Friday
August 22, 2014

Posts by Reiny


Total # Posts: 26,966

math
FF -- x DD -- y RR -- z x+y+z = 41.70 , #1 2x + z = 37.95 , #2 x+y = 26.75 , #3 #1 - #3" z = 14.95 sub into #2 2x + 14.95 = 37.95 2x = 23.00 x = 11.50 sub into #3 11.50 + y = 26.75 y = 15.25 FF costs 11.50 DD costs 15.25 RR costs 14.92
May 20, 2014

Math
your slope of -2/5 or -.4 for line AB is correct The slope of a line can be any real number, both positive and negative If the slope is positive the line leans to the right If the slope is negative the line leans to the left if the slope is zero, the line is horizontal.
May 20, 2014

Precalculus
Since you are given the slope and the y-intercept, the problem becomes a matter of just subbing in the values y = (5/8)x + 4
May 20, 2014

Algebra
19 P 2 = 19!/(19-2)! = 19(18)(17!)/(17! = 19(18) = 342 If by "if there is no r" you mean "if the value of r = 0" then 4P0 = 4!/(4-0)! = 1
May 20, 2014

Algebra
Damon, I think you forgot to divide by 7 before taking the square root. SD = √(80/7) = 3.3806 The amazing Wolfram supports this http://www.wolframalpha.com/input/?i=standard+deviation+4%2C+8%2C+5%2C+12%2C+3%2C+9%2C+5%2C+2
May 20, 2014

geometry
So you need the length of the hypotenuse sin 13° = 186/x x = 186/sin13° = 826.8 ft
May 20, 2014

algebra
width --- x length -- 2x+4 x(2x + 4) = 400 2x^2 + 4x = 400 x^2 + 2x = 200 x^2 + 2x + 1 = 200 + 1 (x+1)^2 = 201 x+1 = ± √201 x = -1± √201 x = appr 13.18 cm or a negative, which we will reject The width is appr 13.2 and the length is appr 30.4
May 20, 2014

math homework help
PV = 125000(1.03)^-5 = $107,826.10
May 20, 2014

Math: Linear Equation
A linear equation of your type will produce a straight line when graphed. So all you need are 2 distinct points. Using the x and y intercepts are a quick and easy way to do this, after all the intercepts are just plain ol' points. Here is an easy way to do this: let x = 0 ...
May 20, 2014

math
distance = 7(55) miles = 385 miles number of gallons of gas = 385/30 = appr 12.8 or 13 gallons
May 20, 2014

no
3 undecillion http://www.thealmightyguru.com/Pointless/BigNumbers.html in scientific notation: 3.0 x 10^36 A rather large number, considering that the total number of grains of sands are estimated to be only about 7.5 x 10^18 and Carl Sagan claimed that there are more stars in...
May 20, 2014

Math
I even tried this to see the median answer http://www.wolframalpha.com/input/?i=sort+19%2C+19%2C+14%2C+14%2C+16%2C+19%2C+19%2C+16%2C+16%2C+15%2C+17%2C+16%2C+17%2C+16%2C+15%2C+14%2C+15%2C+15%2C+17%2C+14%2C+16%2C+15
May 20, 2014

Math
Wow, I didn't know that Wolfram does even this stuff This wonderful webpage amazes me more all the time. http://www.wolframalpha.com/input/?i=mean+19%2C+19%2C+14%2C+14%2C+16%2C+19%2C+19%2C+16%2C+16%2C+15%2C+17%2C+16%2C+17%2C+16%2C+15%2C+14%2C+15%2C+15%2C+17%2C+14%2C+16%2C+...
May 20, 2014

statistics
prog(right) = 1/5 prob(wrong) = 4/5 prob of your stated event is, getting none right --> C(12,0)(1/5)^0 (4/5)^12 = .0687 getting one right --> C(12,1) (1/5) (4/5)^11 = .20616 getting two right --> C12,2) (1/5)^2 (4/5)^10 = .2835 getting three right --> C(12,3) (1/5...
May 20, 2014

Algebra
z-score = (given value - mean)/sd -1.7 = (13 - 18.1)/sd -1.7sd = -5.1 sd = -5.1/-1.7 = 3
May 19, 2014

Need help with pre cal hw
1. I sketched a triangle, and noticed I could use the cosine law: R^2 = 8^2 + 6^2 - 2(8)(6)cos 50° = 38.2923... R = appr 6.189 km or use vectors first vector = (8cos30 , 8 sin 30) = (6.9282 , 4) 2nd vector = (6cos160, 6sin 160) = (-5.63815.. , 2.05212) sum = ( 1.29004...
May 18, 2014

math
a reflection across the y-axis causes the x value to become opposite, while the y stays the same using your wording: (x,y) ----> (-x + 1, y - 2) A(1 , -3) ----> A' (0, -5) B(4 , -5) ----> B' (-3 , -7) C(3 , -1) ----> C' (-2 , -3) You should really have ...
May 18, 2014

RE-TYPE
Oh no, log6 is not a number, it is an operator. You can't factor out log6 (that would be doing something like √8 - √3 = (√)(8-3) ) You have to use your rules of logs. log6(x+3) - log6(x-5) = 2 log6 ( (x+3)/(x-5) ) = 2 which by definition is (x+3)/(x-5) = ...
May 18, 2014

Calculus
Oh no, 6 is not a number, it is an operator. You can't factor out 6 (that would be doing something like √8 - √3 = (√)(8-3) ) You have to use your rules of logs. 6(x+3) - 6(x-5) = 2 6 ( (x+3)/(x-5) ) = 2 which by definition is (x+3)/(x-5) = 6^2 = 36 36x - ...
May 18, 2014

Calculus
log5 16807^5 - log57^3 = log5A log5 (16807^5/7^3) = log5A A = 16807^5 / 7^3 = 49(16807)^4 = appr 3.91 x 10^18
May 18, 2014

maths
I strongly recommend that you mind your p's and q's
May 18, 2014

Calculus
The way you typed R(t), we have to read it as R(t) = 9/2.718 ( t(t-3)^3) then R' (t) = (9/2.718) [ t (3)(t-3)^2 + (t-3)^3 ] = (500/151)(t-3)^2 ( 3t + t-3) = (500/151)(4t - 3)(t-3)^2 How did the base of (t-3) suddenly turn into (t-4) ?
May 17, 2014

algebra
balance on home = .08(118,000) = $94,400 i = .095/12 = .00791666... n = 30(12) = 360 paym( 1 - 1.00791666..^-360)/.00791666.. = 94400 payment = $793.77
May 17, 2014

algebra
a) since 0% interest, the monthly payment would simply be 42500/60 = $708.33 b) I believe in the US , add-on-interest is done this way: amount to be financed = 42500-5100 = 37400 interest = 37400(.025)(5) = 4675.00 total of loan = 37400 + 4675 = 42075.00 monthly payment = ...
May 17, 2014

math
Unfortunately , the expression and measurement of time is not metric, so we have to make some changes. (similar to the US method of working in miles, yards, feet and inches) (14 hrs, 3 min)/3 = (13 hrs, 63 min)/3 = 4 1/3 hrs, 21 minutes = 4 hrs, 20 min , 20 min = 4 hrs and 41 ...
May 17, 2014

math
Does it fit the description I gave you? How about some thinking on your part after all your posts ?
May 17, 2014

math
in a reflection in the x-axis, all the x values stay the same, but the new y's become opposites of the old ones now, which matches that description.
May 17, 2014

math
prob(under 25) = .55 prob(over 25) = .45 prob (exactly 4 of 6 are under 25) = C(6,4) (.55)^4 (.45)^2 = .27795
May 17, 2014

Math
(-8x)(3x^2) = -24x^3
May 17, 2014

math
10 ---> 1 , looks like it went left 9 3 ---> 6 , looks like it went up 3
May 17, 2014

math
just evaluate y for the given x's and plot the points e.g , when x = -2 y = (1/3)(2) - 2 = 2/3 - 2 = -4/3 ------> so you have the point (-2, - 4/3
May 17, 2014

math
Actually I just noticed your equation is not quite clear. is the exponent 3 ? then you would have written it as y = 2x^3 or did you forget to type the exponent ? It would be highly unusual for a text to put the + sign in front of the exponent like you typed it.
May 17, 2014

math
evaluate the y for the given x's, then plot the points. Join them with a smooth curve. You will get a parabola
May 17, 2014

Math
Assuming your ã is √ #3 , the -11√8 becomes -22√2 the rest are correct
May 17, 2014

alegbra/stressed
in each case you divide the rate by the annual compounding frequence, and multiply the years by that annual compouding frequency e.g. if compounded quarterly, the annual compounding frequencey is 4 I will do that one, you try the others. 6.9 %> compounded quarterly i = .069...
May 17, 2014

Math
I think we should use compound interest here. i = .09/12 = .0075 let the payment be p p( 1 - 1.0075^-36)/.0075 = 100000 p = $3179.97
May 17, 2014

Chemistry, not Math
label your problem using the right subject
May 17, 2014

math
for the 1st pair, since you know what y is , just plug that value into the first equation and solve for x #2: 3x - 14y = 0 x - 4y + 1 = 0 3x - 14y = 0 multiply the 2nd by 3 3x - 12y = -3 subtract them -2y = 3 y = -3/2 sub into x - 4y = -1 x - 4(-3/2) = -1 x + 6 = -1 x = -7 x...
May 17, 2014

math
4(2x-9)-4x= 4-6x 8x - 36 - 4x = 4 - 6x 10x = 40 x = 4 16y plus 4 =-10 16y + 4 = -10 Does your keyboard not have a + sign? 16y = -14 y = -14/16 = -7/8
May 17, 2014

Math
it is called a subscript it is not an actual mathematical operator, but instead is an indicator. e.g. you often see it to label two points (x1 , y1) and (x2 , y2) to state that you have two points of the form (x,y) but the x's and y's are different e.g. if you have two...
May 17, 2014

maths
What does "works up to" mean in mathematics ????
May 17, 2014

Math
942!/(15n) = 942x941x940x939x938!/(15n) = 942(941)(188)(313)(938!)/n I divided by 5 and by 3 leaving the division by n
May 17, 2014

Math
multiply top and bottom by √6 + √3 (2 √ 6 + √ 3)/ ( √ 6- √ 3) * (√6 + √3)/(√6 + √3) = ( 12 + 3√18 + 3)/(6-3) = (15 + 9√3)/3 = 5 + 3√2
May 17, 2014

Calc Help Please Again Last one!
I will split it up for you ... (6x-58)/( (x+9)(x-7) ) let A/(x+9) + B/(x-7) = (6x-58)/( (x+9)(x-7) ) A(x-7) + B(x+9) = 6x - 58 let x = 7 0 + 16B = -16 B = -1 let x = -9 -16A + 0 = -112 A = -7 so .... (6x-58)/( (x+9)(x-7) ) = -7/(x+9) - 1/(x-7) now it integrates easily using ln...
May 16, 2014

Calc Help Please Again!
can't tell if your equation is y = e^(x+4) or y = e^x + 4 , why is there a 1 in front of the x ?
May 16, 2014

Calc Help Please
I got (1/4) (ln(x-2) - ln(x+2) ) + c how did your x-2 from the original denominator turn into 2-x) I used partial fractions
May 16, 2014

Geometry
make a sketch to see that height/36 = tan 25° height = 36tan25 = appr 16.8 ft
May 16, 2014

Algebra
yes
May 16, 2014

alegbra
my equation, (very close to yours) 225500 = PV e^(8.4246575(.0855)) 225500 = PV e^(.720308219) , now press 2nd ln 225500 = PV (2.055066524) PV = 109,728.81 I let the calculator carry all the decimal places and only rounded off my final answer to the nearest cent. You were off ...
May 16, 2014

math
distance = √( (-3-8)^2 + (-10+10)^2) = √(121 +0) = √121 = 11 We can see this without any calculation. Since the x values are the same for both points, the line is a vertical one. So all we have to do is take the difference between -3 and 8 , which is 11
May 16, 2014

math
number of $5 tickets --- x number of $10 tickets --- y number of $15 tickets ---- 180-x-y x + (180-x-y) = 2y x + 180 - x - y = 2y 180=3y y = 60 income equation: 5x + 10y + 15(180-x-y) = 1900 5x + 600 + 15(120-x) = 1900 5x - 15x + 600 + 1800 = 1900 -10x = -500 x = 50 x=50 y=60 ...
May 16, 2014

math(compound interest )
What you wanted as an equation is ... [ x( 1 + .1/360)^20 - 600 ](1+.1/360)^108 = 8900 x(1+.1/360)^20(1+.1/360)^108 - 600(1+.1/360)^108 = 8900 x((1.00557024)((1.03045024) - 618.2701442 = 8900 x(1.036190095 = 9518.270144 x = 9185.83
May 16, 2014

math trigonometry
I don't understand your question. Are we looking at two different equations ? Are we solving 10 sec Ø + 13sinØ = 0 and 5tan Ø - 12 = 0 ???? or .... ? is (0,90°) the domain?
May 15, 2014

Algebra 1
first equation: -2x - 2y = 4 ----> x+y = -2 2nd equation: 2y = -2x - 4 2x + 2y = -4 x + y = -2 looks like they are the same line, so you have one line any ordered pair that works in one of them, will work in the other. There will be an infinite number of solutions.
May 15, 2014

Math-- Ms. Sue??
#1 , wrong. If you plot your points you will see that it is (8,5) notice that now two pairs of points have the same x , making the lines vertical, and 2 pairs of points have the same y, making the horizontal. #2, ok #3, ok #4, your answer: (5,-4) and (-2,1) -- slope = (1-(-4...
May 15, 2014

Math
prob(brown, then violet) = (8/16)(1/16) = 1/32
May 15, 2014

Math - Int Trig
y = √x shift up 4 units -----> y = √x + 4 reflect about the y-axis ---> y = √-x + 4 , for x ≤ 0 shift right 2 units -----> y = √(-(x-2)) + 4 , x≤2 again, Wolfram verifies this http://www.wolframalpha.com/input/?i=y+%3D+√%28-%...
May 15, 2014

Math - Int Trig
start: y = |x| shifted right : y = |x-3) stretched by factor of 3 : y = 3|x-3| vertically down 2: y = 3|x-3| - 2 reflected about x-axis y = -3|x-3| + 2 behold the wonders of Wolfram http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx-3%7C+%2C+y+%3D+3%7Cx-3%7C+%2C...
May 15, 2014

math
multiply each of the prob. answers I just gave you by 100
May 15, 2014

math
Four possible outcomes: HH HT TH TT prob(HH) = 1/4 prob(TT) = 1/4 prob (TH or HT) = 2/4 = 1/2 notice the 3 answers add up to 1, since one of those possibilities must happen
May 15, 2014

Geometry
(-3,-1) ---- dilation factor of 2 ----> (-6, -2) show it by plotting the two points how does the distance to the origin change ?
May 15, 2014

Algebra 1
looks like f(3) = 2 then g( f(3) ) = g(2) = -3
May 15, 2014

Trig 3
sloppy way of writing the trig expressions ( when you write tan2, you are asking for the tan(2 radians. What you meant was something like tan^2 Ø It has to be the sine of something, the cosine of something, or the tangent of something. anyway ..... (1 - cos^2 Ø)/...
May 15, 2014

Geometry
Any regular n-gon can be changed to n isosceles congruent triangles by drawing all radii to the vertices of the polygon. the area of a triangle = (1/2)(base)(height) the area of one of these = (1/2)(side)(apothem) where the apothem is the distance from the centre of the ...
May 15, 2014

math(compund interest )
Major Hint: Did you notice that from 16 April to 16 Oct is 6 months? So your time can be very easily expressed in half-years, and quarter-years. From all the knowledge you have gained by having received many answers for similar questions to the above, you should now be able to...
May 15, 2014

mathematics for management
NO you used the concept of continuous compounding but it said it was compounded monthly Even with the above in consideration your expression of 8888(e^0.06(0.25)) makes absolutely no sense. i = .06/12 = .005 n = 3(12) = 36 months PV = 8888(1.005)^-36 = $7427.21 For a single ...
May 15, 2014

math
How do you expect us to know what table you are working from. With today's excellent scientific calculators, the use of "tables" that were found in the back of most textbooks in the past is no longer common practise. Your question is simply PV = 100000(1.05)^-50...
May 15, 2014

math
what is 20000(1.06)^15 ?
May 15, 2014

math(urgent)
Just use the formula. Amount = payment( (1+i)^n -1)/i Amount = 1000(1.08)^3 -1)/.08 = 3246.40
May 15, 2014

Trig
3x^2 + 4y^2 = 12 divide by 12 x^2/4 + y^2/3 = 1 we know sin^2 t + cos^2 t = 1 so sin^2 t = x^2/4 = (x/2)^2 ---> sin t x/s ----> x = 2sin t and cos^2 t = y^2/3 = (y/√3)^2 cos t = y/√3 ----> y = √3cos t x = 2sint y = √4cost confirmation: http://...
May 14, 2014

Calculus
dy/dx = 2tan (x^4) * sec^2 (x^4) * 4x^3
May 14, 2014

ALGEBRA
using the ratios, let the width be 8x and the length be 15x led d be the diagonal d^2 = (8x)^2 + (15x)^2 = 64x^2 + 225x^2 = 289x^2 d = 17x or x = d/17 width = 8x = 8d/17 length = 15x = 15d/17
May 14, 2014

geometry
volume of similar solids is proportional to the cube of their corresponding sides so ratio of volume = 3^3 :^3 = 27 : 125
May 14, 2014

Math
so you want 9(2)(t/9) = 1000000 2^(t/9) = 111,111.111.. t/9 log2 = log111111.11 t/9 = log111111.11../log 2 = 16.7616.. t = 150.8548 years so 1909 + 150.8548 yrs = appr 2060 just what Ms Sue got by continuing her chart.
May 14, 2014

math
1.75 years = 21 months monthly rate = .18/12 = .015 PV = 900(1.015)^-21 = $658.35
May 14, 2014

math
100% of something = the whole thing or 1 50% of something = .5 or 1/2 of the whole thing = .5 145% of something = 1.45 yes, C is the right choice.
May 14, 2014

math (urgent )
my answer confirmed by Wolfram http://www.wolframalpha.com/input/?i=13.875-0.1875%2856.375%29%2F8-2+%281%2F8%2B27.125%2F300.875%29+
May 14, 2014

math (urgent )
This is what you typed: 13.875-0.1875(56.375)/8-2 (1/8+27.125/300.875 I added a bracket at the end, or else they are mismatched. Followed the order of operation, and got 12.1234035... The way you wrote it, there is now way to get 1.1908 check how you placed your brackets.
May 14, 2014

Geometry Help & Proofs
based on : ratio of volumes is proportional to the cube of their corresponding sides. so ratio of volumes: A : B = 1 : 5 A : C = 1^3 : 2^3 = 1 : 8 B : D = 1^3 : 3^3 = 1 : 27 A/B = 1/5 B = 5A A/C = 1/8 C = 8A B/D = 1/27 D = 27B ratio of volume of C :D = 8A : 27B = (8/27)(A/B...
May 14, 2014

Math
9/9 = 1 = 12/12 2/3 = 8/12 5/6 = 10/12 4/12 = 4/12 0/2 = 0 , obviously the smallest now can you tell ?
May 12, 2014

Algebra
(x - y) (3x + xy - 4y) + xy^2 - x^2y = (x-y)(3x + xy - 4y) - xy(x - y) = (x-y)(3x + xy - 4y - xy) = (x-y)(3x - 4y)
May 12, 2014

Math
The total of the first 16 students' marks was 16x66 or 1056 the total of the new students' marks was 6x74 or 444 so the total of the 22 students was 1500 giving an average of 1500/22 or appr 68.2
May 12, 2014

finance
WoW! I recognize the formula Future Value = Present Value (1 + i/n)^(cn) where n is the frequency of compounding per year and c is the number of years from your (1.089/12)12*5 I gather that the interest rate was 8.9 % per annum compounded monthly , for a time of 5 years and ...
May 12, 2014

Algebra 1 Answer Evaluation
anything squared cannot be negative in the real number set, so your first one has no real number solution 2. correct
May 12, 2014

math
distance (d) ∝ time (t) d = kt case 1: when t = 2 , d = 90 90 = k(2) k = 45 so d = 45t , the constant of proportionality is 45 the unit rate is 45 mph check on the others t = 3 --> d = 45(3) = 135 ✔ t = 5 --> d = 45(5) = 225 ✔ t = 6 --> d = 45(6...
May 12, 2014

Algebra 1 (Reiny)
x^2 + 3x - 18 = 0 (x+6)(x-3) = 0 x = -6 or x = 3
May 12, 2014

MATH: TRIG
you should recognize the 3-4-5 right angled triangle. so if cosx = 3/5 then sinx = 4/5 sin 2x = 2sinxcosx = 2(4/5)(3/5) = 24/25 you can always check your result with a calculator.
May 12, 2014

Maths
use substitution x^2 + 3x - 5 = x-2 x^2 + 2x - 3 = 0 (x+3)(x-1) = 0 x = -3 or x = 1 check with Wolfram http://www.wolframalpha.com/input/?i=Y%3Dx-2+%2C+Y%3Dx%5E2%2B3x-5 if x = -3, y = -3-2 = -5 if x = 1 , y = 1-2 = -1 x=-3, y=-5 ---> point (-3,-5) x = 1 , y = -1 --->...
May 12, 2014

Algebra II
quick way: for any linear equation written in the form Ax + By + C = 0 the slope is -A/B so here, the slope is -6/5
May 12, 2014

math
Don't post the same question using different names please.
May 12, 2014

math
3+x/7+x= 3/7 + 3/7 I would multiply each term by 7 , the LCD 21 + x + 7x = 3+3 8x = -15 x = -18/8 I seriously suspect a typo
May 12, 2014

math
3(40+x) = (2+3)(3+4)(4+5) 120 + 3x = 5(7)(9) = 315 3x = 195 x = 65
May 12, 2014

geometry
He has not seen 5 of the comedies and 7 of the dramas Since you want the non-seens from one OR the other there are 12 movies he has not seen prob(nonseen) = 12/18 = 2/3
May 12, 2014

Algebra 1--Please, help me!
1. 4x^2 + 8x = 32 4x^2 + 8x - 32 = 0 x^2 + 2x - 8 = 0 let y = x^2 + 2x - 8 now graph this, and look at where it crosses the x-axis. From Wolfram's graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+%2B+2x+-+8 we can see x = -4 or x = 2 2. x(x + 3) = 32 x^2 + 3x - 32 = ...
May 12, 2014

oops - MATH
just noticed an arithmetic error.. in my evaluation of y, should be 60 - 2x = 60-2(20) = 20 so ..... max profit is 30(20) + 50(20) or 1600 , when 20 of the first product and 20 of the second product are made
May 12, 2014

MATH
let the number of the first product be x let the number of the 2nd product by y So we need to look at the regions 2x+y ≤60 and x+y≤30 and x+3y≤80 The profit function is 30x+50y which has a slope of -3/5 move that profit line to the right, parallel to itself, ...
May 12, 2014

Math
I tried a slightly different approach I looked at the trapezoid, and drew two verticals upwards from the base, creating a rectangle of 25 by 50 cm and two right-angled triangles , each of height 50 and base 75/2 I drew a water line, of height h and width of r in each of the ...
May 12, 2014

Math
You don't have an equation, so "solving" is the wrong instruction. are you expanding 2a(a^2 + 4a) ? then... = 2a^3 + 8a^2
May 11, 2014

algebra
I don't know what h=−16t<E> 6<E>+s is supposed to say, but I know that h = -16t^2 is the relation between t seconds and the distance fallen in feet Since we just want to find the distance, let's use h = 16t^2 when t = 3 h = 16(9) = 144 feet If this is...
May 11, 2014

Math
slope for the first 2 points = (0-1)/(4-2) = -1/2 y = -1/2 x + b , but (2,1) lies on it 1 = -(1/2)(2) + b b = 2 y = -(1/2)x + 2 check if third point is on it LS = -1 RS = (-1/2)(6) + 2 = -1 yes, all is good y = (-1/2)x + 2
May 11, 2014

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