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3 years ago

What is the solution to the following system of linear equations?

1 answer:

8 0

x − 2y = −1 => x = 2y -1

2x + y = −12
2(2y - 1) + y = -12
4y - 2 + y = -12
5y = -10
y = -2
x = 2·(-2) - 1
x = -4 - 1
x = -5

Answer D (-5,-2)

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2 years ago

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3 years ago

A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at ra

Soloha48 [4]

Answer:

$P(M4\ n\ V) = 2.083\%$

Step-by-step explanation:

Given

Paper = 20 slips

Word: PENNSYLVANIA

Required

Determine P(Multiple of 4 and V)

The sample size of the 20 slips is:

$n(S) = 20$

The outcomes of multiples of 4 is:

$M4= \{4,8,12,16,20\}$

$n(M4) = 5$

So, the probability of multiples of 4 is:

$Pr(M4) = \frac{5}{20}$

$Pr(M4) = \frac{1}{4}$

The sample size of PENNSYLVANIA is:

$n(S) = 12$

The outcome of V is:

$n(V) = 1$

So, the probability of V is:

$P(V) = \frac{1}{12}$

So, the required probability is: P(Multiple of 4 and V)

$P(M4\ n\ V) = P(M4) * P(V)$

$P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}$

$P(M4\ n\ V) = \frac{1}{48}$

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Express as percentage

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3 years ago

A manufacturer of skis produces two types: downhill and cross country. The times required for manufacturing and finishing each s

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Answer:

So to maximize profit 24 downhill and 20 cross country shouldbe produced

Step-by-step explanation:

Let X be the number of downhill skis and Y the number of cross country skis.

Time required for manufacturing and finishing each ski are: manufacturing time per ski, downhill 2.5 hours, cross country 1.5 hours

Finishing time per ski: downhill 0.5 hours, cross country 1.5 hours.

Total manufacturing time taken = (2.5) x+ (1.5+) y = 2.5x+1.5y≤90

total finishing time taken = 0.5x+1.5 y≤42

Profit function

Z = 50x+50y

Objective is to maximize Z

Solving the two equations we get intersecting point is

(x,y) = (24,20)

In the feasible region corner points are (0.28) (36,0)

Profit for these points are

i) 2200 for (24,20)

ii) 1400 for (0,28)

iii) 1800 for (36,0)

So to maximize profit 24 downhill and 20 cross country shouldbe produced.

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2 years ago