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2 years ago

8

Tommy is baking a cake. He knows that he needs 2/3 cups of flour to make 4 cakes. How many cups of flour will Tommy need to make

8 cakes?

1 answer:

mash [69]2 years ago

4 0

1. 1/3 cups..... ok vthen have a good day

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Is this correct ? My answers 10 btw. NO BEGINNERS , & whoever answers first gets a thanks :)

borishaifa [10]

The answer would be 54

6 0

3 years ago

Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

2 years ago

Read 2 more answers

Mr. Nelson lost one of his students' test

amid [387]

Complete question :

Mr. Nelson lost one of his students' test papers. He knows that the other 4 students scored as follows: 60, 62, 56, 57. He also knows that the average score is 59.2. What is the score on the missing paper?

Answer:

61

Step-by-step explanation:

Given the following :

Total number of students = 4 + 1 missing = 5

Score on the four avaliable papers = 60, 62, 56, 57

Average score of the 5 papers = 59.2

Score on missing paper :

Sum of each score / number of papers

Sum of each score = sum of available scores + missing score

Let missing score = m

(60 + 62 + 56 + 57 + m) = 235 + m

Recall:

Average = total sum / number of observations

Hence,

59.2 = (235 + m) / 5

59.2 × 5 = 235 + m

296 = 235 + m

m = 296 - 235

m = 61

Missing score = 61

6 0

2 years ago

Mary's team scores 18 points in the first half and 7 points in the second half. Mary scored a total of 5 points. What fraction o

jek_recluse [69]

Answer:

.2 <em>or </em>1/5

Step-by-step explanation:

First, calculate the total points by adding the two half's totals together.

7 + 18 = 25

Now, divide the number of points Mary scored by the total.

5 / 25 = 1/5

7 0

3 years ago

Your grandfather placed $5,000 in a trust fund for you. In 12 years, the fund will be

PolarNik [594]

Answer:

fv/pv=(1+r)^n

10,000/5000=(1+r%)^12

2=(1+r%)^12

r= 5.95

4 0

2 years ago

Read 2 more answers