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AVprozaik [17]
3 years ago
15

Use Synthetic Division to divide 6x^3-10x^2+20 by x+1 Quotient:_____ Remainder:_____

Mathematics
1 answer:
exis [7]3 years ago
6 0

Answer:

the quotient is 6x^2 - 16x + 16, and the remainder is just 4

Step-by-step explanation:

The polynomial 6x^3-10x^2+20 has coefficients {6, -10, 0, 20}.  Division by the binomial x + 1 requires that we use -1 as the divisor.  The synthetic division setup becomes:

-1   /    6    -10    0    20

                 -6    16   -16

     -----------------------------

          6     -16   16       4

Taking the coefficients {6, -16, 16}, we write the quotient as

6x^2 - 16x + 16, and the remainder as just 4.

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Mark spends $36 at a basketball game. He buys a T-shirt for $22. He then buys a bottle of water for $4 and 2 tacos. How much is
Arturiano [62]

Answer:

each taco is $7.

Step-by-step explanation:

In total he spent $36. He bought a shirt for $22 and a bottle of water for $4.

22+4= 26

36-22= 14

14 divided by 2= 7

5 0
3 years ago
Read 2 more answers
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights
Fed [463]

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

  • Given that,  A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams

  • Since the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

  • P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.

Next, multiply that by the sample size of 732.

  • Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171  

 

  • For part b, use the same method except x is now 1591.    

Z = (1581 - 3311)/860 = -2    

  • P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.

 

  • For part c, we now need to get two Z scores, one for 3311 and another for 5031.

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

5 0
3 years ago
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability
erik [133]

Answer:

First choice:

               \large\boxed{\large\boxed{5/19}}

Explanation:

<em>The probability that the first is a man's card and the second, a woman's card</em> is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards  in the hat has changed.

In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.

<u>1. Probability that the first is a man's card</u>

  • Number of cards in the hat = 20 (the 20 business card)

  • Number of man's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.

<u />

<u>2. Probability that the second is a woman's card</u>

  • Number of cards in the hat = 19 (there is one less card in the hat)

  • Number of wonan's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/19.

<u>3. Probability that the first is a man's card and the second, a woman's card</u>

<u />

  • (1/2) × (10/19) = 5/19

That is the first choice.

5 0
3 years ago
Read 2 more answers
The perimeter of a rectangular swimming pool is 160 feet . The length of the swimming pool is four times its width. Find the dim
Murrr4er [49]
Formula for Perimeter of Rectangle:

P = 2(L + W)

Plug in 160:

160 = 2(L + W)

L = 4W
So we can plug in '4W' for 'L' in the first equation.
<span>160 = 2(L + W)

160 = 2(4W + W)

Combine like terms:

160 = 2(5W)

160 = 10W

Divide 10 to both sides:

W = 16

Now we can plug this back into any of the two equations to find the length.

L = 4W

L = 4(16)

L = 64

So the width is 16, and the length is 64.</span>
6 0
3 years ago
Read 2 more answers
I will give brainliest if correct !!
qwelly [4]

Answer:

acute isosceles

Step-by-step explanation:

3 0
3 years ago
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