Monday
January 23, 2017

Posts by Reiny

Total # Posts: 37,369

Math
I think you have a typo and you must mean that there were 104 African pupils, then total number of boys --- x total number of girls --- 121-x (8/9)x + (4/5)(121-x) = 104 times 45 to clear fractions 40x + 36(121-x) =4680 40x + 4356 - 36x = 4680 4x = 324 x = 81 <---- total ...
October 9, 2016

MATH
2/3 < A/10 < 3/5 times 30 20 < 3A < 18 grammatically I read "but" to mean that both conditions apply, so this is not possible
October 9, 2016

Math
was expecting a complex number in the denominator. I will assume you meant: (4-2i)/(3+i) = (4-2i)/(3+i)*(3-i)/(3-i) = (12 - 4i - 6i + 2i^2)/(9 - i^2) = (10 - 10i)/(9+1) = 1 - i
October 8, 2016

Maths
let the tenth digit be x then the unit digit is 2x-6 the number is 10x + (2x-6) the number reversed is 10(2x-6) + x 10(2x-6) + x - (10x + (2x-6)) = 9 20x - 60 + x - 10x - 2x + 6 = 9 9x = 63 x=7 then 2x-6 = 8 then number is 78 check: 87-78 = 9 , looks good
October 8, 2016

Math
(7-13i)/(2i) = (7-13i)/(2i) * i/i = (7i - 13i^2)/(2i^2) , remember i^2 = -1 = (7i + 13)/-2 = (-13 - 7i)/2 check my arithmetic
October 8, 2016

math
You must have meant: y = 100(.2)^x so just plug in x = 4 Use you calculator, you can check how they got the first 3 values, and then do the same thing with x = 4
October 8, 2016

Maths
I will assume you mean (√15-3)/(√10-3) , those brackets are critical = (√15-3)/(√10-3) * (√10+3)/(√10+3) = (√150 -3√15 - 3√10 - 9)/1 = 5√6 + 3√15 - 3√10 - 9
October 7, 2016

Math
make a sketch Draw a line showing the car going one way ending at A, and the truck going the other way ending at B. So you know AB = 350 let the distance gone by the car be x miles, then the distance gone by the truck must be 350-x miles but the car has gone 70 miles more, x...
October 7, 2016

Math
look for a pattern ... 10^0 ÷ 9 leaves a remainder of 1 10^1 ÷ 9 leaves a remainder of 1 10^2 ÷ 9 leaves a remainder of 1 10^3 ÷ 9 leaves a remainder of 1 .... 10^99 ÷ 9 leaves a remainder of 1
October 7, 2016

Math
find the circumference of the circle with radius 11
October 7, 2016

Math
find the area of the inner rectangle, and the area of the larger rectangle. take the difference, that will give you the area of the walkway in square feet. Multiply that by the cost of each square foot.
October 7, 2016

math
what is 4 4/5 ÷ (1 2/5) ?
October 7, 2016

Probability-Cards
1) there is only 1 four of spades, so prob(4ofspades) = 1/52 2. There are 13 diamonds and 13 hearts, so prob(your event) = 26/52 = 1/2 3. you do it. How many of the 52 cards are less than 7 ?
October 7, 2016

Trig
Just noticed that you posted this new question after Steve showed you how to do it. In the one Steve answered for you, it had asked for sin(2A) This time they are asking for cos(2A), surely you can make that minor adjustment. Did you even look at his solution?
October 7, 2016

Math please help
amount of Columbian stuff --- x lbs amount of Peruvian stuff ----- 40-x lbs 5.5x + 4.25(40-x) = 4.6(40) solve for x
October 7, 2016

Math please help
let Jasmine's speed be x ft/m then Lanah's speed is x+25 ft/min time of Lanna's run = 30 min time of Jasmine's run = 20 min distance of Jasmine's run = 20x ft distance of Lanah's run = 30(x+25) clearly at that moment, Lanah is 3500 ft ahead that is, 30(...
October 7, 2016

Math
each adult costs $53.50 , so 12 adults cost 12(53.5) = $642 each child costs 19.25, so 18 of them cost 18(19.25) = 346.50 add them to get the total cost
October 6, 2016

Algebra
let the point be (x,0) distance = √(x-4)^2 + (0+5)^2 ) = 10 square both sides: (x-4)^2 + 25 = 100 x^2 - 8x = 75 completing the square x^2 - 8x + 16 = 75+16 (x-4)^2 = 91 x - 4 = ±√91 x = 4 ± √91 or consider a circle with centre (4,-5) and radius ...
October 6, 2016

simple interest and compound interest
x(1+r)^3 = x + 1815 ** x(1+r)^4 = x + 1996.5 *** divide *** by ** 1+r = (x+1996.5)/(x+1815) x + 1815 + rx + 1815r = x + 1996.5 rx + 1815r = 181.5 r(x + 1815) = 181.5 r = 181.5/(x+1815) so it looks like it depends on the value of x if x = 10000 r = 181.5/11815 = .01536 if x = ...
October 6, 2016

Math
the equation of a circle is x^2 + y^2 = r^2 ---> radius is r yours: x^2 + y^2 = 1.44(10^8), so the radius is 1.2(10^4) you are correct to find 8000^2 + 98000^2 = r^2 r^2 = 9668000000 = 9.668(10^9) , which is clearly > 1.44(10^8) So the point lies outside the circle of ...
October 6, 2016

Trig
Steve had already given you a good hint how to do these types in your previous trig question, this is the same type. You have to know the definitions of the trig functions in terms of x, y, and r and you have to know the CAST rule tanA = 5/1 = y/x , but we are in III, so y = -...
October 6, 2016

Expected Value
expected(gold) = $4(2/32) = 0.25 expected(silver) = $2(7/32) = .4375 expected(black) = -1(23/32) = -0.71875 add them up to get -0.03125 A "losing" game
October 6, 2016

Math (Expanding logarithms)
yes, you are correct log (AB) = logA + logB
October 6, 2016

Math
We have 3 isosceles triangles In triangle xyw, xw = yw, as stated mark angle x = angle xyw = a in triangle xyz, xy = xz, as stated mark angle xyz = angle xzy = b in triangle wyz, yw = yz, as stated mark angle wyz = b-a also angle ywz is an exterior angle in triangle xyw, so ...
October 6, 2016

@ Dip - math please help
Simply stating the answer is of no help to anybody. 3 ​|4x−3​|−3=8 3 ​|4x−3​|=11 ​|4x−3​| = 11/3 (4x-3) = 11/3 OR -(4x-3) = 11/3 4x = 11/3 + 3 OR -4x = 11/3 - 3 4x = 20/3 OR -4x = 2/3 x = 5/3 or x = - 1/6
October 6, 2016

Math
3/4 = .75 12/15 = .8 mmmhhh?
October 6, 2016

Math
you got it
October 6, 2016

Math
Just sub in the given point to see if the equation is true. e.g. for (6,3) is 3 = 6-3 ?? , NO, so (6,3) is not a solution etc. or To me the equation simply says that the y value is 4 less than the x value, so by just looking at the given points, I can tell . e.g. (4, 0) , is 0...
October 6, 2016

Word problems
So far you have spent 1/2 + 1/4 + 1/8 of your money or 7/8, leaving you with 1/8 of your money. (1/8)x = 3.28 x = 8(3.25) = £ 26
October 6, 2016

math
so 30% of his shots = 12 .3x = 12 x = 12/.3 = 40 he took 40 shots check: 70% of 40 = 28 so he hit 28 , must have missed 12
October 6, 2016

calculus
or: let the point of minimum distance from A(4,1) be P(a,b) slope AP = (b-1)/(a-4) 2y dy/dx = 4 dy/dx = 2/y so at A the tangent has a slope of 2/b but AP is a normal to the tangent at A , so the slopes of the tangent and the slope of AP must be negative reciprocals of each ...
October 6, 2016

Algebra
assuming your incomplete sentence is "... how long will it take to fill the tank if both pipes are open " rate of first = 1/90 rate of 2nd = 1/60 combined rate = 1/90+1/60 = 1/36 time at combined rate = 1/(1/36) = 36 minutes
October 5, 2016

Math
did you mean (27-r)^3 ? then you have 27^3 + 3(27)^2 (-r) + 3(27)(-r^2 + (-r)^3 = 19683 - 2187r + 81r^2 - r^3
October 5, 2016

Math
60 L in 5 min ----> 12 L in 1 minute = input 14 L in 2 min ----> 7 L in 1 minute = output net input = 5 L/min time to fill 100L = 100/5 L/min = 20 minutes
October 5, 2016

Math
let the number of weeks be w let the amount in Sam's account be A dollars A = 10w + 150
October 5, 2016

math
Collin's last reply is correct.
October 5, 2016

Mathematics
Your calculator is programmed to follow the order of operation. Since exponents are to be done first, it is doing -1(2^2) = -1(4) = -4 Brackets on your calculator allow you to change BEDMAS trying entering it as (-2)^2 and you will get +4 Suppose you were to calculate 5 - 2^2...
October 5, 2016

Algebra
let the two number be x and y then x+y = 105 ---> y = 105-x x/3 = y/4 times 12 4x = 3y 4x = 3(105-x) 4x = 315 - 3x 7x=315 x = 45 , -----> y = 55
October 5, 2016

algebra
Sounds like an isosceles triangle. Let the base be x each of the other sides = (1/2)x + 1 x + 2((1/2)x + 1) = 22 x + x + 2 = 22 x = 10 so the sides are 6 , 6, and 10
October 5, 2016

jkuat
log 30 = log( 3 x 10) = log 3 + log 10 = .477 + 1 = 1.477 looks like the log2 was not needed, but the question probably contained other cases where it might be needed e.g. log 60 = log (3 x 2 x 10) = log 3 + log 2 + log 10 etc
October 5, 2016

Maths
just plug into the formula ... i = .10/2 = .05 n = 5 amount = 1000( 1.05)^5 = ....
October 5, 2016

Math
Jayden's time ---- x days Lana's time = 1.5x 1.5x = 15 x = 15/1.5 = 10 days
October 5, 2016

Math
How about that ! That ball knows to follow the laws of physics. Is there a question?
October 5, 2016

Math Pre- Algebra
method 1 , straightforward way: daily rate = 75 + 7.50 = 82.50 charge for two days = 2(82.50) = 165 method 2, using distributive property: charge for 2 days = 2(75 + 7.50) = 150 + 15 = 165
October 5, 2016

maths-plz just tell me the two factor am okay
Not even Wolfram was able to find "nice ones". http://www.wolframalpha.com/input/?i=factor+4m%5E4-24m%5E3%2B33m%5E2%2B9m-9
October 4, 2016

Math
I would clean them up first 1st times 10 ----> 4x + 5y = 30 2nd times 6 ----> 3x - y = 12 now multiply that last one by 5 15x - 5y = 60 4x + 5y = 30 Add them: 19x = 90 x = 90/19 y = 3x-12 = 42/19
October 4, 2016

Math
let the larger number be x then the smaller is x-7 "the larger number is decreased by five, then doubled" ---> 2(x-5) 2(x-5) = x-7 +5 2x - 10 = x - 2 x = 8 Finish it up, and check
October 4, 2016

percentage
original numbers : x and y each is increased by 10 ---> x+10 and y+10 percentage increase for first time = 10/x and 10/y so new number is x+10 + 10/x (same thing for the y) x + 10 + 10/x = 72 times x x^2 + 10x + 10 = 72x x^2 - 62x = -10 completing the square: x^2 - 62x + ...
October 4, 2016

math
find the expected value of each case 1 comes up ---> 1/6 (-10) = -10/6 3 comes up ---> 1/6 (-30) = -30/6 5 comes up ---> 1/6 (-50) = -50/6 2 comes up ---> 1/6 (10) = 10/6 4 comes up ---> 1/6 (20) = 20/6 6 comes up ---> 1/6 (30) = 30/6 sum = 1/6 (-10 -30 -50 +...
October 4, 2016

math
Don't know what the "empirical rule" is, but in real normal distribution calculations, I got 95.45% http://davidmlane.com/normal.html
October 3, 2016

Algebra
side of square --- x side of triangle = x+5 so 4x = 3(x+5) 4x = 3x + 15 x = 15 perimeter of square = 4x = 60
October 3, 2016

Algebra
-3-5(3x+7)=0 expand .. -3 - 15x - 35 = 0 -15x = 38 x = -38/15
October 3, 2016

math
number of choices = C(44,6) one of those is correct, prob(big win) = 1/C(44,6) = 1/7059052 = appr .000000141 The probability of getting struck by lightning is about 10 times that.
October 3, 2016

Maths
You are starting off with a wrong premise log 200 = 2.301, not as given log 1000 = 3, not as given If not stated, log x is assumed to have base 10 If you are working with some mysterious unknown base, then loga 200 = .301 a^.301 = 200 .301 loga = log200 a = 44,118,214.29 ...
October 3, 2016

Maths
circumference is a linear measurement, thus it is proportional to the lengths of the radii. ratio of AREA is proportional to the square of the linear measurement Area P : Area Q = 25 : 16
October 3, 2016

math
what is 10000(1.03)^5 ??
October 3, 2016

Mathematics(indices)
Square root of xy^2 = (xy^2)^(1/2) = x^(1/2) y fourth root of 16x^4/x^3y^2 = (16x^4/(x^3 y^2) )^(1/4) = 2 x^(1/4) y^(-1/2) so we have: x^(1/2) y * 2 x^(1/4) y^(-1/2) = 2 x^(3/4) y^(1/2)
October 3, 2016

Derivative
let's look at it http://www.wolframalpha.com/input/?i=plot+f(x)%3Dx%7Cx%7C two cases: y = x^2 for x≥0 or y = -x^2, for x ≤ 0 remember |x| will always be positive, so the sign can only come from the factor of x at the front for y = x^2, f '(x) = 2x f '(0...
October 3, 2016

maths
so the base will be 10 cm by 10 cm by 1 cm. (you are cutting of 1 cm from either end of the 12) Volume = (10)(10)(1) cm^3 = 100 cm^3 follow the same steps for the second part.
October 3, 2016

maths
pi/3+7-2root3 = π/3 + 7 - 2√3 = 4.583095936... on my calculator There is a field of study in "numerical methods", where one has to find the best fraction that could serve as an approximation for a given number. This deals with a topic called "...
October 3, 2016

Math
I believe you mean, round it off to "two significant digits" 439,264 km = appr 440,000 km etc
October 3, 2016

emmy norberton
Jack is 3 and Sam is 3 Is Tom, who is 6, three years older than Sam? yes Is Tom, who is 6, twice as old as Jack ? yes
October 3, 2016

MATH
term(40) = a+39d = -3 ** term(9) = a+8d = 12 *** subtract them: 31d = -15 d = -15/31 back in *** a + 8(-15/31) = 12 a = 492/31 "and some of the frist 7th term" I will assume that is supposed to mean: find the sum of the first 7 terms sum(7) = (7/2)( 984/31 + 6(-15/...
October 3, 2016

math 115
Bosnian, you are correct, I should look at the units more carefully Volume= (100)(.290)(.029) km^3 = .841 km^2 etc thanks for catching my error, the answers seemed unreasonably hight.
October 3, 2016

math 115
volume = (100)(290)(29) km^3 = 841000 km^3 = 8.41 x 10^5 km^3 1 km = 1000 m 1 km^3 = (1000m)^3 = 10^9 m^3 1 m = 1000 mm 1 m^3 = (1000 mm)^3 = 10^9 mm^3 then 1 km^3 = (8.41 x 10^5)(10^9)(10^9) mm^3 = 8.41 x 10^23 mm^3
October 3, 2016

Ignore my gibberish - calculus 1
Just go with Steve. I was answering a totally different question I had in my mind.
October 2, 2016

calculus 1
I assume you meant: y=4x^3−19x+40 let's take a quick look at the graph http://www.wolframalpha.com/input/?i=y%3D4x3%E2%88%9219x%2B40 looks like we will have 3 different tangents from the point A(2,2) let the point of contact be P(a,b) obviously b = 4a^3 - 19a + 40 ...
October 2, 2016

Algebra
"with −2 as a zero of multiplicity 3" ---> (x+2)^3 "0 as a zero of multiplicity 1. " ---- x f(x) = a x(x+2)^3 , where a is a constant , a≠0
October 2, 2016

MATHS
I read that your function is f(x) = 3x^2 - 2x^3 and I will assume that [A=3,0] [B=2,0][C=1,0] are your answers stated in an unusual way. lets' see .... f ' (x) = 6x - 6x^2 for a max/min this equals zero 6x + 6x^2 = 0 6x( 1- x) = 0 x = 0 or x = 1 f(0) = 3(0) - 2(0) = 0 ...
October 2, 2016

Algebra
follow my steps for you previous like question, let me know what you got
October 2, 2016

Calc AB
assuming you meant: y = 32t^2 + 16t + 64 and assuming that D2/t [y] stands for the second derivative y' = 64t + 16 y'' = 64, which is a constant, so no matter what x you give me, y'' = 64 none of your choices are correct, unless D2/t [y] represents ...
October 2, 2016

math
ahhhh, just finished all that stuff below, but it appears that the given point is NOT on the curve, so the question is bogus. Which shows that the first thing you should check for this kind of question is to check if the given point lies on the curve. 2(x^2+y^2)^2=25(x^2+y^2) ...
October 2, 2016

math
Hard to tell, since you did not define your x I will let Isabella's age be x years then John is 2x - 17 x + 2x-17 = 40 3x = 57 x = 19 So Isabella is 19, but it asked for John's age. John is 2(19) - 17 = 21
October 2, 2016

maths need help
(a/k)^y=k^m take log of both sides: y(log (a/k) = mlogk y(log a - logk = mlogk yloga = mlogk + ylogk yloga = logk (m+y) logk = yloga/(m+y) also: a^x = k^m xloga = mlogk logk = xloga/m xloga /m = yloga/(m+y) divide by loga x/m = y/(m+y) ym = x(m+y) ym = xm + xy ym - xm = xy m(y...
October 2, 2016

Algebra
Assuming you meant: 18-4x=6-6x 2x = -12 x = -6 Since we can't see any "following values of x" x = -6 better be part of the list
October 1, 2016

Math
circumference is a linear measurement, so you can immediately rule out any area or volume. the linear units I see are feet, metres, miles, and kilometres
October 1, 2016

Math
Only your last question is correct a) at least 2 blue ----> 2 blue, or 3 blue or 4 blue or 5 blue or total - 0 blue - 1 blue number with no restriction = C(19,5) = 11628 number with 0 blue = C(10,5) = 252 number with 1 blue = C(9,1) x C(10,4) = 1890 number with at least 2 ...
October 1, 2016

Math
I am sure you meant permutations. In a combination, the order does not matter, so there would be only one way For permutation, what is 3 x 2 x 1 ? check by listing them
October 1, 2016

Trigonometry
You should have learned that the slope of a line is equal to the tangent of the angle that line makes with the x-axis so slope = tan 60° = √3/1 = √3 so the equation is: y - 6 = √3(x - 2) y = √3 x + 6 - 2√3
October 1, 2016

Steve, Damon, bob - differential equations
The last time I did differential equations was 55 years ago, perhaps one of our other math tutors can kick in here
October 1, 2016

math
correct, except I would keep the k in the calculation old y = k x^2 new y = k (4x^2) change in y = 3k x^2 percentage change = 3k x^2/(k x^2) = 3 or 300% e.g. enter 1 and 4 for the following applet, http://www.marshu.com/articles/calculate-percentage-increase-decrease-percent-...
October 1, 2016

Probability
Damon's answer represents the prob of the particular order of AAAKK but it could have been AKAKA, etc that is, we have to multiply his product by 5!/(2!3!) btw, there are 52 cards in a deck, not 54 so his product is 4/52 x 3/51 x .... Once changed to that and multiplied by...
October 1, 2016

math
The question is not clearly stated. Ms Sue's answer is correct based on that interpretation I will interpret it that you want to know how many different teams of 5 students you can pick e.g. ABCDE would be a different team from ABCDF etc number of possible 5 member teams...
September 30, 2016

mathematics
first number ---- x second number ---- 2x-1 Their sum = 3x - 1 let's increase it by 2 ----> sum is now 3x + 1 3x+1 = 13 solve for x and all mysteries shall be revealed.
September 30, 2016

math
250/1200 = ???
September 30, 2016

quadratic functions
did you sub in your given value of t ? i.e. how about evaluating height = -16(1.5)^2 + 25(1.5) + 6 follow the instructions regarding rounding.
September 30, 2016

English - for Reiny
I have no idea what that means. Sounds like a Trump-like potpourri of word salad.
September 30, 2016

math
let the number who play both tennis and badminton be x then 45 = 30+26-x x = 11 badminton only ---> 30-11 = 19 tennis only ------> 26-11 = 15 Illustrate and confirm with a Venn diagram if you need to.
September 30, 2016

calculus help
I assume you meant: y=(cosxcosy-sinxsiny)/(sinxcosy+cosxsiny) = cos(x+y) / sin(x+y) , using your identities = cot(x+y) dy/dx = - csc^2 (x+y) (1 + dy/dx) dy/dx = -csc^2 (x+y) - dy/dx csc^2 (x+y) dy/dx + dy/dx csc^2 (x+y) = -csc^2 (x+y) dy/dx(1 + csc^2 (x+y) ) = -csc^2 (x+y) dy/...
September 30, 2016

maths
recall that any multiple of a Pythagorean triple is also a Pythagorean triple I know the "smallest" case is 3-4-5 so using 6 it would be 6-8-10
September 30, 2016

math
In one hour Kyle can do 1/3 yard In one hour Andres can do 1/4 yard so in 8 hours they can do 8(1/3) + 8(1/4) = 8(1/3 + 1/4) yards = 8( 7/12) yards = 14/3 yards or 4 2/3 yards They can do 14/3 yards (houses) in 8 hours then they can do 14 yards in x hours (14/3) / 14 = 8/x (14...
September 30, 2016

Math
Assuming you meant: (x+3)(3x^2 - 20x - 7) = 0 (x+3)(x-7)(3x+1) = 0 carry on
September 30, 2016

Math
common difference = 2k/3 - k = -k/3 given: 20th term is 15 so k + 19(-k/3) = 15 times 3, (I don't like fractions) 3k - 19k = 45 k = - 45/16 first term is -45/16 common difference = -k/3 = 15/16 term 6 = a + 5d = -45/16 + 5(15/16) = 15/8 term n = a + (n-1)d = a + nd - d = -...
September 30, 2016

Algebra
which property would apply to something like 5 x 6 = 6 x 5 ? I would immediately rule out A and D , since we are NOT adding.
September 30, 2016

Math
ok, looks like you are saying that you have a box with a square base of r inches each and a height of x inches volume = r^2 x = 78 so x = 78/r^2 cost = 4(area of base) + 3(4 sides) = 4r^2 + 12 rx = 4r^2 + 12(78/r^2)(r) = 4r^2 + 936/r b) makes no sense to me, since the volume ...
September 30, 2016

Math
original price --- $x after reduced price ---- 89% of x = .8x .8x = 13 solve for x by dividing both sides by .8
September 30, 2016

math
I don't see the choices you made for this assignment. So how can I check it ?
September 29, 2016

math
since it is linear, find the slope of the two ordered pairs that you have: assume 2007 ----> t = 0 then for 2012 , t = 5 slope = (28200 - 35250)/(5-0) = -1410 (interpretation: the town loses 1410 each year) so using the point (0,35250) the equation can be written as P = -...
September 29, 2016

Algebra
Do you like C(L) = .92L better? so the horizontal axis will be labeled L and the vertical axis as C(L)
September 29, 2016

Algebra
I just paid $11.04 for 12 litres of gas, while last week I paid $$59.80 for 65 litres of gas at the same price. If L is the number of litres, and C is the cost in dollars per L, find the equation for the cost in terms of L So you have 2 points of the form (L,C) and they are (...
September 29, 2016

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