P(a ∪ b) = p(a) + p(b) - p(a ∩ b)
p(a ∩ b) = p(a) + p(b) - p(a ∪ b)
p(a ∩ b) = 1/3 + 2/5 - 3/5
p(a ∩ b) = 2/15
Answer:
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Step-by-step explanation:
Answer:
Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line
is
Step-by-step explanation:
Given:
To Find:
Equation of line passing through ( 16, -7) and is perpendicular to the line
Solution:
...........Given
![\therefore y=\dfrac{2}{3}\times x-4](https://tex.z-dn.net/?f=%5Ctherefore%20y%3D%5Cdfrac%7B2%7D%7B3%7D%5Ctimes%20x-4)
Comparing with,
Where m =slope
We get
We know that for Perpendicular lines have product slopes = -1.
![m1\times m2=-1](https://tex.z-dn.net/?f=m1%5Ctimes%20m2%3D-1)
Substituting m1 we get m2 as
![\dfrac{2}{3}\times m2=-1\\\\m2=-\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7D%5Ctimes%20m2%3D-1%5C%5C%5C%5Cm2%3D-%5Cdfrac%7B3%7D%7B2%7D)
Therefore the slope of the required line passing through (16 , -7) will have the slope,
Now the equation of line in slope point form given by
Substituting the point (16 , -7) and slope m2 we will get the required equation of the line,
Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line
is
You were right already it’s A
Answer:
After 22 seconds the projectile reach its maximum height of 4,840 units
Step-by-step explanation:
we have
![h(t)=-10t^{2}+440t](https://tex.z-dn.net/?f=h%28t%29%3D-10t%5E%7B2%7D%2B440t)
This is a vertical parabola downward (because the leading coefficient is negative)
The vertex is a maximum
Find out the coordinates of the vertex
Convert the quadratic equation in vertex form
Factor -10
![h(t)=-10(t^{2}-44t)](https://tex.z-dn.net/?f=h%28t%29%3D-10%28t%5E%7B2%7D-44t%29)
Complete the square
![h(t)=-10(t^{2}-44t+22^2)+(10)(22^2)](https://tex.z-dn.net/?f=h%28t%29%3D-10%28t%5E%7B2%7D-44t%2B22%5E2%29%2B%2810%29%2822%5E2%29)
![h(t)=-10(t^{2}-44t+22^2)+4,840](https://tex.z-dn.net/?f=h%28t%29%3D-10%28t%5E%7B2%7D-44t%2B22%5E2%29%2B4%2C840)
Rewrite as perfect squares
![h(t)=-10(t-22)^{2}+4,840](https://tex.z-dn.net/?f=h%28t%29%3D-10%28t-22%29%5E%7B2%7D%2B4%2C840)
The vertex is the point (22,4,840)
therefore
After 22 seconds the projectile reach its maximum height of 4,840 units