Tuesday
July 22, 2014

Posts by Reiny


Total # Posts: 26,842

math
45000(1.03)^n = 50000 1.03^n = 1.1111... n log 1.03 = log 1.111.. n = 3.5644.. about 3 1/2 years

Math
let the present value of the deposit be P P(1.075)^6 = 55000 p = 55000/1.075^+ = $35637.88 (elope, skip the expensive wedding, and use it as a downpayment for a house)

Algebra
What? No interest involved? So, let the number of months be n 500 + 95n = 800 + 75n 20n = 300 n = 15 check: 500 + 15(95) = 1925 800 + 15(75) = 1925

Bronies
Never heard of that, so I googled it. Does GOOGLE not work on your computer ?

Algebra (Age Problem)
present age --- x age five years ago --- x-5 age five years from now -- x+8 "Five years ago Rico's age was half of the age he will be in eight years" x-5 = (1/2)(x+8 times 2 2x - 10 = x + 8 x = 18 Rico is now 18 yrs old check: 5 years ago: 13 8 years from now: 26...

Math (Variation)
cost = k r^2 when r = 6, cost = 148 148 = k(36) k = 37/9 cost = (37/9) r^2 so when r = 11 cost = (37/9)(121) = 497.44 or cost1/cost2 = r1^2/r2^2 148/cost2 = 36/121 36cost2 = 148(121) cost = 148(121)/36 = 497.44

math
denominator --- x numerator ---- x-6 (x-6)/x = 3/4 4x-24 = 3x x = 24 check: (24-6)/24 = 18/24 = 3/4 , YUP

Pre-Alegebra
25/20 = 6/x 25x = 120 x = 120/25 = 24/5 or 4.8 ft

maths
time = distance / rate = 300 km/(60 km/h) = 5 hrs

algebra 2
since cotØ = 1/tanØ by definition, given the tangent of an angle, just take the reciprocal to find the cotangent of that same angle eg, given tanØ = 4/7 then cotØ = 7/4

Math
I would first of all change the ratio from 1/4 in : 6 ft , to 1 inch: 24 ft a) for 18 ft, x in/1 in = 18ft/24ft x = 18/24 = 3/4 inch b) x/1 = 66/24 = 11/4 inches or 2.75 inches c) you do it.

Maths
current: number of girls -- 3x number of boys --- 4x after change: number of girls -- 3x+3 numbr of boys --- 4x-1 new ratio of girls to boys = (3x+3) : (4x-1) more data needed to get numerical answer. e.g. if we let x = 5 we had 15 girls and 20 boys, notice 15:20 = 3:4 after c...

Probability
Assuming of course that he would try the same password more than once, we want success within 2 attempts ----> He could log in on his first try, or if that fails on his second try. FS for failure, then success is Prob(S) + Prob(FS) = 1/8 + (7/8)(1/7) = 2/8 = 1/4

Math
using my favourite normal distribution graphing calculator (same as tables in back of text books) http://davidmlane.com/hyperstat/z_table.html click on "value from an area" then enter: area = .9 (to be in top 10%, 90 must be "below" ) mean = 620 SD = 220 cl...

math
total now = 24 let the number of oranges to be added be x so (4+x)/(24+x) = 1/4 16 + 4x = 24+x 3x = 8 x = 8/3 8/3 buttons ??? Questions is flawed, check your data or your typing.

math
number of rooms rented = 450 - 7x price per room = 750 + 4x revenue = (450-7x)(750+4x) expand, then either find the vertex of the resultiong quadratic function, or differentiate, set equal to zero, and solve for x

MATH HELP!!!!!!!!
Do you know how to find the inverse of a 3by3 matrix? I got the following: 28 -51 1 40 -18 -26 4 27 7 each is divided by 192 so multiply the above inverse matrix by 46 12 60 then divide each result by 192 for your x1, x2, x3

Algebra 1 (Reiny!)
a) correct b) correct, but do you know why the volume is zero ? c) this will also answer part b) the given volume = c(8.5-2c)(11-2c) in expanded form notice if c = 4.25, the size of the cut-out, you would be cutting away 4.25 on each side of the width but the width is only 8.5...

math
do you know Calculus? If so, then dP/dx = -80x + 1000 = 0 for a max of P 80x = 1000 x = 1000/80 = 12.5 I assume you can't make a partial product , so either make 12 or 13 to get the same maximum profit If you don't know calculus .... the x value of the vertex is -b/(2a...

math
let magnitude 3 be represented by c then maginitude 4 would be 10c and magnitude 6 would be 10^2 x 10c = 1000c it would be 1000 times as great.

algebra
number of quarters --- x number of dimes ----- x + 6 25x + 10(x+6) = 165 solve for x, sub into my definition

math
let the amounts be 2x , 3x, and 5x solve 2x+3x+5x = 8000, then sub the x back into the three different definitions (hint: the largest share should be $4000 )

math!!!!
9 laps = 9(1/8) or 9/8 miles speed = (9/8) / 2.5 minutes = 1.125/2.5 mpm = .45 miles/min

MATH
yellow : red = (3/4) : (5/4) = 3 : 5 y:1 = 3:5 y/1 = 3/5 y = 3/5 He needs 3/5 L of red check: (3/5) : 1 = 3 : 5, the ratio as needed

Geometry
Area of a kite = (1/2)product of the diagonals So the width and height would be diagonals let the height diagonal be h (1/2)(15)h = 60 15h = 120 h = 8 , looks like C

Maths
I will assume you meant: x^2 = (y^2 - r^2)/y^2 , (or else it becomes a real mess involving a quadratic equation in y^4) Let me know otherwise on my assumption, x^2 y^2 = y^2 - r^2 y^2 - x^2 y^2 = r^2 y^2(1 - x^2) = r^2 y^2 = r^2/(1 - x^2) y = ± r/(√(1-x^2) , where...

math
Assume there were no babies in the group number of children --- x number of adults ----- y number of seniors ---- 6-x-y 17x + 27y + 25(6-x-y) = 115 17x + 27y + 150 - 25x - 25y = 115 -8x + 2y = -35 8x - 2y = 35 The left side of this equation is even, the right side is odd, this...

pre calculus
.72 = 1 (e^-.000124t -.000124t ln e = ln .72 but lne =1 t = ln .72 /-.000124 = appr 2649 years check my arithmetic

pre calculus
i = .10/12 = .008333.. n = ? months 5000(1.008333..)^n = 10000 1.008333..^n = 2 n log 1.0083333..= log2 n = appr 83.5 months or 6 years and appr 11.5 months

pre calculus
a) amount = 1000(1.025)^10 = 1280.08 b) amount = 1000 e^(5(.05)) = 1000 e^.25 = 1284.03

Math
cos 4Ø = 2cos^2 2Ø - 1) = 2(2cos^2 Ø - 1)(2cos^2 Ø -1) -1 = 2(4cos^4 Ø - 4cos^2 Ø + 1) - 1 = 8cos^4 Ø - 8cos^2 Ø + 2 - 1 = 8cos^4 Ø - 8cos^2 Ø + 1 now let cosØ = x and we have f(x) = 8x^4 - 8x^2 + 1

maths
number(baseball OR football) =number(baseball) + number(football) - number(baseball AND football) 29 = 21 + 12 - x x = 4 4 of them play both sports.

Math
And exactly what part of Steve' answer and mine did you not like ? http://www.jiskha.com/display.cgi?id=1391831037

statistics
W - wrong R - right a) prob RRR = (1/3)(1/3)(1/3) = 1/27 b) prob WWW = (2/3)^3 = 8/27 c) 2 right could be WRR, RWR, or RRW prob(of that) = 3 x (2/3)(1/3)^2 = 6/27 (notice the other case is 2 wrong prob of that = 3(1/3)(2/3)^2 = 12/27 and notice that 1/27 + 8/27 + 6/27 + 12/27 ...

Math
the first line of my explanation should have said: 72 = 2x2x2x3x3 = (2^3)(3^2) Looks like I had 12 on my mind

Math
To find the number of factors of a number, list its prime factors. e.g. 12 = 2x2x2x3x3 = (2^3)(3^2) so now we argue as follows: the 2's can be used in 4 ways: that is, we can use none, one, two , or all three of them. similarly the 2's can be used in 3 ways, none, one ...

statistics
I use this fantastic webpage for these kind of questions http://davidmlane.com/hyperstat/z_table.html enter the mean and SD, click on "between" and enter 69 and 70 to get .1779

LINEAR EQUATIONS
Noting to "solve" here, since you have 2 unknowns there would be an infinite number of solutions. What can you do with it? - perhaps graph it, by ... sub in any x you feel like e.g. let x = 3, then y = -2) ---> point (3,-2) let x = 0 , then y = 4 ---------> poi...

math
let time taken until they meet be t hrs distance covered by first train = 115t miles distance covered by 2nd train = 105t miles 115t+ 105t = 1200 220t = 1200 t = 5.454545.. hrs or 5hrs and .4545..*60 min = 5hrs and appr 27 minutes (let's hope the trains are on different tr...

Math
I tried dividing the given number by number that reflect teenagers. That is, I started with 13 61150 = 13*47040 47040 = 14*3360 3360=15*224 224=14*16 so the factors are: 13*14*14*15*16 So there are 5 factors, thus 5 members in the club For the second part, start with 12, then ...

math
I must disagree with that answer. There are 2 pizzas, each cut into 10 pieces. So they had 20 pieces, and ate 14 part of the pizzas eaten = 14/20 = .7

Algebra 1 (Reiny)
both 8 and 27 are perfect cubes, so the cube root will be exact and 2. (8/27)^(1/3) = 2/3 for (8/27)^(2/3) = [(8/27)^(1/3) ]^2 = (2/3)^2 = 4/9

Math
889/12 = 74 with remainder 1 961/12 = 80 with remainder 1 1009/12 = 84 with remainder 1 1189/12 = 99 with remainder of 1 So 12 is it! I am not sure if you know anything about modular arithmetic, so I made up a silly little old-fashioned computer program. Here is a listing of i...

Algebra 1 (Reiny)
If you meant: the cube root ∛(8m^3) then you would have = 2m , not both 8 and m^3 are perfect cubes 2. very confusing way of typing it, if you represent the square root correctly with an exponent of 1/3, why not represent the cube root with an exponent of 1/3 so we have ...

Math:A.P.
for AP: term1 = a term3 = a+2d term9 = a+8d but term7 = 19 = a+6d so a = 19-6d so re-defining: term1 = 19-6d term3 = 19-6d+2d = 19-4d term9 = 19-6d + 8d = 19+2d these 3 are supposed to be a GP, so (19-4d)/(19-6d)= (19+2d)/(19-4d) 361 - 152d + 16d^2 = 361 -76d - 12d^2 28d^2 - 7...

Math
x=2 is a vertical line, thus not a function the others are non-vertical lines All non-vertical straight lines are functions.

Math
The lab would measure 180 inches by 216 inches case 1: longer side of tile along longer side of floor 216/18 = 12 180/12 =15 number of tiles = 12x15 = 180 case 2: shorter side of tile along the longer side of floor 216/12 = 18 180/18 = 10 number of tiles = 10x18 = 180 Of cours...

Fractions
original number ---- x Juan ate (1/3)x , leaving (2/3)x Maria ate 3/4 of that , leaving (1/4)((2/3)x = (1/6)x (1/6)x = 10 x = 60 There were 60 j-beans check: Juan ate 1/3 of the 60 or he ate 20 , leaving 40 Maria ate (3/4) of the 40 , or 30, which would leave 10

Only math nerds should read
If you are estimating to get 2/17, and then using a calculator to divide, why not just divide 204/1700 to get .12 or 12% (Some of us old timers actually had to memorize the 12 times table. I recognized 204 = 120 + 84 120 = 10x12 84 = 7 x 12 so 204 = 17 x 12 then 204/1700 = 204...

Math - Alg
Did that one last night http://www.jiskha.com/display.cgi?id=1391650592

Math
1. height of tree above her line of sight: h1/44 = tan28 h1 = 44tan28 height of tree below her line of sight: h2/44 = tan36 h2 = 44tan36 height of tree = h1 + h2 = ... (not a good idea to have her view to be below the tree line) 2. make a sketch. Label the top of the tree T, h...

math
I suspect a typo If I am more than 1000 and more than 2000, then I am more than 2000 there would be an infinite number of solutions e.g. 3660 5579, 9481,9482,9483,....

Math - Alg
amount of pure acid to be added -- x L 1(x) + .3(60-x) = .5(60) 10x + 3(60-x) = 5(60) 10x + 180 - 3x = 300 7x = 120 x = 120/7 or appr 17.14 L

Math - Alg
solve for x, the amount of water to be added 0(x) + .8(50-x) = .7(50) 40 - .8x = 35 -.8x = -5 x = 6.25 So they had 43.75 ml of the 80% solution, and by adding 6.25 ml of water they now had 50 ml of a 70% solution.

math
You keep changing the question. now we have √(2 + √(1+k) ) = √5 square both sides 2 + √(1+k) = 5 √(1+k) = 3 square again 1+k = 9 k = 8

math
see your previous post

math
area = 10x40 = 400 square yds number of bags= 400/50 = 8 cost = 8($4.99) = $39.92 ignoring tax HUHH, where does the new lawn come in??

math
sure

math
I read that as √2 + √(1+k) = √5 √1+k = √5 - √2 square both sides 1+k = 5 - 2√10 + 2 k = 6 - 2√10 or appr -0.325

Algebra
Chessville : 50000(1.07)^n Checkervill: 70000(.96)^n when is 50000(1.07)^n = 70000(.96)6n 5(1.07)^n = 7(.96)^n log both sides and use rules of logs log5 + nlog1.07) = log7 + nlog.96 nlog1.07 - nlog.96 = log7 - log5 n(log1.07 -log.96) = log7 - log5 n = ( log7 - log5)/(log1.07 -...

quanitative methods
enter your data into http://davidmlane.com/hyperstat/z_table.html click on "below" and enter 40

Trigonometry
Just tried you first question again, using cos30° in my cosine law and got 22.6 which is D BUT, according to your wording of N 60° E, the angle between the two paths would be 60, and not 30 So to get your answer it should have been N 30° E

Trigonometry
This time I get a triangle with sides 30 and 10 and the contained angle between them is 150° , (90+60) again by the cosine law, dist^2 = 30^2 + 10^2 - 2(30)(10)cos150 = 1519.62 distance = √1519.62 = appr 38.98 nm which is choice B The next question you posted is a re...

Trigonometry
looks like a rather straight-forward case of the cosine law. distance^2 = 42^2 + 28^2 - 2(42)(28)cos60 = 1372 distance = 37.04 nm or vector of first leg = (42cos270, 42sin270)=(0, -42) vector for 2nd leg = (28cos30,28sin30) = (24.249, 14) adding them to get (24.249 , -28) magn...

Math help
What is 6000(1.04)^70 ?

math - interest rates
annual payments on a car loan? Never heard of that, but, anyway..... Cash value of car = 5000( 1 - 1.06)^-5)/.06 = 21061.82 a) value of loan after 1 year had you made no payments at all = 21061.82(1.06) = 22325.53 but you just made a payment of 5000 So balance after one year =...

Math
if y = -x+3 and y = x+4 then x+4 = -x + 3 2x =-1 x = -1/2 and y = -1/2 + 4 = 7/2

math
let the width of the walkway be x m area of walkway = (6+2x)(15+2x) - (6)(15) = 46 90 + 42x + 4x^2 - 90 = 46 4x^2 + 42x - 46 = 0 2x^2 + 21x - 23 = 0 (x-1)(2x + 23) = 0 x = 1 or x = -23 which would be inadmissable The border should be 1 m wide check: area of garden = 6x15 = 90 ...

oops - precalculus II
go with bobpursley's solution I don't know how my "-" suddenly turned into a + in my third line. should have been: 5^x( x-2 - 5^2) = 0 5^x(x - 27) = 0 5^x = 0 or x = 27 but 5^x = 0 has no solution, so x = 27 , the same as bob had

precalculus II
(x-2)5^x - 5^(x+2) = 0 I see a common factor of 5^x 5^x( x-2 + 5^2) = 0 5^x(x + 23) = 0 5^x = 0 or x = -23 but 5^x = 0 has no solution, so x = -23

Math
Didn't I just show you that it was ? Did you not look at my answer ?

Math
first notice the common factor of x x^3 - 3x^2 - 28x = x(x^2 - 3x - 28) now do the quadratic = x(x-7)(x+4) (notice (-7)(+4) = -28 and -7+4 = -3 )

alegebra
In this forum we type powers using the ^ to show exponents e.g 4x^2 , not 4x2 anyway 1. 4x^2 + 12x + 5 = (2x+1)(2x+5) 2. 2x^2 + x - 3 = (x-1)(2x+3) 3. ok 4. 16x^2 - 16x - 12 = 4(4x^2 - 4x -3) = 4(2x+1)(2x - 3) which is D) 5. = 3(x^2 + 7x - 8) = 3(x+8)(x-1) which is A) looks li...

Math
no need to do FOIL, just sub in n=11 (n-3)^2 = (11-3)^2 = 8^2 = 64 now just put n=11 into the different choices for answers

Math
if n=11, then (n-3)^2 = 64 A) is 17(5) ≠64 B) is 16(4) = 64 ahhhh!!! I assume there is only one answer, but check the others anyway.

math
let the three pieces be x , 3x, and 6x 6x - x = 2.5 5x = 2.5 x = .5 three pieces are .5 , 1.5, and 3 ft the piece was x+3x+6x or 10 long so 10x = 10(.5) = 5 ft mmmhh, what about the wood lost due to the sawdust? You must have one of those fancy new laser saws.

Finance
I will do the first, you do the others in the same way Let me know what you get. PV = ? Amount = 5000 i = .05 n = 10 PV(1 + i)^n = Amount PV(1.05)^10 = 5000 PV = 5000/1.05^10 = 5000/1.628894627 = $3069.57

Algebra 2
Jane, from your wording it is not clear if the first card drawn is returned to the deck or not. Suppose it is not returned could be F4 or 4F = (12/52)(4/40) + (4/52)(12/40) = 3/130 + 3/130 = 3/65 Your answer suggests that the card is returned after it is drawn. Then it would b...

trig
Just supposing you meant what you typed cot^2x+csc=x cos^2 x/sin^2 x + 1 sinx = x wolfram shows 4 answers in your domain http://www.wolframalpha.com/input/?i=solve+cot%5E2%28x%29+%2B+csc%28x%29+%3D+x x = appr. 1.211, 2.343, 3.523 and 5.964 When substituted all are within an er...

math
Oscar is definitely out of line.

Math
draw in an altitude to the base , which would bisect the base. So now you have a right angled triangle, let the equal sides be x cm each sin 43° = 7/x x = 7/sin43 = appr 10.26 cm For the second, I will assume that the 170 yrds is measured along the ski run then sin42 = x/1...

Algebra
mmmh, have you tried substituting t = 4 into the equation and comparing that answer to your graph result when t = 4 on the horizontal axis ?

Algebra
in 5 hours , (from 1:00pm to 6:00pm), he did 5 driveways. (7-2) so he does 1 driveway per hour or he takes 1 hour per driveway.

Algebra
it is in that form

algebra
y-0 = (-2/3)(x-5)

math
treat it as having 2 ordered pairs (28, 8) and (47,17) in the form (m,g) slope = (17-8)/(47-28) = 9/19 using (28,8) g-8 = (9/19)(m-28) 19g - 152 =9m - 252 9m - 19g = 100 or -19g = -9m + 100 g =(9/19)m - 100/19

Math
Notice what happens when you state a problem in a misleading way? I interpreted that you wanted the cost after a 40% discount. Steve thought that the $99 was the cost after the 40% discount. Besides, "$99 watch with a 40% discount. ", is a statement, not a question.

Math
discount = $ 99(.4) = $39.60 So cost of watch = $ 59.40 (how can you get $ 247 ? . That is 2 1/2 times the original cost !! )

algebra
amount needed to rent 5 movies is 3(5) + 10 = $25 He already has $10, so he needs an extra $15

Math
The tens place can be filled in 4 ways for each of those, the unit place can be filled in 3 ways number of such numbers = 4 x 3 = 12 (count the numbers that Ms Sue gave you)

Math
done by Steve http://www.jiskha.com/display.cgi?id=1349250036

math
Are you preparing for a test or exam? The question that you have asked and I have answered for you are of an elementary nature in this topic. I have a feeling that you have some major studying to do.

math
solve -6x^2 + 4x + 7 = 0 6x^2 -4x - 7 = 0 use the quadratic formula, since it does not factor.

math
how about just adding 15 ?

math
f(x) = (x+2 - 12)^2 = (x-10)^2

math
it factors .... (x-8)(x+5) = 0 x = 8 or x = -5

Math
the first term would be S1 = (5/2)(1) + (7/2)(1) = 6 the sum of the first 2 terms is S2 = (5/2)(4) + (7/2)(2) = 17 so the 2nd term = S2 - S1 = 17-6 = 11 which means the common difference must be 5 (just checking: the first 4 terms would be : 6, 11, 16, 21 and the sum of the fi...

algebra
2x + 2(x-4) = 64 take it from there.

Trig
sin Ø = .6 = 6/10 = 3/5 you should recognize the famous 3-4-5 right-angled triangle. so in quadrant II, construct your right-angled triangle in quadrant II sinØ = opposite/hypotenuse = y/r y = 3, r = 5 and in II, x = -4 so ... sinØ = 3/5 , csc Ø = 5...

statistics
enter your data into http://davidmlane.com/hyperstat/z_table.html click on "below" you should get 0.2638 so 26.38 % are less than 38 inches tall

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