Posts by Reiny

Total # Posts: 38,877

Algebra 2
(?8+?5)(?8 - ?5) (1 + i?2)(1 -i?2)

Algebra word problem
job done = time x rate let job done = 1, since it is a constant John's rate --- 1/12 Mike's rate ---- 1/x combined rate = 1/12 + 1/x = (x+12)/(12x) after John worked for 3 hours job done = 3(1/12) = 1/4 so job left to be done = 3/4 (3/4) / ((x+12)/(12x)) = 5 (3/4)(12x...

Math 253 algebra
Ann's rate ---- 1/2 The job is a constant, let job = 1 Job = rate x time sister's rate ----- 1/x combined rate = 1/2 + 1/x = (x+2)/(2x) 1/( (x+2)/2x ) = 5/4 2x/(x+2) = 5/4 8x = 5x+10 3x=10 x=10/3 alone, her sister would take 10/3 hrs or 3 hours and 20 minutes.

Algebra
using the vertex: y = a(x+12)^2 - 1 but (-10,5) lies on it, so ... 5= a(2^2) - 1 6 = 4a a = 3/2 y = (3/2)(x + 12)^2 - 1 expand to get the other form

Maths
Notice the scale of 1 : 200000 has no units. that means we could use any units, that is, 1 cm on the map represents 200000 cm 1 mm on the map represents 200000 mm 1 inch on the map represents 200000 inches so if 1 cm represents 200000 cm then 2.5 cm represents 2.5(200000) cm ...

Calculus Antiderivatives
Any linear function would do How about f(x) = 4x + 5 f ' (x) = 4 Since the derivative of a function represents the slope of that function, and the slope of a straight line is constant, the slope of the function I gave is always 4

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 ...

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

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...

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 ...

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

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

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

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!

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...

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) ...

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.

Math

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

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...

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 ...

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

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 ...

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

math
What is (3/5)(2/5) ?

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

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/...

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

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 ?

Math
no 45000(.98)^15 = appr 33236

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

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

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 - ...

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

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...

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

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

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

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

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...

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 ...

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...

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.

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

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...

Math
2l + 2w = p 2l + 600 = 800 ... l = ...

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.

Maths
What is (26/52)(26/52) ???

Maths

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

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

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

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 ?? ...

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.

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 ??

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

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 ...

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: (-...

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.

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.

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

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 ...

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

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, ...

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? )

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 ...

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

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

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

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

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

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

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...

Algebra1
term(5) = a r^4 plug in your given values

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.

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 ...

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.

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...

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

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

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)

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

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: ...

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

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

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

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...

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

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

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 ...

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

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 ...

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= ...

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.

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°

Math
so the odds against the event = 59 : 41

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

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

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.

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) ??