Reverse foil or quadratic formula.
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The Math Help Thread
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cpp_is_king
Member
If it's not a quadratic (e.g. has an exponent of 3 or more), then the easiest way is often to apply the rational root theorem and find 1 root manually.
There are just so many different situations for factoring. If you post some examples I wouldn't mind stepping through them with you.
MisterLuffy
Member
I have another problem I need help on:
Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The accompanying data was read from a comparative boxplot in the article "Fatal Excited Delirium Following Cocaine Use"(J. of Forensic Sciences, 1997: 25-31).
ED: 0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3 .3 .4 .5 .7 .8 1.0 1.5 2.7 2.8 3.5 4.0 8.9 9.2 11.7 21.0
Non-ED: 0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2 .3 .3 .3 .4 .5 .5 .6 .8 .9 1.0 1.2 1.4 1.5 1.7 2.0 3.2 3.5 4.1 4.3 4.8 5.0 5.6 5.9 6.0 6.4 7.9 8.3 8.7 9.1 9.6 9.9 11.0 11.5 12.2 12.7 14.0 16.6 17.8
a) Determine the medians, fourths, and fourth spreads for the two samples.
b) Are there any outliers in either sample? Any extreme outliers?
c) Construct a comparative boxplot, and use it as a basis for comparing and contrasting the ED and non-ED samples.
Can anyone help me, please?
Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The accompanying data was read from a comparative boxplot in the article "Fatal Excited Delirium Following Cocaine Use"(J. of Forensic Sciences, 1997: 25-31).
ED: 0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3 .3 .4 .5 .7 .8 1.0 1.5 2.7 2.8 3.5 4.0 8.9 9.2 11.7 21.0
Non-ED: 0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2 .3 .3 .3 .4 .5 .5 .6 .8 .9 1.0 1.2 1.4 1.5 1.7 2.0 3.2 3.5 4.1 4.3 4.8 5.0 5.6 5.9 6.0 6.4 7.9 8.3 8.7 9.1 9.6 9.9 11.0 11.5 12.2 12.7 14.0 16.6 17.8
a) Determine the medians, fourths, and fourth spreads for the two samples.
b) Are there any outliers in either sample? Any extreme outliers?
c) Construct a comparative boxplot, and use it as a basis for comparing and contrasting the ED and non-ED samples.
Can anyone help me, please?
You need to figure out the median (middle score) for the full data set.
And then your quartile 1 and 3 medians: Q1, Q3
(middle score for the bottom and top half of your data.)
Your whiskers for your box plot are <= 1.5*(IQR) Interquartile range
where, IQR is your Q3-Q1
For your ED set of data. Median = .4
Q1 = .1
Q3 = 2.8
Box plots are formed by building a rectangle on a number line using the Q1, Q3, and your median value. So it will look like a rectangle with a dividing line in it which will be your median. Your whiskers extend to the lowest and highest values that come next in your data set.
MisterLuffy
Member
For question a), how did you determine the Quartile would be 1 and 3? How do I determine whether its Quartile 2 and 4?
MisterLuffy
Member
Thank you
Hey GAF quick question:
I'm in an intro comp science class and we're doing some base conversions
One question on the homework asks to convert 749 base 8 to base 2. Is this impossible because there is no 9 in base 8?
111 for 7, 100 for 4, so 11110 but then what's 9? Am I missing something or is this question a mistake?
Thanks!
I'm in an intro comp science class and we're doing some base conversions
One question on the homework asks to convert 749 base 8 to base 2. Is this impossible because there is no 9 in base 8?
111 for 7, 100 for 4, so 11110 but then what's 9? Am I missing something or is this question a mistake?
Thanks!
Have a statistics problem I need help with.
Show, by using moment generating functions, that if X is an element of L(1), then X has the same distribution as Y_1 - Y_2, where Y_1 and Y_2 are independent, exponentially distributed random variables (Exp(1)).
Now, using the characteristic function I get 1/(1+t^2) for Y_1 - Y_2, and 1/(1+t^2) for L(1), and using the m.g.f, I get 1/(1-t^2) for L(1), assuming I've done right. I'm supposed to use the m.g.f to prove that both have the same distribution but I'm missing something because I can't get things to add up.
Show, by using moment generating functions, that if X is an element of L(1), then X has the same distribution as Y_1 - Y_2, where Y_1 and Y_2 are independent, exponentially distributed random variables (Exp(1)).
Now, using the characteristic function I get 1/(1+t^2) for Y_1 - Y_2, and 1/(1+t^2) for L(1), and using the m.g.f, I get 1/(1-t^2) for L(1), assuming I've done right. I'm supposed to use the m.g.f to prove that both have the same distribution but I'm missing something because I can't get things to add up.
Yeah, this is a mistake. 749 base 8 is not a number.
KugelBlitz
Neo Member
I wish I could understand things like this...
I am absolutely terrible at maths - but I don't really know where to start, nor do I have the motivation to learn it.
That feel when you are too lazy to help yourself...
*Sigh*
MisterLuffy
Member
Sorry for asking again, I need help on another problem.
Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A) = .5, P(B) = .4, and P(A and B) = .25
a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the even A and B).
b) What is the probability that the selected individual has neither type of card?
c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.
Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A) = .5, P(B) = .4, and P(A and B) = .25
a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the even A and B).
b) What is the probability that the selected individual has neither type of card?
c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.
cpp_is_king
Member
Draw a Venn Diagram.
FUBAR McDangles
Member
Hey fellas, how do I find the derivative of this function?
(3x^3 + 3x^2 + 6x -8) / x
I know the answer is 6x+3+8x^-2 but I have no idea how to actually get there. I went to my professor and asked, and she just told me to break it into parts, like:
((3x^3)/x) + ((3x^2)/x) + ((6x)/x) - (8/x)
But I have no idea where to go from there. Anybody care to help?
(3x^3 + 3x^2 + 6x -8) / x
I know the answer is 6x+3+8x^-2 but I have no idea how to actually get there. I went to my professor and asked, and she just told me to break it into parts, like:
((3x^3)/x) + ((3x^2)/x) + ((6x)/x) - (8/x)
But I have no idea where to go from there. Anybody care to help?
FUBAR McDangles
Member
We just went over the quotient rule and I'm not really comfortable with it yet.
But see I looked at that kinda like you said with the dividing to simplify but I wasn't sure how exactly to do that with the -8/x. I get it now, but for whatever reason that part was blowing my mind :lol
Thanks for the help, I appreciate it.
Partial Gamification
Banned
Checkout the wolfram example.
edit: nvm I think you might be finding volume with the shell method...
you got it, 2pi(x)(cos(x^(2))dx, integrate w/ respect to x or y [?], think about it.
its the x-axis, its a misleading trick question.
cpp_is_king
Member
FWIW, I've only used the quotient rule a few times. I dislike remembering things. I almost always treat the denominator as having exponent -1. In any case, the quotient rule is easy to derive just by treating the denominator as having exponent -1 and applying chain rule.
f(x) / g(x) = f(x) * g(x)^(-1)
[f(x) / g(x)]' = -f(x)g'(x)^(-2) + f'(x) g(x)^(-1)
Now convert the negative exponents back into denominators, make the denominators the same, and voila. quotient rule.
Partial Gamification
Banned
The integration is good, up to plugging in the limits.
Are the limits of integration [ 0 and 1/(2*sqrt(pi)) ] or [ 0 and (1/2)*sqrt(pi) ] ?
maybe its this line:
[ sin(1/2pi^2)]--------- pi [sin(pi/4)]
from pi*sin(x^2) evaluated at the limits, [ 0 and 1/(2*sqrt(pi)) ]
pi*( sin(1/(4*pi)) - sin(0) ) = pi*sin(1/(4*pi))
but... [ 0 and (1/2)*sqrt(pi) ]
pi*( sin(pi/4) - sin(0) ) = (pi*sqrt(2))/2 <-what you got!
Memento_Mori15
Member
Perhaps because it's late and I'm tired but this is bothering me:
What is the sample space of a die thrown 3 times having at least one odd number?
1 - - <- 6 possibilities each blank. Total 12.
3 - -
5 - - <36 outcomes
- 1 -
- 3 -
- 5 -
- - 1
- - 3
- - 5
So 108 outcomes, a half...yet I looked at it another way. What's the possibility of actually throwing straight evens? If I don't, I'll have at least one odd. I worked it out to be 27/216 since u can have:
222
224
226
244
242
246
262
264
266
Do it again 2 more times thus 27.
So in the end, 189/216. Now I think this is correct but where did I mess up in my logic in the former?
What is the sample space of a die thrown 3 times having at least one odd number?
1 - - <- 6 possibilities each blank. Total 12.
3 - -
5 - - <36 outcomes
- 1 -
- 3 -
- 5 -
- - 1
- - 3
- - 5
So 108 outcomes, a half...yet I looked at it another way. What's the possibility of actually throwing straight evens? If I don't, I'll have at least one odd. I worked it out to be 27/216 since u can have:
222
224
226
244
242
246
262
264
266
Do it again 2 more times thus 27.
So in the end, 189/216. Now I think this is correct but where did I mess up in my logic in the former?
It's been a while, but I'm pretty sure that you multiply the possibilities for each blank instead of adding them. For example, 1 - -, 3 - -, and 5 - - would each have 36 possible outcomes. Remember to account for any previously rolled odd numbers for the second and third rolls; otherwise, you'll be counting some outcomes multiple times.
cpp_is_king
Member
There are a couple of errors in your first strategy. The first is that you added instead of multiplied. 6 possibilities for 2 different blanks is a total of 36. If you do it that way however, you get 36 * 9 = 324, and we can see that's too many. Now it's because you're overcounting. For example, consider the combination 1 3 5. That would be counted by 1 - -, by - 3 -, and by - - 5.
Ultimately, the best way to solve this problem is how you did in the second approach - by complementary counting.
Don't know if this has been posted.. but everyone should check out this site
http://www.wolframalpha.com/
It can be extremely helpful for just about any subject but I use it quite often to check integration/derivations, plotting equations, solving systems of equations, etc.
http://www.wolframalpha.com/
It can be extremely helpful for just about any subject but I use it quite often to check integration/derivations, plotting equations, solving systems of equations, etc.
Yeah, it's great for most questions. It can behave a bit strange for certain transforms, though.
campfireweekend
Member
So this is a problem involving finding volumes using slicing and integration.
A dam has a rectangular base 1400 meters long and 160 meters wide. Its cross-section is shown in Figure 8.15 (The Grand Coulee Dam in Washington state is roughly this size.) By slicing horizontaily, set up and evaluate a definite integral giving the volume of material used to build this dam.
I get that the slice is a 3d rectangle whose formula is l*w*h. The length is not variable and is 1400 meters. Both the width and height are variable. What I cannot figure out, is how to express width in terms of height (still talking about the 3d rectangle garnered from slicing.
Help?
Figure in question.
A dam has a rectangular base 1400 meters long and 160 meters wide. Its cross-section is shown in Figure 8.15 (The Grand Coulee Dam in Washington state is roughly this size.) By slicing horizontaily, set up and evaluate a definite integral giving the volume of material used to build this dam.
I get that the slice is a 3d rectangle whose formula is l*w*h. The length is not variable and is 1400 meters. Both the width and height are variable. What I cannot figure out, is how to express width in terms of height (still talking about the 3d rectangle garnered from slicing.
Help?
Figure in question.
Partial Gamification
Banned
Is this a correct diagram, I included the dam for good measure?
It looks like a trapezoidal prism and the horizontal slices will be 2D rectangles, variable length and width. Does that help? Think about how the stacked 'thin' slices yeild the height, the whole volume for that matter.
edit: maybe I'm just reading it all wrong because it seems like the trapezoidal vertical slices would let you manipulate the top-base and height of the trapezoids, here: 1/2 (160 +b)(h) or 1/2 (160 + 10)(150) as shown in the figure. edit: horizonatally will work too, using angles.
campfireweekend
Member
Is this a correct diagram, I included the dam for good measure?
It looks like a trapezoidal prism and the horizontal slices will be 2D rectangles, variable length and width. Does that help? Think about how the stacked 'thin' slices yeild the height, the whole volume for that matter.
edit: maybe I'm just reading it all wrong because it seems like the trapezoidal vertical slices would let you manipulate the top-base and height of the trapezoids, here: 1/2 (160 +b)(h) or 1/2 (160 + 10)(150) as shown in the figure. edit: horizonatally will work too, using angles.
Thanks for the help! How exactly would you go about developing it horizontally using angles? I know that a horizontal slice of this 3d object is a 3d rectangle. I guess I'm just confused as to how I should manipulate it to yield what I need. Probably rooted in geometry
Partial Gamification
Banned
Its 2D areas from the slicing, a 3D rectangular prism isn't coming form a slice but that might just be a typo. If you think of the angles at the base-vertices determining the slope of the side of the dam, then the slices are "squeezed" by the slanted sides as one goes up the dam - assuming top < base in the vertical trapezoids. Its seems more difficult than what you're doing, but out of trig and the algebra required (variable height and maybe the top-base of the trapezoid) not the calculus.
Is the figure used for another problem and the "150" and "10" measures are to be ignored?
edit: let me not throw you for a loop here; this is how I'm seeing your problem. The lower figure is the horizontal cross-section
edit: and the horizontal slice willl have 1400-x = 1400, or x=0 if the length is invariable.
Snarfington
Member
Okay, I'm meant to prove the Cauchy-Schwarz inequality for vectors ( (uv)^2 is less than or equal to ||u||^2 * ||v||^2 ) and I've got to do it independently of the cosine function with the suggestion of "consider the scalar product of u-tv with itself for an arbitrary t" and I have NO IDEA how to even start. And my advisor had no idea so I can't get any help before it's due. Any advice?
Memento_Mori15
Member
I didn't even consider that at the time. Thanks for this, really helpful. "Counting is hard"
Now another question. I know the answer(72) but I'm not getting how we got there.
Say we're at a round table, 8 chairs, 4 men and 4 women. Each must sit alternatively. Well, u have 2 choices and when you use up a man or woman, it decreases. Thus 2*4!*4! Now that's right if it's a non-rounded table. Instead, we must divide that by 8*2. Why?
hemtae
Member
Partial Gamification
Banned
That's an approximation, and the right one.
11y - 1 + (1) = 4y + 1 + (1)
11y +0 = 4y + 2
11y-4y = 4y - (4y) +2
7y = 0 + 2
y = 2/7
2/7 ≈ 0.285714
You can always plug the value back in to test your answer.
11*(2/7) - 1 = 4*(2/7) + 1
22/7 - 7/7 = 8/7 + 7/7
15/7 = 15/7
edit: too slow, beaten.
This may sound bad but I have a test on Monday in my Pre-Calc/Calc class and it's going to be about graphing polynomial and rational functions. I'm having a hard time figuring out how to graph Parabolas and graphing one after reading an equation like:
f(x) = - 4 ( x - 2 )^2 + 1
for example. Any online resources I can use? My Math Lab is ok, but not ideal since my teacher shows how it is done, but not explained.
f(x) = - 4 ( x - 2 )^2 + 1
for example. Any online resources I can use? My Math Lab is ok, but not ideal since my teacher shows how it is done, but not explained.
Thanks, I think i was looking for the fraction.
So to get that I don't actually have to solve 2/7, on the step where y and 2 is divided by 7, y becomes equal to the fraction, and if the fraction were unsimplified I could simplify it for the answer?
Partial Gamification
Banned
Yes, if y = 4/14, then it would also equal 2/7.
Likewise, y = 12/42 is also equal 2/7.
Partial Gamification
Banned
Know how the equations shift the graph.
From the (x-2) term, the graph is 2 to the right, think where x zeros f(x).
Think of y=x^2 versus y= (x-2)^2, graph these.
Expand the polynomial, -4*(x^2 - 4 + 4) + 1 to find the y-intercept when x=0.
Compare: y=x^2 versus y= 4*x^2 versus y = (1/4)*x^2 versus y = (-1)*x^2
If you take the derivative, you'll get the equation for the rate of change.
Test points to find where f ' (x) is positive, negative, and equal to zero;
this will indicate the increasing/decreasing nature of f(x) and its critical point.
Maybe you've seen this done in table-form for the organization when listing values.
Best to try a few from your materials and test the plots you come up with against an online grapher, there are many.
Graph Translation and Stretching
Videos on youtube too, if you want walkthroughs. The title of link should bring up plenty more resources in search queries.
Memento_Mori15
Member
Use wolfram.
If it's an x and u subtract it, you go to the right. ^2 tells you it's a parabola. Negative outside flips it and expands it by 4. +1, you go up one on the y axis. Break it down step by step. Still stuck? You plug random numbers like 0,1,2 and then go from there. Like for the equation you gave, I wanna set x to 2 so I can get right whatever is on the left side of the + a zero. Thus Y is simply 1. Then go from x=1 and x=3. Get the points and then graph using what you get. I will probably go more in detail if I wasn't on my iPod.
I'm pretty sure Patrickjmt has videos on these.
cpp_is_king
Member
I didn't even consider that at the time. Thanks for this, really helpful. "Counting is hard"
Now another question. I know the answer(72) but I'm not getting how we got there.
Say we're at a round table, 8 chairs, 4 men and 4 women. Each must sit alternatively. Well, u have 2 choices and when you use up a man or woman, it decreases. Thus 2*4!*4! Now that's right if it's a non-rounded table. Instead, we must divide that by 8*2. Why?
I'm not sure where you're getting the 2's from, but I get an equivalent answer that doesn't use any 2's.
Fix a starting seat, and then place the women in a circle starting from that seat. There are 4! ways to do that. Once its done, there are an additional 4! ways to place the men. This is a total of 4! * 4! = 576 ways to place the people at the round table. However, there are 8 ways of symmetry (for each configuration, the configuration obtained by rotating the entire table 1,2,3,...,8 spaces to the right is equivalent. So we divide by 8. This gives (4! *4!) / 8 = 72.
This is equivalent to your idea about (2*4!*4!) / (2*8), but I'm not sure where the 2 is coming from, so perhaps it's easier to understand using my explanation.
w1 = 100 lbs
p1 = $1.80 / lbs
w2 = pounds to be mixed
p2 = $0.80 / lbs
p12 = $1.20 / lbs
p12 = (w1*p1 + w2*p2) / w1 + w2
1.20 / lbs = (w1*p1 + w2*p2) / w1 + w2
1 unknown, 1 equation. Solve for w2.
cpp_is_king
Member
We're looking for how many pounds of meal. Let's say M is the number of pounds of meal we're looking for (i.e. the answer to the problem).
We want to mix that meal with 100lbs of grain. How heavy is the resulting meal+grain mixture? It's 100+M pounds. How much is the meal worth? $0.8M.
Now, the total value of this mixture is $180 + $0.8M and the total weight is 100+M. We want the mixture to cost $1.20 / pound.
($180 + $0.8M) / (100+M) = $1.20
Solve for M.
$180 + $0.8M = $120 + $1.20M
$60 = $0.4M
M = 150
Let's make sure this works. If we've got 150 pounds of meal, we've got 250 pounds of mixture. The price of the mixture is (100)($1.80) + (150)($0.80) = $300. Therefore, the mixture is $300/250lb = $1.20 / lb.
Hey guys, just wondering if anyone knows a good link or site for like a "Proofs for dummies" thing.
I'm taking discrete math, and while intro to proofs was not required, it feels like everyone else in the class has had it, or somehow knows what the fuck is happening... either way I'm having a hard time keeping up because the proofs are really confusing me.
I'm taking discrete math, and while intro to proofs was not required, it feels like everyone else in the class has had it, or somehow knows what the fuck is happening... either way I'm having a hard time keeping up because the proofs are really confusing me.
cpp_is_king
Member
Well, maybe someone has a less discouraging response for you, but I feel Discrete Math is the proofs for dummies class
Maybe your best strategy is to post some questions here and clearly articulate exactly what it is you don't understand or where you're getting lost.
Partial Gamification
Banned
Introduction to mathematical arguments
(background handout for courses requiring proofs)
I was hoping to find something that had truth tables in it. cpp_is_king is right, just bring specific questions. Make a key for the math-symbols that are unfamiliar. I wouldn't be surprised if half the stuff you were proving in class came from Euclid's Elements. Cross the pons asinorum! Its practice (I'm not great at it), and not many people in this World even bother to try and understand it, so don't get discouraged or feel like a "dummy." We're all dummies in one way or another.
Well, maybe someone has a less discouraging response for you, but I feel Discrete Math is the proofs for dummies class
Maybe your best strategy is to post some questions here and clearly articulate exactly what it is you don't understand or where you're getting lost.
thanks for the advice guys. I've got the truth tables and euclids symbols kind of down already... so yea I guess it's mostly just practice (and yes I took discrete because I thought intro to proofs would be a pain, never should have minored in math!).
Anyway, seems like I'm getting confused on the last steps... like I can follow the logic, step for step, but then we get to the end and everybody says "Yes, this proves that, we're done." and I just don't see it.
For example, (here's the problem I'm working on now, I hope it comes out here in a way that is readable))
Theorm:
For every n in the integers such that n is greater than or equal to 1, 2+4+6+...+2n=n^2+n
Proof:
P
= 2+4+6+...+2n = (n^2)+nP(1) = 2(1) = ((1)^2)+1, so P(1) is true.
P(k) = 2+4+6+...+2k = (k^2)+k, assume P(k) is true.
P(k+1) = 2+4+6+...+2(k+1) = ((k+1)^2)+(k+1) the next step is where I go wrong, on the left side of the equation I want to multiply out 2(k+1) to 2k+2, and then fill in the previous integers in the sequence to get:
= 2+4+6+...+2k+(2k+1)+(2k+2) = ((k+1)^2)+(k+1) and then I can substitute P(k) and simplify both sides, but it doesn't work out. The book says the sequence for P(k+1) simplifies to 2+4+6+...+2k+2(k+1) "by making the next to last term explicit", but I don't see how 2k comes before 2(k+1)..... oh son of bitch, I get it now... fucking MATH! Damn you. I'm not going to delete all this, I'm just going to post it, because fucking math, that's why.
fake edit: In case anyone read this and can't figure it out: I screwed up because I kept thinking (2k+1) is in the sequence, but it's not because the sequence is only the even numbers and (2k+1) is odd.
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