Answer:
Box A = 37.3333333333
Box B = 23.33333333333
Box C = 9.33333333333
Step-by-step explanation:
Answer:
6%
Step-by-step explanation:
Step 1
The fist step is to define the probabilities.
The events are independent from each other. Each team wins with probability
and looses with probability
Let
be probability that Roses win and
be the probability that Roses loose.
Step 2
The second step is to calculate the probabilities by multiplying the probabilities with the first 3 terms in the product being the probability of a win and the last term being the probability of a loss.
The calculation is shown below,
![P(W_R)\times P(W_R)\times P(W_R)\times P(L_R)=\frac{1}{2} \times \frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} =\frac{1}{16}](https://tex.z-dn.net/?f=P%28W_R%29%5Ctimes%20P%28W_R%29%5Ctimes%20P%28W_R%29%5Ctimes%20P%28L_R%29%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7B1%7D%7B16%7D)
Step 3
The last step is to convert this probability into a percentage. Converting this probability to a percentage is done as shown below,
![\frac{1}{16} \times 100\%=6.25\%.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%20%5Ctimes%20100%5C%25%3D6.25%5C%25.)
Step 4
The next step is to round down the percentage . The value of 6.25% rounded down is 6%. The correct answer is 6%.
Answer:
Part a) Exactly values
The width of the rectangle is ![\frac{\sqrt{70}}{2}\ cm](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B70%7D%7D%7B2%7D%5C%20cm)
The length of the rectangle is ![2\sqrt{70}\ cm](https://tex.z-dn.net/?f=2%5Csqrt%7B70%7D%5C%20cm)
Part b) Approximately values
The width of the rectangle is ![4.2\ cm](https://tex.z-dn.net/?f=4.2%5C%20cm)
The length of the rectangle is ![16.7\ cm](https://tex.z-dn.net/?f=16.7%5C%20cm)
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The area of rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
we have
![L=4x\ cm\\W=x\ cm](https://tex.z-dn.net/?f=L%3D4x%5C%20cm%5C%5CW%3Dx%5C%20cm)
substitute the values in the formula
![A=4x(x)](https://tex.z-dn.net/?f=A%3D4x%28x%29)
![A=4x^2](https://tex.z-dn.net/?f=A%3D4x%5E2)
![A=70\ cm^2](https://tex.z-dn.net/?f=A%3D70%5C%20cm%5E2)
so
![70=4x^2](https://tex.z-dn.net/?f=70%3D4x%5E2)
Solve for x
Divide by 4 both sides
![\frac{70}{4}=x^2](https://tex.z-dn.net/?f=%5Cfrac%7B70%7D%7B4%7D%3Dx%5E2)
square root both sides
![x=(+/-)\frac{\sqrt{70}}{2}](https://tex.z-dn.net/?f=x%3D%28%2B%2F-%29%5Cfrac%7B%5Csqrt%7B70%7D%7D%7B2%7D)
The solution is the positive value
![x=\frac{\sqrt{70}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Csqrt%7B70%7D%7D%7B2%7D)
therefore
<em>Exactly values</em>
![L=4\sqrt{70}}{2}=2\sqrt{70}\ cm\\\\W=\frac{\sqrt{70}}{2}\ cm](https://tex.z-dn.net/?f=L%3D4%5Csqrt%7B70%7D%7D%7B2%7D%3D2%5Csqrt%7B70%7D%5C%20cm%5C%5C%5C%5CW%3D%5Cfrac%7B%5Csqrt%7B70%7D%7D%7B2%7D%5C%20cm)
<em>Approximately values</em>
![L=4\sqrt{70}}{2}=16.7\ cm\\\\W=\frac{\sqrt{70}}{2}=4.2\ cm](https://tex.z-dn.net/?f=L%3D4%5Csqrt%7B70%7D%7D%7B2%7D%3D16.7%5C%20cm%5C%5C%5C%5CW%3D%5Cfrac%7B%5Csqrt%7B70%7D%7D%7B2%7D%3D4.2%5C%20cm)
If you multiply 2x2 you get 4 and multiply another 2 which is 8. Two answers are 8 and 2x2x2.