What is the measure of

Answer:

Option d

Step-by-step explanation:

The population of interest talks about the group that was research into or what type of participants, a research wants to draw a conclusion about.

The population of interest in this case study is all children within the ages of 5 and 15. A sample of 160 children were then drawn out from this total population.

Answer and Step-by-step explanation:

Let x and y be two positive integers and their sum is 14:

X + y = 14

And the sum of square of this number is:

f = x2 + y2

 = x2+ (14 – x)2

Differentiate with respect to x, we get:

F’(x) = [ x2 + (14 – x)2]’ = 0

        2x + 2(14-x)(-1) = 0

        2x +( 28 – 2x)(-1) = 0

     2x – 28 +2x = 0

        2x + 2x = 28

         4x = 28

       X = 7

Hence, y = 14 – x = 14 -7 = 7

Now taking second derivative test:

F”(x) > 0

For x = y = 7,f reaches its maximum value:

(7)2 + (7)2 = 49 + 49

                   = 98

F at endpoints x Є [ 0, 14]

F(0) = 02 + (14 – 0)2

       =  196

F(14) = (14)2 + (14 – 14)2

  = 196

Hence the sum of squares of these numbers is minimum when x = y = 7

And maximum when numbers are 0 and 14.

Final answer:

To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Explanation:

To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:

• 1 and 13: 1^2 + 13^2 = 170
• 2 and 12: 2^2 + 12^2 = 148
• 3 and 11: 3^2 + 11^2 = 130
• 4 and 10: 4^2 + 10^2 = 116
• 5 and 9: 5^2 + 9^2 = 106
• 6 and 8: 6^2 + 8^2 = 100
• 7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.

Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:

• 1 and 13: 1^2 + 13^2 = 170
• 2 and 12: 2^2 + 12^2 = 148
• 3 and 11: 3^2 + 11^2 = 130
• 4 and 10: 4^2 + 10^2 = 116
• 5 and 9: 5^2 + 9^2 = 106
• 6 and 8: 6^2 + 8^2 = 100
• 7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Learn more about Optimization Problems here:

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Answer:

2400 + (0.05X) = 2900

Therefore, the amount of sales that Liz will have to make to meet her goal is $ 10,000.

Step-by-step explanation:

Since Liz earns a salary of $ 2,400 per month, plus a commission of 5% of her sales, and she wants to earn at least  $ 2,900 this month, to find amounts of sales that will meet her goal, the following equation must be solved:

5/100 = 0.05

2400 + (0.05X) = 2900

0.05X = 2900 - 2400

0.05X = 500

X = 500 / 0.05

X = 10,000

Therefore, the amount of sales that Liz will have to make to meet her goal is $ 10,000.

The mean of all the data will be equal to 8.

What is mean?

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. Mean is generally the average it is calculated by adding all the data and dividing by the number of the data.

Given that a basketball team played six games. In those games, the team won by 8 points, lost by 14, won by 9, won by 10, lost by 1, and won by 6.

The mean of the data will be calculated as:-

Mean = ( 8 + 14 + 9 + 10 + 1 + 6 ) / 6

Mean = 8

Therefore, the mean of all the data will be equal to 8.

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Answer:

C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.

Step-by-step explanation:

Volume=576π cubic centimeters

Radius=8 cm

h=?

Her work:

Volume of a cyclinder=πr^2h

Step 1:

576π= π8^2h

Step 2:

576π = 64πh

Step 3:

576π / 64π = 64πh / 64π

Step 4:

h=9π cm

Correct workings:

Step 1:

576π= π8^2h

Step 2:

576π = 64πh

Step 3:

576π / 64π = 64πh / 64π

Step 4:

h= 9 centimeters

Her error is in step 4

C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.

Answer:

the error was made in step 4,  should have also been cancelled making the correct answer as 9 cm.

Step-by-step explanation: