Hampton ate 7 slices of fruit at lunch. After dinner, he ate

Mathematics

1 answer:

vovikov84 [41]3 years ago

7 0

Answer:

If you are trying to find the answer its 8 obviously, but if you are looking for an equation to find the answer it would be 15 - 7 = x or 7 + x = 15.

Step-by-step explanation:

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A model for the population in a small community after t years is given by P(t)=P0e^kt.

LUCKY_DIMON [66]

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}$

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}$

$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t$

b)

A = 10,000, t = 3

$\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I$

3 0

3 years ago

Select the correct answer.

Nina [5.8K]

Answer:

D. $x^2 + 3x - 88$

Step-by-step explanation:

Area of rectangle = $length (l) * width (w)$

Length of rectangle = (x - 8)

Width = (x + 11)

Area of rectangle = $(x - 8)(x + 11)$

Expand the expression

$x(x + 11) -8(x + 11)$ (distributive property of multiplication)

$x^2 + 11x - 8x - 88$

Combine like terms

$x^2 + 3x - 88$

Expression for the area of the rectangle = $x^2 + 3x - 88$

7 0

3 years ago

A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 25

Klio2033 [76]

Answer:

$\mathrm{Best\:course\:grade\:possible:\:}87.25\%,\\\mathrm{Minimum\:score\:on\:final\:to\:earn\:at\:least\:a\:75\%\:for\:the\:course:\:}51\%$

Step-by-step explanation:

Assuming the maximum score for the final is $100\%$ , we can multiply each score by its respective course weight and add them together to give a final score. If your friend did receive this maximum score of $100\%$ , their overall grade for the course would be: