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Quadratic_Equations/44343: Carlos scored 15 more points than John in the basketball game. If the product of the two point totals is 154, how many points did each boy score?
1 solutions
Answer 29273 by fractalier(2101)   on 2006-06-29 16:23:07 (Show Source):
You can put this solution on YOUR website!Let their totals be C and J.
Then C = J + 15 and
CJ = 154
Now substituting we get
J(J + 15) = 154
J^2 + 15J = 154
J^2 + 15J - 154 = 0
(J + 22)(J - 7) = 0
J = -22 or J = 7
but since you can't score negative points,
J = 7 and C = 22
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Trigonometry-basics/44341: What are the possible answers?
sin(x) - sin(3x) = 0
1 solutions
Answer 29272 by fractalier(2101) on 2006-06-29 16:20:28 (Show Source):
You can put this solution on YOUR website!This will take a while...please follow along...from
sin x - sin 3x = 0 we get
sin x - sin (x + 2x) = 0
sin x - (sin x cos 2x - sin 2x cos x) = 0
sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos * cos x) = 0
sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos^2 x) = 0
how factor out sin x
sin x(1 - cos^2 x + sin^2 + 2 cos^2 x) = 0
sin x(1 + cos^2 x + sin^2) = 0
2 sin x = 0
sin x = 0
x = 0, pi
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Probability-and-statistics/44279: An African hospital is treating patients who have Lhassa Fever. Seventy percent of patients with this disease die, and each patient lives or dies independently of other patients.
Suppose over along period, the hosptial expects to treat 100 patients. What is the mean number of deaths expected during this period? My answer is 100 x .70 = 70 patients.
The 2nd part of that is suppose over a long period, the hospital expects to treat 100 patients. What is the standard deviation of the number of deaths expected during this period? (I am not sure how to begin finding this answer)
1 solutions
Answer 29269 by fractalier(2101) on 2006-06-29 16:03:33 (Show Source):
You can put this solution on YOUR website!Your expected mean of 70 is correct.
I believe that sigma is found by
sigma = sqrt(np(1-p))
but it has been a while since I did this kind of stat problem, but if this is a binomial setting, then this is correct...and if so
sigma = sqrt(100*.7*.3)
sigma = sqrt(21) or about 4.58
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Equations/44319: This question is from textbook INTERMEDIATE ALGEBRA
Write each equation in quadratic form and solve it by factoring.
x(3x + 22/5)= 1
1 solutions
Answer 29268 by fractalier(2101) on 2006-06-29 15:57:14 (Show Source):
You can put this solution on YOUR website!From x(3x + 22/5)= 1, we get
3x^2 + (22/5)x = 1
now multiply five and bring everything to the left...then factor...
15x^2 + 22x = 5
15x^2 + 22x - 5 = 0
(5x - 1)(3x + 5) = 0
so that
5x - 1 = 0 and 3x + 5 = 0
which leads to
x = 1/5 and x = -5/3
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Radicals/44333: Reduce each expression to the lowest terms. Show steps and solution.
This is written in fraction form:
4x^2/2x^9
1 solutions
Answer 29252 by fractalier(2101) on 2006-06-29 14:11:39 (Show Source):
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Complex_Numbers/44334: solve log(2x+3) = log(4x)+ 2, for x giving your answer correct to 3 significant figures
1 solutions
Answer 29249 by fractalier(2101) on 2006-06-29 14:04:26 (Show Source):
You can put this solution on YOUR website!Provided the problem is correctly stated we have
log(2x+3) = log(4x) + 2
log(2x+3) - log(4x) = 2
log [(2x+3) / 4x] = 2
so that when we exponentiate we get
(2x+3) / 4x = 10^2 = 100
2x + 3 = 400x
3 = 398x
x = 3/398 or about .00754
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Polynomials-and-rational-expressions/44332: Factor each Trinomial using the “ac” method. Showing work and solution.
15x² - 7x – 2
1 solutions
Answer 29248 by fractalier(2101) on 2006-06-29 13:59:51 (Show Source):
You can put this solution on YOUR website!From 15x² - 7x – 2, we factor by looking at the product of a times c, here that is 15 times 2...or 30...then we ask, what are the factors of 30 that have a difference of 7...that would be 10 and 3 and than adjust our binomial factors to reflect such products...so we get
15x² - 7x – 2 =
(5x + 1)(3x - 1)
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Equations/44327: k^2+10k+24 over k^2+11k+30 * k^2+5k over k^2-2k-24
help
1 solutions
Answer 29246 by fractalier(2101) on 2006-06-29 13:53:24 (Show Source):
You can put this solution on YOUR website!We always factor and cancel in problems like these...so we get
k^2+10k+24 / k^2+11k+30 * k^2+5k / k^2-2k-24 =
(k+6)(k+4) / (k+6)(k+5) * k(k+5) / (k-6)(k+4) =
Now the k+6, k+5, and k+4's cancel, leaving
k / k-6
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Polynomials-and-rational-expressions/44316: Hi, I have the solutions to a problem but I don't know if they are correct. The problem is x^3-x=0. The solutions I got are x=-3/2 and-1/2. If they are not correct, can you show me how to do them? Thanks.
1 solutions
Answer 29243 by fractalier(2101) on 2006-06-29 13:43:56 (Show Source):
You can put this solution on YOUR website!Okay, from
x^3 - x = 0
we factor out x first and then factor what is left...
x(x^2 - 1) = 0
x(x + 1)(x - 1) = 0
so that
x = 0, x = 1, and x = -1
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Systems-of-equations/44228: find the solutions of each system
3x+2y=5
4x+3y=5
1 solutions
Answer 29236 by fractalier(2101) on 2006-06-29 12:25:24 (Show Source):
You can put this solution on YOUR website!Let us multiply the top one by 4 and the bottom one by 3 and subtract them...we get
3x + 2y = 5
4x + 3y = 5
which becomes
12x + 8y = 20
-(12x + 9y = 15)
and thus
-y = 5
and
y = -5
so that when we substitute this into the first equation we get
3x + 2(-5) = 5
3x - 10 = 5
3x = 15
x = 5
Our solution is (5, -5)
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Radicals/44246: Find the time required for an ojbect to fall to ground from the building is 1400 Ft high. t=1/4 square root is s.
1 solutions
Answer 29235 by fractalier(2101) on 2006-06-29 12:20:48 (Show Source):
You can put this solution on YOUR website!What I think you mean is
t = (1/4) * sqrt(s) where t is time and s is the distance....thus if we plug in 1400 feet for s we get
t = (1/4) * sqrt(1400)
t = 9.35 seconds
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Quadratic_Equations/44286: Find the roots of the equadratic equations by the method of completing the square. Express the roots, if they are not rational, in simplest radical form.
3x2 - 2x - 5 = 0
1 solutions
Answer 29234 by fractalier(2101) on 2006-06-29 12:15:37 (Show Source):
You can put this solution on YOUR website!From
3x^2 - 2x - 5 = 0
divide by 3 first and get
x^2 - (2/3)x - 5/3 = 0
Now half of 2/3 squared is 1/9, so
x^2 - (2/3)x + 1/9 - 5/3 = 0 + 1/9
x^2 - (2/3)x + 1/9 = 5/3 + 1/9 = 15/9 + 1/9
(x - (1/3))^2 = 16/9
Now take the square root of both sides
x - (1/3) = ± 4/3
x = 1/3 ± 4/3
so that
x = 5/3 or -1
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Graphs/44200: Find the slope and the y-intercept of the line.
6x - 9y = -18
1 solutions
Answer 29218 by fractalier(2101) on 2006-06-29 11:05:37 (Show Source):
You can put this solution on YOUR website!If we solve 6x - 9y = -18 for y, it will be in slope-intercept form, y = mx + b, so we have
6x - 9y = -18
-9y = -6x - 18
y = (2/3)x + 2
so that the slope is 2/3 and the y-intercept is 2
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