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4 days ago

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from

$9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue?
A. $9.00 per backpack gives the maximum revenue; the maximum revenue is $32.00.
B. $12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.
C. $12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.

Mathematics

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Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two

PIT_PIT [12445]

There are 2 beginner, 6 intermediate, and 3 advanced books, totaling 11.

P(advanced) = 3/11
replaced
P(beginner) = 2/11

P(both) = 3/11 * 2/11 = 6/121 <=

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3 months ago

If Ana devotes all her time to making fudge, she can make 3 pounds of fudge an hour, and if he devotes all her time to making to

lawyer [12517]

Answer: Ana should produce more fudge, and Leo should produce more toffee.

Step-by-step explanation:

Comparative advantage defined: A person or country has a comparative advantage producing a good if their opportunity cost for it is lower than someone else's.

In this case, Ana and Leo will both benefit if they focus on the product for which they have the lower opportunity cost.

(a) Ana’s production possibilities:

If she spends all her time making fudge: 3 pounds; or toffee: 2 pounds.

Opportunity cost of 1 pound fudge = 2/3 = 0.66 pounds toffee

Opportunity cost of 1 pound toffee = 3/2 = 1.5 pounds fudge

(b) Leo’s production opportunities:

All time making fudge: 4 pounds; or toffee: 5 pounds.

Opportunity cost of 1 pound fudge = 5/4 = 1.25 pounds toffee

Opportunity cost of 1 pound toffee = 4/5 = 0.8 pounds fudge

Since Ana’s opportunity cost for fudge is lower than Leo’s, she should specialize in fudge production.

Conversely, Leo has a lower opportunity cost for toffee, so he should focus on producing toffee.

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3 months ago

In how many ways can you receive four cards of the same face value and one card from the other 48 available cards?

Zina [12379]

A deck contains 13 groups of 4 cards, indicating 13 unique ways to select four cards sharing the same face value. Any subsequent card drawn will necessarily represent a different face value. Consequently, the total combinations for selecting 5 cards—4 of which share the same face value and 1 diverging—amount to 13 x 48.

13 x 48 = 624.

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2 months ago

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a

babunello [11817]

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.

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3 months ago