4-33. Lucy keeps track of how long it takes her to do the newspaper's crossword puzzle each day. Her recent times, in minutes, were: 8 22 19 12 18 19 10 35 12 19 16 21

This question is incomplete

Complete Question

Lucy keeps track of how long it takes her to do the newspaper's crossword puzzle each day. Her recent times, in minutes, were: 8 22 19 12 18 19 10 35 12 19 16 21

a. What is the median of her data? b. What is the mean?

a) 18.5

b) 17.583

Step-by-step explanation:

8 22 19 12 18 19 10 35 12 19 16 21

a. What is the median of her data?

The first step is to rearrange the numbers for least to greatest

8, 10, 12, 12, 16, 18, 19, 19, 19, 21, 22, 35

The formula for median = (n + 1)/2

n = number of terms = 12

= (12 + 1)th/2

= 13/2

= 6.5 th value

This means the value is between the 6th and 7th value

= 6th value = 18

7th value = 19

Hence, Median = 18 + 19/2

= 18.5

b. What is the mean?

Mean = Sum of terms/ Number of terms

= 8+ 10+ 12+ 12+ 16+18+19+19+19+21+ 22+35/12

= 211/12

= 17.583333333333

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