Answer:
171 newspapers.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
How many newspapers should the newsstand operator order to ensure that he runs short on no more than 20% of days
The number of newspapers must be on the 100-20 = 80th percentile. So this value if X when Z has a pvalue of 0.8. So X when Z = 0.84.
So 171 newspapers.
the formula for area of a rectangle is
Area = length x width
since both the length and the width of the rectangle lie on the same x and y axis, we can find the distance between the width and the distance between the length by subtracting
(-4,9) (-4,-3)
these points lie on the same x axis, so they create a vertical line
9-(-3) = 12
12 units is the distance between them
(-4,-3) (-1,-3)
these points lie on the same y axis, so they create a horizontal line
-1-(-4) = 3
3 units is the distance between them
now that we have the length and the width, we can find the area
A = 12 x 3
A = 36 units²
Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x
Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x
Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6
Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160
Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224
And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
Your answer should be -8y + 6.6z + 10
Answer:
5 (5x1) , -10 -(5x2), 20(10x2), -40 -(20x2), 80(40x2)
so the next number should be previous number in the sequence multiplied by 2 and a negative sign.
-`(80x2) = -160
