Answer:
x=5.7
Step-by-step explanation:
sin(35=x/10
![\bf \begin{array}{ccll} \stackrel{t}{months}&\stackrel{A}{books}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 0&80\\ 1&100\\ 2&125 \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%0A%5Cstackrel%7Bt%7D%7Bmonths%7D%26%5Cstackrel%7BA%7D%7Bbooks%7D%5C%5C%0A%5Ctext%7B%5Ctextemdash%5Ctextemdash%5Ctextemdash%7D%26%5Ctext%7B%5Ctextemdash%5Ctextemdash%5Ctextemdash%7D%5C%5C%0A0%2680%5C%5C%0A1%26100%5C%5C%0A2%26125%0A%5Cend%7Barray%7D)
, we know that on Month 0, the Books were 80
![\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &80\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ \end{cases} \\\\\\ 80=I(1+r)^0\implies 80=I\qquad therefore\qquad \boxed{A=80(1+r)^t}](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BAmount%20for%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DI%281%20%2B%20r%29%5Et%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5Cto%20%2680%5C%5C%0AI%3D%5Ctextit%7Binitial%20amount%7D%5C%5C%0Ar%3Drate%5Cto%20r%5C%25%5Cto%20%5Cfrac%7Br%7D%7B100%7D%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%260%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A80%3DI%281%2Br%29%5E0%5Cimplies%2080%3DI%5Cqquad%20therefore%5Cqquad%20%5Cboxed%7BA%3D80%281%2Br%29%5Et%7D)
we also know that on the first month there were 100 books,
![\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &100\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &1\\ \end{cases} \\\\\\ 100=80(1+r)^1\implies \cfrac{100}{80}=1+r\implies \cfrac{5}{4}=1+r \implies \cfrac{5}{4}-1=r \\\\\\ \cfrac{1}{4}=r\implies 0.25=r\qquad therefore\qquad \boxed{A=80(1+0.25)^t}](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BAmount%20for%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DI%281%20%2B%20r%29%5Et%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5Cto%20%26100%5C%5C%0AI%3D%5Ctextit%7Binitial%20amount%7D%5C%5C%0Ar%3Drate%5Cto%20r%5C%25%5Cto%20%5Cfrac%7Br%7D%7B100%7D%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%261%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A100%3D80%281%2Br%29%5E1%5Cimplies%20%5Ccfrac%7B100%7D%7B80%7D%3D1%2Br%5Cimplies%20%5Ccfrac%7B5%7D%7B4%7D%3D1%2Br%0A%5Cimplies%20%0A%5Ccfrac%7B5%7D%7B4%7D-1%3Dr%0A%5C%5C%5C%5C%5C%5C%0A%20%5Ccfrac%7B1%7D%7B4%7D%3Dr%5Cimplies%200.25%3Dr%5Cqquad%20therefore%5Cqquad%20%5Cboxed%7BA%3D80%281%2B0.25%29%5Et%7D)
now, how many books when t = 8? A=80(1+0.25)⁸, or A=80(1.25)⁸.
Answer:
![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
Step-by-step explanation:
Assuming a total of ten students were asked,
chose football and
chose other sports.
simplified is
, so that's the experimental chance that the next student favors football.
Answer:
The answer is B) 1/25
Step-by-step explanation:
This is because given that f(x) = 5^x
Hence, f(-2) would be 5^-2, which is equal to (1/5^2) => 1/25
Because a^-b can be written as 1/a^b
Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:
![\begin{gathered} FH=2EI, \\ GI=EI. \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20FH%3D2EI%2C%20%5C%5C%20GI%3DEI.%20%5Cend%7Bgathered%7D)
Substituting the given expression for each segment in the first equation, we get:
![3x+6=2(2x-2).](https://tex.z-dn.net/?f=3x%2B6%3D2%282x-2%29.)
Solving the above equation for x, we get:
![\begin{gathered} 3x+6=4x-4, \\ 3x+6+4=4x, \\ 3x+10=4x, \\ 4x-3x=10, \\ x=10. \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203x%2B6%3D4x-4%2C%20%5C%5C%203x%2B6%2B4%3D4x%2C%20%5C%5C%203x%2B10%3D4x%2C%20%5C%5C%204x-3x%3D10%2C%20%5C%5C%20x%3D10.%20%5Cend%7Bgathered%7D)
Substituting x=10 in the equation for segment EI, we get:
![EI=2*10-2=20-2=18.](https://tex.z-dn.net/?f=EI%3D2%2A10-2%3D20-2%3D18.)
Therefore:
![GI=18.](https://tex.z-dn.net/?f=GI%3D18.)
Now, to determine the measure of angle IEH, we notice that:
![\Delta HFG\cong\Delta GEH,](https://tex.z-dn.net/?f=%5CDelta%20HFG%5Ccong%5CDelta%20GEH%2C)
therefore,
![\measuredangle GHF\cong\measuredangle HGE.](https://tex.z-dn.net/?f=%5Cmeasuredangle%20GHF%5Ccong%5Cmeasuredangle%20HGE.)
Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:
![m\measuredangle IEH=90^{\circ}-35^{\circ}=55^{\circ}.](https://tex.z-dn.net/?f=m%5Cmeasuredangle%20IEH%3D90%5E%7B%5Ccirc%7D-35%5E%7B%5Ccirc%7D%3D55%5E%7B%5Ccirc%7D.)
<h2>Answer: </h2>