Knowing the amount doubles every 30 days, we'll have to find how many times it'lll double in the 210-day time frame:
210 / 30 = 7
It doubles 7 times. If we were to write a rough, not worked on expresion representing that, knowing the starting population was of 20, we would write:
(((((((20 * 2) * 2) * 2) * 2) * 2) * 2) * 2) = 2560 rabbits
Hope it helped,
Happy homework/ study exam!
My favorite is probably aweSAMdude
Answer:
x = 18
m∠HCB = 36
Step-by-step explanation:
The measure of angle FBC is 8x and the measure of angle HCB is 2x. If you add the measures of both angles it will equal to 180 degrees. This can be represented in an equation:
8x + 2x = 180
10x = 180
Divide both sides of the equation by 10 to isolate the x:
10x/10 = 180/10
x = 18
Now that we know the value of x, we can find the measure of angle HCB:
2x
2(18)
36
The measure of angle HCB is 36.
I hope this helps :)
Answer:
To find the x-intercept, substitute in 0 for y and solve for x
. To find the y-intercept, substitute in 0 for x and solve for y
.
x-intercept: (−
45
,
0
)
y-intercept: (
0
,
−
15
)
You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5C%2C%5Cmathrm%20dx%3D710)
and the second moment is
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B1%2C513%2C900%7D3)
The second moment is useful in finding the variance, which is given by
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2%3D%5Cdfrac%7B1%2C513%2C900%7D3-710%5E2%3D%5Cdfrac%7B1600%7D3)
You get the standard deviation by taking the square root of the variance, and so
![\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B%5Cdfrac%7B1600%7D3%7D%5Capprox23.09)
