Thursday
July 24, 2014

Posts by Reiny


Total # Posts: 26,863

Math
nope f(-3) = (-3)^2 - 5(-3) + 1 = 9 + 15 + 1 = 25

If 12 people are playing in a tournament and?
number of subsets of 2 elements from a sample space of 12 = C(12,2) = 66

Math
yes

Math
f(4) = 16+9 = 25 g(-1) = 24-4 = 20 so what is the problem?

Math ~ Check Answers ~
use the first pair of points (2,1) and (4,0) slope = -1/2 so y = mx + b ----> y = -(1/2)x + b sub in (4,0) 0 = (-1/2)(4) + b b = 2 y = (-1/2)x + 2 use our non-used point to check: does (6,-1) lie on it? LS = -1 RS = (-1/2)(6) + 2 = -3+2 = -1 your answer is good.

Algebra 1--Please, help me!
((n-5)/(n^2 - 2n -3)) / ((n-3)/(n^2 -4n - 5)) multiply both sides by (n^2 - 2n -3)(n^2 - 4n - 5) , sometimes called cross-multiplying n^3 - 4n^2 - 5n - 2n^2+ 8n + 10 = n^3 - 2n^2 - 3n - 3n^2 + 6n + 9 -n^2 = -1 n^2 = 1 n = ± 1

word problem?
prob(going to amusement park) = 8/18 = 4/9 so number of the 225 who would go = (4/9)(225) = 100 notice Ms Sue's equation will yield the same answer.

Algebra 1
did that for you here http://www.jiskha.com/display.cgi?id=1401816411 #2, was also done somewhere, can't find it, so ... The way you typed it: 2/t + 4/3t = 4/t + 2 times 3t 6 + 4t^2 = 12 + 6t 4^2 - 6t - 6 = 0 2t^2 - 3t - 3 = 0 t = (3 ± √33)/4 somehow I don'...

Scientific notation
area = (5x10^4)(6x10^3) = 30x10^7 = 3.0 x 10^8 m^2

Probability???
yes, but I would rather have you think of (1/520)(7800) = 7800/520 ---> see, there is your division by 520 = 15

Math
|5m-11| = 9+3m case 1: 5m-11 = 9+3m 2m = 20 m = 10 case 2 -5m + 11 = 9+3m -8m = -2 m = 1/4 product of answers = 10(1/4) = 5/2 oe 2.5

Algebra 1--Please, help me!
let the amount to be added by x ml so we have 300+x ml of the new mixture .3(300+x) = .4(300) 3(300+x) = 4(300) 900 + 3x = 1200 3x = 300 x = 100 Add 100 ml of water check: Do we have the correct amount of acid? in original: .4(300) = 1200 ml in new: .3(400) = 120 ml -----> ...

Algebra/can you ck my anwers
my sum was 1770 divide that by 25 gave me a mean of 70.8 your mean of 1616 should have hit you as absurd. range is correct, your median and mode sound logical

Algebra 1--Please, help me!
#3 no need for all those brackets ... (d + 2)/(d + 8) = (-6)/(d + 8) multiply both sides by (d+8) d+2 = -6 d = -8 ahhh, trick question. Notice in the original, d≠ -8 So there is no solution. #4 correct #5 handled by bobpursley #6 (x -6)/(x^2-6) = (-4)/(x-4) x^2 - 10x + 2...

Algebra 1 (Reiny)
Sorry I misread your original question So here is the correct one: right now : amount of orange juice = .25(8) = 2 cups amount of apple juice = .75(8) = 6 cups let the amount of pure orange juice to be added be x cups so just looking at the orange juice: 2 + x = .4(x+8) times ...

algebra
Bosnian was right in his first post. (think I will have a third cup of coffee to wake up)

algebra
sorry, did not register the "linear" part, and concentrated on the "increasing" actually I think it is a), the slope between any two points is 3/2 all points satisfy the equation 3x-2y=7 http://www.wolframalpha.com/input/?i=interpolate+%281%2C-2%29%2C%283%2...

algebra
correct http://www.wolframalpha.com/input/?i=plot+%281%2C-3%29%2C%283%2C5%29%2C%285%2C11%29%2C%287%2C18%29

statistics
You have the subtraction backwards A score of 90 is above the mean, so the z-score should be positive z-score = (90-84)/8 = +.75

Algebra 1--Please, help me!
Argggghhh Duplicate question Didn't see that Steve had already answered it

Algebra 1--Please, help me!
cups of orange juice --- x cups of apple --------- 8-x .25x + .75(8-x) = 4.(8) 25x + 75(8-x) = 40(8) I will let you finish it 2. For your type of perfect-square trinomial the first and last terms would have to be positive. ---- the -9 takes this one out of the category. It is ...

Algebra 1--Please, check my answer!
correct

Trig
(320cos120 , 320sin120) + (35cos60 , 35sin60) you should be familiar with the trig ratios of the 30-60-90 triangle, and the multiples of those angles using the CAST rule = (320(-1/2) , 320(√3/2) + (35(1/2) + 35(√3/2) = (-160 , 160√3) + (35/2 , 35√3/2) =...

Algebra
Your equation doesn't even match your given data length --- x width ---- 2x - 2 area = x(2x-2) = 82 2x^2 - 2x - 82 = 0 x^2 - x - 41 = 0 use the formula ... x = (1 ± √165)/2 = appr 6.92 or some negative length = 6.92 , length = 11.85 check: 6.92x11.85 = appr 82

statistics
Looks like that professor is still giving those A's See the first 3 "Related Questions" below

algebra
let the number of boxes be x 45x + 4000 = 11200 I will let you solve this equation.

trigonometry, check please
I got 10.064.. which to the nearest tenth is 10.1

Algebra ll
hope you got -23 -48

trigonometry ans.
yes, to the nearest foot it is 66 ft

trigonometry ans.
correct in reference to your angle you are involving the opposite and the adjacent side since tanØ = opposite/adjacent your choice of tangent was correct.

algebra.can you ck my answers
216 = 6^3 <-----> log6 216 = 3 How did you ever get 0 as an answer? That is not even an equation ! I suggest you memorize the definition of logs 16-(1/4)^-2 1/2 No idea what that is supposed to be. Was that supposed to be an equation like your question suggested?

math
so the $72.09 represents 70% of the original price .7x = 72.09 x = 72.09/.7 = $102.99 check by taking off 30% of that

Math
you would have 6 equal surface areas 6x^2 = 24 x^2 = 4 x = √4 = 2

Math
length of side of the larger --- x length of side of the smaller -- y x+y = 5 So what do we see? We see 4 side faces of the larger = 4x^2 we see 4 side faces of the smaller = 4y^2 If we look straight down, we see a small face on top of the large face exposing the edge of the l...

Math
Since you already have the second part, let's work on the number of pennies , dimes and quarters we have to make $5.98 number of pennies -- x number of dimes ---- y number of quarters -- 52-x-y x + 10y + 25(52-x-y) = 598 x+10y + 1300 - 25x - 25y = 598 -24x - 15y = -702 8x ...

Algebra
amount into lower rate account --- x amount into higher rate account --- 8000-x .04x + .07(8000-x) = 480 4x + 7(8000-x) = 48000 4x + 56000 - 7x = 48000 -3x = -8000 x = 8000/3 = 2666.67 amount into CD = $2666.67

Algebra 1
Since F lies on DE, all we need is the equation of DE We don't even need F slope DE = (-2-2)/(-3-3) = 2/3 so y = (2/3)x + b but (3,2) lies on it, so 2 = (2/3)(3) + b b = 0 y = (2/3) x is the equation check: F is the origin (0,0) which satisfies y = (2/3)x A rather strangel...

Algebra 1
#1 and #2 ok #3, I agree with you, there is little that can be done All I could see is to divide top and bottom by 2g #4 ok #5, careless error, 2/2p = 1/p , not p #6 you have a common denominator, so add them 8m^2/(4m^5) = 2/m^3 #7, according to BEDMAS, division is done in the...

Math
if arithmetic, then 8 - (5+x) = (1+2x) - 8 8 - 5 - x = 1 + 2x - 8 -3x = -10 x = 10/3 check: terms are 25/3 , 8 , 23/2 or 25/3 , 24/3 , 23/3 which is an AS

Math
Sum(all terms) = a/(1-r) = 200/(1/2) = 400

statistics
Tools like this below replace tables traditionally found at the back of textbooks http://davidmlane.com/hyperstat/z_table.html enter your mean and sd, click on "above" for "exceeds 0.83" and enter the data to get .1587 ,or .159 correct to 3 decimals

College Algebra
Your last one 3/(x-4)=7/(x-8) is the easiest of the three equations just multiply each side by (x-4)(x-8) , which is sometimes called "cross-multiplying" 7(x-4) = 3(x-8) 7x - 28 = 3x - 24 4x = 4 x = 1

College Algebra
z^2 +iz -(5+i) = (2-5i)^2 + i(2-5i) - (5+i) = 4 - 20i + 25i^2 + 2i - 5i^2 - 5 - i = 4 - 20i - 25 + 2i + 5 - 5 - i = -21 - 19i

Math
value = 84000(.8)(.9)^4 = ....

College Algebra
(-5 - i)/(3 - 3i) = (-5 - i)/(3 - 3i) * (3+3i)/(3+3i) = (-15-15i -3i -3i^2)/(9 - 9i^2) = (-15 - 18i + 3)/(9 + 9) = (-12 - 18i)/18 = -2/3 - i (-5/2)i / ((-1/5)i ) = (-5/2) / (-1/5) = (-2/5)(-5/1) = 2 (-2i)^3 = -8i^3 now i^3 = (i^2)(i) = -i so -8i^3 = -8(-i) = 8i I do not unders...

College Algebra
expand it 3.14 i - 3i^2, but i^2 = -1 = 3.14 i + 3 or in the form a+bi 3 + 3.14 i

algebra
multiply both sides by (x+7)(x+3) , some people call it cross-multiplying 5(x+3) = 3(x+7) 5x + 15 = 3x + 21 I will let you finish it from here.

Math
looks like a geometric series with a = 3 r = 2 sum(n) = a(r^n -1)/(r-1) 765 = 3(2^n - 1)/1 255 = 2^n -1 256 = 2^n 2^8 = 2^n n = 8 there are 8 terms

math
1st times 2 8x + 18y = 20 5x + 18y = 19 subtract them 3x = 1 x = 1/3 sub x = 1/3 into the 1st and solve for y to get y = 26/27

Math
yes, good job however, you should reduce 26/56 to 13/28

decimals
so the number would look like 12.ab given: a+b = 9 b is odd, a is even, b>a easy to see that a=4, b=5 or a = 2 , b = 7 or, if we count 0 as even a = 0 , b = 9 12.45 12.27 12.09

MATH
prob(pink) = 4/14 = 1/7 prob(not pink) = 1 - 1/7 = 6/7

Math
all these are standard angles for which you should know the trig ratios cos 180 = -1 , look at the cosine curve sin 90 = 1 , look at the sine curve cot 45 = 1/tan45 = 1/1 = 1 , look at your 45-45-90 triangle csc 30 = 1/sin30 = 1/(1/2) = 2 , look at the 30-60-90 triangle sec 24...

calculus
I assume you meant f(x) = x √(10 - x^2) and not the way you typed it Of course the function would only be defined for -√10 ≤ x ≤ √10 f' (x) = x (1/2)(10-x^2)^(-1/2) (-2x ) + (10-x^2)^(1/2) = (10 - x^2)^(-1/2) [ -x^2 + 10-x^2] = (10-2x^2)/ͩ...

Algebra/can you ck my answer
correct remember , this would be statistical probability

Precal, please help asap!
let's use the sine law ... sin B/34 = sin 117°/42 sin B = 34sin117/42 = .72129... B = 46.2° or by the CAST rule B could be 133.8° But, that would mean the angle has 2 obtuse angle, which is not possible so angle B = 46.2° and there is only one triangle poss...

maths
nasty and tricky the way you typed it did you mean: 3^(n-1) = 2^(n+1) ?? I sure hope so, and will assume that. take log of both sides log [3^(n-1) ] = log [2^(n+1) ] (n-1) log3 = (n+1) log2 n log3 - log3 = n log2 + log2 n log3 - n log2 = log2 + log3 n(log3 - log2) = log2 + log...

Math (Pre-calc)
1 rotation = 2π(14) or 28π inches In 1 minute he goes 280(28π) inches = 7840π inches In 1 hour he goes 60(7840π) inches = 60(7840π)/12 feet = 60(7840π)/(12*5280) miles = appr 23.3 mph sin(2π/3) = sin 120° = sin 60° = √3/2 ,...

Algebra 1
a) is correct, but you should have brackets around the complete denominator. The way you typed it, it is only divided by (2x+10) x(x + 10)/( (2x + 10)(2x + 9) ) b) So now we have an actual numerical case and let's just follow the same argument you did in a) blacks = 5 whit...

math
rise/run = 400/1600 = 1/4 = tan Ø Ø = appr 14°

math
number of sales = .2(150) = 30 commission = 6(30) = 180

Algebra
Since the positions are specific, this is a permutation, not a combination. number of ways = 33*32*31*30*29 = ...

Albebra
both numbers 2's ----> 22 less than 6 ----> 11 12 13 14 21 22 23 31 32 41 total = 10 , (not counting 22 twice) prob of your event = (36-10)/36 = 26/36 = 13/18

Albebra
that would simply be C(4,1) * C(13,5) / C(52,5) = 5148/2598960 = 99/49980 = 33/16660 = appr .00198 Note, I included the royal flush in the above, you did not say anything about exclusion. What about other hands that are both a flush and something else? e.g. what about the 4,5,...

Algebra
you want 2 out of the 4 aces prob = C(4,2)/C(52,2) = ....

math help plzzz!!!!!!!!!
-8<1-3(x-2)<13 let's just work on it as it sits -8 < 1-3x+6 < 13 -8 < 7-3x < 13 subtract 7 , (does not affect inequality sign) -15 < -3x < 6 divide by -3 , (switches the < to a > sign) 5 > x > -2 better form: -2 < x < 5

math help plzzz
the easy one first: 2(x+7)-4>5(x-3) 2x + 14 - 4 > 5x - 15 -3x > -25 x < 25/3 for the 1st, I don't know why you put brackets around the left side, since it serves no purpose did you mean 2/(5x) > 7 or (2/5)x > 7 I will assume the last case: mulitply both s...

trig
not enough information to make any distance calculations.

HeLP MATH !!!!
2.903t - 1.98 = 18 2.903t = 19.98 t = 6.88 years or 7 years from 2000 in the year 2007

math
how about cos 66° = 11.3/L L = 11.3/cos66 = appr 28 ft

Math
log7 49(3√(x^5) ) = log749 + log73 + log7 x^(5/2) = 2 + log7 3 + (5/2)log7 x it can't be evaluated unless you give me a value for x

math
You don't need an "angle of elevation formula" Just make a sketch and use your basic trig ratios I see it as tan Ø = 350/1000 = .35 Ø = appr 19.26°

hectorr
Why do you call this a fractional equation ? I see no fraction in the equation. 3[2x-(x+7)]=5(x-3) 3[x-7] = 5x - 15 3x - 21 = 5x - 15 -2x = 6 x = -3 check: if x = -3 LS = [3(-6 - 4] = 3[-10] = -30 RS = 5(-6) = -30 = LS my solution is correct.

trig length
Make a sketch to see that sin 69° = 603/L L = 603/sin69 = appr 562.95 m

6th grade math
a) let x=0 is 4(0) - 5 < 3 -5 < 3 ???, YES ... d) let x = 4 is 4(4) - 5 < 3 16 - 5 < 3 11 < 3 ??? , NO do the others the same way

maths
By the definition of logs loga b = c <------> a^c = b so if log10( (5x-1)/(x-2) ) = 2 , then 10^2 = ( (5x-1)/(x-2) )

maths
log(5x-1) = 2 + log(x-2) log(5x-1) - log(x-2) = 2 log ( (5x-1)/(x-2) ) = 2 (5x-1)/(x-2) = 10^2 = 100 100x - 200 = 5x-1 95x = 199 x = 199/95

math
since it is parallel it must look like this: 3x - 4y = c, that is, it will differ only in the constant plug in your given point, find c, and you are done

math
the only numbers divisible by 5 from 1 to 35 are 5,10,15,20,25,30, and 35 there are 7 of them prob of your stated event = 7/35 = 1/5

geometry
the arc-length can be found this way arc = rØ, where r is the radius and Ø is the angle in radians. 92/180 = Ø/π Ø = 92π/180 16 = r(92π/180 r = 16(180)/(92π) = appr 9.96 units check: 92° is very close to a right angle, so the...

math
correct

math
I assume you meant (x+2)/2 = 4/x multiply each side by 2x , (sometimes called cross-multiplying) x^2 + 2x = 8 x^2 + 2x - 8 = 0 (x+4)(x-2) = 0 x = -4 OR x = 2 , which is choice 2) (if the way they presented the answer used the word AND, they they are technically incorrect. x ca...

Math - Personal Finance
To use the formula for a series of payments, such as carpayments, and mortgages, the period of compounding and the period of payments must be the same. Yours has the interest compounded semi-annually, and the payments are monthly, which does not match up So we have to find the...

math
looks like tan Ø = 169/500 = .338 Ø= appr 19°

Algebra 1
dh/dt = -32t + 148 = 0 for a max of h 32t = 148 t = 148/32 = 4.625 when t = 4.625 h = -16(4.625)^2 + 148(4.625) + 3 0 = 372.25 looks like d

Algebra
I think you are referring to one of the alternate ways to represent a combination see: http://laurashears.info/math122/unit5/notation/ Steve found the value of each of your combinations, so just multiply them 84*15*3 = .......

Geometry
I will assume you meant (x + 6)^2 + (y + 4)^2 = 36 , ( notice how the exponent is shown ) which is a standard equation of a circle with centre at (-6,-2) and a radius of 6 units Just noticed that I answered the same question back in 2012 http://www.jiskha.com/display.cgi?id=13...

Algebra 2
I will assume that your light is parabolic and the bulb is placed at its focal point The standard form of the equation with vertex at the origin and focal point (p,0) is y^2 = 4px so you have a focal point of (6,0) then y^2 = 24x is our equation if the diameter is 36 inches, t...

HELP!!!! MATH
Did you make your sketch? If the depth is y you should see that h/24 = cos15° h = 24cos15 = appr 23 ft

math
number of participants --- x number passed first part = 7x/8 (failed = 1/8, so passed = 7/8) number who passed 2nd test = (2/7)(7x/8) = (1/4)x so 1/4 of the original passed the exam check: suppose 56 took the test so 49 passed of those (2/7)(49) or 14 passed 14/45 = 1/4

math
let the number of red marbles be x number of green marbles = (1/3)x = x/3 yellow marbles = 6x red : green : yellow = x : x/3 : 6x = 3x : x : 18x for a total of 24x so yellows would be 18x/24x = 3/4 of his collection

geometric
Next time you are near a big truck, you will notice that most of the trailers will have the notation 53' written along the side, showing that the standard length of the trailer is 53 feet. It asked for the customary way, so it is feet.

calculus
Wolfram amazes me more every day. http://www.wolframalpha.com/input/?i=area+between+y%3D+ln%281-x%29+%2C+y%3D3+%2C+x%3D0 notice that Damon took horiontal slices, while Wolfram took vertical slices. Same result of course.

math
So the length of the base of the continuous rectangle = 10(2) + 10(4) = 60 inches so the distance around the whole thing = 2(60) + 2(3) = 126 inches

trig
make a sketch to see that sin10° = height/35 height = 35sin10 = appr 6.1 ft

math
Let the distance run by the dog be 7x m let the distance run by the cat be 4x m so 7x = 4x + 12 3x = 12 x = 4 So the dog has to run 7(4) or 28 m to catch the cat. check: In the same time that the dog ran 28 m , the cat ran 16 m but the cat had a 12 m head-start , giving us als...

Algebra where did I go wrong
Mark, the correct answer is 10 Please trust Damon.

Algebra
prob (2 yellow) = (6/15)(6/15) = 36/225 = 4/25 Since you are returning the first marble picked, the second probability is the same as the first one.

Precalculus
I followed your description ok. so we get: -8 + 2x + 15 = 9 2x = 2 x = 1 10 + 3x + 25 = 38 3x = 3 x = 1 , confirming our first answer 4 - 3x + 5 = y 4-3+5=y y = 6 So x = 1 , y = 6

algebra
let d be the number of DVD's rented 2d + 6 = 48 2d = 42 d = 21 If the customer borrows less than 21 DVD's the first plan is better If the customer borrows 21 DVD's s, the cost is the same If the customer borrows more than 21, the flat rate of $48 is best.

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