All categories

2 years ago

I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!

Mathematics

1 answer:

marissa [1.9K]2 years ago

5 0

Answer:

2. Eunju is right

3. $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ .

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

$f(x)=(x+b)^3+(x+c)^2-(b-c)$

To find out if x+b is a factor of f(x), we find f(-b):

$f(-b)=(-b+b)^3+(-b+c)^2-(b-c)$

Operating:

$f(-b)=(-b+c)^2-(b-c)$

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

$x^2+5x+6 =(x+2)(x+3)$

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

$f(x)=x^4+5x^3+2x^2-20x-24$

Find f(-2):

$f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24$

$f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0$

Find f(-3):

$f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24$

$f(-3)=81-5*27+2*9+60-24$

$f(-3)=81-135+18+60-24 =0$

Since both f(-2) and f(-3) are zero, $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ .

You might be interested in

An angle in standard position measures 5pie/8 radians.

GrogVix [38]

Answer:

Step-by-step explanation:

It's easier to convert the angle into degrees.

5π/8 ≅ 112.5°, which is in quadrant II

3 0

3 years ago

Some scientists believe alcoholism is linked to social isolation. One measure of social isolation is marital status. A study of

frez [133]

Answer:

1) H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

2) The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

3) $\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

4) $df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 21 37 58 116

Not Married 59 63 42 164

Total 80 100 100 280

Part 1

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

The level os significance assumed for this case is $\alpha=0.05$

Part 2

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

Part 3

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{80*116}{280}=33.143$

$E_{2} =\frac{100*116}{280}=41.429$

$E_{3} =\frac{100*116}{280}=41.429$

$E_{4} =\frac{80*164}{280}=46.857$

$E_{5} =\frac{100*164}{280}=58.571$

$E_{6} =\frac{100*164}{280}=58.571$

And the expected values are given by:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 33.143 41.429 41.429 116

Not Married 46.857 58.571 58.571 164

Total 80 100 100 280

And now we can calculate the statistic:

$\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

Part 4

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

7 0

3 years ago

If h(x) is the inverse of f(x), what is the value of h(f(x))? OO 0 1 f(x)

kozerog [31]

Answer:

Step-by-step explanation:

h(f(x) = x.

For example the inverse of f(x) = 2x is g(x) = x/2

f((gx)) 2 (x/2)

= 2x / 2

= x.

8 0

2 years ago

Read 2 more answers

Graph the six terms of a finite series where a1 = −3 and r = 1.5.

s344n2d4d5 [400]

We are given the first term and the common ratio, this means they belong to a geometric series.

For the given series:

$a_{1}=-3 \\ 
r=1.5$

Each term of the geometric series is obtained by multiplying the previous term by common ratio.

So the next terms will be:

-4.5, -6.75, -10.125, -15.1875, -22.78125

The general formula for the G.P would be:

$a_{n}=-3(1.5)^{n-1}$

On plotting the series, the result will be like this:

6 0

3 years ago

Read 2 more answers

What is 4 divided by 2 3/4. for 6th grade math

Goshia [24]

Answer:

3 1/3

Step-by-step explanation:

4/(2 3/4)

4/(6/4)

4÷6/4

4*4/6

20/6

3 2/6 =3 1/3

8 0

2 years ago