Answer:
a) 0.4
b) 0.133
c) 
Step-by-step explanation:
We are given the following information in the question:
The load is said to be uniformly distributed over that part of the beam between 90 and 105 pounds per linear foot.
a = 90 and b = 105
Thus, the probability distribution function is given by
a) P( beam load exceeds 99 pounds per linear foot)
P( x > 99)
![=\displaystyle\int_{99}^{105} f(x) dx\\\\=\displaystyle\int_{99}^{105} \frac{1}{15} dx\\\\=\frac{1}{15}[x]_{99}^{105} = \frac{1}{15}(105-99) = 0.4](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_%7B99%7D%5E%7B105%7D%20f%28x%29%20dx%5C%5C%5C%5C%3D%5Cdisplaystyle%5Cint_%7B99%7D%5E%7B105%7D%20%5Cfrac%7B1%7D%7B15%7D%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Bx%5D_%7B99%7D%5E%7B105%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D%28105-99%29%20%3D%200.4)
b) P( beam load less than 92 pounds per linear foot)
P( x < 92)
![=\displaystyle\int_{90}^{92} f(x) dx\\\\=\displaystyle\int_{90}^{92} \frac{1}{15} dx\\\\=\frac{1}{15}[x]_{90}^{92} = \frac{1}{15}(92-90) = 0.133](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_%7B90%7D%5E%7B92%7D%20f%28x%29%20dx%5C%5C%5C%5C%3D%5Cdisplaystyle%5Cint_%7B90%7D%5E%7B92%7D%20%5Cfrac%7B1%7D%7B15%7D%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Bx%5D_%7B90%7D%5E%7B92%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D%2892-90%29%20%3D%200.133)
c) We have to find L such that
![\displaystyle\int_{L}^{105} f(x) dx\\\\=\displaystyle\int_{L}^{105} \frac{1}{15} dx\\\\=\frac{1}{15}[x]_{L}^{105} = \frac{1}{15}(105-L) = 0.4\\\\\Rightarrow L = 99](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7BL%7D%5E%7B105%7D%20f%28x%29%20dx%5C%5C%5C%5C%3D%5Cdisplaystyle%5Cint_%7BL%7D%5E%7B105%7D%20%5Cfrac%7B1%7D%7B15%7D%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Bx%5D_%7BL%7D%5E%7B105%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D%28105-L%29%20%3D%200.4%5C%5C%5C%5C%5CRightarrow%20L%20%3D%2099)
The beam load should be greater than or equal to 99 such that the probability that the beam load exceeds L is 0.4.
Perpendicular means that the slopes are negartive inverses, aka
slope1 times slope2=-1
y=mx+b
slope=m
y=-1/2x-2
slope=-1/2
we need to find negative inverse
-1/2 times what=-1
answer is 2
y=2x+b
input the point (2,-2) to find b
(x,y)
(2,-2)
-2=2(2)+b
-2=4+b
minus 4 from both sides
-6=b
y=2x-6
the equtaion is y=2x-6
Answer: 7x + 2y + 2
Step-by-step explanation:
4(3x) + 7 - 5x - 5 + 3y - y
= 12x + 7 - 5x - 5 + 3y - y
= 7x + 2y + 2
Answer:
Part a) 
Part b) 
Part c) 
Step-by-step explanation:
<u><em>The complete question is</em></u>
If $10,000 is invested at an interest rate of 10% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
a)6 years
b)12 years
c)18 years
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part a) 6 years
we have
substitute in the formula above
Part b) 12 years
we have
substitute in the formula above
Part c) 18 years
we have
substitute in the formula above
Answer:
(-2, -16)
Step-by-step explanation:
the minimum is at the vertex which can be found using -b/2a for the x-value of the vertex.
y = 3x^2 + 12x - 4
= ax^2 + bx - c
b = 12, a = 3
-12/(2(3))
-12/6
x = -2
y = 3(-2)^2 + 12(-2) - 4
y = -16
(-2, -16)
