Friday
April 18, 2014

Posts by Reiny


Total # Posts: 26,007

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

Statistics
number of subsets of 6 elements = 2^6 = 64 which includes the nullset (plain pizza) and all elements ("the works")

Math
number of small trucks --- x number of vans -----2x number of large trucks --- 320 - 3x 30000x + 35000(2x) + 80000(320-3x) = 13000000 divide by 10000 3x + 7x + 8(320-3x) = 1300 -14x = -1260 x = 90 so 90 small trucks 180 vans and 50 large trucks

math
speed of boat --- x mph time to go downstream = 39/(x+12) time to go upstream = 39/(x-12) , clearly x > 12 39/(x+12) + 39/(x-12) = 4 1/3 = 13/3 (39(x-12) + 39(x+12))/(x^ - 144) = 13/3 78x/(x^2 - 144) = 13/3 13x^2 - 1872 = 234x 13x^2 - 243x - 1872 = 0 x^2 - 18x - 144 = 0 com...

EASY Volume of shapes
area = area of base x heigh so the hard part is to find the area of the equilateral triangle with sides 5 1. easiest way: area = (1/2) side^2 x sin60 = (1/2)(25)*√3/2 = 25√3 2. draw in the height of the triangle, call it h h/5 = sin60 h = 5sin60 area = (1/2)(base x...

SICK
What post are you talking about? Looked back in search for "anna" and all seem to have been answered.

Math
You should be able to do this mentally area = (1/2)( 3 + 7)(12) = (1/2)(10)(12) = (1/2)(120) = 60 How did you ever get 81.6 ??

CALCULUS
noticed an error from line 2 to line 3 y^2 - y = x y^2 - y + 1/4 = x + 1/4 (y - 1/2)^2 =(4x+1)/4 y - 1/2 = ±√(4x+1)/2 y = 1/2 ± √(4x+1)/2 = (1 ± √(4x+1) )/2 , x ≥ -1/4

math
Is the relation supposed to be linear? If so, then you have two ordered pairs, (0,20) and (12.5 , 25) Find the equation of that line using your usual method.

algebra
The y-intercept, by definition, lies on the y-axis Any point on the y-axis has an x value of 0 (you haven't gone either left or right from the origin)

math
The steeper the line, the larger the slope since 5/3 is greater than 4/3, consider it explained

Ghana National Lotto game
Wow, are you under the impression that lottery number outcomes can be predicted??? Please let me know how.

Algebra 1 (Reiny)
t^-6 = 1/t^6 when t = 2 1/2^6 = 1/64 If this is in relation to your other post , notice that in that question you had #1 t^6 , when t = 2

Algebra 1 Answer Evaluation (Reiny)
I messed up in #3 and #4 #3, I looked at your answer and saw the y's, should have looked at the original question which had no y values. answer is x^10 , see Steve's #4. a^-3/b^-2 = b^2/a^3, see Steve's We have the same answers for the rest

Algebra 1 Answer Evaluation (Reiny)
1. 2^4 = 64 , not 1/64 2. ok 3. x^4 y^6 , your first choice is incorrect 4. a^-3/b^-2 = a^(-3 -(-2)) = a^-1 or 1/a 5. 0.5 = 5.0 x 10^-1 6. 3^2 = 9 , they probably want the actual answer 7. a^3 x a^-6 x a^-2 = a^-5 or 1/a^5 , notice 3-6-2=-5 8. ok 9. (-4d^7)^2 = +16 d^14 looks ...

GEOMETRY MIDPOINT FORMULA steve how did this hapn
looks like Steve was using vector geometry Perhaps the following approach might make sense to you: make a sketch. since AC = 4AB AB : BC = 1 : 3 for the x's : (2 - (-2))/(-2-x) = 1/3 12 = -2-x x = -14 for the y's: (3-0)/(0-y) = 1/3 9 = -y y = -9 so point C is (-14, -9)

Math
any equation of the simple form x = k , where k is a constant is a vertical line. All vertical lines have an undefined slope

Math
y-8 = -8(x-1) y -8 = -8x + 8 y = -8x + 16 or 8x + y = 16 or 8x + y - 16 = 0

Math - Quart to Gallon Ratio
2.5 gallons = 320 oz punch : grape juice = 64 : 16 = 320 : g 64/16 = 320/g 4 = 320/g 4g = 320 g = 80 it would take 80 oz of grape juice number of quarts = 80/32 = 2.5 quarts (Editorial: Go metric to avoid such silly calculations)

math
original perimeter = 2L + 2w new length = 2L new width = 3W new perimeter = 4L + 6w 4L+6w - (2L+2w) = 92 2L + 4w = 92 L + 2w = 46 L = 46-2w area of original = lw = w(46-2w) = 46w - 2w^2

math
children tickets ---- x adult tickets ------- 3x 9x + 5.3(3x) = 872.10 take over from here

math
3hex + 4trap = 200 3hex = 200 - 4trap 1 hex = (200-4trap)/3 or 4trap = 200 - 3hex 1 trap = (200 - 3hex)/4

Math Pre-Cal
to know the "value" of the quadratic function, you must know the value of x simply plug in your given value of x and work it out.

Math Pre-Cal
Use the vertex form first y = a(x-h)^2 + k, where (h, k) is the vertex, so ... vertex is (1,-1) so f(x) = a(x-1)^1 - 1 but (2,2) lies on it, so 2 = a(2-1)^2 - 1 2 = a(1) - 1 3 = a so you have f(x) = 3(x-1)^2 - 1 now expand this ... f(x) = 3(x^2 - 2x + 1) - 1 = 3x^2 - 6x + 3 - ...

Math
let the height be h h^2 + 12^2 + 4^2 = 14^2 h^2 + 144 + 16 = 196 h^2= 36 h = √36 = 6

pre cal
mmmhhh? (0+3)^2 = 3^2 = 9

pre cal
Look back at my explanation in the previous post for vertex (h,k), we get y = a(x-h)^2 + k so for vertex (-3,5), we get y = a(x-(-3) )^2 + 5 or y = a(x + 3)^2 + 5 Now plug in the other point (0, -4) -4 = a(0+3)^2 + 5 -4 = a(9) + 5 -9 = 9a a = -1 y = -(x+3)^2 + 5

pre cal
Two points only is not enough to establish a quadratic, unless one of those points is the vertex. If one of the points is a vertex, use the method I just showed you in your previous post. Let me know what you think.

Math help
Well,you are told that y has a value of 3 so in the 2nd equation, simply replace y with that value and solve for x 4(3) = 2x + 18 12 - 18 = 2x -6 = 2x -3 = x so x=-3, y = 3 Done!

Math
taking a stab at .75

Pre cal
in your text or in your notes, you should have the usual form of the equation if you have the vertex if vertex is (h, k) then the equation of the quadratic is y = a(x-h)^2 + k compare the values of (h,k) with your vertex of (3,-13) the value of a govern which way the parabola ...

Pre cal
Since you are using the word "vertex" I will assume you might be talking about a quadratic function. with vertex (3,-13) the parabola would be y = a(x-3)^2 -13 but (0,-4) lies on it, so .... -4 = a(9) - 13 9a = 9 a = 1 f(x) = (x-3)^2 - 13

Algebra
yes, you are correct example of exponential growth graph http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex example of exponential decay graph http://www.wolframalpha.com/input/?i=plot+y+%3D+%281%2F2%29%5Ex

Math
Let the number be x 2(x-2) + 7 = 57 2x - 4 = 50 2x = 54 x = 27

math
MN = √( (11-3)^2 + (-2+4)^2 ) = √(64 + 4) = √68 or 2√17

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