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3 years ago

Can someone help me with this? its a relatively simple problem for extra credit in algebra 1.

Mathematics

1 answer:

suter [353]3 years ago

4 0

(2x^2+3x+4)(x^3+4x^2+3x)(x+4)

First use the distributive property for the first two:

(2x^5+8x^4+6x^3+3x^4+12x^3+9^2+4x^3+16x^2+12x)(x+4)

And then combine like terms:

(2x^5+11x^4+22x^3+25x^2+12x)(x+4)

Continue use the distributive property:

(2x^6+11x^5+22x^4+25x^3+12x^2+8x^5+44x^4+88x^3+100x^2+48x)

Continue combine like terms:

(2x^6+19x^5+66x^4+113x^3+112x^2+48x)
And that is your final answer.

Hope that help:)

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Suppose we roll a fair die and let X represent the number on the die. (a) Find the moment generating function of X. (b) Use the

Likurg_2 [28]

Answer:

(a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{2 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

Step-by step explanation:

Given X represents the number on die.

The possible outcomes of X are 1, 2, 3, 4, 5, 6.

For a fair die, $P(X)=\frac{1}{6}$

(a) Moment generating function can be written as $M_{x}(t)$ .

$M_x(t)=\sum_{x=1}^{6} P(X=x)$

$M_{x}(t)=\frac{1}{6} e^{t}+\frac{1}{6} e^{2 t}+\frac{1}{6} e^{3 t}+\frac{1}{6} e^{4 t}+\frac{1}{6} e^{5 t}+\frac{1}{6} e^{6 t}$

$M_x(t)=\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) Now, find $E(X) \text { and } E\((X^{2})$ using moment generating function

$M^{\prime}(t)=\frac{1}{6}\left(e^{t}+2 e^{2 t}+3 e^{3 t}+4 e^{4 t}+5 e^{5 t}+6 e^{6 t}\right)$

$M^{\prime}(0)=E(X)=\frac{1}{6}(1+2+3+4+5+6)$

$\Rightarrow E(X)=\frac{21}{6}$

$M^{\prime \prime}(t)=\frac{1}{6}\left(e^{t}+4 e^{2 t}+9 e^{3 t}+16 e^{4 t}+25 e^{5 t}+36 e^{6 t}\right)$

$M^{\prime \prime}(0)=E(X)=\frac{1}{6}(1+4+9+16+25+36)$

$\Rightarrow E\left(X^{2}\right)=\frac{91}{6}$

Hence, (a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$ .

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

6 0

4 years ago

You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to paint a wall with the given dimen

Allisa [31]

Answer:

25.2 min

Step-by-step explanation:

3 0

3 years ago

What is the square root of 64 multiplied by 2

Tamiku [17]

Answer:

its 16

as we know the square root of 64 is 6 and when it is multiplied by 2 its answer is 16.

Step-by-step explanation:

6 0

4 years ago

Flying against the wind, an airplane travels 7520 kilometers in 8 hours. Flying with the wind, the same plane travels 6500 kilom

bezimeni [28]

Answer:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

Step-by-step explanation:

Let the rate (speed) of the plane in still air = u km/h

Let the rate (speed) of the wind = v km/h

Formula for speed is:

$Speed = \dfrac{Distance}{Time}$

Given that against the wind, airplane travels 7520 km in 8 hours.

The speed against the wind will be slower so,

Against the wind, speed = (u -v ) km/h

Using above formula:

$(u-v) = \dfrac{7520}{8} km/h\\(u-v) = 940 km/h ..... (1)$

Given that with the wind, airplane travels 6500 km in 5 hours.

The speed with the wind will be faster so,

With the wind, speed = (u +v ) km/h

Using above formula:

$(u+v) = \dfrac{6520}{5} km/h\\(u+v) = 1300 km/h ..... (2)$

Adding (1) and (2) to solve for u and v:

$2u = 2240\\\Rightarrow u = 1120\ km/h$

Putting u in (1):

$1120-u=940\\\Rightarrow u = 180\ km/h$

So, the answers are:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

6 0

3 years ago

H squared equals 121

Afina-wow [57]

H^2=121 so you take the square root of 121 and get h=11

7 0

4 years ago

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