Answer:
x cubed minus y cubed is equal to 504
Step-by-step explanation:
First we need to know what the values of x and y are. We can do this pretty easily, by just solving both equations for x, and equating them to each other:
With the first:
x + y = 10
x = 10 - y
And with the other
x - y = 6
x = 6 + y
Now that we have two definitions of x, we can say that the expressions are equal, and solve for y:
10 - y = 6 + y
10 - 6 = y + y
4 = 2y
y = 2
And now that we know what y is, we can find x:
x = 10 - y
x = 10 - 2
x = 8
So x is equal to eight. We can check our answer by plugging x into the other equation and seeing if we get the same value for y:
x - y = 6
8 - y = 6
-y = 6 - 8
-y = -2
y = 2
So we know we solved that correctly.
Now if we cube each number, eight cubed is equal to 512, and 2 cubed is equal to 8. If we subtract the latter from the former we get 504.
so x cubed minus y cubed is equal to 504
Answer:
The probability that the instrument does not fail in an 8-hour shift is 
The probability of at least 1 failure in a 24-hour day is 
Step-by-step explanation:
The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

Let X be the number of failures of a testing instrument.
We know that the mean
failures per hour.
(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:
For an 8-hour shift, the mean is 

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:
For a 24-hour day, the mean is 

Answer:
5 units
Step-by-step explanation:
The <u>volume of the cylinder</u> is the area of the circle multiplied by it's height. Therefore, the volume of the cylinder is πr² × h, which when simplified, gives us πr²h. Let's substitute the volume and the radius in the formula to find the height.
⇒ πr²h = Volume of cylinder
⇒ (π)(3²)(h) = 45π
Now, simplify the equation to evaluate the area of the cylinder.
⇒ (π)(3²)(h)/(3²)(π) = 45π/(3²)(π)
⇒ (h) = 45π/(9)(π) = 45/(9) = 5 units
They equal 5*5=25 and 35*35=1225