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Klio2033 [76]
3 years ago
15

1. Lucy has a jewelry business. To make a certain necklace, she spends $3.38 on materials and $5.57 on labor. She then sells the

necklace for $15.99. Lucy’s profit on the necklace is equal to the sale price minus the cost of materials and labor.
(a) How much profit does Lucy earn when she sells a necklace? Show your work.
(b) Write a fraction of the profit per sale price of the necklace. Record your answer as a fraction using whole numbers.
(c) What decimal of every dollar of the sale price of the necklace is profit using the fraction from Part (b)? Show your work. Round your answer to the nearest hundredth.
(d) Lucy collected $223.86 selling necklaces at a craft fair. How many necklaces did Lucy sell? Show your work.
(e) How much profit did she earn from the number of necklaces she sold? Show your work.
Mathematics
2 answers:
VARVARA [1.3K]3 years ago
7 0
A. Profit is calculated by subtracting the total cost from total revenue.

    TR = $15.99 and TC = $3.38 + $5.57

           P = $15.99 - ($3.38 + $5.57)
   <em>          P = $7.04</em>

b. The fraction of the profit and sale price is,

    F = Profit / sale price = 7.04 / 15.99

Simplifying,

   <em>F = 704/1599</em>

 c. If the fraction in b is expressed in decimal places to the nearest hundredths is<em> 0.44</em>.

d. To determine the number of necklaces sold, divide the total amount collected by the price of each.

     n = $223.86 / $15.99 = 14

Answer:<em> 14</em>

e. The profit is calculated by multiplying the answers from a and d.
   
     TP = 14($7.04)
    <em>  TP = $98.56 </em>
son4ous [18]3 years ago
5 0
<span>(a) $7.04 (b) 704/1599 (c) 0.44 (d) 14 (e) $98.56 (a) How much profit does Lucy earn when she sells a necklace? Since the problem states that her profit is the sale price minus the cost of materials and labor, we have the following equation. P = $15.99 - $3.38 - $5.57 P = $12.61 - $5.57 P = $7.04 So her profit is $7.04 per necklace. (b) Write a fraction of the profit per sale price of the necklace. Record your answer as a fraction using whole numbers. The raw fraction is 7.04/15.99, to get rid of the decimal point, multiply top and bottom by 100, getting 704/1599. The prime factors of 704 are 2,2,2,2,2,2,11 and the prime factors of 1599 are 3,13,41. Since neither 704, nor 1599 share any common factors, the fraction can't be reduced and the final answer is 704/1599. (c) What decimal of every dollar of the sale price of the necklace is profit using the fraction from Part (b)? Pardon the lack of formatting 704/1599 = 0.4403 Rounded to the nearest hundredth gives 0.44 (d) Lucy collected $223.86 selling necklaces at a craft fair. How many necklaces did Lucy sell? Show your work. This question is asking for total cost. So divide the $223.86 by the sale price of $15.99. $223.86 / $15.99 = 14 14 necklaces were sold. (e) How much profit did she earn from the number of necklaces she sold? Show your work. Since we know from (a) that she has $7.04 profit per necklace, just multiply the amount of profit by the number sold. So $7.04 * 14 = $98.56</span>
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Step-by-step explanation:

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Answer:

Final graph is attached.

Solution is x=2, y=3

Step-by-step explanation:

As we have to solve by graphing to let's graph y=2x-1 first.

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Answer:

a) Probability of ending up wearing 2 blue socks is 1/11.

b) Probability of ending up wearing no grey socks is 7/22.

c) Probability of ending up wearing at least 1 black sock is 5/11.

d) Probability of ending up wearing a green sock is 0.

e) Probability of ending up wearing matching socks is 19/66.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

In your sock drawer, you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing: a) 2 blue socks. b) no gray socks. c) at least 1 black sock. d) a green sock. e) matching socks.

The explanation of the answer is now given as follows:

The following are given in the question:

n(B) = number of Blue socks = 4

n(G) = number of Gray socks = 5

n(K) = number of black socks = 3

Therefore, we have:

n(T) = Total number of socks = n(B) + n(G) + n(K) = 4 + 5 + 3 = 12

To calculate a probability, the following formula for calculating probability is used:

Probability = Number of favorable outcomes / Number of total possible outcomes ……. (1)

Since this is a without replacement probability, we can now proceed as follows:

a) 2 blue socks

P(B) = Probability of ending up wearing 2 blue socks = ?

Probability of first pick = n(B) / n(T) = 4 / 12 = 1 / 3

Since it is without replacement, we have:

Probability of second pick = (n(B) – 1) / (n(T) – 1) = (4 – 1) / (12 – 1) = 3 / 11

P(B) = Probability of first pick * Probability of second pick = (1 / 3) * (3 / 11) = 1 / 11

b) no gray socks.

Number of favorable outcomes = n(B) + n(K) = 4 + 3 = 7

P(No G) = Probability of ending up wearing no gray socks = ?

Probability of first pick = Number of favorable outcomes / n(T) = 7 / 12

Since it is without replacement, we have:

Probability of second pick = (Number of favorable outcomes – 1) / (n(T) – 1) = (7 – 1) / (12 – 1) = 6 / 11

P(No G) = Probability of first pick * Probability of second pick = (7 / 12) * (6 / 11) = 7 / 22

c) at least 1 black sock.

Probability of at least one black sock = 1 - P(No K)

Number of favorable outcomes = n(B) + n(G) = 4 + 5 = 9

Probability of first pick = Number of favorable outcomes / n(T) = 9 / 12 = 3 /4

Since it is without replacement, we have:

Probability of second pick = (Number of favorable outcomes – 1) / (n(T) – 1) = (9 – 1) / (12 – 1) = 8 / 11

P(No K) = Probability of first pick * Probability of second pick = (3 / 4) * (8 / 11) = 24 / 44 = 6 / 11

Probability of at least one black sock = 1 - (6 / 11) = 5 / 11

d) a green sock.

n(Green) = number of Green socks = 0

Since, n(Green) = 0, it therefore implies that the probability of ending up wearing a green sock is 0.

e) matching socks.

This can be calculated using the following 4 steps:

Step 1: Calculation of the probability of matching blue socks

P(matching blue socks) = P(B) = 1 / 11

Step 2: Calculation of the probability of matching gray socks

P(matching green socks) = Probability of matching gray socks = ?

Probability of first pick = n(G) / n(T) = 5 / 12

Since it is without replacement, we have:

Probability of second pick = (n(G) – 1) / (n(T) – 1) = (5 – 1) / (12 – 1) = 4 / 11

P(matching gray socks = Probability of first pick * Probability of second pick = (5 / 12) * (4 / 11) = 20 / 132 = 5 / 33

Step 3: Calculation of the probability of matching black socks

P(matching black socks) = Probability of matching green socks = ?

Probability of first pick = n(K) / n(T) = 3 / 12 = 1 / 4

Since it is without replacement, we have:

Probability of second pick = (n(K) – 1) / (n(T) – 1) = (3 – 1) / (12 – 1) = 2 / 11

P(matching black socks) = Probability of first pick * Probability of second pick = (1 / 4) * (2 / 11) = 2 / 44 = 1 / 22

Step 4: Calculation of the probability of ending up wearing matching socks

P(matching socks) = Probability of ending up wearing matching socks = ?

P(matching socks) = P(matching blue socks) + P(matching grey socks) + P(matching black socks) = 1/11 + 5/33 + 1/22 = (6 + 10 + 3) / 66 = 19/66

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Answer:

C = 17 - R

Step-by-step explanation:

In this scenario, 17 cars would be the initial starting point. While C would be the final number of cars, meaning that our equation would have to equal C. If she rents R number of cars then this number is being subtracted from the initial number of cars because Charmaine would no longer have them in his/her possession. Therefore, it is being subtracted. Using this information we can create the following equation.

C = 17 - R

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