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March 25, 2017

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Posts by Reiny

Total # Posts: 38,076

math
Best illustrated with a Venn diagram. Draw two intersecting circles, label one barking, the other whining. place 29 in the intersection of the two circles In the non-intersecting part of the barking circle place 49-29 or 20 In the non-intersecting part of the whining circle ...
March 4, 2017

math
1. product of 4 tens and 2 ones = 40(2) = 80 x - 80 = 30 x = 110 2. do it the same way
March 4, 2017

Math
start with x dollars and go through the steps after CD's : x-18 spend 1/2 of that, leaving (x-18)/2 after lunch, amount left = (x-18)/2 - 11 spends 1/3 of that on book leaving with (2/3)( (x-18)/2 - 11), let's simplify that a bit = (2/3)(x/2 - 9 - 11) = (2/3)(x/2 - 20...
March 3, 2017

maths binomial expansion
(x+y/2)^1/3 = x^(1/3) + (1/3)(x^(-2/3) (y/2) + (1/3)(-2/3)/2! (x^(-5/3) )(y/2)^2 + (1/3)(-2/3)(-5/3)/3! (x^(-5/3))(y/2)^3 + .... = x^(1/3) + (1/6)(x^(-2/3)y - (1/36)(x^(-5/3)y^2 + (5/648)x^(-8/3)y^3 + ??? I left out the 5th term for you to finish. I am sure you can see the ...
March 3, 2017

Math
The question is vague. Is the interest simple or compound? Assuming no payments were made in those 4 years: at compound interest, as is usual for times over 1 year .... Amount = 1000(1.15)^4 = 1749.01 So the interest is $749.01 at simple: I = 1000(.15)(4) = 600
March 3, 2017

Statistics
You want the specific case of HHHHHMM, where H is success and M is a miss. prob(HHHHHMM) = (.7)^5 (.3)^2 = ....
March 3, 2017

Finance
The $6000 won't matter, all you need is 1.03^n = 2 log it n log 1.03 = log 2 carry on
March 2, 2017

Finance
7500(1+r)^50 = 1000000 (1+r)^50 = 400/3 take 50th root of both sides 1+r = 1.1028.. r = .1028 = appr 10.28% Good luck!
March 2, 2017

Math, Pre-calculas
original piece ---- x cm by x cm base is (x-6) by (x-6) x(x-6)^2 = 243 x^3 - 12x^2 + 36x - 243 = 0 I don't know what method you have to solve a cubic. Since this one does not factor it becomes complicated. Newton's Method is one algorithm. I sent it through Wolfram and...
March 2, 2017

Math - Linear Approximation
"a) Find a linear approximation of y=sinx at x=pi/6 " no linear approximation needed here, you MUST know that sin(?/6) = 1/2 for b) sin(61?/360) = sin(60?/360 + ?/360) = sin(?/6 + (?/360) so we will now use the formula that you stated: f(x+a)=f(a)+f'(a)(x-a) ...
March 2, 2017

Math
Angelina, we don't just do a whole assignment for you. I will gladly check what your answers are for each of those 11 questions, but I am not just going to give you the answers.
March 2, 2017

Math
I can't see your choices.
March 2, 2017

Math
I do this: 7 - 3 5/12 = 84/12 - 41/12 = 43/12 or 3 7/12 some folks do this 7 - 3 5/12 = 6 12/12 - 3 5/12 = 3 7/12
March 2, 2017

Pre calculus
let the rise be x ft, then , 1/2 < x < 8 the run will be 8-x ft slope of ramp ? tan 4.8° or slope ? .08397... slope = x/(8-x) ? .08397.. x ? .671778... - .08397x 1.08397.. x ? .671778.. x ? .6197 ft So the rise has to be from .5 ft to .6197 ft and the length would be...
March 2, 2017

Urgent math question help!!!
4(x?2)+1=9 --> 4x?8+1=9 you used the distributive property 4x?8+1=9 --> 4x - 7 = 9 you simplified or added like terms 4x - 7 = 9 --> 4x = 16 you added 7 to both sides, rules of equation 4x = 16 ----> x = 4 you divided both sides by 4, rules of equation I don't ...
March 2, 2017

math help plz?!
in/h ---> inches per hour cm/h ---> cm per hour these are the only two that make sense. If you are in the US, it would be in/h elsewhere it would be cm/h
March 2, 2017

math
20% + 50% is 70% accounted for, so 30% are yellow and those are 27 .3x = 27 x = 27/.3 = 90 90 t-shirts in all, 18 are red, 45 are green, 27 red finish the question ...
March 2, 2017

Maths
greens --- x reds ----- 4x x + 4x = 90 take over Just noticed in Related Questions below that I answered the same question in 2014
March 2, 2017

math
What is (3/5)(2/5) ?
March 2, 2017

maths
2x + 2y = 18 x + y = 9 y = 9-x also , xy = 20 x(9-x) = 20 9x - x^2 - 20 = 0 x^2 - 9x + 20 = 0 (x-4)(x-5) = 0 x = 4 or x = 5 if x = 4, then y = 5 if x = 5, then y = 4 you have symmetric answers, the field is 4 m by 5 m
March 2, 2017

calculus
intersection of y =1 and y = x^8 is (1,1) and (-1,1) because of the nice symmetry we could just go from 0 to 1 and double. V = 2?? ( (5-x^8)^2 - (5-1)^2 ) dx from 0 to 1 = 2? ? (25 - 10x^8 + x^16 - 16) dx from 0 to 1 = 2? [9x - (10/9)x^9 + (1/17)x^17 ] from 0 to 1 = 2?(9 - 10/...
March 2, 2017

calculus
The line and the parabola intersect at (3,0) and (0,3) http://www.wolframalpha.com/input/?i=plot+x%2By+%3D+3,+x+%3D+4%E2%88%92(y%E2%88%921)%5E2 from the straight line: x = 3-y V = ?? ((4 - (y-1)^2 )^2 - (3-y)^2 ) dy from 0 to 3 = ..... I would expand first, then integrate
March 2, 2017

math
Why not take the easier equation? x+2y=6 ---> x = 6-2y now plug that into the other, 5x+3y=2 5(6-2y) + 3y = 2 30 - 10y + 3y = 2 -7y = -28 y = 4 then x = 6 -2(4) = -2 see how easy it is ?
March 1, 2017

Math
no 45000(.98)^15 = appr 33236
March 1, 2017

math
daily wage/man = 34000/( (12)(17) ) = 500/3 so for 16 men for 18 days wages = (500/3)(16)(18) = 48000
March 1, 2017

Math
Smaller --- x larger ----- x+4 1/x + 1/(x+4) = 14(1/x)(1/(x+4) multiply by x(x+4) x+4 + x = 14 2x = 10 x = 5 the two integers are 5 and 9 check: 1/5 +1/9 = 14/45 14 times product = 14(1/5)(1/9) = 14/45 my answers are correct
March 1, 2017

math
Let arcsin(x) = A let arctan(x) = B then cos(arcsin(x) + arctan(x)) = cos(A+B) = cosAcosB - sinAsinB ** from arcsin(x) = A sinA = x/1 cosA = ?(1-x^2) , using Pythagoras from arctan(x) = B tanB = x/1 , then sinB = x/?(x^2 + 1) cosB = 1/?(x^2 + 1) back into ** cosAcosB - ...
March 1, 2017

Math (Business)
1000(1+.0155/4)^20-1/(.0155) careful with brackets, secondly you already did .062/4 , so why are you dividing .0155 by 4 ?? amount = 1000 ( 1.0155^20 - 1)/.0155 = 1000( 23.237857...) = $ 23237.86
March 1, 2017

Calculus
given : dl/dt = 3 cm/s, dw/dt 3 cm/s P = 2l + 2w dP/dt = 2 dl/dt + 2 dw/dt plug in the values d^2 = l^2 + w^2 I assume you want the rate of change of the perimeter, not just its length. Your wording is confusing. 2d dd/dt = 2l dl/dt + 2w dw/dt you are given l and w, so you can...
March 1, 2017

Maths
M+T+W = 3(39) =117 W+TH+F+SA = 4(39.5) = 158 Add them M + T + 2W + TH + F + SA = 275 Finally: M+T+W+TH+F+SA = 240 Let's subtract those last two equations: ahhh, W = 35
March 1, 2017

Maths
I picked M as the midpoint of AB, and N as the midpoint of DC let P be the intersection of AN and DM in triangle ADM but not in triangle ADN --> triangle AMP by simple ratio calculations, the area of triangle AMP = (1/8)the square. so prob(of your event) = 1/8
March 1, 2017

maths
from x+y=-1, y = -1-x plug that into the first to find x, then back into x+y=-1
March 1, 2017

Math
distance for first leg = 240 km distance for 2nd leg = 180 km Interpretation 1: total distance traveled is the hypotenuse d^2 = 240^2 + 180^2 etc average speed = d/6 = ... interpretation 2: total distance = 240+180 = 420 total time = 6 avg speed = 420/6 = 70
March 1, 2017

Calculus Reposted
the rate at which x changes is given as 2 cm/sec which is dx/t. so you have to find the derivative with respect to time (t), you found the rate of change of y with respect to x xy = 12 x dy/dt + y dx/dt = 0 now plug in our given stuff. 4 dy/dt + 3(2) = 0 4dy/dt = -6 dy/dt = -6...
March 1, 2017

Maths B
Look at it as being given 2 ordered pairs (25,20000) and (50,30000), and being asked to find the equation of the straight line. Your general point will be (n,C) slope = (30000-20000)/(50-25) = 400 now you have the slope and using one of the given points, find the equation ...
March 1, 2017

Calculus
The rate of $200 per year is dp/dt, so we need to differentiate with respect to t 5p+4x+px=100 5 dp/dt + 4 dx/dt + p dx/dt + x dp/dt = 0 we need x when p = 1.5 in the original: 5(1.5) + 4x + 1.5x = 100 5.5x = 92.5 x = 185/11 so we have: p = 1.5, x = 185/11 , dx/dt = .2, and dp...
March 1, 2017

Calculus- Related rates
dV/dt = 4? r^2 dr/dt 1 = 4?(2.25) dr/dt dr/dt = 1/(9?) <----- nice, you had that dA = 8?r dr/dt = 8?(1/(9?) = 8/9 you had 4/3, looks like a "sloppy" error.
March 1, 2017

Calculus- Related rates
V = (4/3)? r^3 dV/dt = 4? r^2 dr/dt given : when r = 1.5 , dV/dt = 1 find dr/dt for b), A = 4?r^2 dA = 8?r dr/dt , you have dr/dt from a) just plug in the given stuff
March 1, 2017

Maths
ok so far. Now use the last piece of information: "In 4 years Harry will be twice as old as Ben" B + 37 = 2(B+4) B + 37 = 2B + 8 29 = B <---- Ben's present age check: Ben is now 29 Harry is now 62 in 4 years: Ben is 33 Harry is 66 Is Harry twice as old as Ben...
March 1, 2017

Math
2l + 2w = p 2l + 600 = 800 ... l = ...
March 1, 2017

Related Rates
V=(?/3)(r^2)h but we are told that h = 2r or r = h/2 V = (1/3)? (h/2)^2 (h) = (1/3)? h^3/4 =(1/12)? h^3 dV/dt = (1/4)? h^2 dh/dt 10 = (1/4)?(625) dh/dt dh/dt = .... you finish it.
March 1, 2017

Maths
What is (26/52)(26/52) ???
March 1, 2017

Maths
0, there is no E to start with.
March 1, 2017

Maths
both are binomial distribution problems prob(boy) = 1/2 prob(girl) a) in 4 children, we want 3 boys and 1 girl = C(4,3)(1/2)^3 (1/2)^1 = 4(1/16) = 1/4 b)2 boys, 2 girls = C(4,2)(1/2)^2 (1/2)^2 = 6(1/16) = 3/8
March 1, 2017

Maths
prob(all women) = C(4,3)/C(10,3) = ... prob(two men, 1 woman) = C(6,2)*C(4,1)/C(10,3) = ....
February 28, 2017

math
umhh, how about y = 15,000 + 75x
February 28, 2017

math
Your question makes little sense. The sum on the two dice is between 2 and 12 What's with all the weird numbers? ok, a) the prob of rolling a sum not more than 1010 = 1 b) prob of sum less than 77 = 1 so prob of sum not less than 77 = 0 c) prob of sum between 33 and 77 ?? ...
February 28, 2017

math
case 1 : Pay = .06s, where s is the total sales case 2: Pay = 1500 + .04s so you want to solve: .06s = 1500 + .04s go for it.
February 28, 2017

Math
A reflection of "what" over the x axis? what does log1/a(x) mean - is the base 1/a ?? like in log 1/a x ??
February 28, 2017

Maths
girls : boys = 3:6 = 1:2 let the number of girls be x let the number of boys be 2x 2x - x = 15 x = 15 we have 15 girls and 30 girls for a total of 45 pupils
February 28, 2017

Math - Linear Approximation
using: f(x)?f(xo)+f?(xo)(x?xo) <-- should be in your text 27.07 = 27 + .07 let f(x) = x^(2/3) f'(x) = (2/3)x^(-1/3) let xo = 27, x = 27.07 f(27.07) ? f(27) + f'(27)(27.07 - 27) = 27^(2/3) + (2/3)(27)^(-1/3) (.07) = 9 + (2/3)((1/3)(.07) = 9 + .01555.. = 9.01555.. by ...
February 28, 2017

Calculus
x^2 + xy + y^2 = 9 2x + x dy/dx + y + 2y dy/dx = 0 dy/dx(x + 2y)= -2x - y) dy/dx = (-2x-y)/(x+2y) <---- you had that, good! to have a vertical tangent, the denominator of the above has to be zero, that is, dy/dx must be undefined. x+2y = 0 x = -2y sub into the original: (-...
February 28, 2017

Math
look for factors so that at least one of the factors is a perfect square. e.g. 162 = 9 * 18 = 9 * 9 * 2 so ?162 = ?9 * ?9 * ?2 = 3*3*?2 = 9?2 You can always check your answer using a calculator.
February 28, 2017

math
?xe^x dx = xe^x - e^x + c, where c is a constant This one should be part of your repertoire of memorized standard integrals.
February 28, 2017

math
so SD = ?400 = 20 mean = 600 use http://davidmlane.com/normal.html and plug in your values
February 28, 2017

algebra
I will interpret that as: a(1) = -15 a(n+1) = a(n) - 8 so each successive term decreases by 8 y = -8x + b when x=1, y=-15 -15 = -8+b b = -7 y = -8x - 7 or in your variables a(n) = -8n - 7 "your best answer" was C, correct There is no "best answer", the ...
February 28, 2017

Maths
i = .12/12 = .01 payment: p(1.01^48 - 1)/.01 = 2000 p = 32.67 outstanding balance after 35 payments = 2000(1.01)^35 - 32.67(1.01^35 - 1)/.01 = .... you do the button pushing
February 28, 2017

Math
Notice the y values decrease by 5 while the x values increase by 1, so the slope is a constant -5 thus the equation is y = -5x + b notice that the pair (0,-1) is the y-intercept which is what the b stands for , so ... y = -5x - 1 check it with some of the other given values, ...
February 28, 2017

math
I would just use a simple ratio ... x/9 = .8/16 x = 7.2/16 = $.45 check: 9 ounces = 9/16 of a pound (9/16)(.8) = .45 (cheese at 80 cents per pound?? where? )
February 28, 2017

optional math
You MUST know the definitions. Seventh term of geometric series is 64 ---> ar^6 = 64 ** sum of its 10 terms is 1023 ---> a(r^10 - 1)/(r-1) = 1023 *** divide *** by ** , the a will cancel (r^10 - 1)/(r^6(r-1)) = 1023/64 64r^10 - 64 = 1023r^7 - 1023r^6 = 1023r^6(r-1) took ...
February 28, 2017

Algebra 1
Just factor 2y^2+5y-42 2y^2+5y-42 = (2y - 7)(y + 6) expand it, to show it is correct
February 28, 2017

DISTANCE TIME AND SPEED
let the distance be d km time at 90 km/h ---- d/90 time at 120 km/h --- d/120 d/90 - d/120 = 1 solve for d hint: multiply each term by 360 to clear fractions
February 28, 2017

math
Choosing 2 girls from the 4 --- C(4,2) Choosing 2 boys from the 6 --- C(6,2) choosing any 4 of the 10 --- C(10,4) make use of that
February 28, 2017

maths
part at 9% -- x part at 8% -- 200,000 -x .09x + .08(200000-x) = 17200 take over
February 28, 2017

pre calculus
height = -16t^2 + 320t + 0 at ground level, height = 0 16t^2 - 320t = 0 16t(t - 20) = 0 t = 0 , at the start or t = 20 b) you want -16t^2 + 320t > 1584 16t^2 - 320t + 1584 < 0 t^2 - 20t + 99 < 0 (t-11)(t-9) < 0 9 < t < 11 , where t is in seconds
February 27, 2017

Calculus
Go with Steve's answer. Mine gives the rate at which the shadow is lengthening, I missed the part where they want the rate at which the shadow is moving. so dy/dt + dx/dt = 5.5 + 3.2 etc
February 27, 2017

Calculus
I trust you made a sketch. On mine I let the distance between the man and the post be y ft, and the length of his shadow be x ft By similar triangles: 5.3/x = 14.5/(x+y) 5.3x + 5.3y = 14.5x 9.2x = 5.3y 92x = 53y 92 dx/dt = 53 dy/dt but we know dy/dt = 5.5 so dx/dt = 53(5.5)/92...
February 27, 2017

Algebra1
term(5) = a r^4 plug in your given values
February 27, 2017

Math,science
Just use your definitions: "5th term of an arithmetic progression is 23" ---> a + 4d =23 "the 12th term is 37" --> a + 11d = 37 You have two equations in two unknows. Solve them. Hint: I would subtract one from the other. Let me know what you get.
February 27, 2017

Algebra
length of side parallel to river --- y length of the other two equal sides --- x 2x + y = 600 ---> y = 600-2x area = xy = x(600-2x) = -2x^2 + 600x this is a downwards opening parabola. Find the vertex by whatever means you were taught to find the vertex, and extract your ...
February 26, 2017

Algebra
let the number of lower tickets be x let the number of upper tickets be y x+y ?10 ---> y ? -x + 10 8x + 5y ? 200 ---> y ? - (8/5)x + 40 sketch both inequalities then pick any two points in their intersection.
February 26, 2017

Trig
ok up to 2sin2x=1 then: sin 2x = 1/2 so 2x = ?/6 or 2x = 5?/6 <--- you had that. good! x = ?/12 or x = 5?/12 <-- again, you had that, now.... the period of sin 2x = 2?/2 = ? so adding ? to any existing answer will yield a new answer, x=?/12+? = 13?/12 x = 5?/12 + ? = 13...
February 26, 2017

Math Word Problem
total number of employees --- x females = .67x = 603 x = 603/.67 = 900 so 900-603 or 297 are male
February 24, 2017

math
Use the formula for the distance between two points (x1, y1) and (x2, y2) distance = ?( (x2-x1)^2 + (y2-y1)^2 ) plug in your given values
February 24, 2017

Math
-6x^2+15x-6 = -(x^2 - 15x + 6) = -(2x-1)(x + __ ) The reason you don't understand is that their second line is incorrect. Perhaps you typed it wrong This is what I would do: -6x^2+15x-6 = -3(2x^2 - 5x + 2) = -3(2x - 1)(x - 2)
February 24, 2017

Math
They would be 7, 14, 21, ... , 896 this is an AP, where a = 7, d = 7, term(n) = 896 a+(n-1)d = term(n) 7 + (n-1)(7) = 896 7 + 7n - 7 = 896 n = 128 , so there are 128 terms
February 24, 2017

Math
Translating what you said into English .... When 8 is divided by a certain number and the result is then divided by 6 the answer is less than 1/4 let the certain number be x (8÷x)÷6 < 1/4 8/(6x) < 1/4 6x/8 > 4 6x > 32 x > 32/6 x > 16/3 test: ...
February 24, 2017

math
Ignoring the grouting gap needed , we can fit 20 tiles along each side, so we need 20x20 or 400 tiles
February 24, 2017

Maths
let the original cost price be c each 1.2(2c) - 2c = 630 .4c = 630 c = 1575 check: cost price of two suits = 2(1575) = 3150 selling price = 1.2(3150) = 3780 profit = 630
February 24, 2017

Math
for #2, go with Steve's answer. I should have called it GCD instead of LCM
February 23, 2017

Math
After subtracting the $20 from the $140 we would know how much we paid for the pizza. How many slices do we have if each slice costs $4 ? 2. This is like finding the LCM of 24, 64, and 56 At this level of arithmetic, you must have learned how to find that. e.g. 24 = 2*2*2*3 64...
February 23, 2017

Problems in three dimensions
The net of a regular tetrahedron consists of 4 equilateral triangles. Look at one of them: If the side is s, then the area = (1/2)(s)(s)sin60° = (1/2)(?3/2)s^2 = ?3/4 s^2 all 4 of them ----> 4(?3/4)s^2 = ?3 s^2 , as required
February 23, 2017

Math
a) just plug in -2 for x b) set 8-4x = 8 and solve for x c) http://www.wolframalpha.com/input/?i=plot+y%3D+8-4x d) set of real numbers for both e) and f), use the graph I gave you
February 23, 2017

Math
cscØ cosØ = -1 (1/sinØ)(cosØ) = -1 cotØ = -1 tanØ = -1, I know tan45° = +1 so Ø is in quadrants II or IV Ø = 180-45 = 135° or Ø = 360-45 = 315° so the additional information would have to be: in which ...
February 23, 2017

Math
Are the tickets put back into the draw after they were picked? Set it up like I showed you in your previous problem.
February 23, 2017

MAth
13 rocks: 8 red, 3 blue, 2 white expected value of Red = (8/13)(0) = 0 expected value of Blue = (3/13)($40) = 9.23 expected value of white = (2/13)($100) = 15.38 expected payout = $24.61 Cost of game = $20 Frank should play this game all day long, each time he is expected to ...
February 23, 2017

Trigonometry
You should have been told about the CAST rule, that is, an acronym telling you in which quadrants trig ratios are positive. Since sinC is positive and cosC is negative then C must be in quadrant II since sinØ = opposite/hyptenuse sinC = 7/25 --> y=7, r=25 x^2 + y^2= ...
February 23, 2017

Math
Your original post mentioned trapezoids and parallograms. None of your last 3 posts indicated which lines are parallel. I also suggested using letters, you did none of that. I still cannot visualize your figure.
February 23, 2017

Math
Describe the figure by using letters such as ABCD, naming them in a counter-clockwise order. More information is needed, such as AB || BC or angleC = 35°
February 23, 2017

Math
so the odds against the event = 59 : 41
February 23, 2017

Math
prob(event) = .41 prob(not event) = 1-.41 = .59 odds in favour of the event = .41 : .59 = 41 : 59
February 23, 2017

math
Let three of the adjacent sides by x, y, and z then the volume is xyz and xy=8 xz=18 yz=25 (xy)(xz)(yz) = 8(18)(25) x^2 y^2 z^2 = 3600 (xyz)^2 = 3600 xyz = 60
February 23, 2017

Math
Why not type in the regular way like you did here ? http://www.jiskha.com/display.cgi?id=1486616450 I can't read your post the way it was typed.
February 23, 2017

Math
expected to see an "=" sign in tn-tn-2(n-3)/(n-1) check your spelling and correct. Also use brackets, eg is it : tn = t(n-2)*(n-3)/(n-1) ??
February 23, 2017

High School Geometry
from 4/ an arc from B to D suggests that the arc passes through A If that is the case, BD is the diameter and your arc is a half-circle. (Any angle subtended by a diameter is 90° ) I am going to guess that half the square lies within the half-circle. If that is the case, ...
February 23, 2017

Math
Visualize slicing a nice round object such as an apple in the way you described. Try to sketch a 3-D diagram. Your slice will have a circular surface. Sketch a right-angled triangle with hypotenuse of 16 and height of 9 The third side will the the radius of you circular slice...
February 23, 2017

Math
I did part a) here http://www.jiskha.com/display.cgi?id=1487781971
February 23, 2017

Math
prob(a 2) = 1/6 prob(not a 2) = 5/6 assuming you want exactly 50 out the 240 to be a 2. prob(50 2's out of 240 throws) = C(240,50)(1/6)^50 (5/6)^190 (my calculator can do the two powers but not the C(240,50) )
February 23, 2017

business math
No calculations needed. You are earning 12% p.a. vs paying 9% compounded monthly Take the loan e.g. Interest payable for the first month on the loan = 20000(.09/12) = 150 interest earned on fund in first month = 20000(.12)(1/12) = 200
February 23, 2017

math
From your sketch, join the end of the chord to the centre, drop a height from the centre to the chord. You have a right-angled triangle, with 2 sides known, base is 5, hypotenuse is 13. By Pythagoras, find the height Find the central angle using basic trig. find the ...
February 23, 2017

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