Answer:
35, if Tim and Dan scored 4 together, 7 if each scored 4 touchdowns
Answer:
Step-by-step explanation:
In order to find who is more efficient at planting carrots, we want to put both ratios in terms of the same amount of time.
For simplicity, lets see how many carrots each can make in 1 hour.
![Janet:\\9ft \: in \: 15 \:minutes](https://tex.z-dn.net/?f=Janet%3A%5C%5C9ft%20%5C%3A%20in%20%5C%3A%2015%20%5C%3Aminutes)
![\frac{9ft}{15min} = \frac{xft}{60min}\\x = \frac{60*9}{15} = 36](https://tex.z-dn.net/?f=%5Cfrac%7B9ft%7D%7B15min%7D%20%3D%20%5Cfrac%7Bxft%7D%7B60min%7D%5C%5Cx%20%3D%20%5Cfrac%7B60%2A9%7D%7B15%7D%20%3D%2036)
Janet can plant 36 feet of carrots in one hour
![Amy:\\\frac{17ft}{30min} = \frac{xft}{60min}\\x = \frac{17*60}{30} = 34](https://tex.z-dn.net/?f=Amy%3A%5C%5C%5Cfrac%7B17ft%7D%7B30min%7D%20%3D%20%5Cfrac%7Bxft%7D%7B60min%7D%5C%5Cx%20%3D%20%5Cfrac%7B17%2A60%7D%7B30%7D%20%3D%2034)
Amy can plant 34 feet of carrots in one hour
So, Janet can plant carrots more quickly
Answer: it will take a combined rate of 2.67 hours
Step-by-step explanation:
Father can do the job on the farm in 6 hours. This means that the father's unit rate of working will be 1/6
The older son can do it in 8 hours. This means that the older son's rate of working will be 1/8
The younger son can do same job in 12 hours. This means that the younger son's working rate is 1/12
When they work together, they will be working simultaneously. It means that their unit rates are additive. The combined unit rates will be
1/6 + 1/8 + 1/12 = (20 + 15 + 10)/120
45/120
Assuming it takes t hours for them to complete the work while doing it together. Their combined unit rate will be 1/t
45/120 = 1/t
45t = 120
t = 120/45 = 2.67 hours
they are the same lines
x and y are the same
Step-by-step explanation:
i dont know for sure so bye god bless
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D)
![\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to & \begin{array}{llll} 485\cdot 12\\ \underline{5280} \end{array}\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{a year, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases} \\\\\\ ](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0AA%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Boriginal%20amount%7D%5C%5C%0A%5Ctextit%7Balready%20compounded%7D%0A%5Cend%7Barray%7D%20%26%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%0A%5Cend%7Barray%7D%5C%5C%0Apymnt%3D%5Ctextit%7Bperiodic%20payments%7D%5Cto%20%26%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A485%5Ccdot%2012%5C%5C%0A%5Cunderline%7B5280%7D%0A%5Cend%7Barray%7D%5C%5C%0Ar%3Drate%5Cto%206%5C%25%5Cto%20%5Cfrac%7B6%7D%7B100%7D%5Cto%20%260.06%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Ba%20year%2C%20thus%20once%7D%0A%5Cend%7Barray%7D%5Cto%20%261%5C%5C%0A%0At%3Dyears%5Cto%20%264%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A)
![\bf A=5280\left[ \cfrac{\left( 1+\frac{0.06}{1} \right)^{1\cdot 4}-1}{\frac{0.06}{1}} \right]](https://tex.z-dn.net/?f=%5Cbf%20A%3D5280%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.06%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%204%7D-1%7D%7B%5Cfrac%7B0.06%7D%7B1%7D%7D%20%5Cright%5D)
Joe is making $485 payments monthly, but the amount gets interest on a yearly basis, not monthly, so the amount that yields interest is 485*12
also, keep in mind, we're assuming is compound interest, as opposed to simple interest