Each of the 492 people who came to a school football game paid $12 for a ticket. How much ticket money did the school collect?
2 answers:
You might be interested in
Answer:
a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm
Step-by-step explanation:
a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.
b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.
So, dV/dx = 0
d(30 - 2x)(16 - 2x)x/dx = 0
-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0
32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0
4x²- 120x + 450 = 0
x²- 30x + 112.5 = 0
Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,
x ≅ 25.61 or 4.4
V = (30 - 2x)(16 - 2x)x
Substituting the values of x into L and B, we have )x
L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22
B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22
Since L and B cannot be negative, we use the other value for x = 4.4, So
L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2
B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2
So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³
Answer:
Step-by-step explanation:
Given:
We know that, conditional probability of B given that A has occurred is given as:
. Expressing this in terms of
, we get
Plug in the known values and solve for . This gives,
Therefore, the probability of events A and B occurring is .