Monday

December 22, 2014

December 22, 2014

Total # Posts: 28,261

**math**

if AP , then d = 2k/3 - k = 2k/3 - 3k/3 = -k/3 term 6 = a+5d = k + 5(-k/3) = -2k/3
*July 22, 2014*

**Math**

2160 = 2*2*2*2*3*3*3*5 1344 = 2*2*2*2*2*2*3*7 1440 = 2*2*2*2*2*3*3*5 HCF = 2*2*2*2*3 = 24 2. let their income be x x/10 + x/3 + x/5 + 1320 = x times 150 , the LCM 15x + 50x + 30x + 198000 = 150x 198000 = 55x x = 3600
*July 22, 2014*

**algebra**

(3+2x)^5 = 3^5 + 5(3^4)(2x) + 10(3^3)(2x)^2 + 10(3^2)(2x)^3 + 5(3)(2x)^4 + (2x)^5 =243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5 by simple observation that a negative base raised to an odd exponent is negative .... (3-2x)^5 = 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5 (3+...
*July 22, 2014*

**algebra 2**

use your formula for S(n) S(n) = a(r^n - 1)/(r-1) 405 = a(3^4 - 1)/(3-1) 405 = a(81 - 1)/2 405 = 40a a = 405/40 = 81/8
*July 22, 2014*

**math**

8+4+2+1+1/2+1/4+...+1/32 = 1/32 + 1/16 + ... + 4 + 8 sum = ∑ 2^(n - 6) for n= 1 to 9
*July 22, 2014*

**math**

sum(n) = (n/2)(first + last) sum(11) = (11/2)(1+6) = 77/2
*July 22, 2014*

**math**

volume = lwh = 18(3)(1/3) = 18 cubic feet
*July 22, 2014*

**coordinate algebra**

I don't see any choices, but it would have to be c = 4h
*July 22, 2014*

**trigonometry**

write it as y = -3sec 2(x-π/6) period = 2π/2 = π no vertical translation phase shift π/6 units to the right
*July 22, 2014*

**Maths**

a = b+2 c = b-11 )a+b+c)/3 = 70 a+b+c = 210 b+2 + b + b-11 = 210 3b = 219 b = 73 a = 75 c = 62 check: (73+75+62)/3 = 70 all looks good
*July 22, 2014*

**Math**

the wonders of Wolfram http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29 actual work did you notice that consecutive differences are -1, -3, -5, -7 ? this forms an arithmetic sequence, so a quadratic will act as the defining function. let the sequence ...
*July 22, 2014*

**Algebra**

e.g. x^2 - 6x = 0 add 9 to both sides x^2 - 6x + 9 = 9 (x-3)^2 = 9 x-3 = ±3 x = 3 ± 3 = 6 or 0 check: by factoring, x(x-6) = 0 x = 0 or x = 6 , as above
*July 21, 2014*

**Algebra**

I betcha I can solve any quadratic equation by completing the square.
*July 21, 2014*

**math**

#2 number of green = x number of marbles after 5 reds are added = x+5 prob of picking red = 1/7 5/(x+5) = 1/7 x+5 = 35 x = 30 there were 30 marbles
*July 21, 2014*

**math**

#1 g/(b+g) = 1/3 3g = b+g b = 2g (g+1)/(b+g+1) = 3/7 7g + 7 = 3b+3g+3 4g - 3b = -4 4g - 6g = -4 g = 2 then b = 4 , which is choice d. #3 1 million is an even number all prime numbers are odd, except the first one, which is 2, thus even so we have the sum of 999,999 odd numbers...
*July 21, 2014*

**math**

looks like a typo in both functions. is it f(x) = x+2 or f(x) = -x+2 ? same for the other one.
*July 21, 2014*

**Alegbra**

If the expression is as you typed it, then -9x - 13x+7 is indeed equal to -22x + 7 and it is your professor who is in error.
*July 21, 2014*

**Algebra**

I will assume you meant to type 9(/x-1)*7/(x-3) which is 63/( (x-1)(x-3) ) or 63/(x^2 - 4x + 3)
*July 21, 2014*

**math**

Make a sketch and set up your ratio. I get height/(30+25) = 20/30 height = 55(2/3) =110/3 ft or 36 ft, 8 inches
*July 21, 2014*

**math**

dimes in box A originally --- x dimes in box B originally --- y case 1: after 25 moved from A to B box A has x-25 box B has y+25 but x-25 = y+ 25 ----> x = y + 50 case 2: after 100 dimes moved from B to A box A has x+100 box B has y-100 but (x+100)/(y-100) = 7/2 7y - 700 = ...
*July 21, 2014*

**Trigonometry**

No need for trig, just use a simple ratio ... height/60 = 5/10 height = 60(1/2) = 30 ft (did you notice the height of the man is 1/2 of his shadow, then the height of the pole must be 1/2 its shadow, or 1/2 of 60, which is 30 )
*July 21, 2014*

**Trigonometry**

done, see your other post above
*July 21, 2014*

**statistics**

prob defective = .05 prob of good = .95 So we want the prob that all are good = .95^14 = .48776... prob of at least one is defective = 1 - .48776.. = appr. .512 The 8000 does not enter the picture, since we have the percentage if we used it then we could proceed as follow ...
*July 21, 2014*

**Algerbra 1**

again, you should type it as (y+5)/(x^2 + 4y - 32) , the way you have it, the only division is 5/y^2 = (y+5)/((y+8)(y-4)) so which values would make the denominator zero ?
*July 21, 2014*

**algerbra 1**

According to your given choices, I suspect you meant 2/( x(x-3) ) so the restrictions are, x = 0 x = 3 namely, those values which make the denominator zero, thus resulting in an undefined answer.
*July 21, 2014*

**math**

This is the best there is for these kind of questions Just fill in the data http://davidmlane.com/hyperstat/z_table.html
*July 20, 2014*

**Math 221**

2 < y and 7 ≥ y 2 < y and y ≤ 7 or 2 < y ≤ 7
*July 20, 2014*

**mat/117**

Use the formula like I showed you in your other post
*July 20, 2014*

**mat/117**

-3x^2+3x+9=0 x^2 - x - 3 = 0 x = (1 ±√13)/2
*July 20, 2014*

**Algebra**

The wording is poor. Did you mean: " The numerical value of the area of the rectangle is 25 more than the numerical value of 4 times the width" ? if so, then ... width --- x length -- x+4 x(x+4) = 4x + 25 x^2 + 4x = 4x + 25 x^2 = 25 x = 5 The width is 5 units (length...
*July 20, 2014*

**Algebra**

slope = (4 -(-9))/(-3 - (-2)) = 13/-1 = -1 Surely you must have the definition of slope in your notes or in your text.
*July 20, 2014*

**Algebra**

x - y ≥ 2 -y ≥ -x + 2 y ≤ x - 2 draw the line y = x-2 and shade in the region below the line. Since the line is included, make it solid (had it been y < x-2, you would have drawn a dotted line to show it is excluded.)
*July 20, 2014*

**Math**

double the first: 6x - 2y = -24 x + 2y = -18 add them: 7x = -42 x = -6 back into the second: -6 + 2y = -18 2y = -12 y = -6 x = -6 , y = -6
*July 20, 2014*

**Algebra**

I would use substitution, from the 1st: y = 5x-18 sub into the 2nd: -4x - 2(5x-18) = -6 -4x - 10x + 36 = -6 -14x = -42 x = 3 y = 5(3)-18 = -3 x=3 , y = -3
*July 20, 2014*

**College math**

let each of the two equal sides be x let the single side by y then y+2x = 5500 y = 5500 - 2x area = xy = x(5500-2x) = -2x^2 + 5500 Since you labeled it "college" math, I will assume you know Calculus d(area)/dx = -4x + 5500 = 0 for a max of area 4x = 5500 x = 1375 y...
*July 20, 2014*

**stats**

must be an old-type "crank on the wall" from The Waltons era .... anyway .... I will assume that none of your 6 digit numbers can start with a zero, and that numbers may be repeated, so we can't have a number with no 8 prob of no 8 = 8 x 9^5/(9x10^5) so prob that...
*July 19, 2014*

**math**

i = .105/12 = .00875 n = 12(30) = 360 payment ( 1 - 1.00875^-360)/.00875 = 130000 payment = $1189.16
*July 19, 2014*

**Math**

In 1959 the inch was internationally defined in terms of the centimetre 1 inch = 2.54 centimetres So if you want any precision you have to go back to that basic definition. c) 80 in = 80(2.54) cm = 203.2 cm = 2.032 metres once you have converted to any of the metric units, the...
*July 18, 2014*

**math**

cost of computer = .8(825) = 660 original amount of money --- x 12x/100 + .25(88/100)x +1320 + 660 = x 34x/100 - x = -1980 66x-100x = -198000 x = 3000 check: car repairs = .12(3000) = $360.00 leaves --- 2640.00 food = .25(2640) = 660 amount to parents = 1320.00 computer = 660 ...
*July 18, 2014*

**math**

Using proper algebra: number of lights --- x white = x/2 red = (1/3)(x/2) = x/6 blue = 4 yellow = 10 x/2 + x/6 + 4 + 10 = x times 6 3x + x + 6(14) = 6x 84 = 2x x = 42 42 lights in total check: whites = 21 leaves 21 red = (1/3)of 21 = 7 sum = 21 whites + 7 red + 4 blue + 10 ...
*July 18, 2014*

**typo - math**

just noticed a typo should have said: if 3 decimal places divide by 1000 but you probably figured that out anyway.
*July 18, 2014*

**math**

1. count the number of decimal places, in this case there are 2 divide by 100 -----> 12/100 2. reduce the fraction to lowest terms 12/100 = 3/25 (if 1 decimal place, divide by 10 if 2 decimal places, divide by 100 if 3 decimal places divide by 100 etc e.g. .2568 = 2568/...
*July 18, 2014*

**Math 221**

Third time for this question. Surely your text or notes must have your "Cowling's Rule" state and explained. Since I have no idea what it is, .......
*July 17, 2014*

**math**

288π , not 268 TT = appr 904.78 cm^3
*July 17, 2014*

**math**

volume of a cylinder is π r^2 h you are given r and h, take it from here.
*July 17, 2014*

**math**

volume of given tank = (45)(70)(10) cm^3 = 31500 cm^3 number of packages = 31500/3000 =10.5 but since we probably can't buy half a package, there will be 11 packages needed
*July 17, 2014*

**math**

according to your wording of the problem, term(n) = √term(n-1) - 2 or √term(n-1) = term(n) + 2 square both sides term(n-1) = term(n) ^2 + 4term(n) + 4 for n = 3, term(3) = 1 term(2) = 1^2 + 4(1) + 4 = 9 term(4) = √term(3) - 2 = -1 so we can't go any ...
*July 17, 2014*

**math (xi)**

looks like the definition of dy/dx for y = secx we know dy/dx = (sec x)(tan x) so lim [sec(x+h)-sec x]/h h>0 = (secx)(tanx)
*July 17, 2014*

**math**

sum of 20 = 10(2a + 19d) = 10(2a - 38) = 20a - 380 sum of 22 = 11(2a + 21d) = 11(2a - 42) 22a - 462 22a - 462 = 20a - 380 2a = 82 a = 41 first term is 41
*July 17, 2014*

**math**

1960 ---> term10 = a + 9d = 2400 1990 ---> term40 = a + 39d = 600 subtract them 30d = -1800 d = -60 then a + 9(-60) = 2400 a = 2940 sum40 = 20(2(2940) + 39(-60)) = 70800
*July 17, 2014*

**Calculus Help!**

let the number of additional dollars be x new price = 7.5+x number of tickets sold = 1500 - 95x Revenue = (7.5 + x)(1500-95x) = 14250 + 787.5x - 95x^2 d(Revenue)/dx = 787.5 - 190x = 0 for a max of Revenue 190x = 787.5 x = 4.14 ticket price = 7.5+4.14 = $11.64 number of tickets...
*July 16, 2014*

**math**

5(3^2) + 3(3)(-3) - (-3)2 = 45 - 27 - 9 = 9
*July 15, 2014*

**Math**

2[-3(2x+4)+8(3x-2)] = 2[-6x-12+24x-16] = 2[18x-28] = 36x - 56
*July 15, 2014*

**Math**

suppose the radius of the original cone is r then the base area of the original is πr^2 Now, the radius of your half-size cone is r/2 so the base area = π(r/2)^2 = πr^2/4 = (1/4) πr^2 Thus the base area of the scaled down cone = 1/4 of the base area of the ...
*July 15, 2014*

**statistics**

Find the z-score of each. The one with the higher z-score is a "better score"
*July 14, 2014*

**math**

You must mean 6 square root of 3, or 6√3 let each side be 2x then x^2 + (6√3)^2 = (2x)^2 x^2 + 108 = 4x^2 3x^2 = 108 x^2 = 36 x = 6 So each side is 12 units long
*July 14, 2014*

**Math**

with replacement: prob = (13/52)(13/52)(26/52) = 1/32 without replacement: prob = (13/52)(12/51)(24/50) = 12/425
*July 14, 2014*

**algebra**

Katie's share ---- x Brandy --------- 2x Steph-----------x-3 x + 2x + x-3 = 56 4x = 59 x = 14.75 Katie --- $14.75 Brandy --$29.50 Steph---$ 11.75 check: 14.75+29.50+11.75 = 56 All is good.
*July 14, 2014*

**Math**

Fraction of female drivers = 48/106 = 24/53 So according to this experimental data number of female drivers = (48/106)(190 million) = appr 86 million
*July 14, 2014*

**Calculus 2**

yup, didn't see that perfect square
*July 14, 2014*

**Calculus 2**

let y = x^5/10+1/(6x^3) here is a picture of y = x^5/10+1/(6x^3) from 3 to 6 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E5%2F10%2B1%2F%286x%5E3%29+from+3+to+6 arc length = ∫√( 1 + (dy/dx)^2) dx from 3 to 6 dy/dx = x^4/2 - 1/(2x^4) (dy/dx)^2 = x^8/4 - 1/2 + ...
*July 14, 2014*

**Alegbra**

slope of #1 is 7 slope of #2 is .... -3y = 21x + 7 y = -7x - 7/3 to be perpendicular, the slopes would have to be opposite reciprocals of each other that is, the 2nd would have had to have a slope of -1/7 no, they are NOT perpendicular
*July 14, 2014*

**Math**

first conditions: x+4 ≥0 ---> x ≥ -4 and 3x+10 ≥0 ----> x ≥-10/3 so we know that x ≥ -10/3 case 1: x+4 = 3x+10 -2x = 6 x = -3 case 2: -x-4 = 3x+10 -4x = 16 x = -4 , also no good, because of above restriction So x = -3 check: if x = -4 LS...
*July 13, 2014*

**Math**

case 1: 1-x = 2x-5 -3x = -6 x = 2 case 2: -1+x = 2x-5 -x = -4 x = 4 x = 2 or x = 4 but by definition of absolute value, 2x-5 ≥ 0 2x ≥5 x ≥ 5/2 so x = 4
*July 13, 2014*

**Math**

The width of 12 m governs the value of x We must have 12 - 2x > 0 x < 6 the square garden must have sides less than 6 m each.
*July 13, 2014*

**Math**

What part don't you understand ? there are 25 skittles, of which 15 are green so prob of green = 15/25 = 3/5 since you are returning the one you picked, the second prob is the same as the first so prob(2green) = (15/25)(15/25) = (3/5)(3/5) = 9/25
*July 12, 2014*

**RE: ALGEBRA**

Improvement over your last post. 25x^2 - 10x = 0 5x(5x-2) = 0 5x = 0 ---> x=0 or 5x-2=0 ---> x = 5/2
*July 12, 2014*

**Algebra**

I suspect a typo, your wording indicates that it should have been a quadratic. the way you have it ... 25^2 - 10x = 0 625 = 10x x = 625/10 = 125/2 or 62.5
*July 12, 2014*

**Math**

prob(2 green) = (15/25)(15/25) = 9/25
*July 12, 2014*

**math**

argggh, what kind of a texbook would mix metric with non-metric units ?? anyway ... 20 inches = 20(2.54) cm = 50.8 cm one rotation would cover 2π(50.8) cm or 319.1858. (I stored it on calculator) 150 km/h = 150(1000)100)/3600 cm/s = 4166.666.. cm/s number of revolutions...
*July 12, 2014*

**math**

cost of one item --- x .2x = 16 x = 16/.2 = 80 So two items without tax would cost 160
*July 12, 2014*

**maths**

good question, Olivia, since if 3x+3 = 0 we would have 0/(6y+1) = 3 0 = 3 which would be nonsense. Jonel was just "lucky" to get the correct answer, since x = -1 works in the simplified equation x = 6y but not in the original equation.
*July 12, 2014*

**maths**

from the given equation, 18y + 3 = 3x+3 18y = 3x x = 6y then 7x/3y = 42y/(3y) = 42/3 = 14 =
*July 12, 2014*

**Math**

width = 2x+2 length = 4x + 4 2(2x+2)(4x+4) = 216 2(2)(x+1)(4(x+1) = 216 4(x+1)^2 = 54 take √ of both sides 2(x+1) =√54 = 3√6 x+1 = 3√6/2 x = 3√6/2 - 1 = appr 2.67 the pool is 7.35 m by 14.70 m check: 2(7.35)(14.7) = 216.09 , not bad
*July 12, 2014*

**silly typo - Math**

the third last line of the solution should of course be (x-2)^2 = 28 and the conclusion line: can't have a negative side, so x = √28 + 2
*July 12, 2014*

**Math**

let the shortest side be x then the longer side is x+5 and the hypotenuse is x+7 (x+7)^2 = x^2 + (x+5)^2 x^2 + 14x + 49 = x^2 + x^2 + 10x + 25 x^2 - 4x - 24 = 0 x^2 - 4x + .... = 24 + ... , going to complete the square x^2 - 4x + 4 = 24+4 = 28 (x+2)^2 = 28 x-2 = ± &#...
*July 12, 2014*

**math**

assuming you are using the [..] operator to have the same meaning as (..) we have Limit x^2/sinx , as x ---> 0 using L'Hopitals Rule lim x^2/sinx = lim 2x/cosx , as x ---> = 0/1 = 0 verification: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2%2Fsinx looks at x...
*July 12, 2014*

**or - Math**

√(4x+1) = 2 - √(x+1) square both sides (√(4x+1) )^2 = (2 - √(x+1) )^2 4x+1 = 4 - 4√(x+1) + x+1 4√(x+1) = 4 - 3x square both sides again 16(x+1) = 16 - 24x + 9x^2 16x + 16 = 9x^2 - 24x + 16 9x^2 - 40x = 0 x(9x-40) = 0 x = 0 or x = 40/9 ...
*July 12, 2014*

**maths**

b = a-2 c = a+1.5 d = c+1.5 = a+1.5 + 1.5 = a+3 a+b+c+d = 66.5 a + a-2 + a+1.5 + a+3 = 66.5 4a = 64 a= 16 box A = 16 box B = 14 box C = 17.5 box D = 19 check: sum = 66.5 All is good.
*July 11, 2014*

**math**

Your statement is false (25+5)(25-5) ≠ 0 it is (30)(20) = 600 What were you trying to do? To "solve" an equation, it must contain a variable Your expression shows the "difference of squares" could be done as 25^ - 5^2 = 625 - 25 = 600
*July 11, 2014*

**College Algebra**

What about it ? did you mean (15x^2-23x-21) / (3x-7) ? are we graphing y = (15x^2-23x-21) / (3x-7) ? are we solving (15x^2-23x-21) / (3x-7) = 0 ?
*July 10, 2014*

**math**

I would let the width = x then the length is x+120 and x(x+120) = 6400 x^2 + 120x - 6400 = 0 which factors to (x-40)(x+ 160) = 0 x =40 or x = -160, which is not possible, can't have negative width width is 40, length is 40+120 = 160 check: area = 40(160) = 6400 , yup!!
*July 10, 2014*

**math**

I will assume you mean (3x-4)/(4x+2) use the quotient rule ... y = (3x-4)/(4x+2) dy/dx = ( (4x+2)(3) - (3x-4)(4) )/(4x+2)^2 = (12x + 6 - 12x + 16)/(4x+2)^2 = 22/(4x+2)^2 or = 11/(2(2x+1)^2)
*July 10, 2014*

**Math**

correct, assuming that repetition of letters and numbers is allowed
*July 9, 2014*

**Algebra**

really ? isn't x^2 a perfect square? isn't 121 a perfect square ? ---- 11^2 = 121 Don't we subtract (-) to take the difference between 2 numbers? Now what do you think??
*July 9, 2014*

**algebra**

http://www.wolframalpha.com/input/?i=plot+4y%3Dx%2B8%2C+x%3D2%2F3y%2B2
*July 9, 2014*

**Statistics/Probability**

prob(Saturday) = 1/7 prob(not Saturday) = 6/7 prob(exactly 4 of 15 years is a Saturday) = C(15,4) (1/7)^4 (6/7)^11 = appr .1043 at least 2 Saturdays ----> 1 - (case of 0 Saturday + case of 1 Saturday) = 1 - (6/7)^15 - C(15,1)(1/7)(6/7)^14 = .6534 check my arithmetic
*July 9, 2014*

**Algebra II**

I will assume p5 is meant to be p^5 and 2x2 is meant to be 2x^2 , then p^5 + 2x^2 + 3px + 17 = 0 2x^2 + 3px + p^5 + 17 = 0 a quadratic with a = 2 , b = 3p and c = p^5 + 17 for real roots: 9p^2 - 4(2)(p^5 + 17) ≥ 0 9p^2 - 8p^5 - 136 ≥ 0 using Wolfram to solve, I got...
*July 9, 2014*

**precalculus**

make a sketch of the positions at t = 0, 1, 2, 3, and 4 and you will see that you need something like height = 5sin(π/2)t + 8 to meet your condition of 6:00 o'clock position being 3 m we do a 1 second shift to the right, height = 5sin [(π/2)(t-1)] + 8 check: when...
*July 9, 2014*

**math**

prob(male) = .4 prob(female) = .6 prob(5 of 6 are male) = C(6,5) (.4)^5 (.6) = ... prob(at least 4 of the 6 are boys) = prob(4 boys) + prob(5 boys) + prob(6 boy s) = C(6,4) (.4)^4 (.6)^2 + C(6,5) (.4)^5 (.6) + .4^6 = --- all boys = .4^6
*July 9, 2014*

**Algebra**

first of all, write it in its general form ax^2 + bx + c = 0 t^2 - 6t + 3 = 0 a = 1, b = -6 , c = 3 t = (-b ±√(b^2-4ac) )/(2a) = (6 ± √(36-4(1)(3))/2 = (6 ± √24)/2 = (6 ± 2√6)/2 = 3 ± √6 No complex roots here.
*July 8, 2014*

**Math**

let me guess, you want to know the speed of the east-bound ship. looks like a Pythagorean problem: (24(22.2))^2 + (24t)^2 = 863^2 ..... see if you can get appr 28.28 km/h
*July 8, 2014*

**math**

a+3d = -3 a+8d = 12 subtract: 5d = 15 d = 15/5 = 3 a + 9 = -3 a = -12 common difference is 3 sum(7) = (7/2)(-24 + 6(3)) = -21
*July 8, 2014*

**trigo**

slope of y = -mx is -m, but m is a positive number, so the slope is negative the slope is also equal to tan Ø the tangent is negative in quadrants II and IV, but x > 0 in IV so 270° < Ø < 360°
*July 8, 2014*

**math**

√3 is an irrational number, which is a subset of the real numbers
*July 8, 2014*

**math**

salary in 1st year --- x salary in 3rd year = x(1.03)^2 salary in 4th year = x(1.03)^2 (1.05) salary in 5th year = x(1.03)^2 (1.05)^2 x(1.03)^2 (1.05)^2 = 100000 x = 100000/((1.03)^2 (1.05)^2) = $87,180.84
*July 8, 2014*

**Algebra**

hint: How many wheels does a tricycle have ? how many wheels does a bicycle have? tri ?? bi ??
*July 7, 2014*

**Math**

amount = 500( 1.08^8 - 1)/.08 = ....
*July 7, 2014*

**math**

.10(1) + .025(1) = x(2) same type as your previous post, I will let you finish it.
*July 7, 2014*

**math**

.02(25) + .06(35) = x(60) 2.6 = 60x x = 2.6/60 = .04333.. The resulting concentration is 4 1/3 %
*July 7, 2014*

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