Answer:
The number of nickel coins is 10 and the number of quarter coins is 5
Step-by-step explanation:
<u><em>The correct question is</em></u>
Mary has 15 coins with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there
Let
x ----> the number of nickel coins
y ----> the number of quarter coins
Remember that


we know that
Mary has 15 coins
so
-----> equation A
The total value of the coins is $1.75
so
----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (10,5)
therefore
The number of nickel coins is 10 and the number of quarter coins is 5
Let's say that the value invested in the account with a rate of 8% is "x", then the amount invested in the account with a rate of 12% is:

To calculate the total interest we need to calculate the interest of each individual account and sum them:

The total interest is the sum of the two expressions above:

The value invested in the account with 8% interest is 830, the one invested in the account with 12% interest is 1280.
Answer:
<u>b(n) = -11 + (n-1)*8</u>
<u></u>
Step-by-step explanation:
Let n be the sequence number, with n=1 the first number b(1) -11
The sequence changes by +8 each step.
<u><em>b(1)</em></u><em> -11</em> + 8 = -3
<u><em>b(2)</em></u><em> -3</em> + 8 = 5
<u><em>b(3)</em></u> <em> 5 </em> + 8 = 13
<u><em>b(4)</em></u><em> </em> <em>13</em>
b(1) = -11
b(2) = -3. or b(1) + 1*8
b(3) = 5, or b(1) + 2*8
b(4) = 13, or b(1) + 3*8
We note that each step adds a multiple of 8 to the initial value of -11. This can be stated as (n-1)*8
The formula for this sequence would be b(n) = b(1) + (n-1)*8
<u>b(n) = -11 + (n-1)*8</u>
Check: Does n=3 return the value of 5?
b(n) = -11 + (n-1)*8
b(3) = -11 + ((3)-1)*8
b(3) = -11 + (2)*8
b(3) = -11 + 16
b(3) = 5 <u><em>YES</em></u>