First find the slope. m=(y2-y1)/(x2-x1)
m=(4225-1990)/(5-2)=745,
m is the slope, this represents the amount of money earned each month that the business operates.
so far we have:
y=745x+b, using any point we can solve for b, I'll use (2,1990)
1990=745(2)+b
1990=1490+b
500=b
b is the y-intercept which is $500, it represents the amount of moeny that the business started with.
Answer:
0
Step-by-step explanation:
First we need to find the value of constant k in equation. To find k we use the formula:
![\int\limits^{100}_0 {ke^{-0.01x}} \, dx =1\\Integrating:\\k\int\limits^{100}_0 {e^{-0.01x}} \, dx =1\\\frac{k}{-0.01}[e^{-0.01x}]_0^{100}=1\\-100k [e^{-0.01x}]_0^{100}=1\\-100k[e^{-0.01*100}-e^{-100*0}]=1\\-100k[e^{-1}-e^0]=1\\-100k(-0.632)=1\\63.2k = 1\\k=0.0158](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B100%7D_0%20%7Bke%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5CIntegrating%3A%5C%5Ck%5Cint%5Climits%5E%7B100%7D_0%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5C%5Cfrac%7Bk%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%20%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%5Be%5E%7B-0.01%2A100%7D-e%5E%7B-100%2A0%7D%5D%3D1%5C%5C-100k%5Be%5E%7B-1%7D-e%5E0%5D%3D1%5C%5C-100k%28-0.632%29%3D1%5C%5C63.2k%20%3D%201%5C%5Ck%3D0.0158)
the probability that a person age 20 will live for at least 20 more years = P(40 ≤ x <∞).
The person would live for at least 40 years
Therefore:
P(40 ≤ x <∞) =
![\int\limits^{\infty}_{40} 0.0158e^{-0.01x}} \, dx \\Integrating:\\0.0158\int\limits^{\infty}_{40} {e^{-0.01x}} \, dx =\frac{0.0158}{-0.01}[e^{-0.01x}]_{40}^{\infty}\\=-1.58 [e^{-0.01x}]_{40}^{\infty}=-1.58[e^{-\infty}-e^{-100*40}]\\=-1.58[e^{-\infty}-e^{-4000}]=-1.58(0-0)=0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%200.0158e%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%5C%5CIntegrating%3A%5C%5C0.0158%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D%5Cfrac%7B0.0158%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%5C%5C%3D-1.58%20%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-100%2A40%7D%5D%5C%5C%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-4000%7D%5D%3D-1.58%280-0%29%3D0)
They are proportional with a ratio of 2:3
Answer:37
Step-by-step explanation:
180-35=145 I got the 180 because that is a straight line. I got the 35 from the angle. I subtracted them because 35 is part of the 180 and does not need to be counted. Then I set 145= to 4m-3. Then I just solved normally. It should look like this
145+3=4m-3+3
148/4=4m/4
37=m
