Answer:
x = 1.8
Step-by-step explanation:
10.4 - 5 = 5.4 (subtract 5 from each side)
to isolate the variable, x, divide each side by 3
5.4/3 = 1.8
The value of P(R = 3) is 0.2854
<h3>Probability</h3>
Probabilities are used to determine the chances of events.
The given parameters are:
--- the number of slots
. --- the number of red slot
. --- the number of black slot
. --- the number of green slot
<h3>Individual probabilities</h3>
The probability that the ball lands on a red slot is calculated as:
![p = \frac{18}{38}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B18%7D%7B38%7D)
Simplify
![p= \frac{9}{19}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B9%7D%7B19%7D)
The probability that the ball does not land on a red slot is calculated as:
![q = \frac{18+2}{38}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B18%2B2%7D%7B38%7D)
![q = \frac{20}{38}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B20%7D%7B38%7D)
Simplify
![q = \frac{10}{19}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B10%7D%7B19%7D)
<h3>
Binomial probability</h3>
The value of P(R = 3) is then calculated using the following binomial probability formula
![P(R = r) = ^nC_rp^rq^{n-r}](https://tex.z-dn.net/?f=P%28R%20%3D%20r%29%20%3D%20%5EnC_rp%5Erq%5E%7Bn-r%7D)
Where:
![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
![r = 3](https://tex.z-dn.net/?f=r%20%3D%203)
So, we have:
![P(R = 3) = ^7C_3 \times (9/19)^3 \times (10/19)^{7-3}](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%20%5E7C_3%20%5Ctimes%20%289%2F19%29%5E3%20%5Ctimes%20%2810%2F19%29%5E%7B7-3%7D)
![P(R = 3) = 35 \times (9/19)^3 \times (10/19)^4](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%2035%20%5Ctimes%20%289%2F19%29%5E3%20%5Ctimes%20%2810%2F19%29%5E4)
![P(R = 3) = 0.2854](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%200.2854)
Hence, the value of P(R = 3) is 0.2854
Read more about probabilities at:
brainly.com/question/15246027
Answer:
The number is -6.
Step-by-step explanation:
Variable x = a number
Set up an equation:
3x + 12 = -6
Isolate variable x:
3x = -18
x = -6
Check your work:
3(-6) + 12 = -6
-18 + 12 = -6
-6 = -6
Correct!
He made a mistake in step #2. It seemed to be a trivial mistake because it involved signs, but it still had a great impact. Since step#2, his solution was already wrong.
Instead of
(-1)²-4(2)(-6) = 1 + 48 = 49
What he did is
(-1)²-4(2)(-6) = -1 + 48 = 47
Answer:
Can you put the picture
Step-by-step explanation: