Posts by Reiny
Total # Posts: 40,239

math
term(1) = a term(n) = a + (n1)d = a + (n1)(4a) = 37a (n1)(4a) = 36a n1 = 9 n = 10 
math
term(1) = a = 6.1 term(14) = a + 13d = 7.1 6.1 + 13d = 7.1 13d = 1 d = 1/13 
Math
so female = (3/8)(5000) = 1875 then male = 3125 total admitted= .4(5000) = 2000 so half were male, half were female male admitted = 1000 female admitted = 1000 percentage of females admitted = 1000/1875 = 53.3% percentage of males admitted = 1000/3125 = 32% 
Math
(k+ 1/k)^2 = k^2 + 2(K)(1/k) + (1/k) = 36 k^2 + (1/k)^2 + 2 = 36 so k^2 + (1/k)^2 = 34 you are correct 
Math
each equation can be solved indivually to get two answers. I suppose you want the value of x which satisfies both equations. so .... x^2 + 5x+6 = x^2  x  6 6x = 12 x = 2 or: x^2  x  6 (x3)(x+2) = 0 so x = 3 or x = 2 x^2 + 5x+6 = 0 (x+2)(x+3) = 0 x = 2 or x = 3 so the... 
Calculus
Since you want the average velocity, you don't even need the derivative when t = 1, s = 6(1) + 2(1) = 8 when t = 4, s = 6(16) + 2(4) = 104 average speed = total distance/total time = (1048)/(41) = 32 mph 
Algebra
Since distance = time x rate number of miles = 66h 
Algebra
Meg m Jill  m2 Beth  m/2 or Meg  2x Jill  2x  2 Beth  x or Jill  x Meg  x+2 Beth  (x+2)/2 or Meg  10x Jill  10x2 Beth  5x or ..... 
statistics
1.00 ? z is the same as z ? 1 or 1  P(z ? 1.00) > .8413 I don't know how old your tables are or what they look like, but for most of them ... here is a typical one: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf find 1.0 in the horizontal under the 00 ... 
math
What is a square qt ?? 
Algebra
You must know the basic formulas for a geometric sequence. term(n) = a r^(n1), where a is the first term, r is the common ratio and n is the term number for yours: ar = 9 and ar^3 = 81 divide one equation by the other: ar^3/(ar) = 81/9 r^2 = 9 r = ± 3 then ar = 9 So if... 
math
Why do you have a double division sign? Did you mean (d+g)/h ?? the way you typed it: d+g/h = 15 + 27/7 = 132/7 , not one of the choices if you meant: (d+g)/h = (15+27)/7 = 42/7 = 6 Now, tell me why you could not have done this yourself? 
math 5th
original: Beena  x Alisha  x+114 after giveaway: Beena  x+96 Alisha  x+114  96 = x + 18 x+96 = 2(x+18) solve for x 
correction  mathh
in the line near the end: x = ?  .60136... = 2.5102 it should be x = ?  .60136... = 2.5402>/b> 
mathh
I am sure bobpursly had already answered this for you, but I could not find the post. I recall he took you as far as the quadratic. Why did you not finish it ?? 2sec^2x 3tanx =5 for [0,2pi) make use of your identities sec^2 A = 1 + tan^2 A 2(1 + tan^2 x)  3tanx  5 = 0 2 + ... 
calc
Because it is customary, and it often makes it easier, if the coefficient of the square term is positive. So I switched all the signs, you must have known that this would not change the solution to the equation. 
calc
Final word: http://www.wolframalpha.com/input/?i=solve+2cos(2x)%3Dsinx look at the graph, let your mouse hover over the red intersection points. 
calc
Nope, my equation is correct, I should not have skipped that one step: 2cos2x=sinx 2cos2x + sinx = 0 2(1  2sin^2 x) + sinx = 0 2  4sin^2 x + sinx = 0 times 1 2 + 4sin^2 x  sinx = 0 4sin^2 x  sinx  2 = 0 checking one of your answers in the original equation: let x = 2.... 
calc
2cos2x=sinx 2cos 2x + sinx = 0 2( 1  2sin^2 x) + sinx = 0 4sin^2 x  sinx  2 = 0 sinx = (1 ± ?1  4(4)(2)) /8 = (1 ± ?33)/8 = appr .84307.... or appr .59307... If sinx = .84307 x is in quads I or II, and x = appr 1.002967 or appr. 2.1386 if sinx = .59307.. ... 
Maths
How does this question and its solution tie in with your problem? /display.cgi?id=1447959082 
Maths
"sum of circumferences of two circles wirh radii r1 & r2" = 2?r1 + 2?r2 "the circumference of a circle of radius r" = 2?r they are equal .... 2?r1 + 2?r2 = 2?r 2?(r1 + r2) = 2?r divide both sides by 2? 
math
really ?? 
math
sum(21) = 28 (21/2)(2a + 20d) = 28 2a+20d = 56/21 sum(28) = 21 (28/2)(2a + 27d) = 21 2a+27d = 42/28 = 3/2 subtract the two equations: 7d = 3/2  56/21 = 7/6 d = 1/6 in 2a + 20d = 56/21 2a  20/6 = 56/21 2a = 6 a = 3 so we need: a + (n1)d = 0 3 + (n1)(1/6) = 0 3  (1/6)n... 
Math
1/4 square inches = 5 ft < makes little sense or 1/4 square inches = 5 square ft ?? is this a continuation of your previous "scale factor" question? if so, the scale was 1 : 24?5 then model : 46950 = 1 : 24?5 model = 874.86 I sure some author did not embarrass... 
math
let the sum be x x(1.05)^2  x  x(.05)(2) = 205 x(1.05^2  1  .05(2) ) = 205 .... let me know what you got 
Math
1/4 square inches > 5 square ft 1/2 inch > ?5 ft 1 inch > 2?5 ft 1 inch  2?5(12) = 24?5 inches scale : 1 : 24?5 or appr 1 : 53.67 , just like Arora had. 
Maths
let the areas of the flats be 5x , 6x, and 8x for a, b, c respectively Now use your given data: "the difference in the area of flat c and flat a is 270 square metres" > 8x  5x = 720 solve for x, and sub into my definitions 
Math
Use your definitions 2nd term : ar = 1 5th term : ar^4 = 1 divide: r^3 = 1 r = 1 the ar = 1 a(1) = 1 a = 1 your GP is 1,1,1,.... (not a very exciting sequence, some authors would exclude r = 1 in a GP) 
calculus 1chemistry
It will reach a max when R '(T) = 0 R'(T) = .1(.15T^2 + 8T) = 0 .15t^2  8t = 0 t(.15t  8) = 0 t = 0 , (at the beginning) or t = 8/.15 sec = 160/3 sec find R(160/3) to get that maximum 
continued  Algebra and Geometry
take a line segment of length 1 , and divide it into a larger and a smaller segment , so that the ratio of the whole line to the larger = the ratio of the larger segment to the smaller. Let the larger segment be x then the smaller is 1  x 1/x = x/(1x) x^2 = 1  x x^2 + x  1... 
continued  Algebra and Geometry
list the first 20 or so Fibonacci numbers. From left to right, divide one number by the number before it, noting the result. What do you notice about the answers ?? 
continued  Algebra and Geometry
after you find the golden ratio, take its reciprocal on your calculator. Notice the decimal sequence does not change. No other number has that property 
Algebra and Geometry
One of my favourite websites: http://www.maths.surrey.ac.uk/hostedsites/R.Knott/Fibonacci/fib.html It would take you weeks to follow all the links and sideinterests of this wonderful webpage It starts with the Fibonacci numbers, which are very closely linked with the Golden ... 
algebra math, 8th grade
Or, to illustrate Scott's concept, just plot the given points. 
Math
R = mE + b case1: R = 530, E = 16000 530 = 16000m + b ** case2: R = 730, E = 3600 730 = 3600m + b *** subtract *** from ** 200 = 12400m m = 1/62 back in *** 3600(1/62) + b = 730 b = 24430/31 R = (1/62)E + 24430/31 so when E = 1300 R = (1/62) + 24230/31 = 23780/31 or appr 767 
Math
well, if 1 inch > 15 ft then 8 inches > 8(15) ft or 120 ft and 12 inches ........ 
Algebra
in 3  3/x , x cannot be zero ! did you mean x ? 0 ?? 3 3/x = x+7 times x 3x  3 = x^2 + 7x x^2 + 4x + 3 = 0 (x+3)(x+1) = 0 x = 3 or x = 1 what do you think? 
AP Calculus 12
I will assume you mean lim (1  cosx)/sinx , as x > 0 = lim (1  cosx)/sinx * (1+cosx)/(1+cosx) = lim (1  cos^2 x)/(sinx(1+cosx) = lim sin^2 x/(sinx(1+cosx) , as x > 0 = lim sinx/(1+cosx) , as x > 0 = 0/2 = 0 
algebra
what is 6 + 5(2) ? = 6  10 = 4 
algebra
just replace n with 6 a(6) = 6 + (5)(2) = 4 2nd question: correct let x = 8, y = 3(8)+7 = 31 let x = 6, y = 3(6)+7 = 25 ... let x = 2, y = 3(2)+7 = 1 so the range is {31, 25, ... ,1} 
algebra 1
from mailroom at floor x : x + 4  7 + 9  6 + 2  8 = 1 x = .... 
Math
in your repertoire of factoring techniques and formulas, you should have: x^3 + y^3 = (x+y)(x^2  xy + y^2) and x^3  y^3 = (xy)(x^2 + xy + y^2) so .... x^3 + 125 = x^3 + (5)^3 = (x+5)(.....) let me know what you get 
Algebra
the domain of the inverse of f(x) is the range of f(x) if f^1 (x) = x^2  4/5 the inverse of that is x = y^2  4/5 5x = 5y^2  4 (5x+4)/5 = y^2 f(x) = y = ±?((5x+4)/5) < the range of that is any real number 
Math
after first discount: cost = .8(149.99) = 119.99 so yes, you qualify for the second discount. cost after second discount = .9(119.99) = 107.99 total savings = 149.99  107.99 = $42.00 none of the choices are correct, unless you have a typo in a) 
Math
Yes 
Math Algebra 1
Cost A = 125 + 50t Cost B = 200 + 25t You really should have been able to do this. 
Math
I am sure you meant: f(x) = (x+1)/(x1) or y = (x+1)/(x1) f(y) = ( (x+1)/(x1) + 1) / ( (x+1)/(x1)  1) multiply top and bottom by x1 f(y) = ( x+1 + x1) / ( x+1  (x1) ) = 2x/2 = x 
math
If I recall those old nonmetric units ... 1 gallon = 4 quarts, so 3 gallons = 12 quarts 2 cups juice : 3 quarts punch = x cups juice : 12 quarts punch 2/3 = x/12 x = 12(2/3) = 8 
math
yes, of course, hit the wrong key 
math
The areas of two similar figures are proportional to the square of their corresponding sides so 225 : 81 = side1^2 : side2^2 then ?225 : ?81 = side1 : side2 side1 : side2 = 15 : 8 
Math
A) 1 cm : 5 m = 1 cm : 500 cm = 1 : 500 B) ... C) 5 cm : 10 m = 5 cm : 1000 cm = 5 : 1000 = 1 : 200 D) ... you work out the other two, then decide 
MATH
correct 
Algebra 1
I would choose elimination: first one times 2 > 6x + 4y = 20 2nd times 3 > 6x  15y = 9 subtract them: 19y = 29 y = 29/19 back into the original first: 3x  58/19 = 10 3x = 58/1910 = 132/19 x = 44/19 
Math
Was there a question? What are those decimals in your second post ? 
Math
Start with y =  x  you should be able to graph this if not, look at Wolfram: http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C a big V with nothing below the xaxis consider: y = x  2 , we just moved the entire graph down 2 units. http://www.wolframalpha.com/input/?i=y+%... 
Math
you stated correctly, that the depth depends on the time?  so doesn't the depth depend on time, making time the independent variable, and depth the dependent one ?? Usually the independent variable goes on the vertical axis, (the yaxis), and the independent variable ... 
@ Candi
Candi, do not put a new question as an answer to somebody else's. It may not be looked at , since we might think the first question has been answered. '2/3 of a given number is 40'  (2/3)x = 40 x = 40(3/2) = 60 now 2/5 of that is (2/5)(60) = 24 Where did the 200... 
Math
No, did you notice that the y values are all powers with base 5 ? (1,5) > (1, 5^1) (2, 25) > (2, 5^2) ... (5, 3125) > (5, 5^5) So y = 5^x , which I don't see as one of the options, unless you have typo in either B or C 
Math
2(18) + 2(1.5) + soda = 10 + 30.25 solve for 'soda' 
math
Draw your sketch and find the intersection of the two straight lines. The y of that intersection point is the height of your triangle. In your head, you can see that the xintercept of x+y=24 is (24,0) and the xintercept of 3x  2y = 12 is (4,0) so you know the base length of... 
math geometry
Find the volume of the first cone. You know r = 5 and h = 18 You MUST know the formula for the second cone you know r = 7.5 and you have to find h sub in r = 7.5 and h in the formula and set it equal to the volume of the first cone. Solve for h let me know what you get. 
Algebra
john's rate = 5 cups/2 min = 2.5 cups/min sam's rate = 6 cups/2.5 min = 2.4 cups/min combined rate = 4.9 cups/min so time to make 245 cups = 245/4.9 = 50 minutes check: in 50 minutes, john can make 50(5/2) = 125 cups in 50 minutes , sam can make 50(6/2.5) = 120 cups ... 
Math
Again, what formula are you using ?? 
Math
That's what I used to call mathemagics  unfortunately you are wrong! "I just added in the numbers to the formula and 59 just appeared"  nonsense! What formula? Show me if you want help 
Math
no show me your work so I can tell you where you went wrong. 
Math
correct, if you use all the digits that you can hold in your calculator's memory, you will get it exactly to the cent. 
Math
i = .05/12 = .0041666.. (keep it in your calculator, don't round off) n = 60 paym( 1  (1.04166...)^60)/ ..041666... = 2000 solve for paym let me know what you got. 
math
original: number of math books  5x number of geogr books  7x number of science books  8x new numbers: math  1.4(5x) = 7x geography 1.5(7x) = 10.5x science  1.75(8x) = 14x new ratio = 7x : 10.5x : 14x = 7 : 10.5 : 14 = 14 : 21 : 28 = 2 : 3 : 4 
calc
or Newton's method: let y = lnx  x^3 + 1 dy/dx = 1/x  3x^2 newx = x  (lnx  x^3 + 1)/(1/x  3x^2) = (1  3x^3  lnx + x^3  1)/(1/x  3x^2) = (2x^3  lnx)/(1/x  3x^2) guess: x = .5 newx1 = .3545... newx2 = .38789... nrwx3 = .39042.. newx4 = .39044046 newx5 = .39044046... 
Math
log?62 = a , 4^a = 62 , I know 4^3 = 64 , so a = appr 3 , but a < 3 log?36 = b , 6^b = 36, so b = 2 log?10 = c , 3^c = 10, I know 3^2 = 10 , so c = appr 2, but c >2 log?20 = d , 5^d = 20 , I know 4^2 = 25, so d < 2 order: log?20 , log?36 , log?10 , log?62 
Calculus
Looks pretty straight forward ... f(x)=9x^(1/3) + (9/2)x^(4/3) f ' (x) = 3x^(2/3) + 6x^(1/3) f''(x) = 2x^(5/3) + 2x^(2/3) for relative max/min, f'(x) = 0 3x^(2/3) + 6x^(1/3) = 0 3x^(2/3) (1 + 2x) = 0 3x^(2/3) = 0 > no solution or 1+2x = 0 x = 1/2 ... 
Calculus
Your lack of brackets leave the interpretation of the equation very ambiguous. e.g. do you mean: f(x)=9x^(1/3) + (9/2)x^(4/3) ? please retype before I attempt it 
Maths
What is a rectangular pentagonal garden? Where is point A ? 
Algebra 2
or , assuming you meant : 4* 4^(x/2) =1024 4^(x/2 + 1) = 4^5 x/2 + 1 = 5 x/2 = 4 x = 8 If you meant: 4* (4^x)/2 =1024, the way you typed it (4^x)/2 = 256 4^x = 512 xlog4 = log512 x = log512/log4 = 4.5 
Math
Your hyperbola has centre (0,1) , a = 3, and b = 1 vertices would be (3,1) and (3,1) To sketch this hyperbola I would faintly sketch a rectangle with corners at (3,2), (3,2) , (3,0) and (3,0) One asymptote would run through (3,2) and (3,0) and of course (0,1) slope = 1/3 y... 
math
I noticed that the coefficients of y are ± 1 , so ... add the first and the second: 6x = 1 x = 1/6 , well that was lucky add the second and third: 3x + 3z = 3 x + z = 1 1/6 + z = 1 z = 7/6 sub into the last: 1/6 + y  7/6 = 6 times 6 1 + 6y  7 = 36 y = 42/6 = 7 
math
Did you make a sketch? draw a horizontal at the 3 m height, and you will get a rightangled triangle with sides 12 and 5. You might recognize the 51213 rightangled triangle, if not ... h^2 = 5^2 + 12^2 = 25 + 144 = 169 h = ?169 = 13 m 
physics
I am going to do this question with actual numbers let u0 = 20 m/s let v0 = 28 m/s let á = 5 m/s^2 let â = 4 m/s^2 case 1: á = 5 m/s^2 then u0 = 5t+ c when t = 0 , 20 = 0 + c velocity1 = 5t + 20 similarly velocity2 = 4t + 28 distance1 = (5/2)t^2 + 20t + k, ... 
Math
just translate and use your definitions of an AS a+3d = a+4d  3 d = 3, hey, we got the common difference already a+6d = 3(a+4d) a + 6d = 3a + 12d 2a = 6d = 18 a = 9 check: terms are: 9 6 3 0 3 6 9 12 15 .... all conditions check out. 
Math
If possible, I prefer to work without fractions (27\8)A+7=(4\9)3A times 72 243A + 504 = 32  216A 459A = 472 A = 472/459 I verified this answer in the left and right sides. 
Algbra
Here is a quick way to find the slope of a line, if written in the form Ax + By + C = 0 the slope of the line is A/B so for #1 2x=10y+6 > 2x  10y + 6 = 0 , slope = 2/10 = 1/5 x+5y=3  slope = 1/5 so the lines have different slope, so they must intersect in 1 ... 
Alegbra 1
Bill, you have now posted this same question 7 times since yesterday. You received a variety of ways to get the answer. Ms Sue even told you not to post it again, so here it is once more 
Math
this is probably a question asking for EXACT values 37.5 = 1/2 of 75 and 75 = 30+45 so find tan75 = tan(30+45) = (tan30 + tan45)/( 1  tan30*tan45) = (1/?3 + )/(1  1/?3) = (1+?3)(?3  1) recall tan 2A = 2tan A/(1  tan^2 A) tan 75 = 2tan37.5/(1tan^2 37.5) let tan37.5 = x (1... 
Algebra 2/ Intermediate
I will assume you mean: log4(x6)= 1 then .. x6 = 4^1 x6 = 1/4 4x24 = 1 4x = 25 x = 25/4 
Math
geeeshhh let her income be x (1/4)x + (1/12)x + (1/2)x + 10000 = x times 12 3x + x + 6x + 120000 = 12x 120000 = 2x x = 60,000 
Math Help
did you notice: 129=3 1512=3 so what is your verdict ? 
Should be the last one
You probably did 3^2 instead of 2^3  neither one of which requires a calculator 
Should be the last one
make sure you follow the order of operations 4 + 3(10  2^3) = 4 + 3(10  8) = 4 + 3(2) = 4 + 6 = 10 how did you get 11 ?? 
correction  MATH
since V = pi(r^2)h if we double r and h new V = pi(2r)^2(2h) = 8pi r^2 h so it increased 8 times or, since they gave you the volume after doubling in the second sentence, just divide 401.9/50.2 = 8.0059... or 8 times or volume of similar objects varies directly with the cube ... 
math
nothing to solve, you don't have an equation. If you are simplifying .... 3loga(2x+1)2loga(2x1) = loga(2x+1)^3  loga(2x1)^2 = loga [ (2x+1)^3 / (2x1)^2 ] not really simplifying, just changing it around a bit 
Mathe
Did you make a sketch ? Draw a perpendicular from the centre to the chord and you have a rightangled triangle. h^2+ 6^2 = 8^2 h^2 = 6436 = 28 h = ?28 cm 
Math again ;;
First you have to expand using the distributive property 5x + 2(x + 6) , remember multiplication comes before addition according to BEDMAS = 5x + 2x + 12 = 7x + 12 
Algebra 1
Since the two y values must be the same .... 2/5 x 17 7/10 = 5/2 x + 20 2x/5  177/10 = 5x/2 + 20 I suggest we multiply each term by 10 4x  177 = 25x + 200 take over , (the x value is a whole number, but the y isn't) 
math
Well, if n is a whole number, then 2n will always be even. When you add 1 to any even, the result will be odd. So 2n+1 is always odd by writing it as 2n^3+n^2+6n+3 = (2n+1)(n^2 + 3) I have shown that one of the factors, namely (2n+1), will always be an odd number, thus 2n^3+n^... 
math
let's factor it ... 2n^3+n^2+6n+3 = n^2(2n+1) + 3(2n+1) = (2n+1)(n^2 + 3) what kind of a number is 2n+1 ?? 
Geometry
let the other endpoint be (a,b) recall how to find the midpoint: for the xcoordinate, add up the x's of the endpoints , then divide by 2 for the ycoordinate, add up the y's of the endpoints , then divide by 2 so for the x of the endpoint: (a+7)/2 = 2 a+7 = 4 a = 3 ... 
PLEASE HELP, MATH
Alternate way: find inverse of f(x) to see if you get g(x) let y = f(x) = (7x2)/4 the inverse is : x = (7y2)/4 4x = 7y  2 4x + 2 = 7y y = (4x+2)/7 which is the given g(x) so yes, they are inverses of each other. 
math  factoring
the pattern for the difference of squares is a^2  b^2 = (a+b)(ab) so for your 25x^2  9 or (5x)^2  (3)^2 , what do you see for a and what for b ? what would you get as the factors ?? 
Math (Check Answers Please)
You might want to "disguise" the equation a bit, so that it is not so obvious such as yours. e.g. 6x + 21 = 3(2x + 5) + 6 In your explanation, you might also want to show the results for the 3 types of condition. 1. If after solving the equation the variable ... 
Does anyone know how to do calculous easy?
Assuming you know and are reasonably good at basic arithmetic, algebra and related topics .... Pay attention in class. Understand the basic concepts. Do lots of questions. Calculus will be easy.