Here is dependence between scores and x-values:
where 
is the mean, 
is standard deviation and i changes from 1 to 2.
1. When i=1, 
then
2. When i=2, 
then
Now solve the system of equations:
Subtract first equation from the second:
Then
Answer: the mean is 62, the standard deviation is 20.
We will form the equations for this problem:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
z = ? Monthly administration fee is notated with z, and that is the this problem's question.
Number of kilowatt hours of electricity used are numbers 1100 and 1500 respectively.
Cost per kilowatt hour is notated with y, but its value is not asked in this math problem, but we can calculate it anyway.
The problem becomes two equations with two unknowns, it is a system, and can be solved with method of replacement:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
----------------------------
(1) z = 113 - 1100*y [insert value of z (right side) into (2) equation instead of z]:
(2) 1500*y + (113 - 1100*y) = 153
-------------------------------------------------
(1) z = 113 - 1100*y
(2) 1500*y + 113 - 1100*y = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y + 113 = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 153 - 113
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 40
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 40/400
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 1/10
------------------------------------------------
if we insert the obtained value of y into (1) equation, we get the value of z:
(1) z = 113 - 1100*(1/10)
(1) z = 113 - 110
(1) z = 3 dollars is the monthly fee.
9514 1404 393
Answer:
c = 81
Step-by-step explanation:
The equation x² -c = 0 can be factored as ...
(x -√c)(x +√c) = 0
which has roots ±√c.
The roots are given as ±9, so we have ...
±9 = ±√c
c = (±9)² = 81
The value c = 81 makes the equation have ±9 as solutions.
Answer:
$351.00
Step-by-step explanation:
P is the principal amount, $900.00.
r is the interest rate, 3.00% per year, or in decimal form, 3.00/100=0.03.
t is the time involved, 13....year time periods.
So, t is 13....year time periods.
To find the simple interest, we multiply 900 × 0.03 × 13 to get the the answer.
Cheers mate!
