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zubka84 [21]
3 years ago
13

Imagine you are having a potluck at your church this week. You are going to bring a dessert to share. This project includes a re

cipe for chocolate chip cookies for desert. You are expecting 120 people, but the recipe does not serve that many people, so you will need to adjust the ingredients so there will be enough. For example, if a recipe serves 8 people and you need to feed 32 people, what would you need to do? You would have to make 4 times as much as the original recipe makes, which means that you would need to multiply the amount of each ingredient by 4, since 8*4 = 32. (If you are struggling with this project, please refer back to the lesson Multiplying Fractions in the unit Fractions) Cookies (makes 24 servings) 1/2 cup unsalted butter, melted. 1/3 cup granulated sugar. 1/2 cup light brown sugar, packed. 1 large egg. 1 teaspoon vanilla extract. 1/2 teaspoon baking soda. 1 ½ cups all-purpose flour. 1 ½ cups chocolate chips (semi-sweet or milk) Answer the following questions: Show your work for a higher score! 1. This recipe serves 24 people, but you need to serve 120 people. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?

Mathematics
1 answer:
harina [27]3 years ago
3 0

Answer: You will need to multiply them by 5

Step-by-step explanation: 120÷24=5. So you would need to multiply all ingredients by 5 to get enough for 120 people.

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Taye recruits two people to be election campaign volunteers. The next week he ask each of those volunteers to recruit two more c
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Using a geometric sequence, it is found that:

a) For the first 5 weeks, the numbers are: 2, 4, 8, 16, 32

b) Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

For this problem, on the first week there are 2 people, and since each new people involve two more, the common ratio is of 2, hence the parameters for the geometric sequence are:

a_1 = 2, q = 2

Hence the number of people after n weeks is:

a_n = 2 \times 2^{n - 1}

For the first 5 weeks, the numbers are:

  • a_1 = 2 \times 2^{1 - 1} = 2
  • a_2 = 2 \times 2^{2 - 1} = 4
  • a_3 = 2 \times 2^{3 - 1} = 8
  • a_4 = 2 \times 2^{4 - 1} = 16
  • a_5 = 2 \times 2^{5 - 1} = 32

There will be 150 volunteers when a_n = 150, hence:

2 \times 2^{n - 1} = 150

2^{n-1} = 75

\frac{2^n}{2} = 75

2^n = 150

n = 7...

The above is because 2^7 = 128 and 2^8 = 256, and 128 < 150 < 256.

Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

More can be learned about geometric sequences at brainly.com/question/11847927

#SPJ1

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