Let h = height of the box,
x = side length of the base.
Volume of the box is
.
So
Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.
![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then
So the box is 4.86 in. wide and 4.87 in. high.
In order to answer the question, we simply substitute the value of p and q to the given expression and solve. We do as follows:
<span>P^2q^2+pq–q^3–p^3
</span>0.5^2(-0.5)^2+0.5(-0.5)–(-0.5)^3–(0.5)^3
-3/16 or -0.1875
Hope this answers the question. Have a nice day.
27.034%
Let's define the function P(x) for the probability of getting a parking space exactly x times over a 9 month period. it would be:
P(x) = (0.3^x)(0.7^(9-x))*9!/(x!(9-x)!)
Let me explain the above. The raising of (0.3^x)(0.7^(9-x)) is the probability of getting exactly x successes and 9-x failures. Then we shuffle them in the 9! possible arrangements. But since we can't tell the differences between successes, we divide by the x! different ways of arranging the successes. And since we can't distinguish between the different failures, we divide by the (9-x)! different ways of arranging those failures as well. So P(4) = 0.171532242 meaning that there's a 17.153% chance of getting a parking space exactly 4 times.
Now all we need to do is calculate the sum of P(x) for x ranging from 4 to 9.
So
P(4) = 0.171532242
P(5) = 0.073513818
P(6) = 0.021003948
P(7) = 0.003857868
P(8) = 0.000413343
P(9) = 0.000019683
And
0.171532242 + 0.073513818 + 0.021003948 + 0.003857868 + 0.000413343
+ 0.000019683 = 0.270340902
So the probability of getting a parking space at least four out of the nine months is 27.034%
A total of 800 people visited the zoo on Monday
Answer:
-3
Step-by-step explanation:
