The ratio of surface areas of 2 similar cones is 16:49. What is the ratio of volumes of similar cones?
1 answer:
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Answer:
See explanation for matching pairs
Step-by-step explanation:
Equations
(1)
(2)
(3)
Solutions
Required
Match equations with solutions
(1) and
Make x the subject in:
Substitute in
Collect like terms
Solve for y
Recall that:
So:
(2) and
Make y the subject in
Substitute in
Collect like terms
Solve for x
Solve for y in
So:
(3)
and
Make y the subject in
Substitute in
Collect like terms
Solve for x
Solve for y in
So:
Answer:
The optimal production quantity is 9,322 cards.
Step-by-step explanation:
The information provided is:
Cost of the paper = $0.05 per card
Cost of printing = $0.15 per card
Selling price = $2.15 per card
Number of region (n) = 4
Mean demand = 2000
Standard deviation = 500
Compute the total cost per card as follows:
Total cost per card = Cost of the paper + Cost of printing
= $0.05 + $0.15
= $0.20
Compute the total demand as follows:
Total demand = Mean × n
= 2000 × 4
= 8000
Compute the standard deviation of total demand as follows:
Compute the profit earned per card as follows:
Profit = Selling Price - Total Cost Price
= $2.15 - $0.20
= $1.95
The loss incurred per card is:
Loss = Total Cost Price = $0.20
Compute the optimal probability as follows:
Use Excel's NORMSINV{0.907} function to find the Z-score.
<em>z</em> = 1.322
Compute the optimal production quantity for the card as follows:
Thus, the optimal production quantity is 9,322 cards.