X + (-4) = -12 what is x?

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

4 years ago

Will mark brainliest for area.

Elena L [17]

Answer:

c

Step-by-step explanation:

first, find the area of the rectangle thing,

A = lw

14 x 8

112

but, there is a semicircle in it so you need to subtract that from it:

A = πr^2/2

A = π(4)^2/2

A = π16/2

A = 8π

A ≈ 25.132741228718346

then subtract that area from the area of the rectangle:

112 - 25.132741228718346

86.867258771281654

or about 89.9

6 0

3 years ago

The vertex of the parabola below is at the point (2, 4), and the point (3, 6) is on the parabola. what is the equation of the pa

Paraphin [41]

Given:

Vertex ===> (h, k) (2, 4)

The parabola passes through the point: (x, y) ==> (3, 6)

Let's find the equation of a parabola.

To find the equation, use the general equation of a parabola with vertex (h, k):

$y=a(x-h)^2+k_{}$

Where:

(h, k) ==> (2, 4)

(x, y) ==> (3, 6)

Substitute values into the general equation:

$\begin{gathered} 6=a(3-2)^2+4 \\ \\ 6=a(1)^2+4 \\ \\ 6=a+4 \end{gathered}$

Subtract 4 from both sides:

$\begin{gathered} 6-4=a+4-4 \\ \\ 2=a \\ \\ a=2 \end{gathered}$

Substitute 2 for a, and input the values of the vertex (h, k) in the general vertex equation:

$y=2(x-2)^2+4$

Therefore, the equation of the parabola is:

$y=2(x-2)^2+4$

ANSWER:

$y=2(x-2)^2+4$

3 0

1 year ago

Find s8 for the following geometric sequence: 3, – 6, 12, – 24.

Alekssandra [29.7K]

Answer:

B. -255

Step-by-step explanation:

This picture is from the user of: DBlaze.

4 0

3 years ago

Answer please! Thanks so much! :)

DanielleElmas [232]

320 is the correct answer

5 0

3 years ago