In this question, we're assuming Ralph had 0 in his saving funds to start with.
The glasses cost 1200 dollars.
There are 12 months in a year.
Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.
Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)
1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50
Ralph should have put 50 dollars per pay check to pay for the glasses.
A is your answer.
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Let us assume the number of hours after which the cost of Pam and Michelle will be same = x
Now let us concentrate on the information's already given in the problem.
Fixed charge taken by Pam = $125
Charge per hour taken by Pam = $15
Fixed charge taken by Michelle = $50
Charge per hour taken by Michelle = $20
Then
125 + 15x = 50 + 20x
20x - 15x = 125 - 50
5x = 75
x = 75/5
= 15
So after 15 hours the charge taken by Pam and Michelle will be the same. I hope the procedure for doing this type of problem is clear to you.
You would be able to fill 9 celery pieces
which simplifies to
Step 
<u>Find the slope of the given line</u>
Let
slope mAB is equal to
Step 
<u>Find the slope of the line that is perpendicular to the given line</u>
Let
CD ------> the line that is perpendicular to the given line
we know that
If two lines are perpendicular, then the product of their slopes is equal to 
so
Step 
<u>Find the equation of the line with mCD and the point (3,0)</u>
we know that
the equation of the line in the form point-slope is equal to
Multiply by both sides
therefore
the answer is
the equation of the line that is perpendicular to the given line is the equation
Answer:
f) a[n] = -(-2)^n +2^n
g) a[n] = (1/2)((-2)^-n +2^-n)
Step-by-step explanation:
Both of these problems are solved in the same way. The characteristic equation comes from ...
a[n] -k²·a[n-2] = 0
Using a[n] = r^n, we have ...
r^n -k²r^(n-2) = 0
r^(n-2)(r² -k²) = 0
r² -k² = 0
r = ±k
a[n] = p·(-k)^n +q·k^n . . . . . . for some constants p and q
We find p and q from the initial conditions.
__
f) k² = 4, so k = 2.
a[0] = 0 = p + q
a[1] = 4 = -2p +2q
Dividing the second equation by 2 and adding the first, we have ...
2 = 2q
q = 1
p = -1
The solution is a[n] = -(-2)^n +2^n.
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g) k² = 1/4, so k = 1/2.
a[0] = 1 = p + q
a[1] = 0 = -p/2 +q/2
Multiplying the first equation by 1/2 and adding the second, we get ...
1/2 = q
p = 1 -q = 1/2
Using k = 2^-1, we can write the solution as follows.
The solution is a[n] = (1/2)((-2)^-n +2^-n).
