(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"
x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)
3x = 12 --> Divide both sides by 3
<u>x = 4
</u>
Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.
(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.
(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards
4(16 - 4d + 4d - d²) = - 80 --> Simplify the expression inside the brackets
4(16 - d²) = - 80 --> Multiply out these brackets by the 4
64 - 4d² = - 80 --> Subtract 64 from both sides
- 4d² = - 144 --> Divide both sides by - 4
d² = 36 --> Square root both sides
<u>d = 6
</u>Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.
<u>
</u><u />1. x - d = 4 - 6 = <u>- 2
</u><u></u>2.<u> x = 4</u>
3. x + d = 4 + 6 = <u>10
</u>
The three terms are - 2, 4, 10.
<u>
</u>
Answer:
a) 13913
b) 4913.82
Step-by-step explanation:
The compound interest formula is given by:
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
In this question:
Investment of 9000, so 
Interest rate of 8%, so 
Compounded quarterly, so 
5 years and 6 months, that is, 5 years and half, so 
(a) How much would the value of her savings at the end of the term?
(b) How much is the interest earned by your savings?
The amount subtracted by the principal. So
13913.82 - 9000 = 4913.82
Answer:
47% of American adult population
Step-by-step explanation:
The reason why polls are carried out is to obtain information that can represent the opinions, status or habits of the population. The polls do not include the total population, then include a small number of participants, but the results are extrapolated to the general population. There are always small margins of error resulting from polls, that is why the confidence levels are usually +/- 3 or 4%.
