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2 years ago

What is the remainder in the synthetic division problem below?

Mathematics

2 answers:

omeli [17]2 years ago

8 0

Answer:

B.2

Step-by-step explanation:

apex

Naddik [55]2 years ago

6 0

Answer:

The remainder is 25 ⇒ answer (C)

Step-by-step explanation:

* The remainder will be the last number in the calculation

* From the picture the dividend is 3x³ + x² + 2x - 7 and x - 2 is the divisor

- In the synthetic calculation we use the coefficient of the dividend with the value of x when the divisor = 0

- From the picture the divisor is x - 2, when x - 2 = 0, then x = 2

∵ The coefficient of the dividend are 3 , 1 , 2 , -7

Step 1 : Write down the coefficients of the dividend , put x = 2 at the left

2 3 1 2 -7

_____________

Step 2 : Bring down the first coefficient to the bottom row.

2 3 1 2 -7

____________

Step 3 : Multiply it by 2, and carry the result into the next column.

2 3 1 2 -7

___6_________

Step 4 : Add down the column

2 3 1 2 -7

___6_________

3 7

Step 5 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_______

3 7

Step 6 : Add down the column

2 3 1 2 -7

___6_14_______

3 7 16

Step 7 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_32______

3 7 16

Step 8 : Add down the column

2 3 1 2 -7

___6_14_32______

3 7 16 25

∴ The quotient is (3x² + 7x + 16) and the remainder is 25

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2 years ago

The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its preci

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The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

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and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

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P(W) = 0.20

P(Th) = 0.20

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The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

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We can obtain each of these probabilities by using the expression for conditional probability.

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P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

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P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

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P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

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2 years ago