Answer:
Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
Take the square root of 256 to find the side length of the mirror
√256 =16
the rectangles width is 16, it length is 2 inches longer
16+2 =18 so the length is 18
to find the area multiply them together
18x16=288
the area is 288 inches² :)
Answer:
(a) 0.20
(b) 31%
(c) 2.52 seconds
Step-by-step explanation:
The random variable <em>Y</em> models the amount of time the subject has to wait for the light to flash.
The density curve represents that of an Uniform distribution with parameters <em>a</em> = 1 and <em>b</em> = 5.
So, 
(a)
The area under the density curve is always 1.
The length is 5 units.
Compute the height as follows:


Thus, the height of the density curve is 0.20.
(b)
Compute the value of P (Y > 3.75) as follows:
![P(Y>3.75)=\int\limits^{5}_{3.75} {\frac{1}{b-a}} \, dy \\\\=\int\limits^{5}_{3.75} {\frac{1}{5-1}} \, dy\\\\=\frac{1}{4}\times [y]^{5}_{3.75}\\\\=\frac{5-3.75}{4}\\\\=0.3125\\\\\approx 0.31](https://tex.z-dn.net/?f=P%28Y%3E3.75%29%3D%5Cint%5Climits%5E%7B5%7D_%7B3.75%7D%20%7B%5Cfrac%7B1%7D%7Bb-a%7D%7D%20%5C%2C%20dy%20%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B5%7D_%7B3.75%7D%20%7B%5Cfrac%7B1%7D%7B5-1%7D%7D%20%5C%2C%20dy%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5By%5D%5E%7B5%7D_%7B3.75%7D%5C%5C%5C%5C%3D%5Cfrac%7B5-3.75%7D%7B4%7D%5C%5C%5C%5C%3D0.3125%5C%5C%5C%5C%5Capprox%200.31)
Thus, the light will flash more than 3.75 seconds after the subject clicks "Start" 31% of the times.
(c)
Compute the 38th percentile as follows:

Thus, the 38th percentile is 2.52 seconds.
You would be able to cut 144 pieces of wire from the spool because 270/1 7/8 (or 1.875) equals 144
The Correct Answer Is...
<u><em>5/8!</em></u>
Any Questions? Comment Below!
<u><em>-AnonymousGiantsFan</em></u>