Mary deposits $500 into her savings account that earns 5% interest compounded annually. If she makes no additional deposits or withdrawals, how many years will it take for the amount in her account to double?
To arrive at our answer, we need to use the equation, amount=principal*(1+interest rate in decimal form/number of times interest is compounded per year)^number of times interest is compounded per year*time in years [A=P(1+r/n)^nt]. Replacing the proper variables, you get 1000=500(1+0.05/1)^1*t (Why 1000? Because we want to know how long it will take to DOUBLE the principle, which is $500; 500*2=1000). Continuing on, we get 2=1.05^t. Then taking the log of both sides of the equation, we get log(2)=log(1.05)*t. Divide log(2) by log(1.05) and you get t=14.2 years.
Fill in the blank with the proper conjugated form of the verb, (hacer): Estoy _______ mi tarea ahora.
We want to insert the proper form of "to do" (hacer) in the sentence. To conjugate, we take off the "-er" ending and change it to "-iendo", which is the proper ending to make it "doing" (because the event is currently taking place, "ahora"). The verb is coming after a conjugated form of "estar", so the sentence reads: I am _______ my homework now. >> I am doing my homework now.
Expand the following factors (to polynomial form): (3x^2+5)(2x+3).
To expand, we must FOIL the factors: First, Outside, Inside, Last First: 3x^2*2x=6x^3 Outside: 3x^2*3=9x^2 Inside: 5*2x=10x Last: 5*3=15 Put it all together and we get: 6x^3+9x^2+10x+15 (All are plus signs because all of the FOIL outcomes are positive.)