So you know that 30 + 30 + w + w = P. We also know the area is 240 square feet. Divide 240 by 30 to find the width of the area. 240 / 30 = 8. w = 8. So add 30 + 30 + 8 + 8 to find that P = 76. HOWEVER, remember that George is using part of his house as a wall instead of a fence. So subtract 8 from 76 to get 68 ft. George will need 68 ft. of fencing for his dog run.
Recall that the PDF is given by the derivative of the CDF:
The mean is given by
![\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\int_0^2\left(x-\dfrac{x^2}2\right)\,\mathrm dx=\frac23](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_0%5E2%5Cleft%28x-%5Cdfrac%7Bx%5E2%7D2%5Cright%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac23)
The median is the number
such that
. We have
but both roots can't be medians. As a matter of fact, the median must satisfy
, so we take the solution with the negative root. So
is the median.
From Plato
30e-0.12t less than or equal to M
40e-0.18t less than or equal to M
Step-by-step explanation:
It is given that compound A decays at a rate of 12% per week, and compound B decays at a rate of 18% per week. Since the rates represent decay, the r-value is negative. A decay rate of 12% is represented by an r-value of -0.12, and a decay rate of 18% is represented by an r-value of -0.18.
The initial amount of compound A is 30 grams and the initial amount of compound B is 40 grams. Substitute the initial amounts of each compound and their respective decay rates into the system of inequalities.
The following system of inequalities can be used to determine when the remaining mass of the two compounds, M, will be the same, after t weeks.
Since the angle is in radians, then s = rθ.
Answer:
45 minutes
Step-by-step explanation:
Distance needed to be covered = 10,000-550= 9,450
Speed= 210ft/min
time: 9450/210= 45 mins
