Answer:
the rate compounded semi-annually is compounded twice in a year. thus, this rate is higher than the rate compounded annually which is compounded once in a year
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
For example, there are two banks
Bank A offers 10% rate with semi-annual compounding
Bank B offers 10% rate with annual compounding.
If you deposit $100, the amount you would have after 2 years in each bank is
A = 100x (1 + 0.1/2)^4 = 121.55
B = 100 x (1 + 0.1)^2 = 121
The interest in bank a is 0.55 higher than that in bank B
Dime value: $0.10
Nickel value: $0.05
For this word problem, you are asked to create an algebraic expression (an equation) for the unknown variables.
Now, we know that a dime is worth $0.10 or 10 cents and a nickel is worth $0.05 or 5 cents. So, all you would have to do is create an equation that takes those values into account.
5n + 10d
Your algebraic expression would be B. 5n + 10d
I hope this helps!
The 15th term will be 71. Why? Well, see below for an explanation!
By subtracting all of these numbers by the term that comes prior to them, we will find that all of them result in 5. Because of this, we know that each time the term increases, 5 is being added to the numbers. Additionally, I noticed that all of the numbers in this arithmetic sequence only end in a 1 or a 6. Because of this, we can apply the same principle when adding 5 each time:
First term: 1
Second term: 6
Third term: 11
Fourth term: 16
Fifth term: 21
Sixth term: 26
Seventh term: 31
Eighth term: 36
Ninth term: 41
Tenth term: 46
Eleventh term: 51
Twelfth term: 56
Thirteenth term: 61
Fourteenth term: 66
Fifteenth term: 71
By adding 5 each time and keeping in mind that the digits all end in only 1 or 6, we will find that the fifteenth term results in 71. Therefore, the 15th term is 71.
Your final answer: The 15th term of this arithmetic sequence comes down to be 71. If you need extra help, let me know and I will gladly assist you.
Answer:
10x² + 6x + 3xy + 3y - y²
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, as shown
(2x + y)(5x - y + 3)
= 2x(5x - y + 3) + y(5x - y + 3) ← distributing
= 10x² - 2xy + 6x + 5xy - y² + 3y ( collect like terms )
= 10x² + 6x + 3xy + 3y - y²
