Answer:
(Correct to 4 decimal places)
Step-by-step explanation:
The probability of a continuous normal variable X found in a particular interval [a, b] is the area under the curve bounded by x=a and x=b and is given by:

where




Using a calculator,
The equation for that line is y=x+5
Please refer to my image where it shows my work as I’m explaining.
Okay, for system 1:
1. I am using the elimination method to solve. So I check if all the terms are lined up and if any are the same. I found that 2X are common in both equations.
2. The goal is to “eliminate” the term hence the name. So I can choose to add or subtract. I chose subtraction because 2 - 2 equals 0 which is our goal. Solve for the rest of the terms. This will lead to getting y =4. Refer to image for the work.
3. Last step to to find the X value. We do this by picking any of the given equations,then substitute y with 4 and solve to eventually get x = 10. Refer to image for the work.
FOR SYSTEM 2:
1. Again, I am using the elimination method to solve. I noticed that NONE of the terms are in common so I will have to intervene. You can chose any term to create a match with but I chose Y since it was the one I could use the smallest number to multiply with. When multiplying, DONT just multiply Y, multiply ALL the terms in the equation or else everything will crash.
2. Now that I have terms in common I can choose to add or subtract. I chose subtraction because 2-2 equals zero which is what we want. Solve look at image for my process which lead to X = -8
3. Last step is to find the value of Y. Chose any of the given equations in system 2 then substitute x with -8. Refer to image to see process. It lead to y = 20
To check the validity of the answers, substitute the x and y values into both equations both side of the equal side should have the same number. Hope that helped!
Answer: Does not exist.
Step-by-step explanation:
Since, given function, f(x) = 6x tan x, where −π/2 < x < π/2.
⇒ f(x) = 
And, for vertical asymptote, cosx= 0
⇒ x = π/2 + nπ where n is any integer.
But, for any n x is does not exist in the interval ( -π/2, π/2)
Therefore, vertical asymptote of f(x) where −π/2 < x < π/2 does not exist.
Answer:
2 Times
Step-by-step explanation:
Simon can see two lights A and B
- Light A flashes every 15 seconds.
- Light B flashes every 18 seconds.
First, we determine the next time both lights will flash together.
This is done by finding the Least Common Multiple of 15 and 18.
15=3X5
18=
LCM of 15 and 18=
This means that lights A and B will first flash together after 90 seconds.
Now, 240/90=
seconds
Therefore, the number of times more both light will flash together in the next 4 Minutes= 2 Times