Monday
April 21, 2014

Posts by MathMate


Total # Posts: 9,948

Mathematics
This is a direct proportion problem. 80% correct means 100-80=20% incorrect. By direct proportions, 20% : 6 problems 100% : X problems? Cross multiply to get X=6*100/20=30

Volume
Like all multiple integral problems, start with drawing a sketch of the bounding curves. I have done that for you for this time, see: http://img687.imageshack.us/img687/811/1342739949.png If curves intersect, find the intersection points. In this case, it is at (5,25). Then de...

PHYSICS !!
Check out Newton's third law.

calculus derivatives - insufficient parentheses
There are insufficient parentheses in the question and the answer. Remember that multiplication and division take precedence over addition and subtraction. So it is mandatory to insert parentheses around numerators and denominators.

Math
Rewrite the equation as: y=(-3/5)x + 19/5 which makes the slope as (-3/5) Lines that are parallel have the same slope. Two lines that are perpendicular to each other have the product of the slope equal to -1. That should be enough for you to make the right choice.

Statistics
I am glad you checked things out. For P(5), we have P(CMMMC)=(2/9)(7/8)(6/7)(5/6)(1/5)=1/36 P(MCMMC)=(7/9)(2/8)(6/7)(5/6)(1/5)=1/36 The same goes for the rest, namely MMCMC, MMMCC, which when added up together gives 4/36. P(2) to P(3) have been calculated before. For P(2) to P...

Statistics
First I will paraphrase the game to make sure I understand the game the same way you're supposed to. Contestant is to select randomly (assuming he doesn't see the digits while selecting) cards, one at a time, out of 9 cards (without replacement). Two cards out of 9 are...

Calculus :)
You're welcome!

Calculus
From the given point P0(x0,y0)=(2,1/2), we draw a line to join a point on the curve f(x)=x^2 at P(x,y). The distance P-P0 will be shortest when P-P0 is perpendicular to the tangent of f(x) at P. The slope of P-P0 is given by: m1=(y0-y)/(x0-x) =(y0-x^2)/(x0-x) since P is on cur...

geometry
Mid point of points P1(x1,y1,z1) and P2(x2,y2,z2) is given by: P(x,y,z)=((x1+x2)/2, (y1+y2)/2, (z1+z2)/2) Post if you wish to confirm your answer.

Geometry
Distance between points P1(x1,y1,z1) and P2(x2,y2,z2) is given by: distance=sqrt((x2-x1)^2, (y2-y1)^2, (z2-z1)^2) Post if you wish to confirm your answer.

geometry
Similarity ratio and ratio of perimeters are both linear ratios. Ratio of areas is the square of the linear ratios. The linear ratios are therefore the square-root of the area ratio, namely: linear ratios = sqrt(18/50)=0.6

Physics
g(moon)=g(earth)/6 weight on moon =m*g(moon) =m*g(earth)/6 =12kg * 9.81 m/s² /6

maths
Assume formula Population in billions at time t (counting from 1987) as P(t)=Ae^(kt) where A and k are constants. At t=0 (1987), P(0)=Ae^(0)=A=5 the formula becomes: P(t)=5e^(kt) P(1)=5*1.02=5e^(kt) [t=1] => e^(k)=1.02 [t=1] Take log both sides k=log(1.02) [natural log] So ...

Math
Given ABC is a right triangle with AC being the hypotenuse, then angle B is a right-angle. Use Pythagoras Theorem to solve thus: AC²=BC²+AB² or 19²=12²+AB² Solve for AB.

Math
Use cross multiplication for direct proportions: Given A:B, then C:X is given by X=CB/A. Here 75 ft : 1/13 sec. X ft : 5 1/2 sec we find X by: X=75*5 1/2 ÷ 1/13 = 75*(11/2)÷(1/13) =...

MAth
Z score for 81 is (81-100)/19=-1 Z score for 119 is (119-100)/19=+1 Use normal distribution table to find the difference in probability between -1 and +1. It should be around 68%.

calculus
Integrate the region between x from 0 to x0, and y=0 to 1/x0, where x0∈R+ and x0≠0.

Mathematics
8-)

conditional probability
Define events N=from NYC, hence N'=not from NYC A=adolescents under 18, hence A'=over 18 Given: P(A|N)=1.0 (prob. of under 18 given person is from NYC) P(A|N')=0.6 (prob. of under 18 given given person is from elsewhere) First calculate probability of finding a per...

conditional probability
P(R1)=5/11 P(R2)=5/25 Since the drawing of the two bags are independent, we have P(R1∩R2)=P(R1)*P(R2) P(R2|R1)=P(R2∩R1)/P(R1) =P(R1)*P(R2)/P(R1) =P(R2) =1/5 as Ms.Sue had it.

Permutations
Each of the first three characters is 26 choices each (repetition permitted). Each of the following digits has 10 choices (numbers can be repeated). Total number of distinct passwords is the product of all these number of choices.

Operating Systems
Don't know if there are other ways, but Ctrl-C interrupts the command, and Ctrl-Z signals end of input (on DOS).

Integrated Math 1
The standard graph is y=x^2. The shifted graph is y=a(x-h)^2+k which shifts the graph h units to the right, and k units up with a vertical multiplication factor a. In the given problem, h=-4, k=0, a=1. Try to interpret the results.

Integrated Math 1 (help please??:( )
The answer can be correct or incorrect. There are many ways to solve a ,atj problem, depending on the conditions. Any way that give a correct answer is a correct way. Here the most obvious way to factor is to note that it is a perfect square: x^2+8x+16 =x^2+2(4x)+4^2 =(x+4)^2 ...

Mathematics :)
You're welcome!

Mathematics
1-x -2x -3x = 6x-1 Isolate x: 6x-1 = 1-6x 12x = 2 x=2/12=1/6

Computers
I assume you have read all the documents recommended to you by others on inventory systems. A flow chart is for describing logic in a program. A Gantt chart is for tracking progress in a project. For the cost, you would have to consider the costs for 1. hardware (computer, scr...

math
Size of sample space = 6*6 = 36 Number of doubles in the sample space = 6 Odd = number of times in favour of ÷ number times against = 6 ÷ (36-6) = 6 ÷ 30 = 1/5

statistics
Assuming a large city (so that the sample size does not affect the population probability), then the probability of a house is NOT burglarized is (1-0.05)=0.95. By the multiplication law, randomly selecting 50 houses not burglarized is P(50)=0.95^50=0.077. If you work the othe...

Differential Equation
"(-infinity sign, infinity sign)" means the interval from -∞ to +∞. If you have f(t) and g(t) and need to know if they are linearly independent, you can calculate the Wronskian, given by the determinant: W= | f(t) g(t) | |f'(t) g'(t)| If the Wrons...

physics
Let u=vel. before, and v=vel. after collision velocities are positive in +x direction. Momentum is conserved for elastic and non-elastic collisions: ∑mu = ∑mv If the collision is perfectly elastic, then kinetic energies are conserved before and after collision : ∑ ...

elem math core
Sample space (Ω) is the set of possible outcomes. (a) the set of possible outcomes is the set each of the coloured marbles: Ω={R,B,G,Y,W} (b) Without replacement means that the two marbles are of different colours, so the sample space is {RB,RG,RY,RW,BG,BY,BW,GY,GW...

physics
acceleration, a = rω² ft/s² g=32.2 ft/s² 1 RPM = 2π rad/60 s =π/30 rad/s Let x=RPM required, then ω=πx/30 rad/s You need g=rω²=r(πx/30)² Solve for x.

geometry
Use the information replied to your other post to construct the compound truth table. Your other post is: http://www.jiskha.com/display.cgi?id=1341805984

geometry
Sorry, I gave the truth table for ∧ when it should be or, ∨, which is false only when both p and q are false, i.e. p q p∨q T T T T F T F T T F F F

geometry
The truth table for ~q is the opposite: q ~q T F F T The truth table for conditional, p→q is true except when p is true and q is false, i.e. p q p→q T T T T F F F T T F F T For p∧q, the result is true only if both are true, i.e. p q p∧q T T T T F F F T F F F ...

INFORMl logic
I vote for the third: they grow exponttenally and become too large for complex arguments

calculus
What character encoding do you use? Using the standard Western 8859-1, we do not see anything mathematical. Unicode does not help either. Remember, if you copy and paste from Microsoft Word or other word processing software, the character encoding will not be understandable.

calculus
What character encoding do you use? Using the standard Western 8859-1, we do not see anything mathematical. Unicode does not help either.

Maths
Let r be the root: x²-(k+3)x+4k= 0 = (x-r)(x+r)=x²-r² equating coefficients, -(k+3)=0, k=-3 4k=-r², r=sqrt(3*4)=2√3 or the equation is x²-12=0 Find k from the equation.

mnhs
Find out what is the minimum and maximum size of the cut out in consideration of the size (12"x10") of the tin piece. The domain of the function consists of all the possible values of x. If it is not clear, draw a rectangle to represent the tin sheet, and draw the fo...

maths
Some ideas: 1. punch a hole at the bottom and see how long it takes to drain. Note that the height of water remaining is not proportional to elapsed time. 2. For long periods, see how long it takes for water to dry out. This is of low precision because the evaporation time dep...

math
Let the original cost price be 1000. 100 computers at 30% markup brings a profit of 100*(1000*30%)=30000 If the original price goes up 10% (cost =1100), the new profit per computer is 1300-1100=200 Number computers required to maintain the same total profit = 30000/200=150

Probability
P(A∪B)=0.71 P(A)=0.3 P(A∩B)=0.19 The visual way to solve this problem is to draw a Venn diagram and fill in the respective probabilities. If you prefer to solve it mathematically, use: P(A∪B)=P(A)+P(B)-P(A∩B)

maths
4x²+5x+γ=4(x-k)(x-1/k) =4x²-4(k+1/k)+1 Equate coefficients of terms: for x²: 4=4 for x: -4(k+1/k)=5 for constant term: γ=1 So the equation is: 4x²+5x+1=0 (4x+1)(x+1)=0

algebra
If order (in the photo) is not important, then we choose 3 from 5, which is 5C3=5!/(3!2!)=10

algebra
Correct!

physics
At 40,000 ft. air resistance becomes important, as the object will likely reach terminal velocity and greatly increases the time it takes to reach the ground. Also, the horizontal velocity comes into play as the terminal velocity caused by air resistance is actually a terminal...

physics
You're almost there. The length of the bar is 5m. In general, we assume the centroid to be in the middle, or 2.5 m from the wall. You have put in 243*2.0 instead of 243*2.5 I'm sure you'd be OK after this correction.

statistics
Sample space, S={0,1,2,3} PDF: -∞<X<0 P(X)=0 P(0)=39*38*37/3! /C(52,3) no heart P(1)=13*39*38/2! /C(52,3) 1 heart, 2 cards of other suits P(2)=13*12/2!*39 /C(52,3) 2 hearts, 1 card of other suits P(3)=13*12*11/3! /C(52,3) 3 hearts 3<X<∞ P(X)=0 Make sure...

computer science
Please make a draft of your diagram and post it at an image depository so we can look at it. Do check against the requirements before posting.

statistics
E=calls by employees C=complaints P(E)=1-0.30=0.70 P(C|E')=0.15 P(C|E)=0.05 P(C)=0.7*0.05+0.3*0.15=0.08 P(E|C)=P(E∩C)/P(C) =P(C∩E)/P(C) =P(C|E)*P(E)/P(C) (Bayes' theorem) =0.05*0.7/0.08 =35/80 =7/16 =

math
Correct! Is this a statement or a question?

Physics
v=rω => 150 m/s = 0.08m*ω θ=150/0.08=1875 rad/s Average ω=1875/2=937.5 rad/s Number of revolutions =937.5 rad/s *100s /(2π rad/rev) =93750/2π =14921 rev. approx. Check my arithmetic.

math
To factorize, arrange it as: x²-3x + 2x-6 =x(x-3) + 2(x-3) =(x+2)(x-3)

phsc
Haha, it's all hypothetical. We're supposed to be playing hockey on a totally frictionless ice rink! I think crutches with sharp ends would help.

phsc
If it is totally frictionless, you only need to throw the hockey stick to one side and wait for yourself to move slowly to the other side. This will happen by the law of conservation of momentum, and Newton's first law (continues to move in a uniform velocity without exter...

Finite Math - Simplex Method
There are plenty of simplex calculators available, such as: http://www.zweigmedia.com/RealWorld/simplex.html

Physics - momentum
Hints: Conservation of momentum dictates that the components of momentum in the two (or any) orthogonal directions (x and y) should sum to zero, very much like forces in equilibrium. You can resolve the momentum of the two known pieces into the x- and y-directions and sum them...

Physics
The height of any object viewed from a horizontal distance d and angle of elevation θ is d*tan(θ). Let's say the top of the roof viewed from the ground 50 ft away is 30°. The height of the roof is therefore H=50tan(30°)=28.9 feet. Use the same formula t...

math
You need to factorize each expression and cancel common factors. Use (x²-y²)=(x+y)(x-y) in many of the cases. x³-16x =x(x²-16) =x(x²-4²) =x(x+4)(x-4) x²-3x-10 =(x+2)(x-5) x²-9 =(x²-3²) =? x²-4 =(x²-2²) =?

physics
Assume: 1. no air resistance 2. initial speed (Vi) = "average speed" = 6000 mph Change in vertical altitude after time t =Vi*sin(θ)t - (1/2)gt² Vi = initial velocity = 6000 mph = 8800 ft/s t=time since launch = 120 s. θ=launch angle above horizontal ...

algebra1
180s^2+300sf+125f^2 Take out common factor of the coefficients, namely 5 5(36s²+60sf+25f²) =5((6x)²+2*(30sf)+(5f)²) the expression inside parentheses is in the form of a perfect square. Try to factorize accordingly.

math
Let L,W and H be the dimensions of the rectangular block. Total surface area A=2(LW+WH+HL) So if H=height=x then W=x+2, and L=2W=2(x+2) Substitute these values of H,W and L into the equation for A and simplify.

database processing-computer management
b is correct. I do not know where the answers 1:01 am and 12:01:00 AM come in. recursive is definitely not simple (if it exists). 1:N is a normal relationship. If it were N:N, it has to be broken down into two, namely N:1 and 1:N, with an intermediate column in order that the ...

algebra
Assuming order matters, i.e. A,B,C,D is counted differently as B,A,C,D. There are 9 choices for the first place, 8 places for the second, 7 places for the third, and 6 places for the fourth. Applying the multiplication rule, there are 9*8*7*6 ways, or P(9,4) [permutations] =9!...

physics :)
Good job!

physics
0.5981 is cos(θ) If you check the post at 7:43pm, June 22: "Sorry, what I meant was cos(θ) is 0.5981. " so cos(θ)=0.5981 This is how it's calculated: Since the rope is tied to the handle of the trap door, which is 1.41 from the hinges (measured a...

physics
Did you solve: 1.13T=mg(W/2)cos(θ) for T?

physics
Sorry, what I meant was cos(θ) is 0.5981. The cosine is necessary to calculate the horizontal distance of the centroid of the trap door from the hinge, i.e. D=(width/2)*cos(θ) So moment = mg*D The opposing moment is T*vertical distance =T*1.13 You can then solve fo...

physics
85.3N is correct. Do not forget that the angle θ of the door with the horizontal is equal to sqrt(1-(1.13/1.41)²)=0.5981 (approx.)

physics
Draw a free-body diagram of the trap door and put in all the forces in the proper directions. Since the hinge reaction is usually not known, you can eliminate it by taking moments about the hinge. Post if you can use more help.

Physics :)
Great!

Physics
Under the radical, you should have (as bobpursley had it) 64-(4)(3)(-44)=592

math
Read up the article and extract the answer required: http://www.drkhamsi.com/classe/polya.html

math :)
Correct! Good job! By the way, are you chchch or Blessing?

math
X=individual yet unknown Left-most is the fastest A,B,C,D=the four individuals. "Chet is the slowest" => XXXC "Dolly is faster than Alamo, but slower than Brushy" => XXX=BDA So can you take it from here?

matemática
10π/3 radians = (10π/3)*180/π ° =600°

Physics
Hints: X-component of resultant = ∑Di*cos(θi) and Y-component of resultant = ∑Di*sin(θi) D(1)=145m, θ(1)=90-20=70° (from x-axis) D(2)=105m, θ(2)=-35° (from x-axis)

algebra
By system of equations: C=number of child tickets sold A=number of adult tickets sold C+A = 25 6C+16A = 260 Solve for A and C (by substitution). Solving the problem in the head without pencils or paper or calculator: Adult tickets cost $10 more than child tickets. If all 25 we...

programming Please respond
Rude or not is a subjective comment, so you have the right to the freedom of expression. In fact, an administrator is a highly prestigeous position. Why would anyone get offended by that? All I wanted to say was if you don't actually get involved in actually programming, t...

programming Please respond
All programming problems will be responded if you 1. show your work, and 2. specify clearly what help you might need. We will be pleased to help you debug, correct your pseudocode, help you find logic errors, etc. Programming is a knowledge which is acquired by doing the work....

programming
See: http://www.jiskha.com/display.cgi?id=1340231473

Physics :)
You're welcome!

Physics
The tension in the string will be equal to T, which connects both masses A and B. For mass A, the force down the incline is Ma*g*sin(θ) which equals T. For mass B, the force due to gravity is Mb*g which also equals T. Thus, equating the two values of T, we get: Ma*g*sin(...

Physics
We don't have your diagram, so we don't know how the masses are connected. Please describe your figure.

math
Assuming the first and second digits are independent, and assuming that there are 10 possible numbers for each digit (0-9), then the probability that the next digit is odd is 5/10=1/2

math
They have fled 30min at 66 mph = 33 miles. For the helicopter to catch up with them, they have to make up 33 miles at the difference of speeds (132-66)=66 mph. So they will catch up in another 30 minutes.

Math
Can you post your pseudocode or your code, and specify where you need help?

math
tan-1(55/2640) =tan-1(1/48) Use your calculator to find the angle.

MATH
x∈P means x stands for a positive integer. since x∈A means 3<x<12, A={4,5,6,7,8,9,10,11} You can do B,C, and D similarly.

Algebra(please help)
Distance between two points =sqrt((x2-x1)²+(y2-y1)²) =sqrt((10-2)²+(7-3)²) =sqrt(64+16) =sqrt(80) =4sqrt(5)

programming in c++
You're welcome to post your pseudocode and ask specific questions so we know where help would be needed.

math
Subtract 5'-6 3/4" from 5'-10 1/2" =10 1/2" - 6 3/4" =9 3/2" - 6 3/4" =3" + 6/4" - 3/4" =3 3/4"

geometry - incomplete
Please complete the question so that help can be provided.

Calculus - :)
You're welcome!

Calculus - please check my work
All correct!

math
Price * (1+0.15) = 520.99 Solve for price. Tax is the difference between 520.99 and the original price.

Calculus - :)
You're welcome!

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