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lutik1710 [3]
11 months ago
8

Divide g(x) = x^4 - 2x^3 + X + 3 by x+3

Mathematics
1 answer:
SVEN [57.7K]11 months ago
8 0

Let's first get the coefficients of the numerator: x^4 - 2x^3 + x + 3 = 1, -2, 0, 1, 3

<em>There is no x^2 in the expression, thus, the coefficient for x^2 = 0</em>

Zero of the denominator: x + 3; x = -3

Using synthetic division,

-3 I 1 -2 0 1 3

I_________________

-3 I 1 -2 0 1 3

I_________________

1

-3 I 1 -2 0 1 3

I_____-3___________

1 -5

-3 I 1 -2 0 1 3

I_____-3__15_______

1 -5 15

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45_132__

1 -5 15 -44 135

The remainder is 135. Which transforms it into 135/x+3.

Thus, the quotient of x^4 - 2x^3 + x + 3 divided by x + 3 ​is:

x-5x^2+15x\text{ - 44 + }\frac{135}{x+3}

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Four buses carrying 146 high school students arrive to Montreal. The buses carry, respectively, 32, 44, 28, and 42 students. One
Naily [24]

Answer:

The expected value of X is E(X)=\frac{2754}{73} \approx 37.73 and the variance of X is Var(X)=\frac{226192}{5329} \approx 42.45

The expected value of Y is E(Y)=\frac{73}{2} \approx 36.5 and the  variance of Y is Var(Y)=\frac{179}{4} \approx 44.75

Step-by-step explanation:

(a) Let X be a discrete random variable with set of possible values D and  probability mass function p(x). The expected value, denoted by E(X) or \mu_x, is

E(X)=\sum_{x\in D} x\cdot p(x)

The probability mass function p_{X}(x) of X is given by

p_{X}(28)=\frac{28}{146} \\\\p_{X}(32)=\frac{32}{146} \\\\p_{X}(42)=\frac{42}{146} \\\\p_{X}(44)=\frac{44}{146}

Since the bus driver is equally likely to drive any of the 4 buses, the probability mass function p_{Y}(x) of Y is given by

p_{Y}(28)=p_{Y}(32)=p_{Y}(42)=p_{Y}(44)=\frac{1}{4}

The expected value of X is

E(X)=\sum_{x\in [28,32,42,44]} x\cdot p_{X}(x)

E(X)=28\cdot \frac{28}{146}+32\cdot \frac{32}{146} +42\cdot \frac{42}{146} +44 \cdot \frac{44}{146}\\\\E(X)=\frac{392}{73}+\frac{512}{73}+\frac{882}{73}+\frac{968}{73}\\\\E(X)=\frac{2754}{73} \approx 37.73

The expected value of Y is

E(Y)=\sum_{x\in [28,32,42,44]} x\cdot p_{Y}(x)

E(Y)=28\cdot \frac{1}{4}+32\cdot \frac{1}{4} +42\cdot \frac{1}{4} +44 \cdot \frac{1}{4}\\\\E(Y)=146\cdot \frac{1}{4}\\\\E(Y)=\frac{73}{2} \approx 36.5

(b) Let X have probability mass function p(x) and expected value E(X). Then the variance of X, denoted by V(X), is

V(X)=\sum_{x\in D} (x-\mu)^2\cdot p(x)=E(X^2)-[E(X)]^2

The variance of X is

E(X^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{X}(x)

E(X^2)=28^2\cdot \frac{28}{146}+32^2\cdot \frac{32}{146} +42^2\cdot \frac{42}{146} +44^2 \cdot \frac{44}{146}\\\\E(X^2)=\frac{10976}{73}+\frac{16384}{73}+\frac{37044}{73}+\frac{42592}{73}\\\\E(X^2)=\frac{106996}{73}

Var(X)=E(X^2)-(E(X))^2\\\\Var(X)=\frac{106996}{73}-(\frac{2754}{73})^2\\\\Var(X)=\frac{106996}{73}-\frac{7584516}{5329}\\\\Var(X)=\frac{7810708}{5329}-\frac{7584516}{5329}\\\\Var(X)=\frac{226192}{5329} \approx 42.45

The variance of Y is

E(Y^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{Y}(x)

E(Y^2)=28^2\cdot \frac{1}{4}+32^2\cdot \frac{1}{4} +42^2\cdot \frac{1}{4} +44^2 \cdot \frac{1}{4}\\\\E(Y^2)=196+256+441+484\\\\E(Y^2)=1377

Var(Y)=E(Y^2)-(E(Y))^2\\\\Var(Y)=1377-(\frac{73}{2})^2\\\\Var(Y)=1377-\frac{5329}{4}\\\\Var(Y)=\frac{179}{4} \approx 44.75

8 0
3 years ago
I will brainliest to whoever can solve this :)
zloy xaker [14]

Answer:

All I can tell you from what you've given me is that the slope is positive, and the y-intercept is 1.

Step-by-step explanation:

<em>Hope </em><em>I</em><em>t</em><em> </em><em>helps!</em>

6 0
3 years ago
Read 2 more answers
Use the elimination method to solve the system of equations.Choose the correct ordered pair. - x + y = - 2 and 2 x - 3y = 4
Zolol [24]

Answer:(2,0) x=2,y=0

Step-by-step explanation:

Let's solve your system by elimination.

−x+y=−2;2x−3y=4

Multiply the first equation by 2,and multiply the second equation by 1.

2(−x+y=−2)

1(2x−3y=4)

Becomes:

−2x+2y=−4

2x−3y=4

Add these equations to eliminate x:

−y=0

Then solve−y=0 for y:

−y=0

−y/−1 =0/−1

(Divide both sides by -1)

y=0

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

−x+y=−2

Substitute0foryin−x+y=−2:

−x+0=−2

−x=−2(Simplify both sides of the equation)

−x/−1 = −2/−1

(Divide both sides by -1)

x=2

8 0
3 years ago
6-x/4=x/8<br> solve for x
mina [271]

Answer:

Hope this helps

Step-by-step explanation:

x = 16

5 0
2 years ago
Read 2 more answers
Can someone help me with this. ^_^ THANKS
Fynjy0 [20]
It would be B. because it's just 7 times 1.5
4 0
3 years ago
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