Answer:
It means the Judy's rate to complete the puzzle is ![\frac{1}{3}.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D.)
Step-by-step explanation:
If Judy completes a puzzle by herself, it takes her 3 hours.
Working with Sal, it only takes them 2 hours
We have been given the rates of time taken by Judy and Sal to complete a puzzle.
We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.
It is given that Judy completes a puzzle by herself, it takes her 3 hours.
so part of puzzle completed by Judy in one hour would be![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Therefore, the part of puzzle completed by Judy in one hour is ![\frac{1}{3}.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D.)
Answer:
A) 63.36 years.
B) 100.42 years.
Step-by-step explanation:
We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.
A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.
![\frac{7.1 \times 2}{7.1} =(1.011)^{t}](https://tex.z-dn.net/?f=%5Cfrac%7B7.1%20%5Ctimes%202%7D%7B7.1%7D%20%3D%281.011%29%5E%7Bt%7D)
![2 =(1.011)^{t}](https://tex.z-dn.net/?f=2%20%3D%281.011%29%5E%7Bt%7D)
Now let us solve for t using logarithm.
![ln(2) =t \cdot ln(1.011)](https://tex.z-dn.net/?f=ln%282%29%20%3Dt%20%5Ccdot%20ln%281.011%29)
![t=\frac{0.6931471805599453}{0.0109399400383344}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B0.6931471805599453%7D%7B0.0109399400383344%7D)
![t=63.3593217267282743049\approx 63.36](https://tex.z-dn.net/?f=t%3D63.3593217267282743049%5Capprox%2063.36)
Therefore, it will take 63.36 years the population to be double.
B) Now we will find the number of years it will take the population to be triple of its size.
![7.1 \times 3=7.1(1.011)^{t}](https://tex.z-dn.net/?f=7.1%20%5Ctimes%203%3D7.1%281.011%29%5E%7Bt%7D)
![3 =(1.011)^{t}](https://tex.z-dn.net/?f=3%20%3D%281.011%29%5E%7Bt%7D)
Now let us solve for t using logarithm.
![ln(3) =t \cdot ln(1.011)](https://tex.z-dn.net/?f=ln%283%29%20%3Dt%20%5Ccdot%20ln%281.011%29)
![t=\frac{1.0986122886681097}{0.0109399400383344}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B1.0986122886681097%7D%7B0.0109399400383344%7D)
![t=100.4221490079915311298\approx 100.42](https://tex.z-dn.net/?f=t%3D100.4221490079915311298%5Capprox%20100.42)
Therefore, it will take 100.42 years the population to triple of its size.
If you want to find out how Addision paid each month, you have to have 36, then divide 36 by 12, and the answer will give you 3. So Addison paid $3 every month.
Hope this Helped
Nate
Answer:
![7.7n=112.42](https://tex.z-dn.net/?f=7.7n%3D112.42)
![n=14.6](https://tex.z-dn.net/?f=n%3D14.6)
Step-by-step explanation:
The product is the result obtained by multiplying two factors. Then, the sentence ""The product of a number n and 7.7 equals 112.42" can be expressed with the following equation:
![7.7n=112.42](https://tex.z-dn.net/?f=7.7n%3D112.42)
To solve for the variable "n", you has two apply the Division property of equality and divide both sides of the equation by 7.7
Therefore, the value of "n" is:
![\frac{7.7n}{7.7}=\frac{112.42}{7.7}\\\\n=14.6](https://tex.z-dn.net/?f=%5Cfrac%7B7.7n%7D%7B7.7%7D%3D%5Cfrac%7B112.42%7D%7B7.7%7D%5C%5C%5C%5Cn%3D14.6)