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3 years ago

Given ∆QRS≅∆TUV, QS=5v+3, and TV=6v−9, find the length of QS and TV.?

1 answer:

7 0

If ∆QRS≅∆TUV, Their corresponding sides would be equal so,
QS = TV
5v + 3 = 6v - 9
6v - 5v = 3 + 9
v = 12

Now, QS = TV = 5(12) + 3 = 60 + 3 = 63

In short, Your Answer would be Option B

Hope this helps!

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If $5,500 is invested in an account that pays 3% interest compounded annually, how much money will be in the account at the end

Citrus2011 [14]

He would have 7150 in his account

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3 years ago

Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least

Tatiana [17]

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

1) The probability of having a face card in the first turn

In this case, the chances are 12 in 52:

$P_1=P(face\, card)=12/52=0.231$

2) The probability of having a face card in the second turn, having a non-face card in the first turn.

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

$P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181$

3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141$

4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_4=(40/52)*(39/51)*(38/50)*(12/49)\\\\P_4=0.769*0.765*0.76*0.245=0.109$

With these four probabilities we can calculate the probability of losing this bet:

$P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662$

The probability of losing is 66.2%, which is the same as saying you have (1-0.662)=0.338 or 33.8% of winning chances. Losing is more probable than winning, so you should not take the bet.

b) If the bet involves 3 cards, the only difference with a) is that there is no probability of getting the face card in the fourth turn.

We can calculate the probability of losing as the sum of the first probabilities already calculated:

$P=P_1+P_2+P_3=0.231+0.181+0.141=0.553$

There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.

5 0

3 years ago

Solve for x. −3x + 2b > 8

RoseWind [281]

I think the answer is
x < (2b -8) / 3
or
x < 2b/3 - 8/3

6 0

3 years ago

Read 2 more answers

Which ordered pair is included in the solution set to the following system? y > x2 + 3 y < x2 – 3x + 2 (–2, 8) (0, 2) (0,

I am Lyosha [343]

The ordered pair that is a solution of the system is (-2, 8).

<h3>Which ordered pair is included in the solution set to the following system?</h3>

Here we have the system of inequalities:

y > x² + 3

y < x² - 3x + 2

To check which points are solutions of the system, we can just evaluate both inequalities in the given points and see if they are true.

For example, for the first point (-2, 8) if we evaluate it in the two inequalities we get:

8 > (-2)² + 3 = 7

8 < (-2)² - 3*(-2) + 2 = 12

As we can see, both inequalities are true. So we conclude that (-2, 8) is the solution.

(if you use any other of the 3 points you will see that at least one of the inequalities becomes false).

If you want to learn more about inequalities:

brainly.com/question/18881247

#SPJ1

3 0

2 years ago

I need an answer plz asap

aleksley [76]

Answer:

1/5,3/10

Step-by-step explanation:

just look at the picture

6 0

3 years ago