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Brilliant_brown [7]

3 years ago

13

The total amount of weight on an airplane cannot exceed 2,500 pounds. The plane is carrying 1,750 pounds of luggage. The average

weight of each passenger on the plane is 150 pounds. Set up and solve an inequality to find the number of passengers, p, the plane could carry.

1 answer:

fiasKO [112]3 years ago

4 0

1,750 + 150x ≤ 2,500

150x≤2500-1750
150x ≤ 750
x ≤ 5

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Solve the following equation for x<br><br> 5(x - 1) = -45

abruzzese [7]

Answer:

solution: x = -8

Step by step:

1) 5x-5+5 = -45+5 : Add 5 to both sides

2) 5x= -40 : Simplify

3) 5x/5 = -40/5 : Divide both sides

Hope that helps

5 0

3 years ago

Y = 2 - 4x input output

tester [92]

Every function is a rule which tells you how to associate inputs and outputs. The input, also known as independent variable, is often indicated with the letter $x$ , while the output, also known as dependent variable, is often indicated with the letter $y$ .

With this notation, we write $y = f(x)$ , read "y is a function of x", in the sense that the value of the variable y depends on the value of the variable x, and f is the function that tells you how y depends on x.

In your example, you have $y = f(x) = 2-4x$ , which means "subtract four times the input (4x) from 2"

So, it doesn't matter which input you chose (i.e. the value for x), because you will always have to behave this way:

Pick an input value, x
Multiply it by four to get 4x
Subtract this number from 2: 2-4x

Here are some examples of explicit calculations: if I choose $x = 2$ and input, the workflow will be

Pick an input value, 2
Multiply it by four to get 8
Subtract this number from 2: 2-8=-6

So, if the input is 2, the output is -6

Similarly, if we choose $x = 0$ as input, we have:

Pick an input value, 0
Multiply it by four to get 0
Subtract this number from 2: 2-0=2

So, if the input is 0, the output is 2. And so on: for every possible value for x you have the correspondant value for y, with the function f telling you how to associate one with the other.

4 0

3 years ago

Describe how equality and democracy represent traditional American values,

user100 [1]

Answer:

The United States was founded on "equality". Our Declaration of Independence was created to ensure the rights given to us as American citizens and state what must be upheld to protect these rights. Equality comes from a very valued form of Government in America called Democracy. Americans are given the right to freedom of speech, and this represents traditional American values.

4 0

3 years ago

Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.

Cloud [144]

If $F_Y(y)$ is the cumulative distribution function for $Y$ , then

$F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)$

Then the probability density function for $Y$ is $f_Y(y)={F_Y}'(y)$ :

$f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_X(\ln y)=\dfrac1yf_X(\ln y)=\begin{cases}\frac1{y\sqrt{2\pi}}e^{-\frac12(\ln y)^2}&\text{for }y>0\\0&\text{otherwise}\end{cases}$

The $n$ th moment of $Y$ is

$E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy$

Let $u=\ln y$ , so that $\mathrm du=\frac{\mathrm dy}y$ and $y^n=e^{nu}$ :

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du$

Complete the square in the exponent:

$nu-\dfrac12u^2=-\dfrac12(u^2-2nu+n^2-n^2)=\dfrac12n^2-\dfrac12(u-n)^2$

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du$

But $\frac1{\sqrt{2\pi}}e^{-\frac12(u-n)^2}$ is exactly the PDF of a normal distribution with mean $n$ and variance 1; in other words, the 0th moment of a random variable $U\sim N(n,1)$ :

$E[U^0]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du=1$

so we end up with

$E[Y^n]=e^{\frac12n^2}$

3 0

3 years ago

an arc welder provides 250 amps of current when operating with a voltage of 40 volts. what is the power required by this welder

FinnZ [79.3K]

The power(P) of the circuits is the product of the voltage (V) in volts and current(I) in amperes.
P = IV

Substituting the known values to the equation,
P = (250 amps) x (40 volts) = 10,000 Watts

Thus, the answer is 10,000 Watts.

3 0

3 years ago

Read 2 more answers