Sunday
February 1, 2015

Posts by Reiny


Total # Posts: 28,810

Stats
Think about how you obtained that mean? didn't you add the total of the 10 children and divide by 10 ? so the total must have been 172 Let the new kid's score be x then (172+x)/11 = 18 172+x = 198 x = 26
January 31, 2015

Math
Elis --- y Samuel --- y-10 David --- y+20 y+y-10+y+20 = 140 3y = 130 y = 130/3 = 43 1/3 newspapers ???? Something is rather bogus about your question. Notice mathematically my answer is correct: Elis sold 43 1/3 Samuel sold 33 1/3 David sold 63 1/3 43 1/3 + 33 1/3 + 63 1/3 = 140
January 31, 2015

Math
women --- x children --- x+6 men ---- (1/3)(x+6) total passengers = x + x+6 + (1/3)(x+6)
January 31, 2015

math
original number: men -- 3x women -- 4x 3x+4x = 126 7x=126 x = 18 so we had 54 men and 72 women new count: men = 56 women = 80 new ratio : men : women = 56:80 = 7 : 10
January 31, 2015

Math
let the height be x cm original volume = (45)(25)x cm^3 = 1125x cm^3 remember 1L = 1000 cm^3 (the beauty of the metric system) volume removed = (45)(25)(x-4) which is 22500 1125(x-4) = 22500 1125x - 4500 = 22500 1125x = 27000 x = 24 the height was 24 cm
January 31, 2015

Add maths form 4
that's not what you had, so make the necessary changes in my solution.
January 31, 2015

Add maths form 4
I will assume that you meant the equation to be 2qx(x+1) - 8x^2 - 1 = 0 2qx^2 + 2qx - 8x^2- 1 = 0 x^2(2q - 8) + 2qx - 1 = 0 a quadratic with a = 2q-8 b=2q c=-1 to have no real roots, b^2 - 4ac < 0 4q^2 - 4(2q-8)(-1) < 0 4q^2 + 8q - 32 < 0 q^2 + 2q - 8 < 0 (q+4)(q-2...
January 31, 2015

Math
let the cost price be x original selling price = x + .4x or 1.4x after 20% discound ... final selling price = (.8)(1.4x) = 1.12x which looks like a 12% profit based on cost b) if x = 448 If by "marked" price you mean final selling price, then 1.12(448) = 501.76 ...
January 31, 2015

Trigo
The angle of "elevation" means it was measured from ground level up So angle QPB = 54 angle QPA = 46 leaving you with 54-46 or 8° or angle APB = 8° In the right-angled triangle APQ, angle P = 54° so angle B = 90-54 = 36°
January 31, 2015

Trigo
Did you make your sketch? On mine, I labeled the bottom of the building Q, the top of the flagpole B and its bottom A I have a right-angled triangle APQ and a scalene triangle ABP. Angles can be easily found In triangle ABP, I have angle BPA = 8° angle PBA = 36° angle ...
January 31, 2015

algebra
old price --- x new price ----x+9 increase in old price = (4/5)(x+9) new price = x+ (4/5)x+9) x+9 = x + (4/5)(x+9) 9 = (4/5)(x+9) 45 = 4x + 36 4x = 9 x = 9/4 cents ?? or 2.25 cents check: old price -- 2.25 cents new price --11.25 cents other way to get new price: increase in ...
January 31, 2015

Calculus
And Math should be and is fun.
January 31, 2015

Calculus
or let x = 2.44535353.. times 100 100x = 244.535353.. subtract them 99x = 242.09 x = 242.09/99 = 24209/9900 or 2 4409/9900
January 31, 2015

Trigo
make your sketch let the point below the ballon be P let the distance from the 60° position to P be x then the other distance is 350-x You have two right-angled triangles let the height be h m (the common side to the two triangles) for the 1st triangle: tan60 = h/x h = ...
January 31, 2015

Calculus
To be concave up the 2nd derivative must be positive, so -x^2 + x + 6 > 0 x^2 - x - 6 < 0 (x-3)(x+2) < 0 looking at y = x^2 - x - 6 , we see from our solution above that it has x-intercepts of 3 and -2, thus it is above ( greater than zero) for x < -2 or x > 3
January 30, 2015

math
very similar to the other question you had http://www.jiskha.com/display.cgi?id=1422645251 10!11!/(7!13!) = (10x9x8x7! 11!)/(7! 13x12x11x10!) = 10x9x8/(13x12x11) (after the 7!10! cancel) = 60/143
January 30, 2015

math
you are correct in the final answer, but I object to your "work" the statement 121a^2b^2 = 11ab is wrong it should be 121a^2b^2 = (11ab)^2 same for your next line you could have checked your answer ... (11ab + 2b)^2 = 121a^2b^2 + 44ab + 4b^2
January 30, 2015

college Algebra
let the sales over $7000 be x 2150 + .08x = 3120 .08x = 970 x = 12125 so he must have sales of 12125+7000 or $19,125
January 30, 2015

MATH
automatically rule out A and D, last terms are not perfect squares Also rule out B, since both front and back must be positive. So it could only be C , if any at all. take √ of both first and last, multiply those results, then double to get the middle term. looks like C ...
January 30, 2015

math
btw, this is true for all values of n, not just positive integers. e.g. let n = 2.3 (2/3)^2.3 (3/2)^(2.3-1) = (2/3)^2.3 (3/2)^(1.3) = (2/3)^2.3 (2/3)^-1.3 = (2/3)^(2.3 - 1.3) = (2/3)^1 = 2/3
January 30, 2015

math
(2/3)^n (1 1/2)^n-1 =(2/3)^n (3/2)^(n-1) = (2/3)^n (2/3)^(1 - n) = (2/3)(n + 1-n) = (2/3)^1 = 2/3
January 30, 2015

Algebra 2
No, Jasmine I gave you the solution and the answer.
January 30, 2015

Algebra 2
really quite simple, just subtract them f(x) - g(x) = -2x+4- (-6x-7) = -2x+4 + 6x+7 = 4x + 11
January 30, 2015

math
quick way: on your calculator find a key usually labeled n! (on mine to find 6!, I keystroke like this: 6 2ndF n! = to get 720 so for (6!8!)/(9!5!) you should get 2/3 or .6666... or use the definitions: also recall that the concept that 9! = 9x8! since this suits our ...
January 30, 2015

Math- check my answers pls
Was told I had to log in to view.
January 30, 2015

math
first term: a common difference = 2 sum of first 3 terms = a + a+d + a+2d = 3a + 6 sum of first 9 terms = (9/2)(2a + 8(2)) = 9(a + 8) = 9a + 72 so 3a+6 = ar and 9a+72 = ar^2 square 3a+6 = ar^2 9a^2 + 36a + 36 = a^2r^2 r^2= (9a^2 + 36a + 36)/a^2 from the other equation, r^2 = (...
January 30, 2015

algebra
first of all, if you are going to factor an equation, get the RS equal to zero x^2 + 5x + 6 = 0 Now can you think of 2 number, which when multiplied gives you 6, and which when added give you 5 ?? How about 2 and 3 ---> 2+3 = 5 and 2x3 = 6 so (x-2)(x-3) = 0 then x-2=0 or x-...
January 30, 2015

Math
Picking up the equation found by Bosnian at A = 12t + 18t^2 dA/dt = 12 + 36t ---> the instantaneous rate of change for any t when t = 2 dA/dt = 12 + 36(2) = 84 cm^2/second
January 30, 2015

math
w = 5/8 L wl = 360 (5/8)L^2 = 360 L^2 = 576 L = √576 = 24
January 30, 2015

math
Same type of problem as the one I just did for you above this post.
January 30, 2015

business math
single equivalent discount = 1 - .9(.8)(.7) = .496 = 49.6% 49.6% off 9500 = 4712 final price = 9500-4712 = 4788 or , the long way 10% of 9500 = 950 after 1st discount: 9500-950 = 8550 20% discount on 8550 = 1710 after 2nd discount:8550-1710 = 6840 30% of 6840 = 2052 after 3rd ...
January 29, 2015

Mathh
10/13 = .7692.. or 77% I don't see that answer
January 29, 2015

algebra
In that case (1/8 + (x+4)/16 )/( (x+4)/x + 4/x ) = ( (2 + x+4)/16) / ( x+4 + 4)/x) = (x+6)/16 * x/(x+8) = x(x+6)/(x+8)
January 29, 2015

algebra
Was it perhaps (1/8 + (x+4)/16 )/( (x+4)/x + 4/x ) ??
January 29, 2015

algebra
ok, taking it the way you typed it (1/8 + x + 4/16)/(x + 4/x^2 + 4/x) = (1/8 + x + 1/4)/(x + 4/x^2 + 4/x)*(16x^2/(16x^2) = (2x^2 + 32x^3 + 4x^2)/(16x^3 + 64 + 64x) which does not come close to any of the given answers, so the original is missing some important brackets
January 29, 2015

algebra
You MUST include brackets to establish the correct order of operation. I will assume you meant: 6/(x-6) + 3x/(x+5) - 1/( (x-6)(x+5) ) notice that the common denominator is (x-6)(x+5) so ... ( 6(x+5) + 3x(x-6) - 1)/( (x-6)(x+5) ) = (6x + 30 + 3x^2 - 18x - 1)/((x-6)(x+5)) = (3x^...
January 29, 2015

math
Daniel -- x John --- x+30 David --- 3(x+30) solve for x, the plug into my definitions x + x+30 + 3(x+30) = 400
January 29, 2015

math
make a rough sketch, let D be (x,y) vector AC = vector AB + vector AD <5,0> = <3,2> + <x-1,y-2> <5,0> = <x+2,y> x+2 = 5 ---> x = 3 y = 0 D is (3,0)
January 29, 2015

math
5 minutes depletes 3% of water 1 minute depletes 3/5 % of water 50 minutes depletes (3/5)(50) % or 30% of water We can't answer the number of gallons, unless we know how many gallons we started with
January 29, 2015

Algebra
written as 4x = y^2, you should realize that you have a parabola, with its axis of symmetry the x-axis, vertex as (0,0), opening to the right. domain: x ≥ 0 range : any real number btw, it is not a function e.g. both (4,4) and (4,-4) lie on it, so we have 2 different y ...
January 29, 2015

Algebra
looks like an AS a = 9 , d = 1 , n = ? a + (n-1)d = 87 9 + (n-1) = 87 n = 87-8 = 79 sum(79) = (79/2)(first + last) = (79/2)(9+87) = 3792 or sum = sum(all of 87) - sum(all of 8) = 87(88)/2 - 8(9)/2 = 3792
January 29, 2015

math
When the x = 0 in any point, that point lies on the y-axis Janine's error is probably not studying or not doing her homework
January 29, 2015

Math
You have made a contradictory statement. Is there a question?
January 28, 2015

mixed number
But he did tell you that in the first place. Did you not look at his solution? Looks pretty straight forward and correct to me.
January 28, 2015

Geometry midpoint formula
midpoint of diameter = ( (6+15)/2 , (8+8)/2) = ( 21/2 , 8) equation: (x-21/2)^2 + (y-8)^2 = r^2 plug in (6,8) 81/4 + 0 = r^2 (x-21/2)^2 + (y-8)^2 = 81/4 any other point? how about the y-intercept, let x = 0 441/4 + (y-8)^2 = 81/4 y-8 = ±√90 = ±3√10 y...
January 28, 2015

Math
Wow, 10 in a row without a single sign from you that you tried or where your difficulty lies. Where are you having difficulties, or did you just assume that we would do this assignment for you?
January 28, 2015

Math
you know A = π r^2 replace r with 2t^2 + 1 and expand differentiate to find the rate of change plug in t = 2
January 28, 2015

Math
rate of change of volume = change in volume / change in time = (30-0)/(5-0) = 6 cm^3 /second so if it fulls up at 6 cm^3 in 1 second , how much will there be in 12 seconds ?
January 28, 2015

math
-32 ≤ 24-2f 2f ≤ 24+32 2f ≤ 56 f ≤ 28 5 + c/9 ≥ -31 c/9 ≥ -31-5 c/9 ≥ - 36 c ≥ -324
January 28, 2015

Geometry
Let's assume that you are hanging the picture vertically, that is, the width is 20 and the length vertically is 25. so you want to maintain the ratio of height : width right now, height : width = 25 : 20 = 5 : 4 new width = 20+10 = 30 new height = x x/30 = 5/4 4x = 150 x...
January 27, 2015

math
number of pages ---- x (5/12)x = 24 x = 24(12/5) = 57.6 ??? You have confusing information. According to your wording the 24 pages he read on Monday were 5/12 of the total, but that came out to a partial page. Is that what you wanted? Were there perhaps 3 days?
January 27, 2015

algebra
2l + 2w = 22 l + w = 11 ---> l = 11 - w area = 30 lw = 30 (11-w)(w) = 30 11w - w^2 = 30 w^2 - 11w + 30 = 0 (w-5)(w-6) = 0 w = 5 or w = 6 if w = 5 , l = 11-5 = 6 if w = 6, l = 11 - 6 = 5 the dimension is 5 by 6 mm
January 27, 2015

Math
If you haven't already done so, you must memorize the basic trig rations of the 30-6-90° right-angled triangle, as well as the 45-45-90 triangle I often make a quick sketch of those and it is then easy to get those trig ratios you should recognize that tan60° = &#...
January 27, 2015

math
base will be 20-2x by 20-2x, and the height will be x Volume = x(20-2x)(20-2x) or x(20-2x)^2 clearly each of the dimensions must be positive, so 20-2x > 0 -2x > -20 x < 10 In my notation, 0 < x < 10, I will let you change it to yours.
January 27, 2015

Calculus
cost to produce 120 units = C(120) = 1000+5.7(120) + .7(120^2) = = 11764 cost to produce 100 units = C(100) = 8570 rate of change = (11764-8570)/(120-100) = 3194/20 = 159.70 dollars/unit repeat the process for 100 to 101
January 27, 2015

algebra 2
You have a typo and don't state how high above the water the diving board is. I will give it an arbitrary value of 6 ft. So the equation of height is h = -16t^2 + 10t + 6, where h is in ft and t is in seconds , where t ≥ 0 for a max height, we need the vertex of that...
January 27, 2015

physics- vectors
You must have meant, "What are (a) the magnitude and (b) the angle (relative to +x) of Vector C " A = (11.6cos36.5 + 11.6sin36.5) = (appr 9.32, 6.90) B = (14cos17.1 + 14sin17.1) = (appr13.38 , 4.12) vector C = (22.71 , 11.02) magnitude = √22.71^2 + 11.02^2) = ...
January 27, 2015

algebra
Algebaric expressions: algebraic expressions that are just plain barbaric.
January 27, 2015

Kate
I made a rough sketch of triangle JKR and filled in the angles. A basic property of triangles is that in any triangle, the smallest side is opposite the smallest angle, and the largest side is opposite the largest angle Since angle J of 75° is the largest, side RK must be ...
January 27, 2015

math
or, stated another way if x = 0 , y = -16 let's plug it in.... 0 + k(-16) + 15 = 0 k = 15/16
January 26, 2015

math
let's just look at the antifreeze, right now the volume of antifreeze is .7(4) L or 2.8 L Let the amount of the current fluid we are draining be x L Now 70% of that is antifreeze, so the amount of antifreeze we lose is .7x So the actual amount of antifreeze left in the rad...
January 26, 2015

Math
co-workers check -- x your check ------- .7x x + .7x = 695 1.7x = 695 x = 408.82 co-wks = $408.82 yours = .7(408.82) = $286.18 add them up to verify my answer
January 26, 2015

Math
Do you have a typo? You said, "What is P ?" but you said P = {1,2,3,4} , so we know it
January 26, 2015

Math
yes, the correct answer is 7/9 I was just objecting to the messy way that Kudum was writing the expression. Please read my answer to Kudum carefully
January 26, 2015

@ Kudum - Math
the expression 2/3/6/7 is in very bad form You MUST use brackets to establish the proper order of operations. the question was (2/3) ÷ (6/7) = (2/3)(7/6) = 7/9 but if you type in your expression 2/3/6/7 into any modern calculator, which are designed to follow the ...
January 26, 2015

math
Are you reading my replies to your posts? http://www.jiskha.com/display.cgi?id=1422288228
January 26, 2015

math
I will assume you are trying to type: A 6 cylinder car has cylinders with ..... volume of one cylinder = π(2.22^2)(3.25) = 50.3198..... so the engine is 6(50.3198..) = 301.9 cubic inches
January 26, 2015

math
same thing again, plug in the straight line equation, and solve
January 26, 2015

math
You could but you don't have to recall that x = (-b ± √(b^2 - 4ac)/(2a) Judging from the type of question you have been asking, I trust you have learned the properties of the "discriminant" b^2 - 4ac I gave them to you in one of the posts.
January 26, 2015

math
Same thing as your last post Just evaluate b^2 - 4ac and decide
January 26, 2015

math
intersect the line with the parabola kx^2 - 5x + 2 = -3x + 4 kx^2 - 2x - 2 = 0 Looks like you are studying the nature of the roots, remember that if b^2 - 4ac > 0 you will have two solutions b^2 - 4ac = 0 you will have 1 solution (2 equal ones) b^2 - 4ac < 0 , there is ...
January 26, 2015

Maths
Outer dimension of the picture : 44 by 34 area whole thing including the frame = 44x34 = ... area of picture = 40x30 so area of frame = ???
January 26, 2015

Math
Perhaps I am missing something, but if we fill each of the labeled bottles just once, the big bottle can contain as little as 18 L 1 x (4L + 6L + 8L) = 18L
January 26, 2015

Math
The is a quadratic equation: sin^2 x - sinx - 2 = 0 (sinx - 2)(sinx + 1) = 0 sinx = 2 , which is not possible or sinx = -1 x = 3π/2 or x = 270° location on unit circle --- (0,-1) period --- 2π general solution x = 3π/2 + 2kπ
January 26, 2015

Add maths form 4
using the properties dealing with the nature of the roots, if there are two equal roots, then b^2 - 4ac = 0 so in hx2 _ 4kx + 9h = 0 16k^2 -4(h)(9h) = 0 16k^2 = 36h^2 4k = 6h h/k = 4/6 So h : k = 4 : 6 = 2 : 3 They should have reduced their answer to 2:3
January 26, 2015

algebra 1
Yes, your question was answered. http://www.jiskha.com/display.cgi?id=1422242533 Always check back to avoid un-necessary duplication of answers such as this. Secondly it does not help if you switch names.
January 26, 2015

Math
let the angles in order of size be x , a , b, 2x "The difference between the smallest and second smallest angles" ---> a-x "the difference between the biggest and second biggest angles" ---> 2x-b 2x - b = a - x 3x = a+b also we know x + a + b + 2x = ...
January 26, 2015

TO REINY
check our previous post for the explanation
January 25, 2015

ALGEBRA
you showed this: x+0.05<632 x<632/0.05 x<??????? following my argument, you should have had x + .05x < 632 x is a common factor x(1 + .05) < 632 x(1.05) < 632 ahhh, now you see where that 1.05 comes from, right ?
January 25, 2015

ALGEBRA
When you pay for an item with sales tax of 5% you pay the price + the sales tax = 100% + 5% = 1 + .05 = 1.05 similary a sales tax of 7% ---> you pay 1.07 etc
January 25, 2015

ALGEBRA
1.05x = 632 x = 632/1.05 = 601.90 The machine should cost less than 601.90
January 25, 2015

Calc
I agree with SJ but I would look at the backend of this thing first. Consider 1/x As x --->0 , 1/x becomes infinitely large but we are taking cos(???) and the result of cos(anything) is a number between -1 and 1 so e^(cos(1/x)) lies between e^-1 and e^1 or between 1/e and e...
January 25, 2015

algebra
let the first odd integer be n then the next even integer is n+1 3n < 4(n+1) by 11 3n = 4(n+1) - 11 3n = 4n + 4 - 11 7 = n the first odd integer is 7, then next even one is 8 check: 3 times the first = 21 4 times the second = 32 Is 21 eleven less than 32 ??, YES
January 25, 2015

calculus
how about y = 7x^2/((x-7)(x-9))
January 25, 2015

Calc 1
1. lim ( √(x+4) - 2)/x , as x-->0 =lim ( √(x+4) - 2)/x * ( √(x+4) + 2)/( √(x+4) + 2) = lim (x+4 - 4)/(x(√(x+4) + 2) = lim 1/( √(x+4) + 2) , x --> 0 = 1/(2+2) = 1/4 #2. In any limit question, the first thing I do is to sub the approach ...
January 25, 2015

Calculus
1. y = x^3 , at x = 1, y=1, so we have the point(1,1) dy/dx = 3x^2 , which is 3, when x = 1 y-1 = 3(x-1) y-1 = 3x-3 3x - y = 2 or y = 3x - 2 2. Lim sinxcos 2x/(3x) = lim sinx/x * cos 2x/3, as x ---> 0 = (1)*(1/3) = 1/3
January 25, 2015

Algebra
original price = x sale price = .85x x - .85x = 180 .15x = 180 x = 180/.15 = 1200 $1200 for a cell phone ?? check: 15% of 1200 = 180
January 25, 2015

ALGEBRA
set the 2 equations equal to each other ... 16x + 150 = -x^2 + 60x - 10 x^2 - 44x + 160 = 0 (x-40)(x-4) = 0 x = 40 or x = 4 when x = 40, y = 16(40) + 150 = 790 when x = 4 , y = 16(4) + 150 = 214 Pick out the choice that matches my solution
January 25, 2015

math
2560 m/60 sec = 2.56 km/min = 60 km/h
January 25, 2015

Quick Alegbra Help
done http://www.jiskha.com/display.cgi?id=1422231991
January 25, 2015

Math
done http://www.jiskha.com/display.cgi?id=1422231991
January 25, 2015

Math
let total distance be x bus: x/4 jog : (1/2)(3x/4) = 3x/8 walk: 800 x/4 + 3x/8 + 800 = x times 8 2x + 3x + 6400 = 8x x = 6400 total distance = 6400 ft
January 25, 2015

Algebra 2 Applications
height = -4.9t^2 when t = 3 height = 4.9(9) m = appr 44.1 m
January 25, 2015

Calculus
You must have done it correctly, since I also got x = appr 389 m Since this does not appear to make any real sense, let's investigate the other 2 cases: 1. he runs all the 300 m on the trail then at right angles through the bush 2. he runs all the way through the bush ...
January 25, 2015

Math( Attn: Reiny)
in any parabola written in the form y = a(x-p)^2 + q, the vertex is (p,q) if a is positive, q will be a minimum when x = p if a is negative, q will be a maximum when x = p if the equation is written in the form y = ax^2 + bx + c, the x of the vertex can be simply found by -b/(...
January 25, 2015

Math( Attn: Reiny)
Yes Wendy, I made the error in copying it from paper to here , should have been 36-2x Look at Kudums solution, he did it correctly using the same variable setup as mine As for #2 (#3 in your earlier post), compare Kudum's with mine and see that we just interchanged our ...
January 25, 2015

math
Using only whole numbers for lengths and widths 1 by 7 2 by 6 3 by 5 4 by 4 ---> notice that the sum is always 8 if you allow sides with fractional measurement, then there would be an infinite number of cases e.g. 2.5 by 5.5 ..... 3.412 by 4.588 ..... etc --------> ...
January 25, 2015

math
start: 22° increase for 5 min: 5(12) = 60° temp after 5 min = 22+60 = 82° decrease for next 3.5 min = 3.5(4) = 14° so temp after 8.5 minutes = 82-14 = 68°
January 25, 2015

algebric exponents
(3^x + 3^x + 1)/8 = (2(3^x) + 1)/8 = 2(3^x)/8 + 1/8 = (3^x)/4 + 1/8
January 25, 2015

Parabola Ques
Woaahhh! , that looks like a major assignment question. I will tell you what I would do if I had to actually do this. let P be (s,t) , but we know that y^2 = 4ax so t^2 = 4as s = t^2/(4a) so we can let P be (t^2/(4a) , t) from y^2 = 4ax 2y dy/dx = 4a dy/dx = 2a/y So the slope ...
January 25, 2015

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