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Hoochie [10]
3 years ago
8

Divide f(x) by d(x), and write a summary statement in the form indicated.

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0

Answer:

The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

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In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S
lys-0071 [83]

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

8 0
2 years ago
Consider the toss of four coins. There are 16 (i.e., 24) possible outcomesin one toss. (a)Calculate the probabilities that there
lana [24]

Answer:

See answers below

Step-by-step explanation:

If 4 coins are tossed. the total possible outcomes are;

H H H H , H H H T, H H T H, H T H H, T H H H , H H T T, H T T H, T T H H, H T H T, T H T H, T H H T , H T T T, T H T T, T T H T, T T T H  and T T T T

Total outcomes = 16

1) zero head = T T T T = 1 outcome

Probability = Expected/Total outcome

Pr(zero head) = 1/16

2) one head = H T T T, T H T T, T T H T, T T T H   = 4 outcomes

Probability = Expected/Total outcome

Probability = 4/16

Pr(one head) = 1/4

3) two heads = H H T T, H T T H, T T H H, H T H T, T H T H, T H H T   = 6 outcomes

Probability = Expected/Total outcome

Pr(two head) = 6/16

Pr(two head) = 3/8

4)  three heads = H H H T, H H T H, H T H H, T H H H   = 4 outcomes

Probability = Expected/Total outcome

Pr(three heads) = 4/16

Pr(two head) = 1/4

5) four heads appearing on the four coins =  H H H H = 1 outcome

Pr(four heads) = 1/16

6 0
2 years ago
Find<br> the<br> Inverse<br> y = x+10/7
Alona [7]

Answer:

x - \frac{10}{7}

Step-by-step explanation:

y = x + 10/7

x = y + 10/7

x = y + 10/7

x - 10/7 = y

y = x - 10/7

x - \frac{10}{7}

3 0
3 years ago
Which graph most likely shows the experimental probability histogram of X based on 100 data points?
Archy [21]

Answer:

  see attached

Step-by-step explanation:

Based on 100 trials, we don't expect the experimental probability to deviate much from the theoretical probability. The scales on the attached graphs are hard to read, but you want to choose the graph that ...

  • has bars that total 100 in their length
  • has bars that are approximately .50, .25, .17, .08 in height, corresponding to the area fraction

We think the appropriate choice may be C, but we cannot tell for sure.

3 0
2 years ago
Help? Thanks!!!!!!!! If possible show work please!
FrozenT [24]

Answer:

B =102

Y = 32

Step-by-step explanation:

Solving (47):

To solve for B, we have:

B + 50 + 28 = 180 --- sum of angles in a triangle

This gives

B + 78 = 180

Collect like terms

B =- 78 + 180

B =102

Solving (48):

To solve for Y, we have:

X + Y+ Z = 180 --- sum of angles in a triangle

This gives

Y = 180 - X - Z

Where

W+ X=180 -- angle on a straight line

Solve for X

X=180 -W

X=180 -100 = 80

So, we have:

Y = 180 - X - Z

Y = 180 - 80 - 68

Y = 32

5 0
3 years ago
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