Answer:
Add the two numbers to find the total number of fidgets.
23+40
63
So, Amy now has 63 fidgets.
:)
Answer:
31.25 or 31 1/4 cups
Step-by-step explanation:
1 1/4 = 36
x = 900
=> 5/4 = 36
x = 900
Cross multiply
=> 5/4 * 900 = 36 * x
=> 4500/4 = 36x
=> 1125 = 36x
=> 1125 / 36 = 36x / 36
=> 31.25 = x
31.25 = 31 1/4
So, 31.25 or 31 1/4 cups are required for 900 cupcakes.
Answer:
a. 4 and 120. b. 260 miles. c. 140 miles.
Step-by-step explanation:
d(t) = 400-70t.
a. (4,120) refers that with t=4 (when the driver has driven 4 hours), he is incorrect: 120 miles from his destination. d(4) = 400-70(4) = 400-280 = 120.
b. After driving 2 hours, that is in t=2, he is d(2)= 400-70(2) = 400-140 = 260 miles from his destination.
c. In his second hour of driving, that is in t=2 he is 260 miles from his destination, so he has driven 140 miles.
![\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=4\\ r=3\\ a_n=324 \end{cases} \implies 324=4(3)^{n-1} \\\\\\ \cfrac{324}{4}=3^{n-1}\implies 81=3^{n-1}\implies 3^4=3^{n-1}\implies 4=n-1 \\\\\\ \boxed{5=n}\\\\](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20a%20geometric%20sequence%7D%5C%5C%5C%5C%0Aa_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ar%3D%5Ctextit%7Bcommon%20ratio%7D%5C%5C%0A----------%5C%5C%0Aa_1%3D4%5C%5C%0Ar%3D3%5C%5C%0Aa_n%3D324%0A%5Cend%7Bcases%7D%0A%5Cimplies%20%0A324%3D4%283%29%5E%7Bn-1%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B324%7D%7B4%7D%3D3%5E%7Bn-1%7D%5Cimplies%2081%3D3%5E%7Bn-1%7D%5Cimplies%203%5E4%3D3%5E%7Bn-1%7D%5Cimplies%204%3Dn-1%0A%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7B5%3Dn%7D%5C%5C%5C%5C)
![\bf -------------------------------\\\\ \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=4\\ r=3\\ n=5 \end{cases} \\\\\\ S_5=4\left( \cfrac{1-3^5}{1-3} \right)\implies S_5=4\left(\cfrac{1-243}{-2} \right)](https://tex.z-dn.net/?f=%5Cbf%20-------------------------------%5C%5C%5C%5C%0A%5Cqquad%20%5Cqquad%20%5Ctextit%7Bsum%20of%20a%20finite%20geometric%20sequence%7D%5C%5C%5C%5C%0AS_n%3D%5Csum%5Climits_%7Bi%3D1%7D%5E%7Bn%7D%5C%20a_1%5Ccdot%20r%5E%7Bi-1%7D%5Cimplies%20S_n%3Da_1%5Cleft%28%20%5Ccfrac%7B1-r%5En%7D%7B1-r%7D%20%5Cright%29%5Cquad%20%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ar%3D%5Ctextit%7Bcommon%20ratio%7D%5C%5C%0A----------%5C%5C%0Aa_1%3D4%5C%5C%0Ar%3D3%5C%5C%0An%3D5%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AS_5%3D4%5Cleft%28%20%5Ccfrac%7B1-3%5E5%7D%7B1-3%7D%20%5Cright%29%5Cimplies%20S_5%3D4%5Cleft%28%5Ccfrac%7B1-243%7D%7B-2%7D%20%20%5Cright%29)
and surely you know how much that is.