Wednesday
April 16, 2014

Posts by MathMate


Total # Posts: 9,948

Calculus
Find the shortest distance from a point P(2,-1,2) to a line L r= [-1,0,7] + t [4,1,-2]. Assume a point Q on the line such that PQ is the shortest possible distance between them. Then PQ is orthogonal to the line L. Given P(2,-1,2). Let Q(-1+4t, 0+t, 8-2t), then PQ=<-3+4t, t...

Calculus grade 12
7. Where does the line r = (1, 2, -5) + t (2, -3, 1) meet the plane 2x + 5y - 3z = 6? Let the intersection point be P on L such that P(1+2t, 2-3t, -5+t) Substitute the values of x,y and z of P into the equation of the plane and solve for t.

Calculus
Did you see the response at : http://www.jiskha.com/display.cgi?id=1337962346 Do you have difficulties completing the suggested calculations? If you do, you will have the same problems at the exams even if you get a 100% grade for you computerized homework.

Algebra
Difference in fixed cost=$16-$11=$5 Difference in per minute call = $0.11-0.08=$0.03 Difference in minutes = $5/0.03=166.67 min. So up to 166 minutes, XYZ offers a better deal.

college math
10.125/100 =10125/100000 =81/800

math
Check the question for typo. If there is none, then x=0

math
Take a piece of paper and note the following on your diagram. It will be difficult to follow without an annotated diagram. Label the (horizontal) diameter as CD, with C on the left. Label the chord 16 units long as PA (P on the left). Label the chord 12 units long as QB (Q on ...

algebra homework check :)
You're welcom!

algebra homework check
Yes, they are all correct!

Calculus
Take a vector that lies on the line (-2,5,7). Check if this vector is perpendicular to the normal vector of the plane (3,4,-2). If the dot product between them is zero, the two vectors are perpendicular, and therefore the line is parallel to the plane.

Calculus
I assume the plane needs to pass through the mid-point between the two points, and perpendicular to the line joining the two points. First find the mid-point by M((x1+x2)/2,(y1+y2)/2,(z1+z2)/2) The normal vector for the plane is just the vector AB, or N(3-(-1),1-2,-4-4)=(4,-1,...

Calculus
Yep, that's it.

Calculus
The line would look very much like the one shown in the question: http://www.jiskha.com/display.cgi?id=1337962346 You only have to replace the point and the vector.

geometry
If ABCD is a parallelogram, then opposite sides are equal, or AB=CD. Equate their lengths and solve for x.

math
I assume the question was: If E and F are events with P ( E ∩ F ) = 0.09 and P ( E | F ) = 0.3 , P ( F | E ) = 0.4 Find P (F ) where P(E|F) and P(F|E) are conditional probabilities. Review your class notes to find that: P(E|F)=P(E∩F)/P(F) and P(F|E)=P(F∩E)/P(E)=P...

Math :)
You're welcome!

Math
dN/dt = rN(1-N/K) is a separable equation by rewriting it as: dN/[rN(1-N/K)] = dt => (K/r)[1/(N(K-N))]dN = dt split into partial fractions (1/r)[1/N + 1/(K-N)]dN = dt Now integrate (1/r)(ln(N)+ln(K-N))=t + C Rewriting, ln(N*(K-N))=r(t+C) At this point, substitute r and K to...

geometry
The inverse of matrix A= a b c d is d -b -c a divided by the determinant ad-bc. So the inverse of 2 10 5 -3 is -3 -10 -5 2 divided by (-3)(2)-(-5)(-10)=-56, or 3/56 10/56 5/56 -2/56 To find the solution of the given problem, pre-multiply the equation by A-1 to get [x,y]=A-1 [7,1]

MATH HELP see other post
See your other post: http://www.jiskha.com/display.cgi?id=1337917428

MATH
Define C(n,r)=n!/(r!(n-r)!)=n choose r Sample space: C(13,5)=1287 ways to choose 0 boy =Choose 5 girls out of 7 and 0 boy out of 6 =C(7,5)*C(6,0)=21 ways to choose 1 boy: =C(7,4)*C(6,1)=210 ways to choose 2 boys: =C(7,3)*C(6,2)=525 ways to choose 3 boys: =C(7,2)*C(6,3)=420 way...

Calculus
Correct!

Calculus
Same as previous question, http://www.jiskha.com/display.cgi?id=1337914331 Except that the dot-product equated to zero results in a quadratic equation. So solve for possible values of t by solving the quadratic.

Calculus
Correct!

Calculus
Two vectors u and v are perpendicular if the dot product u.v=0. Do the multiplication and equate to zero to solve for t.

Calculus
Correct!

Calculus
A vector perpendicular to both m and n is the cross product. After that, you only need to normalize it to make a unit vector. Post if you need more help.

Integral Calculus :)
No problem!

Integral Calculus
x^2/(x^2+1) = 1 - 1/(x^2+1) You can easily integrate that.

geometry
See the answer for a nonagon and proceed the same way: http://www.jiskha.com/display.cgi?id=1337912555

math
The area A of any regular polygon of n sides with side length s, apothem a is A=nas/2. Since ns=perimeter, p, we can also write the area as A=ap/2 An apothem is the distance from the centre of the polygon to the side. We assume the given nonagon is regular, i.e. all sides and ...

math
"Step 3:forty minus one equals thirty-nine " We add the integer and decimal portions, not subtract.

ALGEBRA
Expected income is ∑ x P(x). you have three cases where x1=445000, P(x1)=1/40 x2=145000, P(x2)=1/20 x3=0, P(x3)=1-1/40-1/20=37/40 Calculate the sum and don't forget to subtract the fixed cost from the expected income.

math
It is a similar problem to an earlier post. Take a look at the other post and see if you can solve it. http://www.jiskha.com/display.cgi?id=1337631545

Algebra
Again the crust will not change the probability. Here the customer chooses 5 toppings out of 10 in C(10,5)=10!/(5!5!)=252 ways. This is the sample space. If the customer is to have onions, jalapenos and tomatoes, he has two other choices out of 7 remaining toppings in C(7,2)=7...

Algebra 2
Sorry I have not noticed that the pizza place sells 5-topping pizzas. The answer (in probability terms) will therefore be different. See other post for details: http://www.jiskha.com/display.cgi?id=1337879558

Algebra 2:)
NOTE: read through the interpretations of the question before deciding if the answer is applicable to you. A classic crust is one choice out of three in the first step of the experiment. The probability for step 1 is therefore 1/3. "Extra cheese, pepperoni, sausage, onion...

Algebra 2
Did you copy the question word for word, or did you paraphrase it? It does not appear too clear for me about the 3 types of ice cream and 4 types of toppings apart from the flavour. Also, the qustion did not mention about multiple flavours, yet it asks for chocolate AND strawb...

Algebra 2
Hm.. There are 3 different types (brands?) ice creams EACH with 8 flavours, and 4 types (styles?) of toppings EACH with 10 flavours. In all, there are 3*8=24 different ice creams and 4*10=40 toppings, for a total sample space of 40*24=960 items. Given that the ice cream has ch...

Consumer math !!!! please check
Up to #9, you have #6 and #8 are correct. I will appreciate if you could show how you worked out the remaining numbers so that any incorrect notions could be corrected accordingly. There is no use throwing a coin to make a guess if you don't know how to get the right answe...

geometry
I do not believe that the 4 given choices correspond to the question. Either there is a typo in the question, or the answer.

geometry
Your answer does not correspond to any of the choices, neither does mine! So there is probably is mistake in posting the question. Once you start using the correct question, think of the following. There is a general misconception about multiple choices in mathematics. The saf...

geometry
All good except P1. Can you spot the error?

geometry
It's almost good. You probably just forgot to divide by the common denominator 2. The answer should therefore be (21+7sqrt(3))/2 =21/2 + (7/2)sqrt(3)

geometry
Did you add the three sides, 3.5, 3.5√3 and 7? Remember that 3.5 is the same as 7/2, and so on.

geometry
Fact: all 30-60-90 triangles are similar. Fact: therefore the ratio of the perimeter to the hypotenuse is the same for all 30-60-90 triangles. We have arbitrarily created a 30-60-90 triangle with hypotenuse = 2. So to get a triangle with a hypotenuse of 7, we need to multiply ...

geometry
The ratios of the sides of the 30-60-90 triangle are: 1 : √3 : 2 So the ratio of the perimeter to the hypotenuse is 3+√3 : 2 Use cross-product to find: perimeter / 7 = (3+√3) / 2

math help
P1=P(3 hearts)=12/52*(11/51)*(10/50) P2=P(3 numbers each less than 6) =P(5 or less out of 52)*P(5 or less out of 51)*P(5 or less out of 50) =(5*4)/52 * (19/51) * (18/50) Add P1 and P2 to get 4/65.

Year 11 Maths B :)
Perfect!

Year 11 Maths B
n1=35, total mass, m1 = 35*49 = 1715 n2=8, total mass, m2 = 8*53 = 424 Total bag count = n1+n2 total mass = m1+m2 New mean mass = (m1+m2)/(n1+n2)

Math :)
You're welcome!

Math
dT/dt=0.1(34-T) dT/(34-T) = 0.1dt Integrate both sides -ln(34-T)=0.1t+c 34-T=Ce^(-0.1t) T=34-Ce^(-0.1t) Initial conditions: t=0, T=4 => 4=34-C => C=30 so T=34-30e^(0.1t) A) Substitute t=15 to solve for T. B) Substitute T=30 to solve for t.

algebra 1
Treat as two fractions, and the common denominator is w²x², so 5/wx² + 2/w²x =(5w+2x)/(w²x²)

math
12 men and 8 women. Define: (n,r)=n choose r = n!/((n-r)!r!) Example: (5,3)=5!/(2!3!)=5*4/2!=10 A. exactly 3 men and 4 women Choose the 3 men in (12,3) ways and the 4 women in (12,4) ways. The number of groups which has exactly 3 men is therefore (12,3)*(12,4)=220*495 ways. B....

math
Usually conveyors are at an angle with the horizontal. Here for lack of more information, we assume that the conveyor is vertical (using pouches) to carry the gravel, or the 3 feet per second is measured vertically. 3 feet/second * 54 seconds = 3*54 feet =162 feet

algebra
Normalize 80 as (80-98)/6=-3 Look up the probability from a normal distribution table for -3 to ∞. (It is the same value from -∞ to +3, depending on the availability of the table). I get 0.9987.

trig
Using sin^2 x = 1-cos^2(x) the equation becomes: cos²(x)+cos(x)-2=0 Use the substitution c=cos(x) to transform the equation to : c²+c-2=0 (c+2)(c-1)=0 c=-2 or c=+1 Since cos(x) cannot equal -2, solution is rejected. Now solve for all values of 0≤x≤2π where c...

algebra 2 :)
You're welcome!

algebra 2
a1=1 a2=(a2-1+1)^2 =(a1+1)^2 =(1+1)^2 =4 a3=(a2+1)^2=5^2=25 a4=(a3+1)^2=(25+1)^2=26^2=676

math
Quarterly means 4 times a year. So (1+0.14/4)^4 =1.035^4 =1.147523 or effective rate =14.7523%

Math
7, -4.2, 2.52, -1.512, ... Divide successive terms, -4.2/7=-0.6 2.52/-4.2=-0.6 -1.512/2.52=-0.6 So the common ratio is r=-3/5 T(1)=7 T(n)=7r^n T(7)=7(-3/5)^7 =-15309/78125 =-0.196 approx.

trig :)
You're welcome!

trig
tan(x) has a period of π, so tan(x)=tan(x+π), in fact, tan(x+kπ)=tan(x), where k∈Z So to evaluate tan(257π/4) =tan((257/4)π) =tan(64π + π/4) =tan(π/4) I will let you figure out which answer to choose.

Geometry
A 30-60-90 triangle has sides in the ratio: 1 : √3 : 2 Find the remaining sides by proportion.

math
1-5t/4 ≥ 6 -5t/4 ≥ 5 5t/4 ≤ -5 5t ≤ -20 t ≤ -4

algebra - conditional probability
Conditional probability P(A|B) is defined as P(A|B)=P(A∩B)/P(B) Hence: P(face card | queen) =P(face card ∩ queen)/P(queen) =P(queen)/P(queen) =1 P(three|not a face card) =P(three ∩ not a face card)/P(not a face card) =(4/52)/(40/52) =1/10

ALGEBRA
So the template is NXXNNNN I interpret the "repeated digit" as any two identical digits appearing anywhere on the licence plate, as opposed to two identical digits next to each other. Also, it was not specified as "exactly one repeated letter or digit", so ...

algebra 2
Part A: Assuming the ring is not symmetrical, i.e. it cannot be worn both ways, then there are 3! ways the stones can be arranged. If the ring is symmetrical, divide by 2. Part B: similar to A, replace 3 by 4. Part C: Leave it to you as an exercise.

geometry
Vj/Ve=(Dj/De)^3=(88000/8000)^3=11^3=1331

Math/Prob
We will have to assume the ESP estimation is correct. The resulting distribution is binomial, with 5 questions, and probability of success p=1-0.6=0.4, q=1-p=0.6 (failure). The probability of getting exactly n question correct (out of 5) is given by the binomial coefficient C(...

algebra 2 :)
You're welcome!

algebra 2
What's left in the bag: 4R, 4G, 3B, 4W = 15 marbles total Expected value = ∑ x P(x) =(4*1+4*2+3*3+4*10)/15 =4.07

Algebra
Any line perpendicular to y=x is y=-x+k where k is a constant to be determined. Since it passes through (0,0), we have 0=-0+k so k=0. The line is therefore y=-x

math
You're looking for: 83*1.07^n=10832 1.07^n=10832/83=130.506 take log and solve for n n log(1.07)=log(130.506) n= 71.99995 = 72 since 10832 is approximate.

Math
What is the question? Which is the part that you cannot do, and what is your attempt at a solution?

algebra - conditional probability
If A and B are independent events, then P(B|A)=P(B)=0.93

algebra - incomplete question
Your question is incomplete. Please check the question after your post.

math
Sum and difference problems can be solved mentally. The bigger number is half of the 24+10=17 and the smaller number is half of 24-10 =7.

programming
If you really don't know where to start, you may review your teacher's class notes, your text book. If there is none, you can also learn by tutorials, such as: http://www.sthurlow.com/python/ Do you have Python installed on your computer, or you have one available at s...

programming
For your information, I will tend to respond to posts on programming / computers in which efforts are shown. Unlike mathematics, where 2+2 always equal 4 (if we are in the decimal system). However, no two computer programs are the same, so every program is a personal version o...

programming :)
You did most of the work, so you deserve the credit too!

programming
It would be along the same lines, just change floors to rooms, and for floors, change 10 to 1 for the number of floors.

programming
Your code looks carefully thought out. For making sure there are 10 storeys or more, you can modify the input segment: System.out.print("How many floors are present: "); floors = input.nextInt(); while(floors<10){ // print Number of floors must be at least 10 floo...

statistics
For equations, see: http://en.wikipedia.org/wiki/Simple_linear_regression

Computer programming
Set k=1 While k<=5 Display k + 1 End While k does not get updated inside of the while loop, so it will print 2 and loop forever. Set k=1 While k<=5 k = k + 2 End While When it hits "while k<=5", the values of k are 1,3,5,7... So how many times does it get ex...

algebra 1
By symmetry, w=7 or -7. Alternatively, w/7-7/w=0 w/7=7/w w^2 = 49 w=±7

Math
4k : k∈Z is an integer which is a multiple of 4. Its square is 16k^2. For 3n=16k^2, we have n=16k^2/3 ∈Z, so 3 must divide k^2, which in turn means that 3 divides k. So the smallest n is when k=3, or n=16*3^2/3=48 assuming n is a positive integer.

Statistics
There are 10 outcomes per urn. Sample space = 10*10*10*10 since the outcome from each urn is independent of the others.

algebra
See response to: http://www.jiskha.com/display.cgi?id=1337744371

algebra 2
yep! That's correct!

algebra 2
How many choices for the first place? 9 How many choices for the second place? 8 (because there are only 8 people left after the first place) How many choices for the third place? 7 How many ways altogether? use the multiplication rule.

Computer Science Computer Programming
Happy to hear that you have got it working! Congrats! Even though the code works as it is, there are traps lurking around to get you as you go on. 1. Your outputting "total" at the end is the proper way to do things, as the showMessageDialog will be used only once fo...

Computer Science Computer Programming
Thank you for posting the original question. It always helps (if accompanied by your efforts)! You may want to review your logic for the prices according to 2 criteria: 1. Basic according to weight: According to following scale: ( = excluding ] = upto and including (0-2] $1.1 ...

Computer Science Computer Programming
First thing that comes to mind is (mile/500) will truncate to the next lower integer, namely zero if mile<500. All you need to do to correct is to write (mile/500.0) which will convert integer division to force floating division. Also, if the program does not work, you will...

math 8
yes. Check: 11x11=121

Math
Divide the output by the input and see if you can find a rule for the quotient, and hence the rule for the function.

math
"...replace it and seect a second sock at random..."

math
With replacement: P(B,R)=P(B)*P(R)=(3/10)*(4/10)=12/100=3/25

ALGEBRA
See: http://www.jiskha.com/display.cgi?id=1337811808

ALGEBRA
Mike, Can you double check if your notation P(spade|spade) means P(spade followed by a spade), usually written as P(spade,spade) or does it means conditional probability P(spade given it is a spade)?

linear programming
Unit Costs: Magnetite: $37 => 0.7 ton of iron =>$52.86/ton limonite: $46 => 0.6 ton => $76.67/ton pyrite: $50 => 0.5 ton => $100/ton taconite: $42=> 0.3 ton => $140/ton Production: magnetite: 350*0.7=245 tons limonite: 0.6*530=318 tons pyrite: 0.5*610=3...

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