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3 years ago

Is the expression 3/4a (16b + 24) equivalent to 12ab + 18a? SHOW YOUR WORK

Mathematics

1 answer:

ipn [44]3 years ago

5 0

Answer:

Yes they are equivalent.

Step-by-step explanation:

since 16 times 3/4 is 12 and a times b is ab. Put those together and you get 12ab. Since 3/4 of 24 is 18 and the variable is a, it is 18a. Hope this helped.

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4 years ago

Stereo speakers are manufactured with a probability of 0.100.10 being defective. TwentyTwenty speakers are randomly selected. Le

olga nikolaevna [1]

Answer:

The expected value of X is 2 with a standard deviation of 1.34.

Step-by-step explanation:

For each speaker, there are only two possible outcomes. Either it is defective, or it is not. The probability of a speaker being defective is independent of other speakers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Stereo speakers are manufactured with a probability of 0.1 of being defective

This means that $p = 0.1$

Twenty speakers are randomly selected.

This means that $n = 20$

Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.

$E(X) = np = 20*0.1 = 2$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.1*0.9} = 1.34$

The expected value of X is 2 with a standard deviation of 1.34.

6 0

3 years ago

4. A company manufactures tires to meet the annual demand of 125,000 production runs. One production run involves producing 100

lyudmila [28]

Answer:

a) Economic order or production quantity = 2,500 tires.

Number of production runs in a year = 50 runs

Hence, 2,500 tires should be produced in each of the 50 runs in a year to minimize total cost.

b) Minimum total inventory cost = Tsh 30,000

Step-by-step explanation:

The total cost for the tire production firm will be a sum of the total production cost and total inventory cost.

Total cost = Total Production cost + Total inventory cost

Total Production Cost = (Number of production runs in a year) × (Setup Cost of one production run)

Number of production runs in a year = (Annual demand)/(Number of units produced per production run)

Let the annual demand = D

Number of units produced per production run = Q

Setup Cost of one production run = S

Number of production runs in a year = (D/Q)

Total Production Cost = (DS/Q)

Total inventory Cost = (Average inventory level) × (Cost of holding 1 unit in inventory)

Average inventory level is usually assumed to be half of the number of units in a production run = (Q/2)

Cost of Holding a unit of product in inventory = H

Total inventory Cost = (QH/2)

Total cost = TC = (DS/Q) + (QH/2)

At minimum cost, (dTC/dQ) = 0

(dTC/dQ) = -(DS/Q²) + (H/2) = 0

(DS/Q²) = (H/2)

Q² = (2DS/H)

Hence,

Economic order/production quantity = Q = √(2DS/H)

For this question

D = Annual demand = 125,000 tires

S = Setup cost for one production run = Tsh 600

H = Holding cost for one unit in inventory = Tsh 24

Q = √(2×125000×600/24) = 2,500 units

Number of production runs in a year = (D/Q) = (125000/2500) = 50 production runs.

b) Total Inventory Cost = (QH/2)

At minimum total inventory cost, Q = 2,500

Minimum total inventory cost = (2500×24/2) = Tsh 30,000

Hope this Helps!!!

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3 years ago