Direct Variation equation: y=kx, k=y/x
42/14=3
k=3
y=3x
y=3(90)
y=270
Answer:
Step-by-step explanation:
a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S
Write the probability of energy supplied by these energy sources in the next 10 years
P(energy supplied) = P(S ∪ F) -----(1)
Rewrite eqn (1)
P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)
substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources
P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)
= 0.85 + 0.7 - (0.595)
= 1.55 - 0.595
= 0.955
Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955
B) write the probability of only one source of energy available
P(only one source of energy available) =
∪
---(3)
Rewrite the equation (3)
P(only one source of energy available) =
![=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)](https://tex.z-dn.net/?f=%3DP%28%5Cbar%20F%20S%29%2BP%28%5Cbar%20S%20F%29%5C%5C%5C%5C%3D%5C%7B%5B1-P%28F%29%5DP%28S%29%2B%5B1-P%28S%29%5DP%28F%29%5C%7D---%284%29)
![=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36](https://tex.z-dn.net/?f=%3D%5C%7B%5B1-0.7%5D0.85%2B%5B1-0.85%5D0.7%5C%7D%5C%5C%5C%5C%3D0.255%2B0.105%5C%5C%5C%5C%3D0.36)
Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36
Answer:
y=-
x+
Step-by-step explanation:
First, calculate the slope of the line that is perpendicular to the equation of line we are asked to find
m=(y2-y1)/(x2-x1)
=(2-(-4))/(-2-1)
=6/-3
=-2
in this equation the slope is 2, and to find the first equation, use y=mx+b
use the point (1, -4) to find b
-4=(2)(1)+b
-4=2+b
b=-6
the first equation of the line is y=2x-6
to find the x intercept of that line substitute 0 for y
0=2x-6
2x=6
x=3
the slope of a line perpendicular to this would be the opposite reciprocal of the slope which would be equal to -1/2
for the second equation of the line to pass thorugh the x-intercept of the first line, it must pass through (3, 0), so substitute and solve for b
y=mx+b
0=(-1/2)(3)+b
b=3/2
thus the equation of the line that is perpendicular to the line through (1,-4) and (-2, 2) and passes through the x intercept of that line is y=-
x+3/2