longmapsto 9x=10x-5

\\ \sf\longmapsto 10x-9x=5

\\ \sf\longmapsto x=5

#2

\\ \sf\longmapsto \dfrac{4}{3}=\dfrac{x}{2.25}

\\ \sf\longmapsto 4(2.25)=3x

\\ \sf\longmapsto 3x=9

\\ \sf\longmapsto x=3

Hope it helps

4 0
2 years ago
Read 2 more answers
The LCM of 12 and 6 is 6. True or False
elena-s [515]

Answer:

false but Least common multiple (LCM) of 6 and 12 is 12.

7 0
3 years ago
Read 2 more answers
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