Population at start : 8,230.
The rate of growth: r = 1.25
x - number of the years;
Answer:
B ) f ( x ) = 8,230 * ( 1.25 ) ^x where 1.25 is the rate of growth.
Answer:
Hence, the limit of the expression:
is:
![\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
We have to estimate the limit of:
![\lim_{x \to 3} \dfrac{x-3}{x^2-2x-3}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%7D%20%5Cdfrac%7Bx-3%7D%7Bx%5E2-2x-3%7D)
We can also represent the denominator of the function in the limit as:
![x^2-2x-3=x^2-3x+x-3\\\\x^2-2x-3=x(x-3)+1(x-3)\\\\x^2-2x-3=(x+1)(x-3)](https://tex.z-dn.net/?f=x%5E2-2x-3%3Dx%5E2-3x%2Bx-3%5C%5C%5C%5Cx%5E2-2x-3%3Dx%28x-3%29%2B1%28x-3%29%5C%5C%5C%5Cx%5E2-2x-3%3D%28x%2B1%29%28x-3%29)
Hence, we have to estimate the limit of:
![\lim_{x \to 3} \dfrac{x-3}{(x+1)(x-3)}\\\\= \lim_{x \to 3}\dfrac{1}{x+1}\\ \\=\dfrac{1}{3+1}\\\\=\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%7D%20%5Cdfrac%7Bx-3%7D%7B%28x%2B1%29%28x-3%29%7D%5C%5C%5C%5C%3D%20%5Clim_%7Bx%20%5Cto%203%7D%5Cdfrac%7B1%7D%7Bx%2B1%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B3%2B1%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D)
Hence, the limit of the expression:
is:
![\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D)
A. ) Addition Property is the answer
Answer:
The probability of getting a nickel, then a dime is 2/21
Step-by-step explanation:
No. of pennies = 9
No. of nickels = 10
No. of dimes = 12
No. of quarters = 5
Total items = 9+10+12+5=36
So, Probability of getting nickel on first draw = ![\frac{10}{36}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B36%7D)
Now the nickle in not replaced
So, Total items = 36-1 = 35
So, Probability of getting dime on second draw =![\frac{12}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B35%7D)
So, the probability of getting a nickel, then a dime = ![\frac{10}{36} \times \frac{12}{35}=\frac{2}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B36%7D%20%5Ctimes%20%5Cfrac%7B12%7D%7B35%7D%3D%5Cfrac%7B2%7D%7B21%7D)
Hence the probability of getting a nickel, then a dime is 2/21
Answer:
$180 for 4 shirts
Step-by-step explanation:
1 shirt costs $50 and you need 4 shirts
50 x 4 = 200
10% of 200 is 20 which means you get $20 off the original price of 4 shirts
200 - 20 = 180
You pay 180 dollars for 4 shirts.
Hope this helps! :)