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Answer:
91
Step-by-step explanation:
P(1) = 0.25
P(3) = 2P(2) = 3P(4)
P(5) = P(4) + 0.1 = P(6) − 0.1
The probabilities add up to 1:
1 = P(1) + P(2) + P(3) + P(4) + P(5) + P(6)
Write each probability in terms of P(4).
1 = 0.25 + 1.5P(4) + 3P(4) + P(4) + P(4) + 0.1 + P(4) + 0.2
1 = 0.55 + 7.5P(4)
0.45 = 7.5P(4)
P(4) = 0.06
Therefore, P(6) = P(4) + 0.2 = 0.26.
The expected value is the number of trials times the probability.
E = 350 × 0.26
E = 91
Direct variation is y = kx, where k is the constant of variation.
But now it says y varies directly with x2 (or 2x), so now the x in the equation is 2x.
The equation is y = k(2x)
Now you find k.
y = 96 when x = 4.
(96) = k(2*4)
96 = k(8)
k = 12
The equation is now y = 12(2x)
To find the value of y when x=2, plug 2 into the equation you made.
y = 12(2*2)
y = 48
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Now it's with a "quadratic variation," which is the same thing except x is squared.
The equation is y = kx^2
But y varies directly with x2 (same thing as 2x), so now it's y = k(2x)^2.
Now you find k by substituting y and x values that were given.
y = 180 when x = 6
(180) = k(2*6)^2
180 = k(12)^2
180 = k(144)
k = 1.25
k, 1.25, is the constant of variation.
9514 1404 393
Answer:
64r -48r -144
Step-by-step explanation:
The January cost expression is ...
62p -48p -144 -432 = profit
The cost is identified as having 3 components, so the profit will have 4 components:
(selling price)×p - ((cost per unit)×p +(fixed monthly cost)) -(first month startup cost) = profit
Comparing this to the given equation, we identify the components as ...
selling price = 62
cost per unit = 48
fixed monthly cost = 144
first month startup cost = 432
We note that 432 = 3×144, so is consistent with the description of startup costs.
Increasing the selling price by $2 will raise it from 62 to 64. In February, the initial month startup cost disappears, so the profit equation becomes ...
(selling price)×r - ((cost per unit)×r +(fixed monthly cost)) = profit
64r -48r -144 = profit
