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Kobotan [32]
2 years ago
9

An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce f

or copper and $20 per ounce for silver. To summarize the situation, a worker writes the inequality: 10c + 20s ≤ 4,000, where c is the number of ounces of copper material and s is the number of ounces of silver material. Which graph's shaded region shows the possible combinations of raw materials the company can buy?

Mathematics
1 answer:
inysia [295]2 years ago
7 0

Answer:

Option B (top of the 2nd column) is the correct answer.

Step-by-step explanation:

An electronics company can spend no more than $4,000 on raw materials for circuit boards.

The raw materials cost $10 per ounce for copper and $20 per ounce for silver.

Let us assume that,

c = the number of ounces of copper,

s = the number of ounces of silver.

The inequalities will be,

10c + 20s \le4000

and

c\ge 0,\\\\s\ge 0

As the number of ounces used can not be in negative.

Plotting the graph and drawing the shaded region by origin test, we get the shaded region as attached below.

Therefore, option B (top of the 2nd column) is the correct answer.

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The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′
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2 years ago
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6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find t
Keith_Richards [23]

Answer:

a) 7.54189*10^-8

b) 0.99999999

c) E ( X ) = 0.39 , s ( X ) = 0.604

Step-by-step explanation:

Solution:-

- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.

- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.

- The random variable is assumed to follow binomial distribution.

- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:

                        X ~ Bin ( 6 , 0.065 )

Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:

                       P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )

a) Find the probability that all 6 are type A-

- We will pmf given above and set r = 6. And evaluate the resulting probability:

                     P ( X = 6 ) = 6C6 * ( p )^6 * ( 1  - p ) ^ ( 0 )

                                      = p^6

                                      = ( 0.065 )^6  

                                      = 7.54189*10^-8

b) Find the probability that at most 4 of them are type A-

- We will pmf given above and evaluate the following expression:

                     P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )

                     P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1  - p ) ^ ( 1 ) - p^6

                                      = 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6

                                      = 1 - 6.50923*10^-8 - 7.54189*10^-8        

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c) Find the mean and standard deviation.

- The mean E ( X ) of the defined random variable distributed binomially is given by:

                     E ( X ) = n*p = 6*0.065 = 0.39 people

- The mean s( X ) of the defined random variable distributed binomially is given by:

   

                    s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604

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Answer:

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Lastly, what determines the facing of the graph (up or down) is the leading coefficient. If positive, the graph ends point up. If negative, the graph ends point down. All even degree graphs will have this shape.


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