<span>1,2,4,53,106,212
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</span>
1)
a) Draw the axis:x-axis is horizontal, y-axis is vertical
b) draw a point on any part of the plane (use color to highlight it)
c) draw a second point on a different part of the plane (again use color)
d) draw the straight line that passes through the two points (use a ruler).
That is it.
2)
a) Draw the axis: x-axis is horizontal and y-axis is vertical
b) Draw a stright line (use a ruler)
c) Draw a second straight line (use a ruler) which is not parallel to the first line. Extend the second line intil it intersects (and passes) the first line. The lines can only intersect in one point (if the lines are parallel they will not intersect each other).
Let's say the length is L, and the width is W
L is one foot more than 2W, so L=1+2W
the area of the rectangle: A=L*W=300
replace L with 1+2W: (1+2W)*W=300 =>2W^2+W-300=0
solve the quadratic equation: (W-12)(2W+25)=0
W=12 or W=-12.5 (impossible)
so the width is 12, and the length is L=1+2*12=25
please refer to this website for how to factor a quadratic equation
http://www.purplemath.com/modules/factquad.htm
Answer:
5 feet away
Step-by-step explanation:
It is a Pythagorean Triple.
The hypotenuse is 13 feet and one of the sides is 12 feet. To find the length of the base, use the Pythagorean Theorem.
13^2=12^2+c^2
169=144+c^2
c^=25
c=5
Answer:
The expected cost is 152
Step-by-step explanation:
Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y
if
and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)
Recall that, by definition

Also, we are given that
. Recall the following properties of the expected value. If X,Y are random variables, then

Then, using this property we have that
.
Thus, we must calculate E[Y] and E[Y^2].
Using the definition, we get that
![E[Y] = \int_{1}^{5}\frac{y}{4} dy =\frac{1}{4}\left\frac{y^2}{2}\right|_{1}^{5} = \frac{25}{8}-\frac{1}{8} = 3](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E2%7D%7B2%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B25%7D%7B8%7D-%5Cfrac%7B1%7D%7B8%7D%20%3D%203)
![E[Y^2] = \int_{1}^{5}\frac{y^2}{4} dy =\frac{1}{4}\left\frac{y^3}{3}\right|_{1}^{5} = \frac{125}{12}-\frac{1}{12} = \frac{31}{3}](https://tex.z-dn.net/?f=E%5BY%5E2%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%5E2%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B125%7D%7B12%7D-%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cfrac%7B31%7D%7B3%7D)
Then
