a previous analysis of paper boxes showed that the standard deviation of their lengths is 15 millimeters. A packers wishes to find the 95% confidense interval for the average length of a box. How many boxes do he need to measure to be accurate within 1 millimeters

864.36 boxes

Step-by-step explanation:

In the question above, we are given the following values,

Confidence interval 95%

Since we know the confidence interval, we can find the score.

Z score = 1.96

σ , Standards deviation = 15mm

Margin of error = 1 mm

The formula to use to solve the above question is given as:

No of boxes =[ (z score × standard deviation)/ margin of error]²

No of boxes = [(1.96 × 15)/1]²

= 864.36 boxes

Based on the options above, we can round it up to 97 boxes.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

i think the answer is true

step-by-step explanation: