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3 years ago

In the expression below, a is an integer. 12^3+ax-20 if 3x+4 is a factor of the expession above, what is the value of a

Mathematics

1 answer:

SVEN [57.7K]3 years ago

4 0

Our function is:

$f(x)=12^3+ax-20$

Now, if $3x+4$ is a factor of $f(x)$ then $x=\frac{-4}{3}$ must satisfy the equation:

So, $f(\frac{-4}{3} )=0$

Putting $x=\frac{-4}{3}$

We get,

$f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0$

$12^3+\frac{-4}{3} a-20=0$

$\frac{-4}{3} a=20-12^3=20-1708$

$a=-1708 \times \frac{-3}{4} =1281$

So, the value of 'a' for the given expression is 1281.

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If a gallon of paint covers 400 square feet, how many gallons are needed to paint a retaining wall that is 269 feet long and 4 f

Nuetrik [128]

The area of a rectangular shape is given by

$A=l\times b$

Given:

It is given that a gallon of paint covers 400 square feet, and wall is 269 feet long and 4 feet high .

Now the area of wall will be

$A=269\times4$

Since,

$\begin{gathered} 400\text{ sq f}eet=\text{ 1gallon} \\ 1\text{ sq f}eet=\frac{1}{400}gallon \\ 269\times4\text{ sq f}eet=\frac{1}{400}\times269\times4 \\ =\frac{269}{100} \\ =2.69\text{ gallon} \\ =3\text{ galllon} \end{gathered}$

So, the ewall requires approx 3 gallon of paint.

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2 years ago

A tour helicopter travels at a constant rate of 80 mph. If the tour takes 2 hours, how far does the helicopter travel?

vodka [1.7K]

Answer:

Step-by-step explanation:

80 miles per hour, each hour it will travel 80 miles so for two hours tou do

80 x 2 = 160

7 0

3 years ago

Read 2 more answers

Suppose X and Y are random variables with joint density function. f(x, y) = 0.1e−(0.5x + 0.2y) if x ≥ 0, y ≥ 0 0 otherwise (a) I

Hatshy [7]

a. $f_{X,Y}$ is a joint density function if its integral over the given support is 1:

$\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\frac1{10}\int_0^\infty\int_0^\infty e^{-x/2-y/5}\,\mathrm dx\,\mathrm dy$

$=\displaystyle\frac1{10}\left(\int_0^\infty e^{-x/2}\,\mathrm dx\right)\left(\int_0^\infty e^{-y/5}\,\mathrm dy\right)=\frac1{10}\cdot2\cdot5=1$

so the answer is yes.

b. We should first find the density of the marginal distribution, $f_Y(y)$ :

$f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\frac1{10}\int_0^\infty e^{-x/2-y/5}\,\mathrm dy$

$f_Y(y)=\begin{cases}\dfrac15e^{-y/5}&\text{for }y\ge0\\\\0&\text{otherwise}\end{cases}$

Then

$P(Y\ge8)=\displaystyle\int_8^\infty f_Y(y)\,\mathrm dy=e^{-8/5}$

or about 0.2019.

For the other probability, we can use the joint PDF directly:

$P(X\le5,Y\le8)=\displaystyle\int_0^5\int_0^8f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=1+e^{-41/10}-e^{-5/2}-e^{-8/5}$

which is about 0.7326.

c. We already know the PDF for $Y$ , so we just integrate:

$E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5$

5 0

3 years ago

Question 24

andreyandreev [35.5K]

Answer:

parallel bc they have same gradient

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

An electrician charges a base fee of $70 plus $45 for each hour of work. The minimum the electrician charges is $160. Create a t

Murrr4er [49]

Answer:

1) See below for table.

2) Domain: $\{1, 2, 3, 4\}$

Range: $\{160, 160, 205, 250\}$

Yes, this is a function.

Step-by-step explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

$y=45x+75$

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

$y_1=45(1)+70$

Multiply and add:

$y_1=45+70=\$115$

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

$y_1=\$160$

2 Hours:

Substitute 2 for x:

$y_2=45(2)+70=90+70=\$160\\$

So:

$y_2=\$160$

3 Hours:

Substitute 3 for x:

$y_3=45(3)+70=135+70=\$205$

So:

$y_3=\$205$

4 Hours:

Substitute 4 for x:

$y_4=45(4)+70=180+70=\$250$

So:

$y_4=\$ 250$

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

$\{1, 2, 3, 4\}$

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

$\{160, 160, 205, 250\}$

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!

8 0

3 years ago