Answer:
0.7698
Step-by-step explanation:
If you call your random variable
, then what you are looking for is

because you want the probability of
being <em>between 87 and 123.</em>
We need a table with of the normal distribution. But we can only find the table with
and
. Because of that, first we need to <em>normalize </em>our random variable:

(you can always normalize your variable following the same formula!)
now we can do something similar to our limits, to get a better expression:


And we transform our problem to a simpler one:
(see Figure 1)
From our table we can see that
(this is represented in figure 2).
Remember that the whole area below the curve is exactly 1. So we can conclude that
(because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then
.
FINALLY:

The volume of <span>Rectangular prism A is 120 inches and the volume of rectangular prism is 960 inches. the volume of prism b is 8 times the size of prism A</span>
Answer:
Step-by-step explanation:
Okay, so I think I know what the equations are, but I might have misinterpreted them because of the syntax- I think when you ask a question you can use the symbols tool to input it in a more clear way, otherwise you can use parentheses and such.
Problem 1:
(x²)/4 +y²= 1
y= x+1
*substitute for y*
Now we have a one-variable equation we can solve-
x²/4 + (x+1)² = 1
x²/4 + (x+1)(x+1)= 1
x²/4 + x²+2x+1= 1
*subtract 1 from both sides to set equal to 0*
x²/4 +x^2+2x=0
x²/4 can also be 1/4 * x²
1/4 * x² +1*x² +2x = 0
*combine like terms*
5/4 * x^2+2x+ 0 =0
now, you can use the quadratic equation to solve for x
a= 5/4
b= 2
c=0
the syntax on this will be rough, but I'll do my best...
x= (-b ± √(b²-4ac))/(2a)
x= (-2 ±√(2²-4*(5/4)*(0))/(2*(5/4))
x= (-2 ±√(4-0))/(2.5)
x= (-2±2)/2.5
x will have 2 answers because of ±
x= 0 or x= 1.6
now plug that back into one of the equations and solve.
y= 0+1 = 1
y= 1.6+1= 2.6
Hopefully this explanation was enough to help you solve problem 2.
Problem 2:
x² + y² -16y +39= 0
y²- x² -9= 0
Answer:

Step-by-step explanation:
To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

So, the average rate of change of:

Over the interval 
Is:


Therefore, the average rate of change of this function over that interval is 3.
Step-by-step explanation:
-3+m/9=10
m/9=10+3
m/9=13
m=13×9
m=117
<u>N</u><u>o</u><u>t</u><u>e</u><u>:</u><u>i</u><u>f</u><u> </u><u>y</u><u>o</u><u>u</u><u> </u><u>n</u><u>e</u><u>e</u><u>d</u><u> </u><u>t</u><u>o</u><u> </u><u>a</u><u>s</u><u>k</u><u> </u><u>a</u><u>n</u><u>y</u><u> </u><u>question</u><u> </u><u>please</u><u> </u><u>let</u><u> </u><u>me</u><u> </u><u>know</u><u>.</u>