Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(5869)
(Show Source):
You can
put this solution on YOUR website!10 years is 120 monthly payments
find the total of the payments
subtract 8400 to find the interest
divide the interest by 10 to find the annual interest
divide the annual interest by 8400 to find the percentage (interest rate)
Answer by josmiceli(6766) 
(Show Source):
You can
put this solution on YOUR website!10 years times 12 months/yr = 120 payments
The total interest paid is
This is the interest over 10 yrs, so the annual
interest is
---------------
The annual interest rate is
The annual interest rate is 7.5%
Hope I got it
Question 424976: 1. Mike’s Sport Shop deposits $3,600 at the end of each year for 12 years at 7% annual interest.
a. How much will this ordinary annuity be worth at the end of the 12 years? (5 points)
Answer:
b. How much more will this annuity be worth (annuity due) if Mike deposits the money at the beginning of each year instead of at the end of each year? (5 points)
Answer:
2. Barb and John Reed want to know how much they must deposit in a retirement savings account today to have payments of $1,750 every six months for 15 years. The retirement account is paying 8% annual interest, compounded semiannually. (5 points)
Answer:
3. Lena Dimock is saving for her college expenses. She sets aside $200 at the beginning of each three months in an account paying 8% annual interest, compounded quarterly. How much will Lena have accumulated in the account at the end of four years? (5 points)
Answer:
Part II. Case Study
Julie has just completed the rigorous process of becoming a Certified Financial Planner (CFP). She is looking forward to working with individuals on saving for retirement. She would like to show her clients the value of an annuity program as one of the best options for investing current earnings in a tax-deferred account.
1. If a client puts the equivalent of $55 per month, or $660 per year, into an ordinary annuity, how much money would accumulate in 20 years at 3% compounded annually? (5 points)
Answer:
2. Jackie, a 25 year old client, want to retire by age 65 with $2,000,000. How much would she have to invest annually, assuming a 6% rate of return? (5 points)
Answer:
3. Another client, Wynona, decides that she will invest $5,000 per year in a 6% annuity for the first ten years, then $6,000 for the next ten years, and then $4,000 per year for the last ten years, how much will she accumulate? [Hint: Treat each ten-year period as as separate annuity and compute the Future Value. After the ten years, assume that the value will continue to grow at compound interest for the remaining years of the 30 years. Use tables from Unit 6 to compute compound interest.
Answer by Hyot(1)
(Show Source):
You can
put this solution on YOUR website!3. Lena Dimock is saving for her college expenses. She sets aside $200 at the beginning of each three months in an account paying 8% annual interest, compounded quarterly. How much will Lena have accumulated in the account at the end of four years? (5 points)
Answer: Number of years times number of intrest periods per year = 4(4) = 16
Annual intrest rate/Number of periods per year = 8/4 = 2%
$200 ( 1.37279) = $274.558
Question 568880: Over 5 years, the total value of a mutual fund account decreases continuously by 15%. find a formula A(x) that calculates the amount of money in the account after x years.
Answer by stanbon(48498) (Show Source):
You can
put this solution on YOUR website!Over 5 years, the total value of a mutual fund account decreases continuously by 15%. find a formula A(x) that calculates the amount of money in the account after x years.
------
Each year 85% of the value of the fund survives.
---
After one year you have 0.85A
After two year you have (0.85^2)A
---
After x years you have (0.85^x)A
----
Equation:
V(x) = (0.85^x)A
=======================
Cheers,
Stan H.
=============
Question 568365: The solution to | 4x | + 3 < 0 is which of the following?
Answer by richard1234(4783) 
(Show Source):
You can
put this solution on YOUR website!|4x| < -3
However, absolute value is always nonnegative, so the absolute value of something can't be "less" than -3. Therefore there are no solutions.
Question 567610: Assume your planning to invest $5000 each year for 6 years earning 10% per year. What is the future value in the first $5000 invested?
Please help solve future value in the first $5000 invested.
Here is what I've thus far:
Future Value = present value X [(1 + interest rate) x (number of years)]
FV= $5000 x (1 + .010 x 6)
FV = $5000 x 1.010 x 6)
FV = $5000 x 6.06
FV = $30,300
30,300 - 30,000 = 300.00 / 6 = $50.00
First year $5000 investment is worth 5,050.00
Answer by bucky(2097) (Show Source):
You can
put this solution on YOUR website!The basic question is that if you invest $5000 at an annual interest rate of 10 percent, what will that investment be worth at the end of 6 years? This presumes that you let the $5000 stay invested for the full 6 years and that all annual dividends stay invested and draw interest also.
.
That being the case, the general formula for calculating such a future value is:
.
.
And the variables are defined as follows:
.
P = Future Value
C = Initial Deposit
R = Annual Interest Rate expressed as a decimal (example 6% = 0.06)
N = The number of times per year the interest is compounded
T = The number of years that the initial deposit remains invested
.
For this problem you are to solve for P, the Future Value. C the Initial Deposit is $5000. R the Annual Interest Rate is 10% or 0.10. N is the number of times per year that the interest is calculated. Although the problem doesn't say so directly, it appears that the interest is awarded at the end of each year. That being the case, N equals 1 for one time per year. And finally, T is the number of years that the $5000 remains invested, which in this case is 6 full years.
.
Substitute these values into the general equation and it becomes:
.
.
which when you account for the fact that N = 1, simplifies to:
.
.
Combining the two terms in the parentheses reduces the equation to:
.
.
If you raise 1.1 to the 6th power (the same as multiplying 1.1 times itself six times) using a calculator you get 1.771561. Substituting this into the equation you now have:
.
.
Using a calculator to multiply out the right side gives you the answer:
.
.
which rounds off to an answer of:
.
or P = $8,857.81
.
What you are doing by using this formula is to recognize that after the first year, you get 10% interest on your $5000 investment. (10% of $5000 is $500.) So at the end of the first year, you will have a total of $5500 in the bank. That stays invested so at the end of the second year, you get 10% of that or $550 in interest. That added to the $5500 that was in your account for the second year means that at the end of the second year you have $6050 in your account which remains invested during the entire third year. At the end of the third year the $6050 draws $605 in interest. This added to the $6050 results in your account at the end of the third year being $6050 + $605 = $6655. In the fourth year the $6655 is invested at 10% and so it earns $665.50 of interest. Adding that to the $6655 you had invested during the year gives you a total of $6655 + $665.50 which, at the end of the fourth years gives you $7320.50. During the fifth year the $7320.50 earns 10% interest. That means that at the end of the fifth year you add interest of $732.05 to the $7320.50 in your account to get a total amount of $8052.55. This amount remains invested throughout the sixth year so that at the end of the sixth year, 10% interest amounts to $805.255 which is then added to the $8052.55 resulting in a total of $8857.805. Note that this agrees exactly with the Future Value that we got by using the formula, and it checks out our answer.
.
Write down the future value equation and the definition of all its variables. It's likely that you will be able to use this formula again in similar problems.
.
Note that 10% converts to 0.10 in decimal form, not to 0.01 as you indicated in your work. And also note that if you had multiplied 1.1 times 6 you would have gotten a future value of $33,000. This is way too high. I'm not sure why you then divided that future value by 6, but if you did the answer would have been $5,500 which is too low when compared to the answer of $8857.81.
.
You can always approximate the answer by multiplying the annual percentage rate times the number of whole years. Then take that answer and multiply it by the original investment. That will give you only an approximate amount of interest earned over the 6 years of investment and you add that to the original investment. In this case 10% or 0.1 times 6 years = 0.6. Multiply that by the original investment of $5,000 and it tells you that the $5,000 will earn $3,000 in 6 years. So at the end of 6 years your account will have $5,000 + $3,000 = $8,000. Gives you a rough idea of what the actual answer should be, but as you can see it is "rough" because it's $857.81 lower than it should be.
.
I hope this helps you to understand the problem a little better and also to see how to use the formula to solve it. Keep working on this. In real life you absolutely need to understand how to work with your money to your advantage! You might try this problem again only using a 0.1% interest rate that banks are paying today on savings accounts. (Yes, that's right. One-tenth of 1% or a rate of 0.001). See how little your $5,000 will return in 6 years. The answer is that in 6 years you will have $5030.08 in your account, about $3,827 less than you would have at a 10% interest rate for the same period. Be smart. Lack of knowledge can be expensive.
.
Good Luck with this!!!
Question 564055: You have $10,000 which you will invest for the next four years. You are considering the following investment alternatives:
(I) Purchase units in a bond mutual fund which pays $210 interest quarterly. Assume that the
interest is reinvested at the coupon rate.
(II) Purchase a 4-year guaranteed investment certificate which pays 3 percent compounded
monthly.
(III)Invest in a stock which promises the following cash flows:
Year 1 $ 0
Year 2 500
Year 3 750
Year 4 2,000
(a)Assume that at the end of year 4, you will get back your $10,000. Which investment alternative do you prefer? Why?
(b)What factors, other than the rate of return, should you consider in making your investment decision?
Answer by cp24(1) (Show Source):
You can
put this solution on YOUR website!You have $10,000 which you will invest for the next four years. You are considering the following investment alternatives:
(I) Purchase units in a bond mutual fund which pays $210 interest quarterly. Assume that the
interest is reinvested at the coupon rate.
(II) Purchase a 4-year guaranteed investment certificate which pays 3 percent compounded
monthly.
(III)Invest in a stock which promises the following cash flows:
Year 1 $ 0
Year 2 500
Year 3 750
Year 4 2,000
(a)Assume that at the end of year 4, you will get back your $10,000. Which investment alternative do you prefer? Why?
(b)What factors, other than the rate of return, should you consider in making your investment decision?
Question 567208: Frank buys last years best-selling novel, in hardcover, for $14.70. this is with a 30% discount from the original price,what was the original price of the novel?
Answer by nerdybill(5399) 
(Show Source):
You can
put this solution on YOUR website!Frank buys last years best-selling novel, in hardcover, for $14.70. this is with a 30% discount from the original price,what was the original price of the novel?
Let x = original price
then
x - .30x = 14.70
x(1 - .30) = 14.70
x(.70) = 14.70
x = 14.70/.70
x = $21
Question 567012: William opened two investment accounts for his grandson’s college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was invested at each rate?
Answer by mananth(10539) 
(Show Source):
You can
put this solution on YOUR website!Investment Part I 5.50% per annum ----x
Investment part II 4.00% per annum ----y
The sum of the investments is $18,000.00
The sum of individual interests = $831.00
x+y 18000 ------------------------1
5.50%x +4.00%y = $831.00
Multiply by 100
5.5x + 4y = $83,100.00 --------2
Multiply (1) by -5.5
we get
-5.5x -5.5y =-99000.00
Add this to (2)
0x -1.5y =-$15,900.00
divide by-1.5
y = $10,600.00 investment at 4.00%
Balance $7,400.00 investment at 5.50%
CHECK
$7,400.00 @ 5.50% $407.00
$10,600.00 @ 4.00% $424.00
Total -------------------- $831.00
Question 566071: Lowell purchased a motorcycle for $17,011. It depreciates about 3.9% each year. What is the value of the motorcycle after eight years?
Answer by Alan3354(21539) 
(Show Source):
You can
put this solution on YOUR website!Lowell purchased a motorcycle for $17,011. It depreciates about 3.9% each year. What is the value of the motorcycle after eight years?
-----------
100% - 3.9% leaves 96.1% of its value = 0.961*worth of the previous year.
value @ years = 17011*(0.961)^8
=~ $12374.19
Question 565566: This really confuses me since it showed be put in the formula I=prt. If this was explained that would help! Thanks.
Madison invested $50,000 for two years. A part of this investment had 10% annual interest and the rest was invested at 15% annual interest. The interest from the investment at 10% was $350 more than the interest from the investment at 15%. How much did she invest at 10%? How much did she invest at 15%?
Answer by lwsshak3(2900) (Show Source):
You can
put this solution on YOUR website!Madison invested $50,000 for two years. A part of this investment had 10% annual interest and the rest was invested at 15% annual interest. The interest from the investment at 10% was $350 more than the interest from the investment at 15%. How much did she invest at 10%? How much did she invest at 15%?
**
I=prt, p=initial investment, r=annual rate of interest, and I=amt after t years
..
let x=$ amt invested at 10%
50000-x=$ amt invested at 15%
..
At 10%
I=(10%*2)x=.2x
At 15%
I=(15%*2)(50000-x)=(15000-.3x)
Since the 10% investment made $350 more than the 15% investment,
.2x-(15000-.3x)=350
.2x-15000+.3x=350
.5x=15350
x=30700
50000-x=19300
ans:
amt invested at 10%=$30,700
amt invested at 15%=$19,300
Question 565509: A salesperson's weekly paycheck is 25% more than a second salesperson's paycheck. The two paychecks total $1675. Find the amount of each paycheck. (Round your answers to the nearest cent.)
Answer by ad_alta(170)
(Show Source):
You can
put this solution on YOUR website!Let 'p' be the smaller paycheck and 'P' the larger paycheck. Then P=1.25p and P+p=1675. Substituting, 1.25p+p=1675. Thus, p=$744.44 and P=$930.56.
Question 565226: Eliana has $2600 to invest for 6 months. If she needs the money to earn $104 in that time, at what rate of simple interest must Eliana invest.
Answer by rfer(10417) (Show Source):
Question 563742: a person borrows $10000 and agrees to repay the loan in equal instalments over 20 years. interest is 12% per annum on any money owing
A) what is the amount of each repayment, if the repayment are made
i) annually, ii) quarterly, iii) monthly, iv) weekly
B) which is the cheapest of the four methods of repayment in (A)
Answer by Theo(2958) 
(Show Source):
You can
put this solution on YOUR website!person borrows $10,000
pays back loan in equal installments.
interest is 12% per year.
amount of repayments if:
annually = 1338.79
quarterly = 331.12
monthly = 110.11
weekly = 25.39
total paid with each method is:
annually = 1338.79 * 20 - 10000 = 16775.8
quarterly = 331.12 * 20 * 4 - 10000 = 16489.6
monthly = 110.11 * 20 * 12 - 10000 = 16426.4
weekly = 25.39 * 20 * 52 - 10000 = 16405.6
the cheapest of the four methods is paying every week.
this is because the balance goes down with each payment so the total interest paid becomes less.
here's an example:
loan is 10000
interest is 10% per year.
loan is paid off in one year.
yearly payments
each payment is 10100.
balance is 10000 * 1.10 = 10100 at the end of the year.
you make a payment of 10100 at the end of the year and the balance becomes 10100 - 10100 = 0.
total interest paid is 1 * 10100 - 10000 = 100.
semi-annual payments.
interest rate is 10% / 2 = 5% every 6 months.
each payment is 5378.04878.
balance is 10000 * 1.05 = 10500 at the end of 6 months.
you make a payment of 5378.04878 at the end of 6 months and the balance becomes
10500 - 5378.04878 = 5121.95122
balance is 5121.95122 * 1.05 = 5378.04878 at the end of 12 months.
you make a payment of 5378.04878 at the end of 12 months and the balance becomes 5378.04878 - 5378.04878 = 0
total interest paid is equal to 2 * 5378.04878 - 10000 = 756.09756
total interest is less because the interest rate is being applied to the remaining balance and the remaining balance becomes less after each payment.
10% of 10000 = 100
5% of 10000 = 500 and then 5% of 5121.95122 = 256.09756 for a total interest of 756.09756
Question 563155: I buy a tank of gas for $41.56. That price is the actual cost of the gas plus
6.25% sales tax. How much sales tax did I pay? How much was the actual price of the gas?
Answer by htmentor(579)
(Show Source):
You can
put this solution on YOUR website!The price paid is the cost of the gas plus the tax
If c = the cost of the gas then the tax paid = 0.0625*c
So the total price = c + 0.0625c = 41.56
c(1+0.0625) = 41.56
c = 41.56/1.0625
c = 39.16
So the actual price of the gas is $39.12
The tax is 41.56 - 39.12 = $2.44
Question 561935: Can you please help me solve 60= [400/(1+r)^3 for r?
Answer by ankor@dixie-net.com(12678) 
(Show Source):
You can
put this solution on YOUR website!solve 60 = [400/(1+r)^3 for r?
:
multiply both sides by (1+r)^3
60(1+r)^3 = 400
:
divide both sides by 60
(1+r)^3 =
(1+r)^3 = 6.667
:
find the cube root of both sides
Using a calc
1 + r = 1.882
;
subtract 1 from both sides
r = 1.882 - 1
r = .882
Question 560716: Please help solve this problem. A couple plans to save for their childs' college education. What principal must be deposited when their child is born in order to have $100,000 when the child turns 18? Assume the money earns 4% interst compounded quarterly.
Answer by stanbon(48498) (Show Source):
You can
put this solution on YOUR website!What principal must be deposited when their child is born in order to have $100,000 when the child turns 18? Assume the money earns 4% interst compounded quarterly.
-------
A(t) = P(1+(r/n))^(nt)
-----
100,000 = P(1+(0.04/4))^(4*18)
----
100,000 = P(1.01)^(72)
----
100,000 = P(2.0471)
P = $48,849.61
=======================
Cheers,
Stan H.
=======================
Question 559161: What is the model for unkowns for this problem: Mrs. B invested $30,000: part at 5%, and part at 8%. The total interest on the investment was $2100. How much did she invest at each rate?
I started here: $30,000-x=7
x=.05
y=.08
Stuck now...
Answer by scott8148(5869) (Show Source):
You can
put this solution on YOUR website!x + y = 30000 ___ x = 30000 - y
(5%)x + (8%)y = 2100
substituting ___ (.05)(30000 - y) + (.08y) = 2100 ___ 1500 + .03y = 2100
solve for y; then substitute back to find x
Question 559038: The park had initially planned to charge $8 for admission and expected to have 2400 visitors a day. Allison and Hannah were assigned the task of analyzing the parks admission revenues.
a) How much revenue would the park have for one day at the current price?
b) Market research shows for every $0.50 the admission price is raised, the park will have 80 fewer visitors. How much would you expect the park revenue to be if the park raised their admission price by $1?
After a few calculations, Allison and Hannah realize the park will make more money if they raise the price of admission. However, they also understand that there must be a limit to how much the park can charge.
As a result, they model the situation with the equation, R = (2400 - 80x)(8 + 0.5x), where R represents the revenue from sales and x represents the number of price increases.
Use this Factored form Quadratic equation to solve for the zeroes, and then use the zeroes to calculate the number of price increases that will generate the maximum Revenue.
Now demonstrate a second strategy for solving such a problem. This process will ultimately double check your results from above...
a) Express this same Quadratic R = (2400 - 80x)(8 + 0.5x), in Standard form: R = ax2 + bx + c.
b) Complete the Square to again determine the number of price increases that will generate the maximum Revenue.
c) What is the Maximum Revenue that can be generated? (from just looking at your results!)
I would be
GRateful for any help you give me
Answer by stanbon(48498) (Show Source):
You can
put this solution on YOUR website!The park had initially planned to charge $8 for admission and expected to have 2400 visitors a day. Allison and Hannah were assigned the task of analyzing the parks admission revenues.
a) How much revenue would the park have for one day at the current price?
2400*8 = $19200
-------------------------
b) Market research shows for every $0.50 the admission price is raised, the park will have 80 fewer visitors. How much would you expect the park revenue to be if the park raised their admission price by $1?
(8+2*0.50)*(2400-2*80) = $20160
------------------------------------------
After a few calculations, Allison and Hannah realize the park will make more money if they raise the price of admission. However, they also understand that there must be a limit to how much the park can charge.
As a result, they model the situation with the equation, R = (2400 - 80x)(8 + 0.5x), where R represents the revenue from sales and x represents the number of price increases.
Use this Factored form Quadratic equation to solve for the zeroes, and then use the zeroes to calculate the number of price increases that will generate the maximum Revenue.
Revenue = (2400 - 80x)(8 + 0.5x)
Zeroes:
2400-80x = 0 when x = 30
8+0.5x = 0 when x = -16
Mid-value = c = (30-16)/2 = 7
-----------------------------------
Maximum Revenue = ?
R(x) = (2400 - 80x)(8 + 0.5x)
R(x) = -40x^2+1200x-640x+8*2400
R(x) = -40x^2+560x+19200
Max occurs when x = -b/(2a) = -560/(80) = 7
R(7) = (2400-560)(8+3.5) = $21,160
----------------------------------------------------
Now demonstrate a second strategy for solving such a problem. This process will ultimately double check your results from above...
a) Express this same Quadratic R = (2400 - 80x)(8 + 0.5x), in Standard form: R = ax2 + bx + c.
R = -40x^2+560x+19200
b) Complete the Square to again determine the number of price increases that will generate the maximum Revenue.
R = -40(x^2-14x+49)+19200+40*49
R = -40(x-7)^2 + 21160
-------------------------------
c) What is the Maximum Revenue that can be generated? (from just looking at your results!)
Max = $21160
==================
Cheers,
Stan H.
======================
Question 557815: A man invested $100,000. Part of it is invested at 10% and the rest at 8%. If the total income is $8800, how mush did he invest at 10%?
Answer by mananth(10539) (Show Source):
You can
put this solution on YOUR website!Investment I 10.00% per annum ----x
Investment II 8.00% per annum ----y
x+y= 100000 ------------------------1
10.00% x+8.00% y=$8,800.00
Multiply by 100
10x+8y= $880,000.00 --------2
Multiply (1) by -10
we get
-10x-10 y =-1000000.00
Add this to (2)
-2 y = -$120,000.00
divide by -2
y = $60,000.00 investment at 8.00%
Balance $40,000.00 investment at 10.00%
CHECK
$40,000.00 $4,000.00
$60,000.00 $4,800.00
Total $8,800.00
Question 557336: iF THE RATE OF DEPRECIATION IS APPROX. 30% how do I find the decay factor?
Answer by Theo(2958) (Show Source):
You can
put this solution on YOUR website!rate of depreciation per year is 30%.
that might also be equivalent to rate of decay.
b^x formula or you can use e^kx formula.
they will both provide you with the same answer.
b^x formula takes your value and raises it to an exponent for the number of time periods of your decay.
assume your original value is 100.
you have 30% depreciation / decay per year.
using the b^x factor, your formula would be:
f = p * (1 - decay factor) raised to the number of time periods.
with your numbers, that formula would be:
f = 100 * (.7)^n
if n = 0, then f = 100
if n = 1 then f = .70 * 100 = 70
if n = 2 then f = .70 * 70 = 49
etc.
using the e^kx factor, your formula would be:
first you would need to find the value of k.
you would do this by using a known decay and finding out what k is.
example:
you know that 30% decay after the first year results in 70
you would use this fact to find the value of k as follows:
70 = 100 * e^kx
e is the scientific constant of 2.718281828...
you would divide both sides of this equation by 100 to get:
.7 = e^(k*1)
you would then take the natural log of both sides of this equation to get:
ln(.7) = ln(e^k)
by the laws of logarithms, this becomes:
ln(.7) = k*ln(e)
since ln(e) = 1, this formula becomes:
ln(.7) = k
you would then find the natural log of .7 to get:
k = -.356674944
that's the value of k that would be used if you are using the e^kx formula.
let's see how both formulas work.
your starting value is 100
your decay factor is .3 per year.
you want to know the end value after 15 years.
using the b^x formula, you would do the following:
f = p * (.7)^15 which becomes:
f = 100 * (.7)^15 which becomes:
f = .474756151
using the e^kx formula, you would do the following:
f = p * e^kx
k = -.356674944
f = p * e^(-.356674944*15) which becomes:
f = 100 * e^(-.356674944*15) which becomes:
f = 100 * e^(-5.350124159) which becomes:
f = .474756151
you get the same answer either way.
the e^kx formula is used a lot in scientific studies.
the b^x formula, in this case, will provide the same answer as the e^kx formula.
Question 557030: What is "k" in -4x + 2y = -2 and how do I get it?
Answer by richard1234(4783) (Show Source):
Question 556991: How can I tell whether -4x + 2y = -2 represents a direct variation?
Answer by stanbon(48498) (Show Source):
You can
put this solution on YOUR website!How can I tell whether -4x + 2y = -2 represents a direct variation?
-----
2y = 4x - 2
y = 2x -1
----
As x increases, y increases.
x and y are directly related.
---
Note: Every linear function expresses a direct variation.
===========================================================
Cheers,
Stan H.
---------
Question 556113: algebraic expression in verbal expression
the sum of b and 21
Answer by fcabanski(385) (Show Source):
You can
put this solution on YOUR website!Sum means add.
21+b
If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com
Question 554413: A waiter earns $10 in tips plus $5 per hour. This is represented by the function y=10+5x. What happens to the graph of the line if the waiter earns $5 per hour but only $3 in tips??
Answer by Theo(2958) (Show Source):
You can
put this solution on YOUR website!the equation of the first line is y = 5x + 10
the equation of the second line is y = 5x + 3
the second equation is parallel to the first equation because the slope is the same.
the total value of the second line will always be 7 less than the total value of the first line.
for example:
when x = 5, y1 = 35 and y2 = 28 for a difference of 35 - 28 = 7
when x = 50, y1 = 260 and y2 = 253 for a difference of 260-253 = 7
this is because the amount of tips are assumed to be fixed at 10 and 3.
this is not realistic, but it's the way the problem was posed.
Question 553978: A university bookstore recently sold a wirebound graph-paper notebook for $1.64, and a college-ruled notebook for $1.17. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $66.02. How many of each type were sold?
Answer by lwsshak3(2900) (Show Source):
You can
put this solution on YOUR website!A university bookstore recently sold a wirebound graph-paper notebook for $1.64, and a college-ruled notebook for $1.17. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $66.02. How many of each type were sold?
**
let x=number of $1.64 notebooks sold
let (50-x)=number of $1.17 notebooks sold
..
1.64x+1.17(50-x)=66.02
1.64x+58.50-1.17x=66.02
.47x=7.52
x=16
50-x=34
ans:
number of $1.64 notebooks sold=16
number of $1.17 notebooks sold=34
Question 553296: How long will it take money to double if it invested at the following rates:
(1) 5.9% compounded quarterly.
(2) 6.3% compounded quarterly.
Thanks!
SuperDuper
Answer by mananth(10539) (Show Source):
You can
put this solution on YOUR website!Principal P = 100
Amount= 200
years=n
compounded (t) 4
Rate = 5.9 0.01
Amount = P*((n+r)/n)^n
200 = 100 *( 1 + 0.01 )^ n*t
2 = *( 1 + 0.01 )^ n* 4
ln 2 = 4 n *ln 1.01
0.69 = 4 0.01 *n
11.83 = n
11.83 years
-------------------------
Principal P = 100
Amount= 200
years=n
compounded (t) 4
Rate = 6.3 0.02
Amount = P*((n+r)/n)^n
200 = 100 *( 1 + 0.02 )^ n*t
2 = *( 1 + 0.02 )^ n* 4
ln 2 = 4 n *ln 1.02
0.69 = 4 0.02 *n
11.09 = n
Question 553175: how do I simpllfy this
7x+ 13X+ 80
Answer by stanbon(48498) (Show Source):
Question 551533: como se puede saber si el resultado que uno busca es correcto o incorrecto
Answer by Earlsdon(6098) (Show Source):
Question 550507: Jessica has 81% more money today than she did this time last year. If Jessica has $94 today, how much money did she make over this past year?
Answer by Alan3354(21539) (Show Source):
You can
put this solution on YOUR website!Jessica has 81% more money today than she did this time last year. If Jessica has $94 today, how much money did she make over this past year?
------------
You have to define the relationship between the money she made and the money she has.
Question 550345: ?*0.3294=$3500.00
Answer by nyc_function(2626) 
(Show Source):
Question 549708: Show that the number of permutations which can be formed from 2n letters which are either a's or b's is greatest when the number of a's is equal to the number of b's.
Answer by Theo(2958) (Show Source):
You can
put this solution on YOUR website!assume the number of letters is equal to 4.
you can have:
0 a's and 4 b's
1 a and 3 b's
2 a's and 2 b's
3 a's and 1 b
4 a's and 0 b's
when you have 0 a's and 4 b's, the permutation formula is:
4! / (0!*4!) = 1 possible permutations.
that would be:
bbbb
when you have 1 a and 3 b's, the permutation formula is:
4! / (1!*3!) = 4 possible permutations.
that would be:
abbb
babb
bbab
bbba
when you have 2 a's and 2 b's, the permutation formula is:
4! / (2!*2!) = 6 possible permutations.
that would be:
aabb
abab
abba
bbaa
baba
baab
when you have 3 a's and 1 b, the permutation formula is:
4! / (3!*1!)
this is the same as 4! / (1!*3!) which we already did to get you a total of 4 possible permutations.
that would be:
aaab
aaba
abaa
baaa
when you have 4 a's and 0 b's, the permutation formula is:
4! / (4!*0!)
this is the same as 4! / (0!*4!) which we already did to get you a total of 1 possible permutation.
that would be:
aaaa
the formula peaks when the number of a's and b's is equal and goes symmetrically down from there on both sides of the peak.
this is characteristic of the formula.
it works with any number of a's and b's.
Question 549512: Find the sum of all numbers greater than 10000 formed by using the digits 1,3,5,7,9, no digits being repeated in any number.
Answer- 6666600
Answer by Edwin McCravy(6927) 
(Show Source):
You can
put this solution on YOUR website!Here's why:
Suppose you had this long list of them to add:
13579
13597
13759
.....
.....
97351
97513
97531
------
There would be 5! or 120 numbers to add. Each vertical column of digits
contains an equal number of 1's, 3's, 5's, 7's and 9's. So since 120÷5
is 24, the sum of each column is 24×(1+3+5+7+9) = 600, The first column
represents 10000's, the 2nd column represents 1000's, etc. Therefore the
sum is:
600×10000 + 600×1000 + 600×100 + 600×10 + 600 =
600×(10000 + 1000 + 100 + 10 + 1) =
600×(11111) = 6666600
Edwin
Question 549276: A DVD costs 7 times what you get when if you add the number of $ in it's price to the number of cents. This gives it's price in cent . What is it ? Thanks.
Answer by ankor@dixie-net.com(12678) (Show Source):
You can
put this solution on YOUR website!A DVD costs 7 times what you get when if you add the number of $ in it's price to the number of cents.
This gives it's price in cent. What is it?
:
Let d = no. of dollars
Let c = no. of cents
:
100(d+.01c) = 7(d+c)
100d + c = 7d + 7c
100d - 7d = 7c -c
93d = 6c
c =
d
reduce the fraction
c =
d
we can see that an integer solution is possible when d = 2, then c = 31
Actually we have 3 integer solutions from this equation (c has to be less than 100)
DVd cost:
d . c
$2.31, 7(2+31) = 231 cents
$4.62, 7(4+62) = 462 cents
$6.93, 7(6+93) = 693 cents
Question 548388: Find the amount that results from the investment. Use the formula A=Pert or A=P(1+r/n)nt.
$480 invested at 10% compounded quarterly after a period of 8 years
Answer by rfer(10417) (Show Source):
Question 548387: A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $34.29. The second group bought 5 slices of pizza and 7 soft drinks for $24.87. How much does one slice of pizza cost?
Answer by mananth(10539) (Show Source):
You can
put this solution on YOUR website! cost/unit
pizza x
soft drink y
Total 750
8 x + 7 y = 34.29 .............1
5 x + 7 y = 24.87 .............2
Eliminate y
multiply (1)by -1
Multiply (2) by 1
-8 x -7 y = -34.29
5 x + 7 y = 24.87
Add the two equations
-3 x = -9.42
/ -3
x = 3.14
plug value of x in (1)
8 x + 7 y = 34.29
25.12 + 7 y = 34.29
7 y = 34.29 -25.12
7 y = 9.17
y = 1.31
pizza $ 3.14
soft drink $ 1.31
m.ananth@hotmail.ca
Question 547066: how can 56000 be invested part at 4% annual simple interest ant the remainder at 10% annual simple interest so that the interest erned by the two accounts is equal at the end if the year
Answer by mananth(10539) (Show Source):
You can
put this solution on YOUR website!x+y=56000
x@ 4%
y@10%
0.04x = 0.1y
0.04x-0.1y=0
x+y=56000 .............1
0.04x-0.1y=0 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by 10
1 x 1 y = 56000
0.4 x + -1 y = 0
Add the two equations
1.4 x = 56000.000
/ 1.4
x = 40000
plug value of x in (1)
1 x + 1 y = 56000
40000 + 1 y = 56000
1 y = 56000 -40000
1 y = 16000
y = 16000
4000@4%
16000@10%
Question 545751: A total of $12,000 is invested in two funds paying 3% and 3.4% simple interest. The annual interest is $378. How much is invested in each fund?
Can you show the steps as well so I can figure out how to do it myself? Thank you!
Answer by mananth(10539) (Show Source):
You can
put this solution on YOUR website!Fund A 3.00% per annum ---x
Fund B 3.40% per annum ---y
x + y= 12000 ------------------------1
3.00% x + 3.40% y= = $378.00
Multiply by 100
3 x + 3.4 y= = $37,800.00 --------2
Multiply (1) by -3
we get
-3 x -3 y= = -36000.00
Add this to (2)
0 x 0.4 y= = $1,800.00
divide by 0.4
y = $4,500.00 investment at 3.40%
Balance $7,500.00investment at 3.00%
CHECK
$7,500.00 --------- 3.00% ------- $225.00
$4,500.00 ------- 3.40% ------- $153.00
Total -------------- $378.00
m.ananth@hotmail.ca
Question 545062: 1.43=1.05(1+g)4 trying to solve for g to give me the dividend growth rate. the answer in the book is .0803 I just forgot how to do this type of algebra.
Found 2 solutions by josmiceli, nerdybill:
Answer by josmiceli(6766) (Show Source):
You can
put this solution on YOUR website!Use logs
I don't have a calculator right now, but you
will end up with:
( n is some number )
Change this to the form
Hope this helps
Answer by nerdybill(5399) (Show Source):
Question 540756: Find the value of x given that 5^3x-2 = 625.
Answer by Alan3354(21539) (Show Source):
You can
put this solution on YOUR website!Find the value of x given that 5^3x-2 = 625.
5^3x = 627
3x*log(5) = log(627)
x = log(627)/(3log(5)) = log(627)/log(125)
x =~ 1.333995
Question 538868: 8v+1=7v-20
Answer by rfer(10417) (Show Source):
Question 536688: Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra?
Answer by fcabanski(385) (Show Source):
You can
put this solution on YOUR website!Assign a number to y. If y=1:
x = 4y+1 = (4*1)+1=5.
x = 4y-1 = (4*1)-1=3
The two equations do not have the same solution.
If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com
Question 536666: 12-e^0.4*t=3
Answer by bucky(2097) (Show Source):
You can
put this solution on YOUR website!Given to solve for t:
.
.
Get all the constants on the right side so that only the term containing the variable is on the left side. Do this by subtracting 12 from both sides to you get:
.
.
On the left side the +12 and the -12 cancel each other out. On the right side the +3 and the -12 combine to give -9 and the equation reduces to:
.
.
Multiply both sides by -1 to get:
.
.
Take the natural logarithm (ln) of both sides:
.
.
Use a calculator to determine that
. Substitute that value for the right side:
.
.
Now, by the rules of logarithms, the exponent can come out as a multiplier and the equation becomes:
.
.
But the value of
. Substituting this reduces the equation to:
.
.
Solve for t by dividing both sides by 0.4 to get:
.
.
And performing the division of the right side results in:
.
.
That's the answer to the problem you were given. Hope this helps you to understand it better.
.
Question 536424: eighteen is what percent of 60?
Answer by algebrahouse.com(914)
(Show Source):
