Yes, because you can multiply $3 by 3 to get $9 and 6 muffins by 3 to get 9 muffins.
Answer:
0.03125
Step-by-step explanation:
If we have a fair coin the probability of landing a head is 50%.
We can think the question as what is the probability of landing four tails and then a head. That is we needed at least 5 tries to get a head.
Since this events are independent we can write it as
Answer:
- r = 12.5p(32 -p)
- $16 per ticket
- $3200 maximum revenue
Step-by-step explanation:
The number of tickets sold (q) at some price p is apparently ...
q = 150 + 25(20 -p)/2 = 150 +250 -12.5p
q = 12.5(32 -p)
The revenue is the product of the price and the number of tickets sold:
r = pq
r = 12.5p(32 -p) . . . . revenue equation
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The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...
p = (0 +32)/2 = 16
The theater should charge $16 per ticket.
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Maximum revenue will be found by using the above revenue function with p=16.
r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue
_____
<em>Additional comment</em>
The number of tickets sold at $16 will be ...
q = 12.5(32 -16) = 200
It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.
Answer:
(a) 1825 = 2.25x + (2.25-1)(x -108)
(b) 560 mi/h
Step-by-step explanation:
(a) distance = speed·time
The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.
The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).
The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...
... 1825 = 2.25x + (2.25 -1)(x -108)
(b) Simplifying the equation gives ...
... 1825 = 3.50x -135
To solve this 2-step equation, we add 135, then divide by 3.50.
.. 1960 = 3.50x
... 1960/3.50 = x = 560
The first airplane's speed is 560 mph.
<u>Check</u>
In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.
In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.
Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.
