Thursday
July 31, 2014

Posts by Reiny


Total # Posts: 26,926

Algebra
yes

calcus
Isn't that just a straight-forward Pythagorean calculation? Surely somebody who studies Calculus MUST know how to do that. Let me know where your problem lies.

maths
Again, having a hard time trying to establish the order of operation. e.g. #3 I put it into Wolfram the way you typed it , and the webpage interpreted it the same way I did http://www.wolframalpha.com/input/?i=+X%5Elogx%2B5%2F3%3D+10%5E5%2Blog+x What a messy equation that woul...

maths
1. by definition of logs x^2 - 12x + 36 = 10^2 (x-6)^2 = 100 x-6 = ±√100 = ±10 x = 6 ± 10 = 16 or -4 2. you have the product of 3 numbers = 0 so one of them is zero but log4 and log2 are non-zero real numbers, so log2x must be 0 that is, x = 1 3.not ...

maths
11^(1/2) = √11 since 11 is not a perfect square, 11^(1/2) is irrational

maths
1st number --- x 2nd number -- 8-x sum of squares = x^2 + (8-x)^2 = x^2 + 64 - 16x + x^2 = 2x^2 - 16x + 64 d(sum of squares)/dx = 4x - 16 = 0 for max/min 4x=16 x = 4 the two numbers are both 4 check: for the answer, sum of squares = 16+16 = 32 let 1st be 3.99, the other 4.01 s...

math
first you need the monthly payment. i = .11/12= .00916666.. n = 12 Paym (1 - 1.0091666..^-12)/.009166.. = 15000 paym = 1325.72 Here are my titles to the amortization table ( they will not line up niceley) Time - payment - interest - repayment - balance now -- 0.00 -- 0.00 -- 0...

math
prob = C(4,3)*C(4,3)/C(52,6) = 16/20,358,520 4/5089630

math-Ms Sue please help
I am pretty sure that for loans lasting 25 years, compound interest would be used. i = .10/12 = .008333... n = 25(12) = 300 payment( 1 - 1.008333^-300)/.0083333) = 73700 I get payment = $ 669.71

math
All your questions deal with the use of our 4 basic compound interest formulas. What exactly do you not understand about these questions ? They all are very straight forward.

math
i = .08/12 = .006666.. n = 18(12) = 216 amount = 225( 1.00666..^216 - 1)/.00666.. = ... you do the button pushing

math
amount(1.02)^12 = 15000 amount = 11827.40

math
amount after 3 years at 5% pa compounded semiannually = 4494(1.025)^6 = 5211.66 so interest = 5211.66-4494 = 717.66

math
how about y = x^3/(x-1) confirmed: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3%2F%28x-1%29

algebra
√50 = √25√2 = 5√2, which is choice A

MAT 221
-10 < -2 + 8x < 22 add 2 -8 < 8x < 24 divide by +8 , (no change in inequality sign) -1 < x < 3 Can't make out your symbols in the 2nd e.g. use <= for ≤ and >= for ≥

Frequency
assuming that they either supported it or not supported it, P(E) = 80/400 = 1/5

Algebra
yes, I would put your answer in set form, using { } brackets, eg. range = {2,-5}

Trigonometry help
Depends on the interpretation of "makes a 15° angle with the boat". If the rope makes a 15° angle with the water line, (parallel to the bottom of the boat) you would have: depth/24 = cos 75° or depth/24 = sin 15° , both giving you depth = 6.21 If the ...

Math
1 term(n) = ar^(n-1) term(10) = 16(-1/2)^9 = 16(-1/512) = - 1/32 2. ar^9 = 3/512 ar^14 = 3/16384 divide the 2nd by the first r^5 = 1/32 r = 1/2 back into the first a(1/2)^9 = 3/512 a(1/512) = 3/512 a = 3(512)/512 = 3

Math
looks like an arithmetic sequence with d = 17 and term2 = -243 a+d = -243 a = - 260 term(67) = a+66d = -260 + 66(17) = ... you should have at your finger-tips the formulas for the sum of n terms you have the a and the d, so plug in

oops - finite math
that should be .25 + .47 for OR the way I had it would have been for AND

finite math
what is .25(.47) ?

finite math
How many of the 59 homeruns went to left field ?

geometry
Did you carefully read the question ?

geometry
let me rephrase the question ... what is the greatest common factor of 720, 1008, and 672 ? 720 = 8*9*10 = 16*3*3*5 1008 = 8*9*14 = 16*3*3*7 672 = 16*3*2*7 so who is common? looks like 16*3 or 48 check: 720/48 = 15 1008/48 = 21 672/48 = 14 , nothing common in any of those 3 an...

Math
well, let's put z=2 into the 2nd z=y + 2 = 5 y = 3 So now we know that z=2 and y = 3 now into the 1st: x - 6 + 2 = 8 z = 12 So, where was your problem with this ? Looks very very easy.

Math
use term(n) = a + (n-1)d here a = -847 , d = 11 , n = ?? , and term(n) = -11 solve : -11 = -847 + (n-1)(11) which should be pretty straightforward to do.

probability and statistics
Ummmh, if everybody got an 85, wouldn't the average be 85 ??? , so mean = 85 and since nobody "deviated" from that score, wouldn't the standard deviation be zero ????

Math
It must be true that (2x-1) - (3x-2) = (4x-3) - (2x-1) -x + 1 = 2x - 2 -3x = -3 x = 1 check: terms would be 1 , 1, 1 strange sequence but it is arithmetic

Math
so you are adding 64 + 81 + 98 + ... for 17 terms a = 64 d = 17 n = 17 use the formula Sum(17) = (17/2)[128 + 16(17)] = 3400

algebra
so -2x^2 + 8x + 5 = 0 x^2 - 4x = 5/2 complete the square ... x^2 - 4x + 4 = 5/2 + 4 (x-2)^2 = 13/2 = 26/4 x-2 = √26/4 ........ since √26 is close to 5 x = appr 2 ± 5/2 = appr 4.5 or .5

Math
I saw this question and have not been able to get a handle on it we know that ln(x) has an expansion formula http://upload.wikimedia.org/math/6/d/b/6dbf56b2e5f34d298c1e71ddd93b3448.png but it only good for |x-1| < 1 so we could create a series of terms = 1/(x+1) ( (x-1) - (...

geometry
let the mean be x (1/8) / x = x / (8/32) x^2 = (1/8)(8/32) x^2 = 1/32 x = ± 1/√32 or ± 1/(4√2) or ± √2/8

Math
a=2 ,d=4 term(12) = a+11d = 2 + 44 = 46

Math
a = x-y d = 2x+y-3 just use your formula term(101) = a + 100d = x-y + 100(2x+y-3) = x-y + 200x + 100y - 300 = 201x + 99y - 300

Maths
You will need brackets to properly identify the order of operations. you probably mean : 5/(1/2) + 14( 5/(1/2) + 14)(1/4) which is 10 + 14(10+14)/4 = 10 + 60 = 70 As to the relationship between the two number ??? yes, you are right, they are both whole numbers or they are both...

Math
surface area = 2π(2.5)^2 + 2π(2.5)(9) = ---

MATH
Your solution is illustrated by http://www.google.com/search?q=intersection+of+3+planes&tbm=isch&imgil=VKeuvId73BKgcM%253A%253Bhttp%253A%252F%252Ft2.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcTP5OK2B8xVEFseHgCh5S25ao2K4pX-fClEpupY9ltfPRK6cZC8NA%253B332%253B265%253BL5ht1c6d...

MATH
if you divide the 2nd by 2, all your equations start with 2x. That is good, since we could add or subtract them to eliminate the x 2x+y-3z=4 2x+z=10 -2x+3y-13z=-8 subtract 1st from the 2nd -y + 4z = 6 , #4 add the 2nd and 3rd 3y - 12z = 2 , #5 #4 times 3---> -3y + 12z = 18 ...

algebra
Did you mean, are the lines through each pair of points parallel or perpendicular to each other ?

Angles,Lines and Triangles
let the angles be x and y x+y = 116 x-y = 24 add them 2x = 140 x = 70 then y = 46 one angle is 70°, the other is 46° leaving 64° for the third angle

math
use a simple ratio ... miles/7 = 64/80 miles = 7(64/80) = 5.6

Math
since it is parallel to y=x/2 + 4 it will differ only in the y-intercept, so let y=x/2 + b plug in the point(10,12) 12 = 5+b b = 7 y = x/2 + 7

algebra 2
Since you labeled it algebra rather than Calculus, I will use an algebraic solution, completing the square h(t) = -16(t^2 - 9t + 81/4 - 81/4) + 24 = -16( (t - 9/2)^2 - 81/4) + 24 = -16(t - 9/2)^2 + 324 + 24 = -16(t-9/2)^2 + 348 this is a downwards-opening parabola with vertex ...

Math
#1 and #2 are the same type as the ones I just did for you Give them a try #3 a=2 , d=4 a+(n-1)d = term(n) 2 + (n-1)(4) = 106 2 + 4n - 4 = 106 4n = 108 n = 27 term(27) = 106

Math
common difference = 4+p - (6-p) = 4+p - 6 + p = 2p - 2 term(101) = a+100d = 6-p + 100(2p-2) = 6-p + 200p - 200 = 199p - 194

Math
a+32d = -2p a+ 60d = 26p subtract: 28d = 28p d = p a + 32p = -2p a = -34p

Maths
R(t) = e^kt, where R(t) is the percentage remaining after t t years, k is a constant given: when t = 50 , R(50) = .6 .6 = e^(50k) ln both sides ln.6 = 50k lne k = ln.6/50 R(t) = e^( (ln.6/50) t)

Math
volume = h(50-2h)^2

add maths
OP /PA = 1/3 3OP = AP now follow the same method I just showed you in your previous post

add maths
let the point be P(x,y) then PA = 2PB √( (x-1)^2 + y^2) = 2√( (x+2)^2 + y^2) square both sides and expand x^2 - 2x + 1 + y^2 = 4(x^2 + 4x + 4 + y^2) x^2 - 2x + 1 + y^2 = 4x^2 + 16x + 16 + 4y^2 3x^2 + 18x + 3y^2 = -15 x^2 + 6x + y^2 = -5 complete the square: x^2 + 6...

Word Problem
let the length and width be 4x and 3x old area = (4x)(3x) = 12x^2 new length = 4x+4 new width = 3x + 2 new area = (4x+4)(3x+2) = 12x^2 + 20x + 8 12x^2 + 20x + 8 = 2(12x^2) = 24x^2 12x^2 - 20x - 8 = 0 3x^2 - 5x - 2 = 0 (x-2)(3x + 1) = 0 x = 2 or x = -1/3, which is not admissibl...

lehman
number of $30 units ---- x number of $20 units ---- 2x number of $10 units ---- 40000-x-2x = 40000-3x 30x + 20(2x) + 10(40000-3x) = 800000 30x + 40x + 400000 - 30x = 800000 40x = 400000 x = 10,000 so 10,000 of the $30 units 20,000 of the $20 units 10,000 of the $10

lehman
amount invested at 10% --- x amount invested at 8% ---- 3x amount invested at 9% ----- 700,000-x-3x = 700,000-4x .1x + .08(3x) + .09(700000-4x) = 60500 times 100 10x + 8(3x) + 9(700000-4x) = 6050000 34x + 6300000 - 36x = 6050000 -2x = -250,000 x = 125,000 amount borrowed at 10...

math
Here is the "magic" square, where not only are your diagonals equal to a sum of 15, but so are each row and column 8 1 6 3 5 7 4 9 2

UGRENT HELP, math
They used the < sign should have used the ≤ for the ones that are equal

UGRENT HELP, math
number = 80(3)^(8/2) = 6480 C is obviously the biggest, followed by A B and D are the same none of the answers match, after you find the typo, I will let you figure it out

finance
first let the 50,000 and the 100,000 ride for the 12 years. Amount = 50000(1.05)^12 + 100000(1.10)^12 = 403,635.65 PLus our annuity of 30,000 for 12 years at 10% = 30000(1.1^12 - 1)/.1 =641,528.51 for a total of $1,045,164.17 Last part: let the rate be i 1,045,164.17 = 102,000...

maths
All four sides are equal, so each side of the rhombus is 8 cm get angle Ø , opposite the 10 cm diagonal 10^2 = 8^2 + 8^2 - 2(8)(8)cosØ cosØ = 7/32, then sinØ = 5√39/32 area = 8(8)sinØ = ... you take over

MAth
4+√(4+x^2) = x √(4+x^2) = x-4 square both sides 4+x^2 = x^2 - 8x + 16 8x = 12 x = 12/8 = 3/2 since we squared the equation, we MUST verify the answer LS = 4 + √(4 + 9/4) = 4 + √(25/4) = 4 + 5/2 = 13/2 RS = 2/3 LS ≠ RS so actually there is no solut...

Math
prob(blue, then red) = (10/24)(1/23) = 5/276

College Algebra
from vertex, y = a(x+9)^2 + 8 but (9,4) lies on it, so 4 = a(18^2) + 8 324a = -4 a = -4/324 = -1/81 etc you messed up here: 4=a(18)^2+8 4=a(332) , you added 8 to 324a , you can't add unlike terms

College Algebra
from the given vertex, the equation must be y = a(x+2)^2 + 4 but (0,2) lies on it, so 2 = a(0+2)^2 + 4 2 = 4a + 4 4a=-2 a = -1/2 y = (-1/2)(x+2)^2 + 4

Math please help
let y = 3/x + 4(1-x) = 3/x + 4(1-x)^-1 dy/dx = -3/x^2 -4(1-x)^-2 (-1) = -3/x^2 + 4/(1-x)^2 = 0 for a max/min of y 4/(1-x)^2 = 3/x^2 4x^2 = 3(1-x)^2 2x = ± √3(1-x) 2x = √3 - √3x 2x + √3x = √3 x = √3/(2 + √3) = appr .4641 or 2x = ...

algebra
D : B = 27 : 16 = D : 64 D/64 = 27/16 D = 64(27/16) = 108

Math
$1 = 82.8/12 francs so he has 12 + 25 or $37 $37 = 37(82.8/12) francs = appr 255.3 francs Time to update that ancient texbook your school is using. France has been using the Euro since 1999

Math
2nd angle --- x 1st angle ---- 4x 3rd angle ---- x+84 x + 4x + x+84 = 180 6x=96 x = 16 1st angle = 4x = 4(16) = 64°

ALgebra
adults --- x children -- 3x solve: 975x + 525(3x) = 30600

math
In terms of cosx cos 3x = 4 cos^3 x - 3cosx , and cos 2x = 2 cos^2 x - 1 so cos 3x = cos 2x 4 cos^3 x - 3cosx - 2cos^2 x + 1 = 0 let cosx = y so we need 4y^3 - 2y^2 - 3y + 1 = 0 I tried y = 1 and sure enough that was a solution. then by synthetic division ... 4y^3 - 2y^2 - 3y ...

math
i = .08 n = 40 years a) amount = 3000 ( 1.08^40 - 1)/.08 = appr $777,170.00 b) change the exponent from 40 to 30

geometry
second angle --- x first angle ------ 4x third angle ----- x+84 x + 4x + x+84 = 180 you finish it

Math
dimes--- x quarters -- x+2 nickels --- 3(x+2) = 3x + 6 10x + 25(x+2) + 5(3x+6) = 180 10x + 25x + 50 + 15x + 30 = 180 50x =100 x = 2 so 2 dimes and 4 quarters and 12 nickels check: 10(2) + 4(25) + 5(12) = 180 all is good

Introductory Algebra
Ummmh, isn't it about your school updated those old textbooks? France hasn't used the franc for years, they use the Euro.

algebra
cost of pound of copper ---- x cost of pound of tin -------- x+2 3(x + 2) + 7x = 10(3.85) 3x + 6 + 7x = 38.5 10x = 32.5 x = 3.25 copper sells for $3.25 per pound, and tin sells for $5.25 per pound

Math
I would write it as y = (8x^3)(3x-2)^(-1/2) and use the product rule dy/dx = (8x^3)(-1/2)(3x-2)^(-3/2) (3) + 24x^2 (3x-2)^(1/2) I will let you clean it up a bit

Math
yes, f(-6) = -18-5 = -23 f(4) = 12 - 5 = ........ f(8) = ........ range = { -23, ..... , .... }

trig
3secØ = 5 secØ = 5/3 then cosØ = 3/5 , since secA = 1/cosA Ø = arccos 3/5 = appr53.13° but you wanted the obtuse angle, so Ø = 360-53.13 = 306.87° , because the cosine is positive in quadrant I and IV to the nearest degree it would be...

Algebra
to get the y-intercept, let x = 0, that would leave you with y = 3 for the x-intercept, let y = 0 , that would leave you with x = 3 if the equation is of the form Ax + By = C do the same thing, usually you can do it your head e.g. 5x + 3y = 20 x-intercept is 4 y-intercept is 20/3

Algebra
of course

Algebra
treat it like two ordered pairs (1,295) and (2,272) slope = (272 - 295)/(2-1) = - 23 so equation in the form y = mx + b would be count = -23x + b , were x is the day number so using (1,295) 295 = -23(1) + b b = 318 count = -23x + 318 so on day 3 , x =3 count = -23(3) + 318 = 2...

data management
a) z-score for 6 days = (6-7)/2 = -1/2 = -.5 b) go to your table at z = -.5 and find the corresponding probability , multiply by 8000 ( I got 2468 c) repeat the above for 4 days I found this website a great replacement for tables http://davidmlane.com/hyperstat/z_table.html

math (please check answer)
prob = (6/20)(2/19) = 3/95 you were right

algebra/what am I doing wrong Please help
You should have definitions for dependent, independent, and incosistent. if there is a unique solution , the system would be independent. since the two lines have different slopes, they MUST intersect in a point, thus independent Wolfram is great ... http://www.wolframalpha.co...

Please help me with this question.!!!!!!
I must admit that I had no idea what a "box and whisker" plot is, even though I taught math for 35 years, so I looked it up and found this video of the very useful Khan Academy by Sal Khan https://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-wh...

Algebra
prob on base = .45 prob not on base = .55 prob (on base 5 of 7 times) =C(7,5) (.45^5)(.55^2) = appr .117

Math
-4x-8>4 -4x > 12 divide both sides by -4 x < -3 You add and subtract jus like you would for an equation, but when you divide by a negative, like I did in the last step, you MUST reverse the inequality sign.

math (cant figure it out)
Prob(vowed, then Q) = (3/6)(1/6) = 3/36 = 1/12 How did you possible get 1/10 ?

math *check*
Strike 2 prob (red from 1st then red from 2nd) = (12/20)(8/13) = 24/65

algebra
what is 4^3 - 5(4^2) + 4 ?

math
1/8 = .125 or 12.5% so to double we would solve 1(1.125)^n = 2 log both sides log (1.125^n = log2 n log 1.125 = log2 n = log2/log 1.125 = appr 5.885 years for tripling, solve 1.125^n = 3 ------> you should get appr 9.33

math *check*
prob(green) = 9/20 prob(not green) = 11/20 odds in favour of green = (9/20) : (11/20) = 9: 11 you are correct.

math (cant figure it out)
Valid point by Writeacher, if they they are numbered from 0-10 , there would be 11 sections. Clarify before I answer it.

math
strange wording .... " Finding three geometrically numbers" I assume you have 3 numbers in a geometric sequence. "30 units exceeds the sum of the other two" ...... which "other two" , the first two, the last two , or the middle two ? the three num...

Math
Use Cartesian geometry let the first be at (1,120) and the last one at (7,12) slope = (120-12)/(1-7) = -18 so for each increase in x, the height drops 18 cm so you want two decreases, height of third = 120-2(18) = 84 or find the equation: y = -18x + b at (7,12) 12 = -18(7) + b...

math -interest
i = .14/12 = .0116666... n = 12 400 = payment (1 - 1.011666...^-12)/.01166.. I get payment = 35.91

Algebra 1
y = x^2 - 4x+ 4 = (x - 2)^2 for x-intercept, let y = 0 (x-2)^2 = 0 x-2 = 0 x = 2 we have a double root at x = 2 , ( x=2 or x=2) see Wolfram: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+-+4x+%2B+4 Usually , I would put my money on Wolfram.

math
If f(x) will "vanish" when x = 1 and x = -2 (x-1) and (x+2) must be factors assume we have f(x) = a(x+b)(x-1)(x+2) given: f(-1) = 4 ---> 4 = a(-1+b)(-2)(1) -2a(-1+b) = 4 2a - 2ab = 4 a - ab = 2 f(2) = 28 ---> 28 = a(2+b)(1)(4) 4a(2+b) = 28 8a + 4ab = 28 2a + ab...

math
I see about 9 questions that you posted all dealing with the factor and remainder theorems. You have shown no effort on your part or let us know where you difficulties are. They all basically follow these two concepts : if for some f(x) , x-a is a factor, then f(a) = 0 if for ...

math
p(4) = 64k + 48 - 3 = 64k + 45 Q(4) = 128 - 20 + k = k + 108 by the remainder theorem , each of these are the remainders when divided by x-4 But they are equal ... 64k + 45 = k + 108 63k = 63 k = 1

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