Step-by-step explanation:
It asks you to choose values for w, the width, and evaluate the equation for each. It describes the constraint "the perimeter of 20 units" The perimeter of a rectangle is the length of all the lines of a regtangle.
Or
2L + 2W = 20 reduce this to simplest for by dividing both sides by 2;
L + W = 10, so the length plus the width is 10. Rearrange it to be W = 10 - L. Values of W can range from 1 to 9. Now sove for a few points in the function.
f(W) = 10W - W^2
3; 10(3) - 3^2 = 30 - 9 = 21.
If we look at the constraint, L = 10 - W, when the width is 3 the length must be 7. The area of a rectangle is L x W, 3 x 7 = 21. That checks against the function.
Solve for additional points.
4; 10(4) - 4^2 = 40 - 16 = 24.
If W is 4 the L is 6 and 4 x 6 = 24
20 times 10=200 fluid ounces
128 fluid ounces per gallon
1 gallon is too little
2 gallons is to much
but you can't buy 1 and 72/100 of a bottle so just buy 2
2 bottles
Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
The margin of error is:
In which:
is the sample mean.
is the standard deviation for the population.
Assuming an uniform distribution, the standard deviation is given by:
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of 
, so the critical value is z = 1.96.
The sample size is found solving for n when the margin of error is of M = 0.006, hence:
n = 142,282.
A sample of 142,282 should be taken, which is not practical as it is too large of a sample.
More can be learned about the z-distribution at brainly.com/question/25890103
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Answer: 3 kids take 3 pieces of candy each
Step-by-step explanation:
Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)
Number of children that took 5 pieces is y ( total take 5*y pieces of candy)
1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.
( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy. So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )
So we have 2 equations or the system of 2 equations:
1). x+y=18
2). 3*x +5*y=84
Multuply both sides of equation 1) by 3
We have 3*x+3*y=18*3
Deduct 3*y from both sides of this equation
3*x+3*y-3*y=54-3*y
3*x=54-3*y
Substitute 3*x in equation 2). by 54-3*y
2) 54-3*y+5*y=84
2*y=30
y=15 ( kids take 5 pieces of candy each)
Using equation 1) find x
x+15=18
x=3 (kids take 3 pieces of candy each)
