Posts by MathMate

Total # Posts: 12,115

Number of ways of choosing 3 distinct kinds of rolls for first guest =(3/9*3/8*3/7)*(3!) =9/28 Number of ways of choosing 3 distinct kinds of rolls for second guest =(2/6*2/5*2/4)*3! =2/5 Number of ways of choosing 3 distinct kinds of rolls for third guest =(1/3*1/2*1/1)*3! =1...

1) After giving $5 to Greg, David has $25. Greg now has 1/5 as much as Davis does. How much did Greg start with? Now David has $25 Greg now has 1/5 of David, or 1/5 of 25, or 5. So before he got $5 from David, Greg had 5-5=0, or nothing. 2) if 3a+4b=4a-4b=21 find the value of ...

p+pq = 4(p-pq) p(1+q) = 4p(1-q) Since pq ≠ 0, then we can cancel out p on both sides. => 1+q=4(1-q) Expand and solve for q 1+q=4-4q 5q=4-1=3 q=3/5 Check: (1+q)=1+3/5=8/5 4(1-q)=4(1-3/5)=4(2/5)=8/5 Therefore the value of q is correct and unique.

We don't need the website. translation 3 units right and 2 units down follows the following rule: (x,y)->(x+3,y-2) So we will need to take the coordinates of A, B and C, and transform each point according to the rule given above. For example, if P(2,5), then P'(2+3,...

Sorry the sketch did not work out! :(

Events: S=Laurel waits 40 minutes or less for hardy. ~S=Laurel waits more than 40 minutes. Assumptions: both arrivals are random and create a uniform probability distribution. Between 1:00 and 1:20, Laurel will be sure to wait 40 minutes or more, since Hardy does not arrive ...

Here's an example of what the question is asking for: If Molly removed 2 orange marbles, the probability of drawing an orange marble from the remaining batch is P(Orange) = (2-2)/(4+3+3+0) = 0/10 = 0 and that does not equal 1/5, so she did not remove 2 orange marbles. ...

Mathematical Range.
Well, I do not know how you got the range as ± 3 to ± 11.1. The interpretation of your answer is -11.1 (excluding) to -3 (including) together with 3 (including) to 11.1 (excluding). This means that (-3,3) is excluded from the range. Confirm that this is the case. If the ...

Twenty members of a group contributed sh 80000 each means contribution from members = 20 members * 80000 =sh 1600000 They already had sh 120000 in a bank out of which sh 20000 was to remain means from bank reserve = 120000 - 20000 = sh 100000 Price of land = sum of ...

University Genetics part 2
The man has Widow's peak (Ww or WW) and attached earlobes (dd), and the woman without widow's peak (ww) and detached earlobes (Dd, the d is inherited from her father). So yes, Man: Wwdd or WWdd (could be either one) Woman: wwDd. Case 1: If man has Wwdd (woman has wwDd...

University Genetics
The fact that fur colour can be tortoise means that both phenotypes are expressed, as a result of codominance of the genotypes black and orange. Since we are given that fur colour is controlled by X-linked alleles, it means that tortoise can only be inherited in females (XX) ...

Hints: Properties of the given dataset: 1. Could have a large number of nodes. 2. Generally very large and sparce. 3. Requires relatively efficient search algorithm given a node. 4. In general, contains cycles. Since cycles are present, we can safely eliminate trees. Lists are...

Here we do not know the initial investment, P. We can still apply the formula to solve for it since we know the future value = $44800. From FV=44800=P(1+0.028/365)^(23*365) we solve for P P=44800/((1+0.028/365)^(23*365)) =23528.98 The interest earned is therefore FV-PV=$21271....

Use binomial distribution because: 1. Bernoulli trials (either girl or boy) 2. number of trials (n=9) known. 3. probability (p=0.5) of outcome known and remains constant throughout trials 4. trials are independent of each other. n=9 p=0.5 P(X=k)=C(n,k)*p^k*(1-p)^(n-k) where C(...

2012 was a leap year, so 366 days. deaths per hour = 31700 deaths /(366 days *24 hour/day) = 7925/2196 deaths / hour = 3.61 deaths per hour (approximately)

inflation rate (increase) =(new value-old value)/old value =(82.4-72.6)/72.6 =9.8/72.6 =.134986 =13.4986% =13.50% (to the nearest hundredth of a percent)

Admission = $9 charged once each ride = $2.5x (x=number of rides) Total cost for x rides =2.5x+9

Yes, $17592.59, to the nearest cent.

Discrete Math
Another way to solve. Let A=# of students who answered the first question B=# of students who answered the second question C=# of students who answered the third question Then we are given B+C-|B∩C| = 10 A+C-|A∩C| = 14 A+B-|A∩B| = 12 Add three equations 2A+2B+2C-(|...

Vector Calc
The equation of a spherical surface centred at (0,0,0) is x^2+y^2+z^2=r^2 centred at (x0,y0,z0) (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2 substituting C(4,-5,0), the equation of the spherical surface is (x-4)^2+(y+5)^2+z^2=10^2=100 Assuming z-coordinate is positive=up, then we have (x-4...

The given quadratic equation has no real roots when the determinant is (strictly) negative. This happens when b^2-4*a*c-p<0, or (-6)^2-4(2)(5)-p<0 => p>36-40=-4 So the condition for f(x)=p has no real roots is when p>-4.

Since the 401k plan is tax free until the money is withdrawn, Sal has a 5% salary contributed to the plan AND deductible at the marginal rate of 20%. The company contribution does not matter for the current year taxes until the money is withdrawn. So the difference in taxes ...

college- math
Use binomial distribution, which requires a known and constant probability of success, a known number of trials, independence of trials. probability of success, p=1/6 number of trials, n=3 the probability of x successes is P(x)=C(n,x)p^x (1-p)^(n-x) where C(n,x) is number of ...

probabilities in statistics
(a) Given a diamond dealt first (without replacement) There are 51 cards left, so 13 clubs from a deck of 51 cards: P(C|D)=13/51. (b) Ace of hearts followed by a black card. P(A∪B)=1/52*26/51=1/102

Oh yes, please add machine cost Y(0)=90000 to negative cash-flows. All other calculations remain valid.

You seem to have deducted machine depreciation as 25000/3 instead of 25000/year. Also, you have provided the first year cash flow without taking into account of the WACC. I suggest you make a cash-flow diagram for three years, using following information (if you agree with it...

To @Writeacher
Personally I do prefer the actual dates over today/yesterday because if and when we save a page, today/yesterday becomes a relative date which is ambiguous. However, today/yesterday could be an addition to the complete date to avoid confusion.

For a simple pendulum, period T=2*π*sqrt(L/g) Substitute T=5T, L=4L 5T=2*π*sqrt(4L/g) => square both sides and solve for g: 25T=4π²(4L)/g g=16Lπ²/25T where L and T are as given in the question.

Your solution: (5!*7*6*5*4)*(3*2*1)+7!*5!*2!*2! =604800+2419200 =3024000 The first term is basically 5!7! which is the number of ways each gender can be permuted separately, and I agree with that, however they are seated. Now coming to the restriction, which is usually solved ...

i=10.5%=.105 n=2 for machine J, =3 for machine K We assume machine J lasts 2 years with no salvage value, same for machine K, but three years. Case J: PV=-11000-1200/(1.105)-1300/1.105^2= =-13150.65 annual expense over 2 years A=P*(A/P,10.5%,3) =-13150.65*((i*(1+i)^n)/((1+i)^n...

Event: S=success for last passenger to get his assigned seat. 1=case 1 2=case 2 Note that cases 1 and 2 are complementary. Case 1: P(1)=1/100 If the first person chose (randomly) his assigned seat Then all the rest of the passengers will also get their assigned seats. => P(...

Given: D (2,2), E (-2,-1), and F (-3,5). The reflection about the y-axis follows the following rule: sy: (x,y)->(-x,y) For example: sy: D(2,2)->D'(-2,2) The translation along a vector (p,q) follows the following rule: T(p,q): (x,y)->(x+p, y+q) Example: T(3,-5): D...

Approximate the earth as a perfect sphere, with radius 6371 km. Change in longitude = 60-20 = 40° = 40π/180 radians Latitude of flight path = 20° N horizontal radius = Rcos(20°) Horizontal arc length from A to B =Rcos(20°)(40π/180) =6371*0.9397*.6981 =...

The given information assumes that the investment is made on the 31st of December (end of year of year of investment), so year 0. At the end of year 3, the NPV is -879.46, and at the end of year 4, the NPV is +2907.51 as you had it. I believe payback period is usually ...

if the prime factors of p²+1, excluding 1 and itself, are of the form {a²,b | a≠b}, then the possible factors are: {1,a,b,a², ab, a²b} total exactly 6 factors. The first few such sums are: 1²+11=12=2²*3 [but 1 is not a prime] 3²+11=20=2&...

When more than two (i.e. 3 or more) lines intersect at the same point, i.e. they intersect each other, these lines are concurrent.

Let interest be i per annum simple interest. 4050(1+i*2)=4526.50 solve for i. 1+i*2=4526.5/4050=1.117654321 i=(1.117654321-1)/2 =0.058827 1 lakh = 100,000 So after 3 years, accumulated amount =100,000(1+3i) =100,000(1.1764815) =117648.15

We know (assume) that each cow and chicken has one head. Chickens have 2 legs and cows have 4 legs. If there are C cows, then there are 30-C chickens. Count total number of legs 4C+2(30-C) = 86 Simplify and solve for C 4C-2C=86-60 2C=26 C=13 So there are 13 cows and 17 ...

If long diagonal is defined as continuous diagonals with 8 squares, then there are only two. The following scheme should work. C C _ _ C C _ _ _ _ C C _ _ C C C C _ _ C C _ _ _ _ C C _ _ C C C C _ _ C C _ _ _ _ C C _ _ C C C C _ _ C C _ _ _ _ C C _ _ C C Each row and each ...

dx/dt=2t, integrate, x=t^2+Cx dy/dt=4, integrate, y=4t+Cy We know x(0)=y(0)=0 => Cx=Cy=0 The trajectory of the particle is therefore <t^2, 4t> Guess you can find displacement at t=2 with the above information.

software development
array length syntax is different for different languages. Please specify language you're using. most use the syntax len(array), or variants.

You don't have to worry about the top, just assume that it was off balance by some random motion, and acceleration will start from there where KE=0, and PE=mg(R) if we take reference elevation at the centre of the sphere. Then at at certain θ<pi/2, mg(cos(?))=mv^2...

Try reaction=centripetal force, mg(cos(θ))=mv^2/R Yes, v^2 (at the time it leaves sphere) can be calculated using energy considerations.

spatial reasoning
I find 8. ||||| =||| |=|| ||=| |||= ==| =|= |==

The rectangle is slanted with respect to the axes. Make a sketch to see if the corners are in order. You can use the graphing tool to help you plot. From the plot, it looks like the three points A, B and C do not form any right-angle, so there must be a typo with ...

Try pairing numbers to make a sum of 9, after taking out, say 1 and 4 for the first digits. leaves 2,3,5,6,7,8, so pair 2,7, 3,6, 5,8 for the other digits. making 1235 and 4768 sum is 6003. Try other combinations to see if it is possible to get closer.

Assuming the order within the day does not matter. Monday: 15C3 ways Tuesday: 12C3 ways Wednesday: 9C3 ways Thursday: 6C3 ways Friday: 3C3 ways Total= product of the above numbers, =455*220*84*20*1 =168168000

Physics 11
(a) Normal force, N= 140g N μs=0.25 frictional force to move crate = μN = 0.25*140g = 343.35 Assuming force of 340N is acting horizontally, crate will move since 390N > 343.35 N (b) μk=0.17 kinetic frictional force = μkN = 0.17*340*9.81 = 233.48 N Net force ...

Volume of object = 40*30*10=12000 cm³ Principle of floatation says that the mass of liquid displaced by a floating object equals the mass of the object. (C.F. Archimedes) For a density of 0.92 g/cc floating on a liquid of density 1.0 g/cc, the mass of liquid displaced is ...

Integer is the set of all numbers without the need to use decimals or fractions, examples, 2,100,0,-4. Counting numbers are positive integers, examples: 1,2,10,10000, etc. Counting numbers are called natural numbers by mathematicians. Depending on the location/country, ...

There is probably a more elegant way to solve the problem, but here's one that works. We know a and b are unit vectors. By the cosine rule, we can find the angle between the two vectors a+b as: cos(φ)=(1^2+1^2-(√3)^2)/(2*1*1)=-1/2 => φ=2π/3. Without ...

49g in 100 mL solution => 490g in 1000 mL solution. molecular mass of H2SO4=2+32+64=98 Molarity = (mass/L)/molecular mass = ?M

Finance charge = average daily balance*interest rate Here average daily balance = 250.82 interest rate = 1.7% = 0.017 Finance charge = 250.82*0.017 = ?

b e t Sofia high school (arethametic)
Let the AP be a(n)=a(0)+(n-1)d then we were given a(p)=q => a(0)+(p-1)d=q a(q)=p => a(0)+(q-1)d=p Subtract one equation from the other a(0)-a(0)+(p-1-(q-1))d=q-p simplify (p-q)d=q-p solving, we find that d=-1 substitute d and p in the AP a(p)=a(0)+(p-1)d =a(0)+(p-1)(-1) ...

Check if you are using these formulas for pressure and temperature. If so, go ahead and feed your calcxulator. If not, please post formulas you use. You may post your answers for checking if you wish, but specify formulas you ...

Mathematics question
In summary, 90% of cats and 10% of dogs think they were cats. So if the population is made up of C cats and D dogs, then (0.9C+0.1D)/(C+D)=0.2 Let x=C/(C+D), then D/(C+D)=1-x 0.9x+0.1(1-x)=0.2 isolate x and solve 0.9x-0.1x=0.2-0.1 0.8x=0.1 x=0.125 => 12.5% of the population...

Assuming there is no limit on the size of the individual pieces, e.g. NOT x pieces of equal area. No cut: 1 slice 1 cut: 2 slices 2 cuts: 4 slices (last cut intersects one previous cut, so adds two pieces) 3 cuts: 7 slices (last cut intersects 2 previous cuts, so adds 3 pieces...

Codominance means both are expressed in the presence of each other. If there is one allele of each, then both A and B will be expressed (giving AB type). If either an A allele is paired with a different one, such as O, then the dominance is expressed and the resulting blood ...

A=biannual payment = 12,000 APR=10% => i=10%/2=0.05 n=number of periods (each six-months) = 10*2=20 Present value P=A*((1+i)^n-1)/(i(1+i)^n) You can substitute values and compute. P is the same as the amount borrowed in a mortgage with a semi-annual payment of 12,000. Post ...

MATH 123
Use amortization equation for monthly payment = A =P*i*(1+i/12)^(12n) / [(1+i/12)^(12n)-1] P=amount borrowed (present value) i=annual interest rate n=duration of loan in years compounding frequency = 12 times per year. Case 1: P=23000 i=4.6% = 0.046 n=3 (years) Monthly payment...

maths - oops
P1=-300/(1.12^3)=-213.53 P2=-1000/(1.12^5)=-567.43 P3=-200/(1.12^15)=-36.54 (negative because money is due in the future)

i=0.12 use P=F*(P/F,i,n)=F/((1+i)^n) P1=-300/(1.12^3)=213.53 P2=-1000/(1.12^5)=567.43 P3=-200/(1.12^15)=36.54 (negative because money is due in the future) P=P1+P2+P3 [present value]

quantitative apptitude
Since the period of time is not mentioned, it will be assumed that it is a perpetual annuity, with initial sum S generating interest of $1200 per month forever. 18% APR = 1.5% per month. Therefore S*0.015=1200, or S=1200/0.015=80000

Each test is graded in R=(3 teachers * 3 hours)/ 40 tesets =9/40 teacher-hour/test 480 tests will require Time=480 tests *R =480* (9/40) tests*teacher-hours/test =108 teacher-hours. 12 teachers will take Time = 108 teacher-hours / 12 teachers =108/12 hours =9 hours.

binomial distribution
The situation calls for binomial distribution because all criteria are satisfied: 1. Bernoulli trials (i.e. either success or failure, one of exactly two outcomes). 2. Probability of success (i.e. failure of engine) is known (p=0.004) and remains constant throughout the trials...

P(7<X<9) =Z((9-12)/2)-Z((7-12)/2) =Z(-3/2)-Z(-5/2) =0.0668072-0.006209665 =0.6060

Again here the keyword is "among" 10 people. Check that the conditions of binomial distribution are satisfied (ref. the airplane problem). Then proceed with the calculation of "at least two" out of 10, namely "not zero", "not one" out of...

Let x-axis => due east y-axis => due north then 100m due east and 50m due north => New position P(100,50) distance by Pythagoras, D=sqrt(100^2+50^2) angle (from x-axis)= tan-1(y/x)=tan-1(50/100)=tan-1(1/2) [ in the first quadrant]

probability - oops
Question asks P(2 red), so Probability of first red=6/10 Probability of second red = (6-1)/(10-1)=5/9 By the multiplication rule, P(2 red) =6/10*5/9 =30/90 =1/3

Probability = P(2 red)+P(2 blue) =6/10*5/9 + 4/10*3/9 =(30+12)/90 =7/15

You're welcome!

With two inequalities, you can have a maximum of one intersection point. The feasible region is therefore open. The feasible region is below the red line, and above the black line. The corner point has already been found correctly, ... by you!

Business Math
Amount to save = 10,000-2500=7500 Use the future value formula: A=F*(A/F,0.08,3) =F(i)/((1+i)^n-1) =7500*0.08/(1.08^3-1) =2310.25 Note: each payment is even less than 7500/3=2500 because the first two payments earn interest at 8%.

For a large population with a known (30%) probability of success with relatively small samples, binomial distribution may be used to model the situation. p=0.3 n=12 P(X=x)=C(n,x)(p^x)(1-p)^(n-x) where C(n,x)=n!/(x!(n-x)!) combination of x objects from n. (A) x=12 P(X=12)=C(12,...

you're welcome!

2,3,5 are coprime to each other. Say the prime factorization is x=(2^p)(3^q)(5^r) where p>0,q>0,r>0 for x>0 To satisfy "2x is a perfect square" => mod(p+1,2)=0 mod(q,3)=0 mod(r,5)=0 => the smallest solution is therefore p=15 Similarly for "3x ...

The supernormal rate and the constant growth rate require us to calculate the annulised rate. If we assume the stock will be kept for 10 years, then the 6 years at 10% will reduce the annulised (kind of average over 10 years) rate to be 13.14%. Do your own calculations to ...

business math
A very nice thinking question! To compare the two jobs, you would first need to tabulate expenditures. House purchase and mortgages aside (important issues though), you need to list, for each city, 1. annual property tax 2. state income tax 3. assume a percentage of income ...

Is the previous response useful? If not, please tell us where you do not understand or cannot do.

ok, I will provide some hints, but you will have to work on the problems, perhaps after reviewing your class notes. Some of the problems are straight from definition of the terms. Not being able to do those problems means you do not have a good grasp of the material. (1) The ...

Without a calculator, you can break it up like the above: 45=40+5=20+20+5 so 192*45=192*20+192*20+192*5 =3840+3840+960 =?

She has seen at least 45 birds/trip * 12 trips/year *16 years =at least 45*12*16 birds You can use a calculator to find the product, and feel free to post what you have for verification.

With a spring balance, there is an additional tension ma upwards, therefore the registered weight = mg+ma=m(g+a) With a pan balance (one pan object, the other weights) Both sides experience the same acceleration, so will exert equally m(g+a) on each side. Hence it will show ...

Statistics - to Barry
What are your thoughts on any of the questions?

Check if the following response helps you:

Yes, basically that, but watch out for parentheses and order of operations. Examples: C(8,5)=8!/(5!(8-5)!) =40320/(120*6) =56 and C(9,6)=9!/(6!(3!)) =362880/(720*6) =84

The number of combinations can be found from the formula C(n,r)=n!/(r!(n-r)!) n=total number of distinct objects r=size of sample For example, there are 9 different fruits to choose from. The number of different samples of 6 fruits is equal to C(9,6)=9!/(6!(9-6)!) =84

S + O2 = SO2 32g+32g = 64g (molecular mass) So the two reactants are in the ratio of their molecular masses (MM) Can you find the mass of sulphur required?

hypergeometric distribution
Here you have a small population N=26 and two classes of identical objects, known and not known. Also, the samples are taken without replacement (we don't get to have the same word tested twice in the same test). Let K=number of known words = 12 U=number of unknown words...

Definition of a coulomb: "A quantity of 1 C is equal to approximately 6.24 x 1018, or 6.24 quintillion. In terms of SI base units, the coulomb is the equivalent of one ampere-second. Conversely, an electric current of A represents 1 C of unit electric charge carriers ...

P(n,r)=n!/(n-r)! C(n,r)=n!/(r!(n-r)!) So P(6,4)=6!/(6-4)! =720/2 =360 C(8,5)=8!/(5!3!) =8*7*6/(1*2*3) =56 Multiply the two to get the answer.

permutations & combinations
Hypergeometric distribution applies to a limited population from which a sample is drawn without replacement. Here we assume all defectives are identical, so are undefectives. D=4 (defective) U=65-4=61 (undefective) => S=U+D=65=size of population=65 d=defectives selected u=...

or the previous problem:

It will be similar to the previous problem.

Events: R=Republican candidate elected D=Democratic candidate elected C=conservative judge appointed M=moderate judge appointed L=liberal judge appointed P(R)=1/3 P(D)=1-1/3=2/3 P(C|R)=1/6 P(M|R)=1/6 P(L|R)=2/3 P(C|D)=2/9 P(M|D)=5/9 P(L|D)=2/9 Need to find P(D|C) or ...

It will be similar to the previous problem. The steps are to use law of total probability and then Bayes theorem. I'll start, and let you finish. Events: A=part was produced by machine A B=part was produced by machine B C=...

Math - to Selena
Most tables give the area below the normal distribution curve on the left (<Z). In that case, yes, you need to subtract. The link Damon gave you has the option of finding area to the right, (>Z). In that case, you do not have to subtract from 1. Also .4052 is straight ...

Exactly! Well done!

Have you come across a strong reducing agent that reduces Fe+++ to Fe++? In fact, Fe++ ions are generally very pale green and not completely colourless.

triangle inequality not satisfied
Length of lines AB, AC and BC do not satisfy the triangle inequality, namely mAB+mBC=8.4cm < mAC=10 cm so a triangle cannot be drawn. Please proofread the whole question.

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