So we have a rectangle, whose area is A=bh. We don't know any of those, so we've got a bit of thinking to do. (Wish I could draw a picture....) First of all, we only need to consider half the rectangle. Since it is bounded by a parabola that is symmetric over the y-axis (ie not moved left or right), the rectangle has the same area on the right and left. So let's just consider the first quadrant. Note that if we maximize this area, we maximize the entire rectangle's area. The width of this half rectangle is x (it's the x coordinate). The height of this rectangle is whatever the y coordinate of the corner is. That corner is directly above the x coordinate, and is on the rectangle. So the upper corner must have coordinates of (x, y), or (x, 8-x2). Those will serve as our base and height. A = x (8 - x2)A = 8x - x3 Maximize implies derivative = 0, so... dA = 8 - 3x20 = 8 - 3x23x2 = 8x2 = 8/3x = ±1.633 Notice that this is giving us two answers -- one of them is on the left (second quadrant), while the other is on the right. The y coordinates will be the same for both, due to the nature of this parabola. y = 8 - (1.633)2y = 8 - (8/3)y = 5.333 Our upper corners are (±1.633, 5.333). The dimensions are: Height: 5.333Width = (2 · 1.633) = 3.266 :)
Answer:
$4
Step-by-step explanation:
40/100=0.4
(10)0.4=4
Work out 6% of $42 which equals to $2.52. The work out what 20% of $42 which is $8.40. Finally add the $8.40 and $2.52 onto $42 to give you your answer of $52.92
DAnswer:
Step-by-step explanation:
Answer:
The minimum score an applicant must receive for admission is 392.
Step-by-step explanation:
Let the minimum score required be 'x₀'.
Given:
Mean score (μ) = 500
Standard deviation (σ) = 100
Percentage required for admission, P > 86% or 0.86
So, we are given the area under the normal distribution curve to the right of z-score which is 86%.
The z-score table gives the area left of the z-score value. So, we will find the z-score value for area 100 - 86 = 14% or 0.14
So, for value equal to 0.1401, the z-score = -1.08
Now, 
So, we find x₀ using the formula of z-score which is given as:
Therefore, the minimum score an applicant must receive for admission is 392.
