Thursday
May 28, 2015

Posts by Reiny


Total # Posts: 30,086

Statistic
for test1 prob correct = 1/4 prob wrong = 3/4 i) could be c or wc or wcc , (c for correct, w for wrong) prof (of that) = 1/4 + (3/4)(1/4) + (3/4)^2 (1/4 = 37/64 ii) less than 4 correct ---> none correct + 1 correct + 2 correct + 3 correct = C(8,0) (1/4)^0 (3/4)^8 + C(8,1)(1...
January 2, 2015

Physics 1
v = -9.8 t so when t = 10 s v = -9.8(10) = -98 m/s The negative indicates the direction of the stone.
January 1, 2015

algebra 2
I will assume you meant to type (x^2 + 8x + 15)/(x+5) and you want to simplify it = (x+5)(x+3)/(x+5) = x+3 , x ≠ -5
January 1, 2015

math
The number of subsets of 6 from 18 is C(18,6) = 18!/(6!12!) = 18564
January 1, 2015

regneing
Very strange question. 2 x 8084506040 ≠ 8002408082
December 31, 2014

Math
You would use ADDITION No need for multiplication, division, or fractions in this case. 360+240=600
December 31, 2014

MATH
If you have two points (a,b) and (c,d) then the distance between them is √( (a-c)^2 + (b-d)^2 ) (notice that since we are squaring the difference, it really would not matter in which direction you are subtracting) e.g. for R(-2,1) and S(-5,1) RS = √( (-2+5)^2 + (1-...
December 31, 2014

Algebra
Olivia, why did you not evaluate the equation given to you in the first reply ? it gives a time of 2.777... or 2.8 years Bob gave you the calculation using compound interest, the most likely scenario in our 21st Century, and the time for this real-life case would be 2.65 years...
December 31, 2014

Algebra 1
What is this? Are you expanding 2x(3xy + 4y² + 8y) ? Then it would simply be = 6x^2 y + 8x y^2 + 16xy What you did is pure mathematical gibberish
December 30, 2014

GRANTHAM
PV = 2000 (1 - 1.06^-14)/.06 = ....
December 30, 2014

Algebra 1
I agree with Steve, I got x = 6/17 , y = 9/17 , which does not match any of the answers given
December 30, 2014

algebra 2
divide each term by -3 x^4 - 9x^2 - 400 = 0 (x^2 - 25)(x^2 + 16) = 0 x^2 = 25 OR x^2 = -16 x = ± 5 or x = ± 4i
December 29, 2014

Algebra 2
The correct statement is Salary = 2000x + 45500 , 0 ≤ x ≤ 10 , x ∈ I so it looks like B is the closest match. James's answer is incorrect, e.g. if x = 1 , the salary based on his formula is 45700 whereas it should be 47500, which is obtained with B
December 29, 2014

Algebra 1
Lucina's conclusion is correct, but based on an incorrect result. The slope of the first line is -2/3 the slope of the 2nd line is 2/3 so they are neither parallel nor parallel Lucina stated that their slopes were equal, if they had been equal, then the lines would have ...
December 29, 2014

Algebra 1
We can see that the slope of the given line is -1/4 So the slope of our new line must be 4 thus: y-5 = 4(x+3) Massage this equation to whatever form you need
December 29, 2014

Precalculus
No you have to expand (800+x)tan33 to get at the x inside the bracket. so ... 800tan33 + xtan33 = xtan35 now get all the x terms to one side 800tan33 = xtan35 - xtan33 x is a common factor: 800tan33 = x(tan35-tan33) divide both sides by tan35-tan33 800tan33/(tan35-tan33) = x ...
December 29, 2014

geometry
Let a point on the locus be P (x,y) then √(x^2 + y^2) = √((x+2)^2 + (y-5)^2) square both sides: x^2 + y^2 = (x+2)^2 + (y-5)^2 x^2 + y^2 = x^2 + 4x + 4 + y^2 - 10y + 25 4x - 10y = -29 which is the perpendicular bisector of the line joining (0,0) and (-2,5) , as ...
December 29, 2014

CAL-Critical points
F ' (x) = (x^2(1/x) - lnx(2x) )/x^4 = (x - 2x lnx)/x^4 = 0 for critical values x - 2x lnx = 0 x(1 - 2lnx) = 0 x = 0 , but for lnx to be defined, x > 0 or 1-2lnx = 0 lnx = 1/2 , x = √e x = appr 1.65 y = (1/2) / (1.65)^2 = appr .18 the critical point is appr (1.65...
December 29, 2014

Algebra
You probably mean, "completing the square", where we take the square root near the end of the process x^2 - 10x + 22 = -2 x^2 - 10x + ..... = -24 + ..... x^2 - 10x + 25 = -24 + 25 (x-5)^2 = 1 take √ of both sides x - 5 = ± √1 = ± 1 x = 5 &...
December 29, 2014

mathematics
height/15 = tan 30° take over ....
December 29, 2014

Mathematics
look for common factors first, looking at the 5x^4 and 20x^3 , that would be 5x^3 looking at the (x-7)^(-1/2) and (x-7)^(1/2) , that would be (x-7)^(-1/2) , (take the lower exponent one) also I would take out the fraction of 1/2 = (1/2)(5x^3)(x-7)^(-1/2) [x + (2/1)(4)(x-7...
December 29, 2014

Mathematics
Use the product rule for the first and the quotient rule for the second. 1. y = (5x^4)(x - 7)^(1/2) dy/dx = (5x^4)(1/2)(x-7)^(-1/2) + 20x^4 (x-7)^(1/2) I found most students find the difficulty not in finding that first derivative line, but rather in simplifying it I don't...
December 29, 2014

Mathematics
y = |x-3| ----> y = x-3 for x>3 or y = -x + 3 for x<3 for y = x-3, dy/dx = 1 , for x > 3 for y = -x+3, dy/dx = -1 , for x < 3 look at the graph of y = |x-3| http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx-3%7C when x = 3, y = 0 for both parts of the ...
December 29, 2014

maths
contradiction ! If your tank is half full and it contains 15 L, then the full capacity must be 30 L If the tank only can hold 18 L as you said, then at 15 L it is not "half filled" If you are asking what fraction 15 is of 18 ??? 15/18 = 5/6
December 29, 2014

Math
No, the point 4,4) ----> (4,-4) after a reflection in the x-a xis but the point (4,4) ---> (-4,4) after a rotation of 90° For a point P(x,y) the slope of PO , where O is the origin is (y-0)/(x-0) = y/x For a point P1(-y,x) , the slope P1O = x/-y, which is the ...
December 28, 2014

AP Calc
f ' (x) = x(1/x) + lnx + (1-x)(-1/(1-x)) + -1(ln(1-x) = 1 + lnx -1 - ln(1-x) = lnx - ln(1-x) = ln(x/(1-x)) = 0 for a min then e^0 = x/(1-x) 1 = x/(1-x) 1-x = x x = 1/2 Proof: confirmed by Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+x+ln+x%2B%281-x%29ln%281-x%29
December 20, 2014

AP Calc
I believe this is the same question, and answered by Steve http://www.jiskha.com/display.cgi?id=1419047350
December 20, 2014

Math - Two-Step Inequalities - Please Help
–3 > –3t + 6 3t > 6+3 3t > 9 t > 3 So for the given numbers, I see that only 4 > 3 so , yes, C is the correct answer.
December 19, 2014

Math
You have to look for some pattern Did you notice that for every 1 unit increase in the x's there is a 5 unit increase in the y's so you know it starts with y = 5x + b, we still don't know the b plug in one of the points , how about (1,2) 2 = 5(1) + b b = -3 ...
December 19, 2014

math
"Using 22/7 for pi is just not rational! " good one, they were selling t-shirts with that slogan to the math-nerds at our University of Waterloo a few years back.
December 19, 2014

math
I think 22/7 is the approximation we used for π in the "olden days" so a + b = π/2 or a and b are complementary angles Construct a right angled triangles with angles a and b along with the right angle since sina = 1/3, the missing side is √8 by ...
December 19, 2014

Algebra
x • b • y • a = (xy)(ab) = (1/37)(37) = 1
December 18, 2014

math
Elimination is a poor choice for this question. I would definitely use substitution. sub the 1st into the 2nd 2(5y) - 3y = 7 10y-3y=7 7y=7 y = 1 , then x = 5 compare this with elimination: 5y = x x - 5y = 0 multiply by 2, 2x - 10y = 0 2x - 3y = 7 subtract them -7y = -7 y = 1 ...
December 18, 2014

Algebra math
In English please.
December 18, 2014

math
number of people ---- n Company A: CostA = 25n + 50 Company B: CostB = 20n + 130 So for n = 100 CostA = 2500+50 = 2550 CostB = 2000+130 = 2130 When is CostA = CostB ? 25n + 50 = 20n + 130 5n = 80 n = 16 break-even number is 16 people.
December 18, 2014

Math
Why not just reverse the process and subtract 2 from top and bottom to get 2/3 ?
December 18, 2014

Calculus
done, look back please
December 18, 2014

math
first one is correct #2, 6.3% of $77 = .063(77) = $4.85 77+4.85 = 81.85 , so #4
December 18, 2014

Calculus
First of all you must understand what the intersection is When you intersect two planes you get a straight line, unless the two planes are parallel In this case they are not, since 1:1:-1 ≠ 2:4:-3 multiply the first by 3 3x+3x-3z = -36 subtract 2x+ 4y - 3z = -8...
December 18, 2014

Math
The inclusive vs exclusive restrictions in rational expressions always leads to debate. I restricted x = -1 and x = -2 since subbing in these values in the original yields 0/0 but subbing those values in my answer (and yours) yields a real number Since I was using the equal ...
December 18, 2014

Math
I read that as: (x^2 - 2x)/(x+1) * (x^2 - 1)/(x^2 + x - 6) =x(x-2)/(x+1)*(x-1)(x+1)/( (x+3)(x-2) = x(x-1)/(x+3) or (x^2 - x)/(x+3) , x ≠ -1,2
December 18, 2014

math
Please number your question, how are we to know who is who and what you want done 1. assuming you want to solve 2/3n = 8 multiply each term by 3 2n = 24 n = 12 2. sub the 2nd into the 1st 4x + 3y = 13 4x + 3(-x+4) = 13 4x - 3x + 12 = 13 x = 1 back into the 2nd, y = -1+4 = 3 x=...
December 18, 2014

Algebra
good job
December 18, 2014

Algebra
first get rid of nasty fractions by multiplying each term by 3 , LCD 3x^2 - 5x + 2 = 0 which factors quite nicely. Let me know what you got
December 18, 2014

algebra
speed of boat --- x speed of current -- y x+y = 21 x-y = 5 add the two equations, and continue
December 18, 2014

Algebra
You typed the equation incorrectly, it should say y = 5 (1/2)^(t/20) so ... 4 = 5(1/2)^(t/20) .8 = (.5)^(t/20) take log of both sides log.8 = log(.5^(t/20)) log.8 = (t/20)log.5 log.8/log.5 = t/20 t = 20(log.8)/log.5) I leave the button-pushing up to you
December 18, 2014

stats
a) prob = (25/32)(24/31) = .. b) prob = (25/32)(7/31) = ... c) prob (both red) = answer to a) prob(both black) = (7/32)(6/31) = .. prob(different colour) = 1 - a) - both black
December 18, 2014

math algebra
Let the length along the front be x let the width be y let the height be z x^2+ z^2 = 25^2 = 625 , #1 y^2 + z^2 = 20^2 = 400 , #2 subtract them x^2 - y^2 = 225 , #3 also x^2 + y^2 + z^2 = 28^2 = 784 , #4 add it to #3 2x^2 + z^2 = 1009, but x^2 + z^2 = 625 from #1 so 2x^2 + z^2...
December 18, 2014

math algebra
recall that if the line is written in the form y = mx + b, then m is the slope so ... 8y = -16 or, how about 8y = 0x - 16 y = (0/8)x - 2 y = 0x - 2 so the slope must be 0 in general if the linear equation can be written in the form y = k, where k is just a constant, you have a...
December 18, 2014

Math
Zyere is not correct 72/60 = x/40 60x = 40(72) 60x = 2880 x = 48 The ratio of height : shadow must be the same note: 72 : 60 = 6 : 5 , and 48 : 40 = 6 : 5
December 18, 2014

Math
use a simple ratio and solve for x 72/60 = x/40
December 18, 2014

math algebra
Use the last two points to find the equation slope = (697-522)/(100-75) = 175/25 = 7 so we have y = 7x + b sub in (75,522) 522 = 7(75) + b b = -3 so we have y = 7x - 3 From your knowledge of y = mx + b, what do you think?
December 18, 2014

math
Let the capacity of the tank be x L (1/4)x + 90 = (3/4)x times 4 x + 360 = 3x 2x = 360 x = 180
December 18, 2014

*repost* - Grade 11 math
sketch a right-angled triangle. On the horizontal base mark W for Wes. let the fireworks be at P and let Q be the point below P, so that angle Q = 90° let the angle at W be 28° let A for Abby be a point between W and Q so that angle PAQ = 40° , and AW = 20 Look at ...
December 17, 2014

Algebra 1
http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx+%2B2%7C
December 17, 2014

math
ar^2 = 25 ar^7 = 25/32 divide the 2nd by the 1st: r^5 = 25/32 ÷ 25 = 25/800 = 1/32 r = 1/2 in ar^2 = 25 (1/4)a = 25 a = 100 where does t come into the picture ?
December 17, 2014

Math (Repost)
1. u^-3 = 1/125 1/u^3 = 1/125 u^3 = 125 u = 5 2. y-1 = 4y - 2/3 each term times 3 3y - 3 = 12y - 2 -9y = 1 y = -1/9 3. your are right 4. number of miles last week --- x x+40 = 4x + 10 -3x = -30 x = 10 She ran 10 miles last week 5. change it into the form y = mx + b (takes 2 ...
December 17, 2014

Algebra 2
= 200(1 + .08/12)^12 = 200(1 + .0066666..)^12 = 200(1.006666...)^12 = appr 216.60
December 17, 2014

Algebra 1
slope of given line = 8/3 so slope of your new line = -3/8 through (-2,3) y = 3 = (-3/8)(x+2) since the original was written in that form, I assume the new one is to be in that same format.
December 17, 2014

Math
(m + s)/2 = 74 m+s = 148 (m + e )/2 = 83 m+ e = 166 subtract them: e - s = 18
December 17, 2014

Math
Did you notice that if you multiply the 2nd equation by 4, you get the second? So , you basically only have one equation, thus an infinite number of solutions.
December 17, 2014

Algebra 2
you know that it must be (x+y)^9 to get a ?x^7y^2 so the term is C(9,7) x^7 y^2 = 36x^7y^2 Observe that the 10th row of Pascal's triangle is 1 9 36 84 126 126 84 36 9 1
December 17, 2014

Algebra
subtract your equations: 1 Sandwich = 4.75 in the 1st: 4.75 + Salad = 8.7 salad = 3.95
December 17, 2014

MATH PLEASE HELP
1 e^.012t = 2 take ln of both sides ln e^.01t = ln2 .012t ln e = ln 2 , but ln e = 1 .12t = ln 2 t = ln2/.012 = 57.76 years or 58 years to the nearest year.
December 17, 2014

Math Help
5^x =125 <----> log5 125 = x I had my students memorize this pattern, 2^3 = 8 <---> log28 = 3
December 17, 2014

Algebra
total area = 12000 ft^2 still to be mowed = (1/2)(12000) = 8000 ft^2 let the width mowed by Lisa be x ft wide area still to be done = (100-2x)(120-2x) = 12000-200x - 240x + 4x^2 4x^2 - 440x + 12000 = 8000 x^2 - 110x + 1000 = 0 (x-100)(x -10) = 0 x = 100 or x = 10 , but clearly...
December 17, 2014

Calculus
Steve , you are right, I read the question rather superficially. (notice it was my last post last night, must have been a bit tired)
December 16, 2014

Calculus
f(x) = e^(4x^2) f(-1/4) = e^(1/4) f(1/4) = e^(1/4) avg value = (e^(1/4) - e^(1/4) )/(1/2) = 0
December 16, 2014

math help!!
This one is easier than the previous question you posted about GS's Give this one a try, you can do it.
December 16, 2014

math please hellp
Done, look back
December 16, 2014

algebra 1
when it hits the water, h = 0 0 = -16t^2 + 20t + 24 4t^2 - 5t - 6 = 0 (t-2)(4t + 3) = 0 t = 2 or t = -3/4, the last answer is inadmissible It will take 2 seconds I have no idea what the last part of your post is. Is that supposed to be a solution ? If so, it makes no sense at ...
December 16, 2014

math help
a + ar = 12 a(1+r) = 12 , #1 a + ar + ar^2 = 62 a(1 + r + r^2) = 62 , #2 divide #2 by #1 (1+r+ r^2)/(1+r) = 62/12 = 31/6 6r^2 + 6r + 6 = 31 + 31r 6r^2 - 25r - 25 = 0 (r-5)(6r + 5) = 0 r = 5 or r = -5/6 if r = 5 , in #1 6a = 12 a = 2 the first 4 terms are 2 , 10, 50, 250 if r...
December 16, 2014

math
Draw a right-angled triangle DAC, AC as a base line Let CD be the height of the building. Let B be a point between A and C, so that AB = 230 angle A = 28° angle DBC = 43° Look at triangle ABD, you know angle A = 28, angle ABD = 180-43 = 137 angle ADB = 15° you can ...
December 16, 2014

Math
Just did this when you posted it as "John"
December 16, 2014

calculus
Just like taking slope C(101) = 101^2 - 10000 = 201 C(100) = 100^2 - 10000 = 0 average rate of change = (201-0)/(101-100) = 201 instantaneous rate of change = 2x at x = 100 rate = 200
December 16, 2014

Algebra 1
y+7 = -.54(x-4)
December 16, 2014

math
double the first: 2x + 4y = 16 subtract from the 2nd x = 4 back into the 1st: 4 + 2y = 8 2y = 4 y = 2 x = 4, y = 2
December 16, 2014

algebra
prob = (10/24(10/24) = 25/144
December 16, 2014

Math
1st + last = 100 2nd + 2nd last = 100 ... ... looks like I can form 50 such pairs sum = 50(100) = 5000 use the same concept for the second question.
December 16, 2014

Literature - the Watch
I am sure that you were not assigned this yesterday. In my days we used to call this "planning ahead". Giving you a summary would be contributing to plagiarism . Here is a page that lets you read the short story on line: http://www.readbookonline.net/readOnLine/22270/
December 16, 2014

MATH
When I divide 56 by 3 , I get 18 packages with 2 brownies left over. So none of your choices fit.
December 16, 2014

math
assuming a and b are constants, we have (1/a^n) x^n + (1/b^n) y^n = 2 (n/a^n) x^(n-1) + (n/b^n) y^(n-1) dy/dx = 0 so for (a,b) (n/a^n)(a^(n-1) + (n/b^n)(b^(n-1) dy/dx = 0 (n/a) + (n/b) dy/dx = 0 dy/dx = -(n/a) (b/n) = -b/a equation of tangent at (a,b) y - b = (-b/a)(x-a) toy ...
December 16, 2014

one math question.
yes
December 16, 2014

contains typo - ^Maths^
You have a typo. the right side of your equation should say 72^y log3(x-7) = 2y --> 3^(2y) = x-7 log2(x-6) = 3y --> 2^(3y) = x-6 then LS = x^2 - 13x + 42 = (x-6)(x-7) = ( 2^(3y) ) ( 3^(2y) ) = (8^y)(9^y) = 72^y = RS
December 16, 2014

math algebra
Obviously the diagonal of 10 must be greater than either the length, width or height, so the height cannot be greater than 10 and you are incorrect Look at the diagonal of the base, call it d d^2 = 8^2 + 2^2 = 68 d = √68 now the diagonal we want is the hypotenuse of the ...
December 15, 2014

algebra
so his effective speed downriver is 4+3 or 7 mph and he goes for 5 hrs distance = rate x time = ....
December 15, 2014

Math
A GS, with a = -4 r = -1/4 sum(∞) = a/(1-r) = -4/(1 -(-1/4) ) = -4/(5/4) = -16/5 or -3.2
December 15, 2014

MATH
= .5^0 + .5^1 + .5^2 + .5^3 + .5^4 = 1 + .5 + .5^2 + .5^3 + .5^4 or = 1 + 1/2 + (1/2)^2 + (1/2)^3 + (1/2)^4 we could just add them up, but I guess this question deals with the sum of a GS a = 1 r = .5 n = 5 sum(5) = 1(.5^5 - 1)/(.5 - 1) = (.03125 - 1)/(-.5) = 1.9375 or 31/16
December 15, 2014

Math
= 2/2 + 3/2 + 4/2 + ... 8/2 = ∑ (1+n)/2 for n = 1 to 7 This answer is not unique, there are many ways to express it
December 15, 2014

Math
a+(a+1)+(a+2)+.....+(a+n-1) looks like an arithmetic series with first term a common difference = a+1 - a = 1 for n terms so sum = (n/2) (2a + (n-1)(1)) = (n/2)(2a + n-1) so (n/2)(2a + n - 1) = 100 2an + n^2 - n = 200 2an = 200 - n^2 + n a = (200 - n^2 + n)/(2n) n .. a 2 - 49....
December 15, 2014

Algebra
Tell me what your answer is and I will critique it.
December 15, 2014

Algebra
The first element of the vertex in this case would be the time it took to reach the highest point, and the 2nd number would be that maximum height.
December 15, 2014

Algebra
the x-intercept would be the time taken to hit the ground
December 15, 2014

Math
Memorize the relationship: π radians = 180° from that you can solve for each unit : 1 radian = (180/π) ° <-------> 1 ° = (π/80) radians so which ever is given, proceed from there (13π/12) rad = (180/π)(13π/12) ° = 195° (...
December 15, 2014

math
one hectare is 10,000 m^2 , (100 m by 100m) so half of that is 5,000 m^2 so let each side be x then x^2 = 5000 for the diagonal d, d^2 = x^2 + x^2 = 2x^2 = 10000 d = 100 m
December 15, 2014

7th grade math
#1, at 10^2 - 1 = 100-1 = 99 #14, leave your answer as an inequality, since that is what you started with, thus c < -12.8 the rest are correct
December 15, 2014

Calculus (math)
if v(t) = t^3 - 5t^2 s(t) = (1/4)t^4 - (5/3)t^3 + c s(6) = (1/4)6^4 - (5/3)6^3 = -36 + c s(-1) = (1/4)(-1)^4 - (5/3)(-1)^3 = 23/12 + c distance traveled = 23/12+c - (-36+c) = 4550/12
December 14, 2014

Steve saw the light - easy geometry
The fact that the sides were not listed sequentially made me interpret the question in an entirely different way, so go with Steve' solution. Anyway, my interpretation led to a nice problem, lol
December 14, 2014

For #1 easy geometry
From my previous reply to this problem http://www.jiskha.com/display.cgi?id=1418471605 (it was called #3 ) I had given you "I drew a figure ABCD , with AD || BC AD = 10 AB = 20 BC = 30, and CD = 10 From A draw a line AP, so that AP is || to DC and P is on BC So AP=10 and ...
December 14, 2014

easy geometry
I'll take care of #2 first. the common formula is A = P(1 + r)^n , where r is the rate per interest period expressed as a decimal (e.g. 3% --> .03 ) and n is the number of interest periods I don't know where your a comes from. so 1690 = 1000(1 + r)^2 (1+r)^2 = 1.69 ...
December 14, 2014

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