Thursday
October 23, 2014

Posts by Reiny


Total # Posts: 27,529

Math
a) prob winning = 1/C(49,6) = 1/13,983,816 b) 10,000/13,983,816 c) x/13,983,816 = 1/2 , solve for x d) prob not winning = 13,983,815/13,983,816 odds against winning = 13,983,815 : 13,983,816 e) expected value = 1,000,000(prob of a) )
April 30, 2014

math
100% + 5% salestax = 1 + .05 = 1.05 to increase something by 5% , just multiply it by 1.05
April 30, 2014

math
.85(1.05)x = 30 x=30/(.85(1.05)) = $33.61
April 30, 2014

Algebra
same type of question here http://www.jiskha.com/display.cgi?id=1397438547 just change the numbers.
April 30, 2014

Algebra 1/2
prob(3 or 5) = 2/8 = 1/4 prob(2) = 1/8 prob(3or5 then 2) = (1/4)(1/8) = 1/32
April 30, 2014

Algebra 1/2
not enough information, what kind of spinner? how many positions are possible ?
April 30, 2014

math
let the time taken by the eastbound plane until they meet be t hrs let the time taken by the westbound plane until they meet be t-1/2 hrs distance covered by the easbound plane = 700t distance covered by the westbound plane = 750(t - 1/2) 700t + 750(t-1/2) = 3420 700t + 750t...
April 30, 2014

math
What about it ? Are we integrating ? if so ... ∫sin(πx+1)dx = (-1/π)cos(πx+1) + C
April 30, 2014

Algebra 2
I answered this as part of the reply to your log question http://www.jiskha.com/display.cgi?id=1398883636 about the third line down ....
April 30, 2014

Probability
doubles --- 6 of them sumof 8 --- 26,35,44,53 62 total = 10 (we have to count 44 only once) prob = 10/36 = 5/18
April 30, 2014

Math
number of reds = 26 number of blacks faces = 6 (I think) prob(red card or black face) = 32/52 =8/13 (I believe face cards are defined as Jack, Queen and King, if not change the numbers above to match)
April 30, 2014

Algebra 2
4x = log5 90 or 5^(4x) = 90 take log of both sides log (5^(4x) = log 90 4x log5 = log90 4x = log90/log5 x = (1/4)(log90/log5) = appr .699
April 30, 2014

Maths
number of white --- n number of non-white -- 12-n prob of choosing at least 1 white = 1 - prob(choosing both non-white) = 1 - (12-n)/12 * (11-n)/11 = 19/33 (12-n)(11-n)/132 = 1 - 19/33 = 14/33 (132 - 23n + n^2)/12 = 14/3 3n^2 - 69n + 396 = 168 3n^2 - 69n +228 = 0 n^2 - 23n + ...
April 30, 2014

math
66 2/3 % is equivalent to 2/3 so (2/3)(81) = 54
April 30, 2014

math
It often helps to see a physical model of the problem Cut out a circular sector with scissors and form it into a cone. You will see that the arc length of the sector becomes the circumference of the circular base of the cone if the cone is to have a radius of 6 cm, then its ...
April 30, 2014

Math
2H + 1F = 8 ===> F = 8-2H 6H + 6F = 30 or H+F=5 using substitution: H + F = 5 H + 8-2H = 5 -H = -3 H = 3 then F = 8-6 = 2 each hamburger costs $3.00 and each fries costs $2.00
April 29, 2014

Math
width --- x lengyth -- x+11 x(x+11) = 2040 x^2 + 11x - 2040 = 0 (x-4)(x+51) = 0 x = 40 or x = - 51 , negative width makes no sense, so x = 40 the rectangle is 40 cm by 51 cm
April 29, 2014

math
I have a feeling you have typos here. Is that supposed to be 24x^2 at the top and 32x^2 ... at the bottom ?
April 29, 2014

calculus
(9x^3+5x-8) ÷ (3x-2) I assume you are studying long algebraic division, I got 3x^2 + 2x + 3 - 2/(3x-2)
April 29, 2014

math
number of tickets bought ---- x 2x ≤ 30
April 29, 2014

Algebra
(89+88+78+95+92+x)/6 = 90 solve for x
April 29, 2014

grade 3 math
There is no such rectangle. I can make the length some ridiculous length and the width very very small. e.g. length = 5000 width = 39/5000= .0078 check: the area is 5000(.0078) = 39 Perimiter is 2(.0078) + 2(5000) = 1000.0156 ft length = 20,000 width = 39/20000 = .00195 ...
April 29, 2014

Trig
This is exactly the same type of question as your previous one. Just follow my steps using these numbers.
April 29, 2014

Trig
if t1 = 7 and t2 = 205 then d = 205-7 = 198 sum(100) = (100/2)(2(7) + 99(198)) = 50(19616) = 980800
April 29, 2014

Trig
Just use your definition of term(2) and plug in the values.
April 29, 2014

Trig
a9 = 120 ----> a + 8d = 120 a14 = 195 ---> a + 13d = 195 subtract them 5d = 75 d = 15 then a+8(15) = 120 a = 0 so term(6) = a+5d = 0 + 5(15) = 75
April 29, 2014

maths
5cosx + 3 = 0 cosx = -3/5, and 180° < x < 306° so that x is in quadrant III did you notice the 3-4-5 right-angled triangle ratios? so sinx = -4/5 tanx = 4/3 3tanx + 25sin^2 x = 3(4/3) + 25(16/25) = 20 ( you can use your calculator to check this result Ø = ...
April 29, 2014

math
let the distance be d miles for Hannah: let her speed be x mph d = 6.5x for Dylan: let his speed be x+30 mph d = 2.6(x+3) 6.5x = 2.6(x+30) 6.5x = 2.6x + 78 3.9x = 78 x = 20 then d = 6.5(2) or 130 miles (I would have that "caps lock" malfunction looked after on your ...
April 29, 2014

math:mensuration plane shapes
If radius of cone is 4 cm, and its height is 3 cm, then the "slant" length of the cone is 5 cm (3^2 + 4^2 = 5^2) If cut open , this translates into a "pac-man" game looking sector with arc length equal to the circumference of the base of the cone and its ...
April 29, 2014

math
2^ = .125 2^x = 1/8 2^x = 1/2^3 = 2^-3 then x = -3
April 29, 2014

Calculus
go with Steve's I forgot to multiply the .02 by the 3 in front
April 28, 2014

Calculus
write it as P(t) = 20 (1 + 3e^(-.02t)^-1 P ' (t) = -20(1+3e^-.02t)^-2 (-.02 e^(-.02t) ) now use the product rule to get the 2nd derivatives I suggest cleaning up the first deriv. a bit
April 28, 2014

Math
I just can't see a pattern even Wolfram, which surprised me with a "pattern" function, could not see anything (I tested to see if Wolfram was able to pick up a pattern. I used n + 2^n to get the terms 3,6,11,20,37 and entered pattern { 3,6,11,20,37} look what it ...
April 28, 2014

Math
from the 1st ---- y = 8-2x so 8 - 2x = -3(x-3) 8-2x = -3x + 9 x = 1 in y = 8-2x, y = 8-2 = 6 looks like D
April 28, 2014

math (1)
Just drop in the values and stir. e.g. c) x = 2, y=1 h(2,1) = (4+8)/(2-1) = 12 That's all there is to it.
April 28, 2014

Math
(3√8 + 4√9)^2 = (3√8 + 12)^2 = 72 + 72√8 + 144 = 216 + 72(2√2) = 216 + 144√2 or appr 419.65
April 28, 2014

math
2x+8=3x+2 2x - 3x = 2 - 8 -x = -6 x = 6
April 28, 2014

math
5x-2(x+4)=3(2x+1) 5x - 2x - 8 = 6x + 3 5x - 2x - 6x = 3 + 8 -3x = 12 x = -4
April 28, 2014

Physics waves- check answers please
agree with all of them
April 28, 2014

Integrated Trig
if compounded annually 1.03^t = 2 t ln1.03 = ln2 t = ln2/ln1.03 = appr 23.45 years
April 28, 2014

Integrated Trig
5000 e^(.03t) = 10000 e^(.03t) = 2 take ln of both sides , and use rules of logs .03t = ln 2 t = ln 2/.03 = appr 23.1 years
April 28, 2014

math
solve for x 2x + 2(3x) = 64
April 28, 2014

Math 1314
width of pond --- x length of pond --- 3x width of whole thing = x+6 , (3 feet on each end) length = 3x + 6 2(x+6) + 2(3x+6) = 100 2x + 12 + 6x + 12 = 100 8x = 76 x = 9.5 ft the pond is 9.5 ft wide and 28.5 ft long
April 28, 2014

Math 120
d = -16t^2 , if we have to consider direction or d = 16t^2 if all we care about is distance when t = 17 d = 16(17)^2 = 4624 ft some deep well !!
April 27, 2014

Math HELP HELP
use Venn diagrams, fill in your data starting with the intersection of all three, then the intersection of two at a time, etc.
April 27, 2014

Maths
check your previous post for this
April 27, 2014

math/ratio
let the number of apples, oranges, and pears be 3x, 5x, and x respectively. 5x+x - 3x = 12 3x = 12 x = 4 so 12 apples, 20 oranges and 4 pears check: oranges + pears = 24 apples = 12 is 24 more than 12 by 12 ?? YES
April 27, 2014

Calculus
area = integral ( e^-x) from 0 to infinitiy = [ - e^-x] from 0 to infinity = [-1/e^x] from 0 to infinity now clearly as x ---> ∞ , 1/e^x --> 0 so we have ( 0 - (-1/1) = 1
April 27, 2014

Math
Do you want the probability of drawing 2 green balls? = (3/5)(2/4) = 3/10
April 27, 2014

Maths
the 17 would cancel, leaving you with 93/97
April 27, 2014

Math
The way you typed it: 5x/6 = 15 5x = 90 x = 18
April 27, 2014

Precalculus
A = {2,3,5,7,11,13} B = {1,2,3,4,6,9,12} c= {4,8,12,16} Just noticed that in your listing of C you don't have the 16 Does that result in your difficulties? A intersect B = {2,3) (A intersect B)' = {1,4,5,6,7,8,9,10,11,12,13,14,15,16} which in "union" with C...
April 27, 2014

Math
18 ft / 2 seconds = 9 ft/sec = (9/5280) miles / (1/3600) hours = (9/5280)(3600/1) m/h = (135/22) mph = appr 6.1 mph or 18 ft in 2 seconds = 9 ft in 1 second = 540 ft in 1 minute = 32400 ft in 1 hour = 6.1 mph
April 27, 2014

algebra
tried: ±1 , ±2 and found x = 2 to be a triple root. successive synthetic divisions shows x^5−8x^4+28x^3−56x^2+64x−32=0 (notice how we show exponents) x=2 to be triple root so x^5−8x^4+28x^3−56x^2+64x−32=0 (x-2)^3 (x^2 - 2x + 4...
April 27, 2014

Math - Trigonomety
What a silly and unrealistic problem, anyway .... I made a sketch the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65° The side opposite the 105° is also the hypotenuse of a right-angled triangle ...
April 27, 2014

Geometry
Ms Sue solved the "same" question. Just change the numbers http://www.jiskha.com/display.cgi?id=1398287442
April 27, 2014

MATHS
x/2 + 2y/3 = -1 ---> 3x + 4y = -6 x - y/3= 3 --------> 3x - y = 9 elimination: subtract them: 5y = -15 y = -3 sub into the 2nd 3x - (-3) = 9 3x = 6 x = 2 x = 2, y = -3 by substitution: from the 2nd: y = 3x-9 into the 1st: 3x + 4(3x-9) = -6 3x + 12x - 36=-6 15x = 30 x = 2...
April 27, 2014

math
to me this says: x = 4sin^3 t y = 7cos^3 t dx/dt= 12(sin^2 t)(cost) = 12cost(sint)^2 dy/dt= 21(cos^2 t)(-sint) or -21sint(cost)^2 both dx/dt and dy/dt must be zero for dx/dt =0 , dy/dt=0 12cost(sint)^2 = 0 , -21sint(cost)^2 = 0 in other words, wherever the sine or cosines are ...
April 27, 2014

Pre algebra
1 km/h = (1/60) km/minute (how many minutes are there in 1 hour? ) You don't post an actual speed (typo?). so suppose you have 80 km/h = (80/60) km/min = (4/3) km/min replace my speed with whatever speed you have, then simplify ??/60 to lowest term fractions.
April 26, 2014

Jim and Mia : - Math (6)
Jim, they do intersect at one point only, thus creating an open region on the left. By squaring you are introducing a part of the graph which was originally undefined. y = √x is defined only for x ≥ 0 Mia: Both Steve and I gave answers to this earlier http://www....
April 26, 2014

math (4)
graph of your function http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1 notice the region will be below the x-axis, so height = 0 - (-xe^(-x^2)) = xe^(-x^2) area = integral (xe^(-x^2)) dx from 0 to 1 = (-1/2) e^(-x^2) from 0 to 1 = (-1/2) e^-1 - (-1/2...
April 26, 2014

math (2)
Here is what your curve looks like from x = -1 to +1 http://www.wolframalpha.com/input/?i=y%3D+2x%2F%28x%5E2%2B4%29+from+-1+to+1 So where is the shaded region? Are you finding the area between the curve and the x-axis? (That is the usual case for this question, but let me know...
April 26, 2014

Trig
Or use the old sum of roots and product of roots property sum of roots = 5+i√2 + 5-i√2 = 10 product of roots = (5+i√2)(5-i√2) =25-2i^2 = 25+2 = 27 x^2 - (sum)x + product = 0 x^2 - 10x + 27 = 0
April 26, 2014

Calculus
draw a sketch of the situation, at a time of t hours after 9:00 am let A1 be the position of Aida let I1 be the position of Ian Join A1 and I1, to get a right-angled triangle let D be the distance between them D^2 = (6t)^2 + (20-8t)^2 = 36t^2 + 400 - 320t + 64t^2 = 100t^2 - ...
April 26, 2014

Deepa
let the number of 50 cents increases be n NOW: number of riders = 10000 cost per ride = 20 after increase number of riders = 10000- 200n cost per ride = 20+ .5n Revenue = (10000-200)(20 + .5n) expand this and you will have a quadratic representing a parabola that opens ...
April 26, 2014

For fizz - math
I answered this for you already http://www.jiskha.com/display.cgi?id=1398482333 I counted about 8 problems dealing with series of discounts, plus numerous questions that have been answered dealing with compound interest. I don't see a single reply by you or even a response...
April 26, 2014

math (trade and cash discount)
let the list price be x .85(.92)x = 239.29 x = 239.29/(.85(.95)) = ....
April 26, 2014

math
One step calculation price = 1780(.7)(.9)(.95) = 1065.33 Discount = 1780-1065.33 = $714.67 or first discount = .3(1780) = 534 leaving 1246 2nd discount = .1(1246) = 124.60 leaving 1121.4 3rd discount = .05(1121.4 = 56.07 leaving 1065.33 Discount = 1780 - 1065.33 = 714.67 as ...
April 26, 2014

MATH
tried: ±1, ±2, ±3 success at x = -3 by synthetic division 21x^3+67x^2-36=(x+3)(21x^2+ 4x - 12) = (x+3)(3x-2)(7x+6) so what do you think?
April 26, 2014

good catch- maths
Good catch Steve, the smallest 3-digit number divisible by 7 is 105 So count one more, 128 of them
April 26, 2014

maths
smallest 3 digit number divisible by 7 is 112 largest 3 digit number divisible by 7 is 994 look at the arithmetic sequence 112, 119, .... 987 , 994 how many terms are there? a=112, d = 7 term(n ) = a+(n-1)d 994= 112 + (n-1)(7) 882 = 7n - 7 889 = 7n n = 127 2. really!? (I will ...
April 26, 2014

maths
I will assume you meant, "How many red marbles should be added" let the reds to be added be x so we have 10+x reds total = 40+x (10+x)/(40+x) = (3/5) 50 + 5x = 120 +3x 2x = 70 x = 35 #5 reds should be added check: reds = 45 total = 75 percentage of reds = 45/75 = .6 ...
April 26, 2014

Maths
a) flipping 2 counters, Cam's outcomes: 11 , 12 , 21, and 22 , two ways to get a 3 ---> prob(3) = 2/4 = 1/2 flipping a die, outcomes 1,2,3,4,5,6 , one way to get a 3 --> prob(3) = 1/6 prob(both get a 3) = (1/2)(1/6) = 1/12 CA DE ---- Cam's loss ---> Dean's...
April 26, 2014

math
amount left of 1 unit after the series of 3 discounts = (.8)(.9)(.96) = .6912 amount left of 1 after a single discount of 32% = .68 which is the better discount?
April 25, 2014

Math
Just like 3(2x+5) = 6x + 15 just like 3(7+2) = 21 + 6 so is √5(2+√5) = 2√5 + √25 = 2√5 + 5 you could also check by evaluating it with your calculator.
April 25, 2014

Math
√5/(2-√5) ?? what about it? If you are rationalizing it, then = √5/(2-√5) * (2+√5)/(2+√5) = (2√5 + 5)/(4-5) = -2√5 - 5
April 25, 2014

Calculus
" 50 m away from you" -measured along the string, or measured along the ground? There is not enough information , there are 3 rates involved, but you only give one. Are we ignoring the fact that the string cannot form a straight line ? Is the kite always 40 m high?
April 25, 2014

Algebra 1
sure, if it exists For a "vertical " parabola there will always be a y-intercept For a sideways parabola, there may not be one.
April 25, 2014

math (9)
picture: http://www.wolframalpha.com/input/?i=plot+y%3D+-x%5E2%2B2x%2B4+%2C+y+%3D-x%2B4 looks like they intersect at (0,4) and((3,1) (the points satisfy both equations) area = ∫( -x^2 + 2x + 4 - (-x+4)) dx from 0 to 3 = ∫( -x^2 + 3x ) dx from 0 to 3 = [ -x^3/3 + 3x...
April 25, 2014

math (2)
we see no shaded region.
April 25, 2014

Math (6)
Since x ≥ 0 for y = √x the graph shows that we cannot have a closed region. see ... http://www.wolframalpha.com/input/?i=plot+y%3D+√%28x%29+%2C+y%3D+x-2
April 25, 2014

math
must exclude no heads and 1 head prob(no heads) = (1/2)^6 = 1/64 prob(1 head) = C(6,1) (1/2)^1 (1/2)^5 = 6/64 prob (more than 1 head) = 1 - 1/64 - 6/64 = 57/64
April 25, 2014

Calculus Please Help4
You appear to have found their intersection correct as (3,3) and (19,-5) USING VERTICAL SLICES: y^2 = x+6 so y = ± √(x+6) = ± (x+6)^(1/2) so for the part from -6 to 3 height = (x+6)^ - ( -(x+6)^(1/2) = 2(x+6)^(1/2) integral of that is (4/3)(x+6)^(3/2) area ...
April 25, 2014

Calculus Please Help3
intersection points: y = 5 with 2y = 3√x ---> (100/9 , 5) y = 5 with 2x+2y = 5 ---> (-2.5, 5) 2y = 3√x with 2x + 2y = 5 ---> 1 , 3/2) So I see it as area = ∫(5 - (5-2x)/2) dx from -2.5 to 1 + ∫((5-(3/2)(x^.5) )dx from 1 to 100/9 = 6.125 + 14....
April 25, 2014

Algebra
Suppose the question had said: when a number is divided by 4 the quotient is 6 with a remainder of 1 we would write: number = 6(4) + 1 = 25 so f(x) = (x^3 + x^2 - 4)(x+3) + 8 = x^4 + 3x^3 + x^3 + 3x^2 - 4x - 12 + 8 = x^4 + 4x^3 + 3x^2 - 4x - 4
April 24, 2014

Calculus Help Please Urgent!!!
height = -1.6t^2 + 32t + 3 b) need the vertex of that parabola t of vertex = -b/(2a) = -32/-32 = 1 second height = -16(1) + 32(1) + 3 = 19 m c) hits the moon ground when h = 0 -16t^2 + 32t + 3 = 0 t = (-32 ± √1216)/-32 = -.089 or 2.09 seconds so , "in the air...
April 24, 2014

Math
prob(H win) = 1/3 , prob(A win) = 2/3 prob(H loss) = 2/3 , prob(A loss) = 1/3 a) not good on trees in this forum, hard to show b) Prob (HH) = (1/3)(1/3) = 1/9 Prob(AA) = (2/3)(2/3) = 4/9 c) to go 3 games, could be AHA or HAH prob of that = (2/3)(1/3)(2/3) + (1/3)(2/3)(1/3) = 4...
April 24, 2014

mathematics
1. What is 1 - 1/13 ? 2. ....... 3. to get a 2 ---> 11 to get a 5 ---> 14, 41, 23, 32 or 4 ways so to get a 2 or 5 ----> 5 possible outcomes prob(2 or 5) = 5/36 so in 1000 tosses we expect (5/36)(1000) or appr 139 times
April 24, 2014

typo correction -Math
my first equation should have been cosØ = 49/50 = .98
April 24, 2014

Math
Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm so we would get cosØ - 49/50 = .98 then Ø = .20033.. (I stored that in my calculator to keep accuracy) so we ...
April 24, 2014

finances
P(1.04^35 - 1)/.04 = 1000000 P = $ 13,577.32
April 24, 2014

Algebra
I did a synthetic division (or you can do a long algebraic division) to get a remainder of (c+1188) So for the division to be exact, x+1188 = 0 c = - 1188 http://www.wolframalpha.com/input/?i=%28x%5E4+-+3x%5E2+-1188%29%2F%28+x%2B6%29 look at "quotient and remainder" ...
April 24, 2014

Math
a) the only even prime is the number 2 so prob = 1/6 b) primes less than 5 are : 2 and 3 so prob = 2/6 = 1/3 c) if not a 6, then it must be: 1, 2, 3, 4, or 5 how many of those are prime? d) which of 1 or 2 is prime ? e) how many even's < 4 are prime? etc.
April 24, 2014

Algebra
(√5a^-2)/(√10a^-1) = (√5 a)/(√10 a^2) = 1/(√2 a)
April 24, 2014

Math
volume of whole apple = (4/3)π(6^3) = 288π cm^3 volume of inner part of apple with radius 5 cm = (4/3)π(5^3) = 500π/3 cm^3 part of apple within 1 cm of outside = 288π - 500π/3 = 364π/3 prob(being in outer part of apple) = (364π/3) / (288...
April 24, 2014

Math
expected income = .2(0) + .3(-1000) .25(-10000) + .25(20000) = 2200
April 24, 2014

Math
Let the line joining (1,-4) and (6,-4) be the base of your triangle. This is a horizontal line, and it should be easy to see that its length is 5 let the height be h (1/2)(5)h = 20 5h = 40 h = 4 so any point on the x-axis (or 4 units above your base) would be such a third ...
April 24, 2014

math
So they must enter in the order G B B B G number of ways = 2 * 3*2*1 * 1 = 12
April 24, 2014

Math
could be 1. YY --->(5/29)(4/28) = 20/812 2. GG ---> (7/29)(6/28) = 42/812 ... 5. BB ---> 4/29)(3/28) = 12/812) Add them up (20 + 42 + .. + 12)812 = ....
April 24, 2014

Math
so prob that 5 of the 10 smoke = C(10,5)(.4^5)(.6^5) = appr .2 40% of college students smoke ??? Are those stats from the 50's ?
April 24, 2014

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