Wednesday
April 16, 2014

Posts by Reiny


Total # Posts: 25,982

business math
interest earned = 1 million(1.02)^4 - 1 million

math for busness and finance
Paym(1.06^8 - 1)/.06 =40000 payment = 4000(.06)/(1.06^8 - 1) = $ 4041.44

math
for this GS a = 23 t(3) = ar^2 92 = 23r^2 r^2 = 4 r = ± 2 sum(n) = 62813 sum(n) = a(r^n - 1)/(r-1) 23(2^n -1)/1 = 62813 2^n - 1 = 2731 2^n = 2732 n log2 = log2732 n = 11.4 something wrong here, n has to be a whole number. check: for 11 terms, sum(11) = 23(2^11 - 1)/1 = ...

algebra
Original number of students = x original number playing = x/4 this year: number of students = x+6 number playing = x/4 + 4 x/4 + 4 = (1/3)(x+6) times 12 3x + 48 = 4x + 24 -x = -24 x = 24 So now there are x+6 or 30 students in the class

alegbra
number = 298(1.08)^n , where n is the number of years so when n = 3 population = 298(1.08)^3 = appr 375

alegbra
I will interpret (g f)(-3) as f(g(-3)) now g(-3) = -3 + 5/-3 = -14/3 then f(g(-3)) = f(-14/3) = 196/9 + 5 = 241/9 , none of your choices match If you meant g(x) = (x+5)/x repeating the above, I get 49/9 but that is not what you typed, but probably meant.

Math
in general the x of the vertex is given by -b/(2a) = -7/-10 = 7/10

math
correct If your x's drop out and you end up with a false statement, such as our 6 = 7, then there is NO solution if, however, the x's drop out and you end up with a true statement, there would have been an infinite number of solutions.

algebra
The values that we need from Pascal's triangle are 1 5 10 10 5 1 (s+2v)^5 = s^5 + 5(s^4)(2v) + 10(s^3)(2v)^2 + 10(s^2)(2v)^3 + 5(s)(2v)^4 + (2v)^5 = .. I will leave the algebraic simplification up to you

Pre-Calculus
I know that sin (π/6) or sin 30° = .5 so (π/4)(x-6) = π/6 or (π/4)(x-6) = π - π/6 = 5π/6 (in II) case 1 times 12 and divide by π 3(x-6) = 2 3x - 18 = 2 3x=20 x = 20/3 case 2 times 12 , and divide by π 3(x-6) = 10 3x - 18=10 3x =...

math
y= -4x - 2 Now, why could you not do this? All you had to do was to subtract the 4x and the +2 form both sides.

math
sort of hard to line numbers up nicely in this format, the .... represents spaces 1 | 1 -2 +2 ......... 1 ..-1 ..... 1 -1 1 so (r^2 - 2r + 2) ÷ (r-1) = r-1 + 1/(r-1) or r-1 with a remainder of 1

math
tickets sold by Minh --- x tickets sold by Jake --- 3x (notice x : 3x = 1 : 3) So number of tickets sold by Zoe = 4x 4x - 36 = x 3x = 36 x = 12 total tickets = x+3x + 4x = 8x or 96 money collected = 96($2) = $192

Math
at each drainage even we are taking out 1/4 of the current mixture and replacing it with 5 L of pure antifreeze, leaving 3/4 of the previous mixture after 1st drainage: amount of antifreeze =5 L after 2nd drainage: amount of antifreeze = (3/4)(5) + 5 = 8.75 L after 3rd drainag...

math
In my diagram , I arbitrarily let the radius of the cylinder be 1 unit let the radius of the cylinder be r , and let the height of the cylinder be 2h That way I can say: r^2 + h^2 = 1 r^2 = 1 - h^2 or r = (1- h^2)^(1/2) Surface area (SA) = 2πr^2 + 2πrh = 2π(1-h^...

Trigonometry
I did not get this sinx = 2/3, then cosx = √5/3 if secy = 5/3, then cosy = 3/5, and siny = 4/5 sin(x+y) = sinxcosy + cosxsiny = (2/3)(3/5) + (√5/3)(4/5) = (6 + 4√5)/15 Your individual trig values are correct, you must have made a substitution error.

Anyone want to help me?
did you mean s=6r^(5t) or s=6r^5t , the way you typed it. I will take it the way you typed it. t = s/(6r^5)

Math
yes, you are correct

Algebra 2 help...
amount = 487 (1/2)^(t/36) where t is the number of days. if t = 5 amount = 487(.5)^(5/36) = 442.302 kg

Math
d/20+1=d/24+ 1 1/4 d/20+1=d/24+ 5/4 times 120 , the LCD 6d + 120 = 5d + 150 d = 150-120 = 30

simultaneous equations
your error is in the 3rd last line from : 10 - 5b = 20 -5b = 10 b = -2 btw, why didn't you sub back into 2a + b = 3, it would have been easier. Also , it is not a good idea to sub into an equation that you have altered, try going back into the easiest-looking of the origin...

Math
3x - 9y = 3 6x - 3y = -24 from the first, divide by 3 x - 3y = 1 x = 3y+1 sub into the 2nd 6(3y+1) - 3y = -24 18y + 6 - 3y = -24 15y = -30 y = -2 then x = -6+1 = -5 for the 2nd system, multiply the 1st by -4 2x -4y = -24 2x + 6y = 19 subtract them 10y = 43 y = 43/10 = 4.3 into...

Calc and Vectors
looks like for each $5 decrease in the price, the attendance rises by 2000 let the number of $5 decreases be n the price of a ticket = 60-5n attendance = 18000 + 2000n revenue = (60-5n)((18000+2000n) factoring .... = 5(12-n)(1000)(18 + 2n) = 5000(12-n)(18+2n) = 5000(216 + 6n -...

Calc and Vectors
It could have yielded a minimum value, and there is no maximum value. setting the derivative equal to zero and solving for x, gives you the x where either a maximum or a minimum occurs.

pre algebra
" When he multiplies this number by 6 and then subtracts 15 from the answer, he ends up with his original number." -----> 6x - 15 = x easy to solve for x

oops - math
Steve, looks like you should have had that early morning coffee. from p + 12 > 9 p+12 - 12 > 9 - 12 p > -3

Math
2nd one: x/4- 8 = 16 - (3/4)x multiply each term by 4 , the LCD x - 32 = 64 - 3x 4x = 96 x = 96/4 = 24 1st one is even easier, give it a try.

Math
What's with the >.< are these supposed to be in-equations? Tell me before I do them

Algebra 2
let f(x) = x^4+3x^3+3x^2-3x-4 f(1) = 1 + 3 + 3 - 3 - 4 = 0 f(-1) = 1 - 3 + 3 + 3 - 4 = 0 f(0) = -4 ≠ 0 f(2) = ..... ≠ 0 so what do you think?

Math
as two equal parts 9/8 + 9/8 = 18/8 = 9/4 as three equal parts, 3/4 + 3/4 + 3/4 = 9/4 9/8 + 9/8 = 2(9/8) = 9/4 3/4 + 3/4 + 3/4 = 3(3/4) = 9/4

Dont get this question..
zeros of a function are those values of x which make y = 0 that is, where does the graph cross or touch the x-axis The ideal expression has the function in factored form, we have that already, so it is easy Just set each of the factors equal to zero and solve e.g. x-3 = 0 x = ...

Algebra 2 help!
which pair works in both equations ? (all pairs work in the 2nd equation, but not in the 1st)

HELP!!!
Of course you have to know that i^2 = -1 so (-5i)(-3i) = 15i^2 = 15(-1) = -15

Math
try making a sketch make the 70's opposite each other, and the 110' opposite each other. What do you notice? Is it possible to have the two 70's adjacent to each other?

Algebra help please!
same thing as x^2 - 5x + 3 = 0 x = (5 ± √13)/2 which is the same as a)

Pre Calc
let the amount of the more expensive mix be x pounds then the amount of the cheaper mix has to be 60-x pounds .80x + .65(60-x) = .70(60) times 100 , (I don't like decimals) 80x + 65(60-x) = 70(60) 80x + 3900 - 65x = 4200 15x = 300 x = 20 Use 20 pounds of the expensive kind...

Algebra 1 (Reiny)
in general if you have y > mx + b, you would shade in the region above the line y = mx + b y < mx + b , you would shade in the region below the line y = mx + b if the inequality contains ≥ or ≤ , the would include the boundary line itself and make it solid if...

Algebra 2 help!
then, as I said before, x = (5 ± √-19)/2 none of the choices match, that's all there is to say.

Algebra 2 help!
first make the equation more presentable .... x^2 - 5x + 11 = 0 x = (5 ± √-19)/2 none of the answers match this, so there has to be a typo. since all answers contain √13 your equation could have been x^2 - 5x + 3 = 0 that would give you x = (5 ± ͩ...

Algebra 2
for x^2 + bx + .... take 1/2 of the coefficient of the x term, in your case 1/2 of 16 is 8 now square that , in your case 8^2 = 64 so you would add 16 to make it into a perfect square test: x^2 - 16x + 64 = (x-8)^2 yup, it works.

Pre Calc
let the tens digit be x then the unit digit is x-4 the number itself is 10x + (x-4) sum of the digits is x + x-4 = 2x - 4 10x + x-4 = 9(2x-4) -3 11x-4 = 18x - 36 - 3 -7x = -35 x = 5 tens digit is 5, unit digit is 1 the number id 51

math
I did this for you before guessing what you might have meant. Tell me what b , c, and Ø are before I attempt it again.

Algebra 2
Actually none of them do the constants were completely ignored in all the choices. You would want what is called the "augmented" matrix -10 -9 13 12 8 -7 -5 15 5 4 -6 -12 btw, the elements of a matrix are not separated by commas

Algebra
let the tens digit of our number be x let the unit digit be y so the number is 10x + y sum of its digit = x+y 10x + y = 7(x+y) - 3 3x - 6y = -3 , #1 the number reversed is 10y+x 10y+x = 10x+y - 18 9y - 9x = -18 y - x = -2 y = x-2 sub this into #1 3x - 6(x-2) = -3 -3x = -3-12 x...

math
make a sketch, notice the 2 given points form a horizontal line, and has length 14 So the other side must be a vertical line let the point below (4,5) be (4,y) then (5-y) + 14 = 22 y = -3 So the point below (4,5) is (4,-3) and the point below (-10,5) is (-10, -3) the point cou...

algebra 1
I will do the last one, you do the others the same way point is (6,-2) line is y = -3x - 6 slopes of perpendicular lines are negative reciprocals of each other. So the new line is y =(1/3)x + b sub in the given point -2 = (1/3)(6) + b -2 = 2 + b -4 = b new equation: y = (1/3)x...

Algebra
we could write n*0 as n(5-5) which is 5n - 5n = 0 for all values of n

Math
Try this on your calculator 5/.01 = .. 5/.00001 = 5/.0000001 = notice I am making my divisor smaller and smaller, almost zero and what is happening to your answer? The closer my divisor gets to zero, the larger the answer. So when I could actually divide by zero, then the answ...

please
since tangent is negative in II and IV and the sine is negative in III and IV , our angle Ø must be in quadrant IV so using our given tanØ = -8/5 y = -8, x = 5 and r^2 = 64+25 = 89 r = √89 sinØ = y/r = -8/√89 cosØ = x/r = 5/√89 csc...

another math
for h2, the height from the base to the top of the flag: h2/34 = tan 48.6° h2 = 34tan48.6° = .. for h1, the height to the bottom of the flag h1/34 = tan 44.6° h1 = 34tan44.6° h2-h1 = 5.1 (this information is not needed when I calculate h2 - h1, I get 5.04 , not...

math
4! means 1x2x3x4 = ....

rational and irrational
no, .3π is not rational since π is irrational, any multiple of π such as .3π is also irrational. (I don't understand what the 67/79 , 75 pi,0.3 pi,13 pi is supposed to be )

Math
let the rise be 2x , and the run be 5x, then the hypotenuse is 1320 (2x)^2 + (5x)^2 = 1320 29x^2 = 1320 x^2 = 1320/29 x = √(1320./29) = appr 6.74665 rise = 2x = appr 13.5 ft run = 5x = appr 33.7 ft don't know what your b and c refers to , but I am sure you can match ...

math
Your first answer is correct. the second: prob(nickel, then penny) = (4/10)(1/9) = 4/90 = 2/45

Math
I read that as 4x + 16 = x^2 - 2x x^2 - 6x - 16 = 0 (x-8)(x+2) = 0 x = 8 or x = -2

math
9 times "What" = 27 What = 27/9 = 3

Math
let the number of prints be n so cost of prints = .19n cost of subscription = 5.95 so .19n + 5.95 = 15.83 .19n = 9.88 n = 9.88/.19 = 52 So .....

Maths
How about this? let a = 2, and b = 2 then a^2 - b^2 = a-b (a+b)(a-b) = a-b divide both sides by a-b a+b = 1 then 2+2 = 1 and 4 = 1 nice , eh?

Maths
2+2 = 5 for relatively large values of 2.

Maths
If the 9th term of an AP is 0 , then a+8d = 0 a = -8d 29th term = a + 28d = -8d + 28d = 20d 19th term = a +18d = -8d + 18d = 10d since 20d = 2(10d) the 29th term is twice the 19th term

Math - Check my answer?
Again, I am not crazy about your second line, since you are solving equations, I don't see one. I suggest this if you have to show your steps -6q + 5.8 = 23.8 -6q + 5.8 - 5.8 = 23.8 - 5.8 -6q = 18 -6q-6 = 18/-6 q = -3

Math - Help!!
I don't like the presentation of your second line, but you last two lines are good If you want to show all your steps, I prefer this: 7x/8 = 21 (7x/8)(8) = 21(8) 7x = 168 7x/7 = 168/7 x = 24

Math - Help!!
multiply each side by 8 7x = 168 divide both sides by 7 x = 168/7 = 24

Check my answer?
I would give it as 88.89% to the nearest hundredth of a percent

Math
1260 = 2x2x3x3x5x7 so their sum is .... ?

Math
looks like an arithmetic sequence with a = 3 d = 4 term(n) = 439 a + (n-1)d = 439 3 + (n-1)(4) = 439 4n - 4 = 436 4n = 440 n = 110 there are 110 terms

geometry
just use a simple ratio .... 5/2 = h/8 h = 8(5/2) = 20

math(please check answers)
I disagree with #7 (5/20) ÷ (1/7) = (1/4)(7/1) = 7/4 or 1 3/4 none of your choices match this. #9, how did you get 6 rooms ? If he takes 1 hour to clean one room, wouldn't it take him 6 hrs to clean the house?

math
You have a couple of typos. I will assume you meant f(x) = √(x^2-1) and g(x) = √(x-1) then f(x)/g(x) = √( (x^1-1)/(x-1) ) = √( (x+1)(x-1)/(x-1) ) = √(x+1) , for all x > -1 Since you didn't supply the choices they gave you ..... btw, the way...

geometry
so we are doing: (x,y) --->(x-1, y+3) ----> (x+4, y-1) so for R(-2,-2) (-2,-2) --->(-3, 1) ----> (1, 0) do the same for the other points (I am not sure why you have quotations around S and T in the final result. Are you saying that only S and T are transformed? If ...

Algebra 2
No, both direct, the variable is in the numerator. I wrote it the way I did, to point that out to you. Notice that to be an inverse variation, the variable must be in the denominator.

Algebra 2
suppose I write c = e/-4 as c = (-1/4) e and u = l/18 as us = (1/8)l now what do you think?

Math
(same as diameter halved, anyway ....) original: radius r, height h surface area = 2πrh + 2πr^2 = 956 πrh + πr^2 = 478 h = (478-πr^2)/(πr) for new cylinder, height = h, radius = r/2 volume = π(r^2/4)(478-πr^2)/(πr) = (478r - πr...

Math
Your question is rather vague. When you say that the circular top is halved, are you taking half of the diameter or half of the area ?

MATH
Delia's money --- d Sarah's money --- s d+s = 225 (7/10)d = (1/5)s 7d/10 = s/5 35d = 10s d = 10s/35 sub into d+s = 225 10s/35 + s = 225 times 35 10s + 35s = 7875 s = 175 then d = 225-175 = 50 Deliah has $50 and Sarah has $175 check: (7/1)(50) = 35 (1/5) of 175 = 35 yea...

math. can someone do this for me please....
Here is a nice picture of your problem http://www.wolframalpha.com/input/?i=plot+f%28x%29%3D1%2Fx+%2B4+%2C+g%28x%29%3D2%2Fx.+ disregard the "parametric graph"

math
Done for you 2 weeks ago http://www.jiskha.com/display.cgi?id=1387130183 and even earlier http://www.jiskha.com/display.cgi?id=1386792229 Steve found the derivative of the function for you, so for b) all you have to do is plug in the given values to get the slope of the tangen...

trig
After you make your sketch, it should be simple to calculate the angle between their flight-paths to be 88° , and after 2 hours the distance covered would be 650 and 600 miles. So a direct application of the cosine law .... d^2 = 650^2 + 600^2 - 2(650)(600)cos88° = ......

math
Read your question more carefully, it said to double the original triangle's LONGEST sides original longest side = 7 new longest side = 14 new recctangle is 5 by 14 new perimeter = 38

math
2(x + x+2) = 24 4x+4=24 4x=20 x=5 the original rectangle is 5 by 7 take it from there

math
So each circle has a diameter of 6 cm or a radius of 3 cm Circumference of one circle = 2πr = 2π(3) = 6π

math
correct

math
Since the radius of the new circle is 1/2 of the original, and the radius is squared in the area formula, the new area must be 1/4 of the original so what is (1/4) of 25 ?

Math
Meenah conjecture is either true or false Assume that it is true, that is, all even numbers are divisible by 4 test some 8/4 = 2 , ok 24/4 = 6 10/4 = 2.5, not exact Since we assumed it to be true and I found a case which was false, my assumption must have been false. Since the...

Business Math
Are we doing simple interest? notice your data did not line up nicely, do we have principal = $50000 rate = ???? time = 9 months interest = $4500 ? rate = interest/(principal x time) = 4500/(50000(9/12)) = .12 So the simple interest rate is 12% per annum

Math
I usually "play aroung" with the y values, I found this .... suppose we double all y values 1 2 = 1x2 2 6 = 2x3 3 12 = 3x4 4 20 = 4x5 5 30 = 5x6 6 42 = 6x7 ... n ----> n(n+1) Did you see the pattern ? but remember we multiplied by 2 so, ..... y = x(x+1)/2

algebra 2 honors
I had answered this for you 3 minutes after you first posted it. http://www.jiskha.com/display.cgi?id=1388971076 Why would you post it again ?

algebra 2 honors
2x^2-12x+32=x^2 x^2 - 12x + 32 = 0 (x-8)(x-4) = 0 x = 8 or x = 4

medical insurance
I thought I answered this for you a few days ago. Did you not read my answer ? http://www.jiskha.com/display.cgi?id=1388407747 Private rooms are not covered by our universal health care, so private room coverage requires some kind of extra medical insurance. Canadians do not n...

maths
profit = 16.75-12.50 = ... Percentage markup based on cost = profit/12.5* 100 % = ...

math
largest 4 digit number = 7654 smallest 3 digit number = 123 take the difference between them

math
b = b/2 + 4 multiply each side by 2 2b = b +8 b = 8 one brick weighs 8 lbs

math
Can't make out your diagram. Please describe it in words.

math
"each of 30 people brought 3 guests" accounts for 30 + 90 or 120 people "each of the 20 brought 2 guest" accounts for 20 + 40 or 60 guests "each of 40 people brought 1 guest" accounts for 40 + 40 = 80 people total so far: 120+60+80 = 260 leaving 3...

math
real time passed from 6:00 am to 10:00 pm is 16 hrs time gained by fast clock = 8 minute will read: 10:08 time lost by slow clock = 8 minutes clock will read: 9:52 pm so fast clock is 16 minutes ahead of slow clock

math
yes, your answer of 7 is correct.

Math
1. strange question Without looking at your last part of the given x and z values, just solving the system .... from the 2nd: 2y = 6x+1 y = (6x+1)/2 from the 3rd: z = x-3 back into the 1st: x + 3y - z = -3 x + 3(6x+1)/2 - (x-3) = -3 times 2 2x + 18x + 3 - 2x + 6 = -6 18x = -15...

Math - Algebra
let the three numbers be a , b , and and c a+b+c=350 a/c = 2 ---> a = 2c or c = a/2 so a + b + a/2 = 350 3a + 2b = 700 b/a = 5 + 25/a b= 5a + 25 in 3a + 2b=700 3a + 10a + 50 = 700 13a = 650 a = 50 b = 275 c = 25 check: 50+275+35 = 350 , check! 50/25 = 2 , check 275/50 = 5.5...

Math
Just do it (3!)!/3! = 6!/3! = 720/6 = 120 btw, you have a typo in your definition of n! n! = 1x2x3x...xn

Math
1000^2/(252^2/248^2) = 10^6 / (252/248)^2 = 10^6 / (63/62)^2 = 3844/3969/3844 * 10^6 = 3844000000/3969 sort of pointless to ask "how do you do it faster" the fastest way would be to simply punch it into a calculator like Ms Sue showed you

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