Wednesday
December 17, 2014

Posts by MathMate


Total # Posts: 10,864

Probability
Choosing r unordered sets from n is given by nCr = n!/((n-r)!r!)
June 22, 2014

Compute
Missing information. You'll need three pieces of information to find the fourth in the following relation: P(A∪B)=P(A)+P(B)-P(A∩B)
June 22, 2014

Probability
7P5, where nPr=ordered set of r items chosen from n. =n!/(n-r)!
June 22, 2014

Trig laws help
Use cosine law: a²=b²+c²-2bc(cos(A))
June 22, 2014

Probability
If P(B)=p, then P(B')=1-p
June 22, 2014

Physics
Friction or not, the work done is W = F.D (scalar product) If force is applied in the same direction as the displacement, then work done is simply the product of the magnitude of the force and the distance travelled, namely W= 21N*3.3m = 69.3 J
June 22, 2014

physics
Not really. For an object which accelerates from rest, the variation of speed with time is given by: final velocity=initial velocity + acceleration * time = 0 + 10 m/s² * 2 s =20 m/s (note how the units cancel to give m/s)
June 22, 2014

Physics
Total distance = 120 km For an average of 60km/h, total time available = 120/60=2 hours Distance left = 120-30=90 km Time left = 2-1 = 1 hour What is the speed need for the remaining distance?
June 22, 2014

Algebra/Steve
Mary Ann, Hope your surgery goes well and have a speedy recovery.
June 21, 2014

math
largest 9 digit number without repeating: - must have 9 digits 999999999 - must use different digits - zero excluded (to have the largest number) - must be in reverse order starting from 9 987654321 - must be even, so invert last two digits Say 987654321 987 654 312 So what is...
June 21, 2014

physics
The fundamental frequency of a wave along a taut string is f=√(T/m)/(2L) T=tension in N m=mass of string in kg/m Since the fundamental mode of vibration consists of only half a wave, the wave velocity is f*2L, or λ=√(T/m). Here N=139 N, m=0.0036 kg/m v=&...
June 21, 2014

math
fraction of tank filled by A per minute = 1/3 fraction of tank filled by B per minute = 1/6 Fraction of tank filled in first two minutes = 1/3+1/6 = 1/2 Can you take it from here?
June 21, 2014

Physics :)
You're welcome! :)
June 21, 2014

Physics
Yes, but only in the first part. m was inadvertently omitted in the second part, my apologies. k=2mgh/x²
June 21, 2014

Physics
Initial velocity=√(2gh) h=height reached. Spring constant=k compression = x = 0.125m Potential energy=(1/2)mv²=mgh =(1/2)kx² solve for k in (1/2)kx² = mgh k=2gh/x²
June 21, 2014

physics
Assuming no air resistance, and PE at bottom of tower to be zero, then At the maximum height, mgh=(224mg+m(80²)/2 h=224+80²/(2g) [assume g=32.2 '/s² =224'+99.38' =323.38' At bottom of tower, mv²/2 = m(80²)/2+mg(224) solve for v to get v...
June 21, 2014

venn diagram
If 10 failed in both, that means 130-10=120 passed at least one subject. Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145-120=25 passed both. Hence (b) 120-25=95 passed (or failed) exactly one subject. For (a), 60 passed ...
June 21, 2014

Maths
Q1. HCF and LCM could be found using 1. factoring 2. Euclidean algorithm Q2. Let H(p,q) denote the HCF of positive integers p,q, and L(p,q) denote the LCM of p,q, then H(p,q)*L(p,q)=pq
June 21, 2014

Physics
26 m/s is about 10% from stalling for a Cessna 150. With a tailwind, the airspeed does not change, but it will be added to the ground speed ("actual velocity"). With a headwind, the airspeed does not change either, but it will be subtracted from the ground speed. ...
June 21, 2014

physics
Explained with the help of diagrams here: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html
June 21, 2014

Math - correction
*1,499,999
June 21, 2014

Math
149,999 is the greatest integer that may be rounded to the nearest million.
June 21, 2014

Physics
It will gather speed because of acceleration due to gravity. The acceleration is g=9.8 m/s²
June 21, 2014

Physics-half way fin.
I get 62.5 using g=9.8
June 21, 2014

mathematics
The same as X or Z.
June 21, 2014

Physics
Kinetic energy is proportional to mass and also varies with the square of the velocity. So the new kinetic energy =(5*105 joules)*(114/50)²
June 20, 2014

ap physics
Magnitude:use Pythagoras theorem (note 90° between the teammate and the green). Angle (from point of view of teammate) = atan(120/60)+75° West of south since the golfer is at 75° west of south from the point of view of the teammate.
June 20, 2014

Physics
Assuming both sides of the canyon are at the same elevation, then use the range equation: range = vi²sin(2θ)/g 6.5=vi²sin(2*9.45°)/9.8 vi=sqrt(6.5*9.8/sin(18.9°) =14.0 m/s
June 20, 2014

Physics-check plz
All correct!
June 20, 2014

physics
vi=-30m/s a=-g=-9.8 m/s² vf=vi+at =-49.6 m/s Height =average velocity*time =(-30-49.6)/2 * 2 sec =-79.6 m The negative sign means that the rock is lower than the initial position.
June 20, 2014

physics
Ignore air resistance => no energy loss PE at 40.0 m = mgh = 40*9.8m J =392 J PE=KE=(1/2)mv² vi=sqrt(2gh)=sqrt(2*9.8*40) = 28 m/s Time = 2 * time it takes to reach highest point = 2*(28/9.8) = 5.71 s
June 20, 2014

physics
vf=vi+aΔt =0-9.8*3 =-29.4 m/s Distance =average velocity*time =-14.7*3 =-44.1 m
June 20, 2014

Survey of Mathamtics
Calculate the effective interest, i.e. actual performance over a year: Local bank = (1+0.065/12)^12 =1.066971852002543 Credit union = (1+0.0675/2)^2 = 1.0686390625 So the credit union pays a little more.
June 20, 2014

engineering economics analysis
You cannot, directly. You can always try to put a link, or copy and paste.
June 20, 2014

college physics
The signal has to make a return trip, so the total distance is 2*1.5=3m Number of round trips per second = 344/3 = 114.7
June 19, 2014

math
Starting from 102, the minimum number of chicken sandwiches has to be divisible by 8 and 3, i.e. 24, that leaves 78 tunas, etc. So possible combinations may be Chicken/Tuna 24 / 78 48 / 54 72 / 30 96 / 6
June 19, 2014

physics
1. Use substitution x=u-&pi/2; dx=du ∫csc(u-π/2)cot(u-π/2)du =∫csc(x)cot(x)dx =∫cos(x)dx/sin²(x) =∫d(sin(x))sin²(x) =-1/sin(x)+C
June 19, 2014

question incomplete
Please complete the question.
June 19, 2014

Physics
To find the velocity in the last two seconds, we need to first find the time it takes to arrive at the end of the street of 250 length, and assuming uniform acceleration. The distance travelled is given by Δx = vi(t)+(1/2)at² where vi=initial velocity (m/s) a=...
June 18, 2014

math please help
I assume you forgot the parentheses in the numerator, Lim (sin(x)-(x^3/6))/x^5 as x->0 It would be easy to change sin(x) to a polynomial, the limits of which are easy to find. If you expand sin(x) by Taylor's series, you'd get sin(x)=x-x³/6+x^5/120... So the ...
June 18, 2014

Math
Each coin can land heads or tails with equal probability of 1/2. Dropping a coin four times has 2^4=16 possible outcomes. (a) three heads By enumeration: There are four possible outcomes, so the probability is 4/16. THHH,HTHH,HHTH,HHHT. The number of combinations for 3H can be...
June 18, 2014

Math
Calculate the product of the net gain (i.e. gain minus the bet of $3) and the probability of each outcome. Add all the products to get the expectation of the game. Note that the probabilities of all the outcomes must add up to exactly 1.0
June 18, 2014

ALGERBRA
Number of possible combinations of 5 (distinct) numbers out of 30 = 30C5 Probability of winning if n different tickets are bought = n/(30C5) where 30C5 =30!/((30-5)!5!)
June 18, 2014

math
There three ways of choosing 1 girl out of three (3C1) and (5C2) ways of choosing 2 boys out of 5. Total number of ways = (3C1)(5C2) = (3)(10) = 30
June 18, 2014

Math
Assuming all three coins are fair, you could use a probability tree or a table to list all possible outcomes (Ω) and calculate the probabilities accordingly. H=head T=tail All 8 possible outcomes HHH HHT HTH HTT HHH THT TTH TTT You can use the table to answer the above ...
June 18, 2014

finite math - answered before
This (or a similar one) question has been answered before. If you have a follow-up to the answer, please respond to the previous question, or make reference to it. If it is a similar question, then please show your efforts by first studying the previous answer, and attempting ...
June 18, 2014

finite math
This question has been answered before. Do you check your previous posts?
June 18, 2014

finite math
B=bachelor's degree H=high income P(H)=0.105 P(H|B) =P(H∩B)/P(B) =0.215 => P(H∩B)=P(H|B)*P(B) =0.215*0.105 >0 So H and B are not independent.
June 17, 2014

finite math
Is it (a) P(F/E), (b) P(F\E), or (c) P(F|E)? If it is (c), conditional probability, then P(F|E)=0.1/0.4=0.25 (a similar question was answered before)
June 17, 2014

finite math
How many are "succesful picks", and how many in total?
June 17, 2014

finite math
Please refer to your previous batch of questions. An almost identical question was answered completely and explained.
June 17, 2014

Physics
equate PE=spring potential energy (1/2)kx²
June 17, 2014

finite math
Judging from other questions, I am sure you are capable of answering this question.
June 17, 2014

probability - question incomplete
There are three statements and no question.
June 17, 2014

finite math
Do you mean P(F|E), the conditional probability that F happens given that E has happened? P(F|E)=P(E∩F)/P(E)=0.1/0.5=0.2
June 17, 2014

finite math
If at least one has not written, then there are only 5 to consider. p=0.29 q=(1-0.29)=0.71 P(at least one out of 5) =1-P(none out of 5) =1-q^5 =1-0.18 =0.82
June 17, 2014

finite math
is part (a) a given condition or you're expected to calculate the said event?
June 17, 2014

finite math
Assume random selections and outcomes. P(1 snake)=0.94461=p P(2 snakes)=p² P(3 snakes)=p³ ...
June 17, 2014

probability
#of orange balls=2 #of red balls = 5 Total number of balls = 25 P(orange ∪ Red) =P(orange)+P(red)-P(orange∩red) =2/25+5/25-0 =7/25
June 17, 2014

probability
P(E∪F)=P(E)+P(F)-P(E∩F) If E and F are mutually exclusive (ME), then P(E∩F)=0, and consequently P(E∪F)=P(E)+P(F)=0.41+0.47=0.88
June 17, 2014

finite math
Do you use "outcome" to mean elementary events? The elementary events of F are 3,6,7.
June 17, 2014

math
Set up: M=J+2000 J=B-400. L=S+1500 S=443 S=B-60 From the chain of equations, it would be possible to substitute backwards from the known values. Given: S=443 and S=B-60, so B=S+60=? L=S+1500=? J=B-400=? M=J+2000=?
June 17, 2014

physics
Angles of incidence and refraction are angles measured from the normal. If n represents the refractive index between air and the medium, the equation that governs the relationship between them is n=sin(θi)/sin(θr) which gives the value of θr as θr=sin-1...
June 17, 2014

statistics
μ=42 σ=1.5 so Z(38)=(38-μ)/σ Look up a normal distribution table for the probability of exceedingZ(38), which is the same as the probability of not exceeding -Z(38). Post your answer for checking if you wish.
June 17, 2014

Stats
Have you started looking at the question? What are your thoughts?
June 16, 2014

Physics
The force required to produce the acceleration is given by Newton's second law F=ma. If m is mass in kg, a is acceleration in m/s² then force F is in newtons. To this force must be addded the frictional force 740 N to overcome friction. Note: the force unit newton is ...
June 16, 2014

Math: Trig
arcsec(-2) is the same angle as arccos(-1/2) The angle 2pi/3 is correct, so is 4pi/3. Depending on the domain required, you may have to put in both values (for 0-2pi). If that is not the problem, then you have to read carefully the instructions how to answer the question, how ...
June 16, 2014

Geometry
If you just want the area, use Hero's formula: Let p = (a+b+c)/2 = half-perimeter Area = √(p(p-a)(p-b)(p-c)) If it's really the altitude you need, then find each angle using the cosine law: cos(A)=(b²+c²-a²)/(2bc) where a,b,c are lengths of sides ...
June 16, 2014

Geometry
* = 2√(3)b
June 15, 2014

Geometry
Hint: Call the lengths of medians 3b, 3b and 3a. The length of the base = 2√((2b)²-a²) The length of one of the congruent sides = 2√((2b)²-b²) = 2&radc;(3)b
June 15, 2014

physics
F=ma => a=F/m F=-(13.4+14.7) N m=71 kg evaluate acceleration (should be negative)
June 15, 2014

Math
Since it is open ended, only "lateral area" is significant. AL = p*h p=perimeter of base h=height of prism
June 15, 2014

physics
Use the same equation as before: F=(m-ρv)g N where v=volume of the iron object, and v=m/8000 m³ Be sure to convert all values into SI units.
June 15, 2014

Algebra II
Is πn a sequence or is it a function? At the beginning of the question define what πn is to represent?
June 15, 2014

Algebra II
To me, Πn=product of integers from 1 to n, which is equivalent to n!. It evidently is not because the expression would way exceed 1. So please explain what Πn is supposed to represent.
June 15, 2014

physics
Archimedes principle states that the buoyant force equals the weight of fluid displaced. Fresh water has a density of ρ=1000 kg/m³ Sea water from deep in the ocean has a mass density of ρ=1050 kg/m³. Average sea water has a mass density of ρ=1030 kg/m&...
June 15, 2014

math
* Y'∪Z'= YΔZ= {30,40,70,80,90,100}
June 15, 2014

math
When you deal with complements, the first question to ask is do we know the universal set E? Here we assume E=Z (integers) X'∩Y = Y\X = {10,20,40,60,90,100} Y'&cup'Z'= YΔZ= {30,40,70,80,90,100} (X\Z)'={10,20,30}' depending what E equals (Y\Z...
June 15, 2014

algebra
hint: x=1/3
June 15, 2014

algebra
At 8%, she gets RM1200. At 7%, she gets RM1050. Let x be the fraction he invested at 8%, the 1-x is what he invested at 7%. we have x*1200+(1-x)1050=1100 Solve for x.
June 15, 2014

Math
Would you like to calculate lateral surface areas or volumes of solids? Please post an example of what you'd like to calculate.
June 15, 2014

math
If you know the rule between exterior angle θ and the number of sides, n: θ=360/n then 360/(n-1)-360/(n+2)=6 Solve for n, then calculate θ for each polygon. (answer is between 10 and 15, reject negative root)
June 15, 2014

physics
The equation for range is R(θ)=v²sin(2θ)/g Examine the values of sin(2θ) to arrive at the correct ratio .
June 15, 2014

Chemistry
One mole of HCl is required to prepare 1 L of 1N solution. Calculate number of moles (n) required to prepare 200/1000 L of 0.5N solution. Find molecular mass M of HCl in g mass of pure HCl required = nM g Volume of given acid required = nM ÷ (1.18*0.37) g÷(g/mL)
June 15, 2014

physics
What is the question? Need to find the period, T? use T=2π√(L/g) for small oscillations.
June 15, 2014

Physics
The minimum initial velocity will create at least the kinetic energy (1/2)mv² to equal the potential energy gained, mgh, where h is the height difference between the horizontal rod and the cg of the person from the ground. Make assumptions to the value of this difference...
June 15, 2014

Physics
Magnitude: F=ma Direction: see figure.
June 14, 2014

physics - insufficient information
Sorry, wish we could help, but without the figure or a text version of it, we do not know what the given data are.
June 14, 2014

physics
This is a problem of levers which can be solved by taking moments. Three forces are involved, L the left hand, R the right hand, and W the weight of the pole equal to 50N. It is not clear but will be assumed that the cg of the pole is 2.00m to the left of the left hand, as ...
June 14, 2014

Physics :)
You're welcome!
June 14, 2014

Physics
Time (hours) = Distance (km) ÷ Speed (km/h) Divide by 24 to convert into days.
June 14, 2014

Physics
T (period) = time/rev = 20 sec/ 30 rev = 2/3 sec/rev ω(angular speed) =30 rev/20 seconds =30/20 rev / sec =30/20*2π radians / s Velocity =rω =0.008m*ω m/s
June 14, 2014

math check
5P5=5!/(5-5)!=?
June 11, 2014

Physics
Upstream=300 metres/(2-1)=300 s Downstream=300/(2+1)=100 s
June 11, 2014

Math
If you follow the rules of PEDMAS, what you wrote means: a + (b/10) = a - (0.1b^2/a) -b Please confirm if you really mean if(a+b)/10 = (a-0.1b²)/(a-b) Also, post what your answer is, and explain.
June 11, 2014

PHYSICS
For a projectile with initial velocity=vi projection angle = θ with horizontal The time of flight =2visin(θ) If time is doubled with θ unchanged, vi is doubled. From range = vi²sin(2θ)/g you can figure out the increase of the range when time (and ...
June 11, 2014

PHYSICS
There is no rule. It depends on the path. Average velocity = (final position-initial position)/Δt Average velocity = ∫c dx /Δt (line integral)
June 11, 2014

physics - figure missing.
Not sure why your answer is wrong when the question is not even complete.
June 11, 2014

Physics
Half way down is 30 m down. Assuming the GPE reference is at the bottom of the cliff, then GPE=mg(30)=27072 J KE=(1/2)mv² Equate GPE and KE.
June 8, 2014

Physics
Let fulcrum be at x cm from the 0 mark. Then 1kg*x cm = 3kg*(100-x) cm Expand and solve for x.
June 8, 2014

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