Wheel of fortune is a popular game show on televis ion. contestants spin a wheel and try to guess a correct letter from a word puzzle. if they guess correctly, they earn the dollar amount from the wheel. if they spin “bankrupt” or “lose a turn” they get nothing and can’t play. to the right is an example of the wheel. the outcome of a spin on the wheel is a discrete random variable. consider x the dollar amount spun on the wheel, where bankrupt and lose a turn = $0, and free play = $500. there are 24 wedges on the wheel.
the following table provides the probability mass function for x. round values to 3 decimal places.
x $0 $300 $350 $400 $450 $500 $550 $600 $700 $800 $900 $5,000
count 2 5 1 2 1 3 1 3 1 2 2 1
p(x) 0.083 0.208 0.042 0.083 0.042 0.125 0.042 0.125 0.042 0.083 0.083 0.042
what is the most likely dollar amount?
how likely is it to spin lose a turn or bankrupt?
what is the average dollar amount? show work!
suppose a contestant spins the wheel three times, how likely is it they spin $0 at least one time? show work!

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

first one because it can't have a fraction in it

step-by-step explanation: