You will have to find what x is to get your answer solve each to find the answer
Answer:
Not true
(x/w)^2 > z
Step-by-step explanation:
(x/w)^2 will be less than 1
z is greater than 1
so (x/w)^2 < z
57% of students studied, which decomposes into 52% who both studied and saw an increase in their exam grade 5% who both studied and did Not see an increase in their exam grade The percentages above are relative to the whole population of 100 students, to get the requested probability, recall that: One way to find out the probability of an event is to Take the ratio of the number of times the event happened, over the total number of times the event could have happened. Total number of times the event happened: 52 = 52% of 100 students studied and saw an increase in their exam grade Total number of times the event could have happened: 57 = 57% of 100 students studied
<span>Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as:
W = (2400 - L)/2
And area is:
A = LW
Substitute the equation for width, giving:
A = LW
A = L(2400 - L)/2
And expand:
A = (2400L - L^2)/2
A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
