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Dima020 [189]
3 years ago
7

Lucy buys 7kg of nuts to sell.

Mathematics
1 answer:
Nikitich [7]3 years ago
3 0

Answer:

Lucy's percentage profit = 33.33% based on Sales Value

and 50% based on Cost.

Step-by-step explanation:

a) Calculations:

7kg = 7,000g of nuts

Cost of 7,000g = £10

350g = 20 bags (7,000/350)

Sales value = £15 (20 x 75p)

Profit = Sales value minus Cost

Profit = £5 (£15 - £10)

Profit percentage based on sales = Profit/Sales x 100 = 5/15 x 100 = 33.33%

Profit percentage based on cost = Profit/Cost x 100 = 5/10 x 100 = 50%

b) Profit is the excess of sales over cost.  There are two ways to express it in percentages.  Profit can be expressed as a percentage of the cost (Markup).  It can also be expressed as the percentage of the sales value (Margin).

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Answer:

a) 0.9

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Step-by-step explanation:

We are given the following in the question:

A marketing firm is considering making up to three new hires.

Let X be the variable describing the number of hiring in the company.

Thus, x can take values 0,1 ,2 and 3.

P(x\geq 2) = 50\%= 0.5\\P(x = 0) = 10\% = 0.1\\P(x = 3) = 18\% = 0.18

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P(x\geq 2) = P(x=2) + P(x=3)\\0.5 = P(x=2) + 0.18\\ P(x=2) = 0.32

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P(x= 0) +P(x= 1) + P(x= 2) + P(x= 3) = 1\\ 0.1 + P(x= 1) + 0.32 + 0.18 = 1\\ P(x= 1) = 1- (0.1+0.32+0.18) = 0.4

\text{P(firm will make at least one hire)}\\= P(x\geq 1)\\=P(x=1) + P(x=2) + P(x=3)\\ = 0.4 + 0.32 + 0.18 = 0.9

b) expected value and the standard deviation of the number of hires.

E(X) = \displaystyle\sum x_iP(x_i)\\=0(0.1) + 1(0.4) + 2(0.32)+3(0.18) = 1.58

E(x^2) = \displaystyle\sum x_i^2P(x_i)\\=0(0.1) + 1(0.4) + 4(0.32) +9(0.18) = 3.3\\V(x) = E(x^2)-[E(x)]^2 = 3.3-(1.58)^2 = 0.80\\\text{Standard Deviation} = \sqrt{V(x)} = \sqrt{0.8036} = 0.89

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3 years ago
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