Ingredients •1 1/2
cups all-purpose flour.
• 31/2 teaspoons baking powder.
• 1 teaspoon salt.
1 tablespoon white sugar.
• 1 1/4 cups milk.
• 1 egg.
• 3 tablespoons butter.


1.) How much of each of the ingredients do you need to make 16 pancakes, 4 pancakes, 12pancakes? Explain which operations with fractions you used to obtain your answer.

Answer:

11 1/2 years old

Step-by-step explanation:

Let Amanda's age be a.

Let the company's age be c.

The company is 24 years older than Amanda. This means that:

c = 24 + a ______(1)

The sum of Amanda's age and the company's age is 121 years. This means that:

c + a = 121 ________(2)

Put (1) in (2):

24 + a + a = 121

2a = 121 - 24

2a = 97

a = 97 / 2 = 48 1/2 years

She has been there for 37 years, therefore, her age when she started working there is:

48 1/2 - 37 = 11 1/2 years old

NOTE: This age doesn't seem right but I worked based on the parameters given.

Answer:

x = 16

Step-by-step explanation:

x - 12 = 4

 + 12 = +12

x = 16

Answer:

16

Step-by-step explanation:

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:

brainly.com/question/32781677

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Answere:

its black

Step-by-step explanation:

black is better and im right