# Posts by MathMate

Total # Posts: 12,095

**Math**

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.

**Math**

Since the 401k plan is tax free until the money is withdrawn, Sal has a 5% salary contributed to the plan AND deductible at the marginal rate of 20%. The company contribution does not matter for the current year taxes until the money is withdrawn.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

**Finance**

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

**Finance**

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.

**physics**

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.

**Math**

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 ...

**Finance**

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...

**probability**

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(...

**geometry**

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...

**Math**

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 =...

**Finance**

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 ...

**maths**

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&...

**maths**

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.

**math**

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

**math**

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 ...

**maths**

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 ...

**Physics**

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.

**Physics**

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...

**Physics**

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. ||||| =||| |=|| ||=| |||= ==| =|= |==

**math**

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 desmos.com 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 ...

**math**

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.

**math**

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 ...

**physics**

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 ...

**math**

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, ...

**Physics**

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 ...

**Science**

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

**MATH**

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) ...

**engineering**

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. https://en.wikipedia.org/wiki/Barometric_formula 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...

**math**

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...

**Biology**

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 ...

**Math**

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)

**maths**

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

**Math**

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...

**math**

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

**Binomial**

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...

**physics**

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**

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

**math**

You're welcome!

**math**

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%.

**statistics**

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,...

**math**

you're welcome!

**math**

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 ...

**Accounting**

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 ...

**Math**

Is the previous response useful? If not, please tell us where you do not understand or cannot do. https://www.jiskha.com/display.cgi?id=1498736044

**Maths**

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 ...

**Math**

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 =?

**Math**

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.

**Physics**

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?

**Econ.**

Check if the following response helps you: http://www.jiskha.com/display.cgi?id=1496657535

**math**

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

**combinations**

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

**Chemistry**

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...

**physics**

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 ...

**math/statistics**

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=...

**math/statistics**

or the previous problem: http://www.jiskha.com/display.cgi?id=1498438280

**math/statistics**

It will be similar to the previous problem. http://www.jiskha.com/display.cgi?id=1498184495

**math/statistics**

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 ...

**math/statistics**

It will be similar to the previous problem. http://www.jiskha.com/display.cgi?id=1498184495 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 ...

**Chemistry**

Exactly! Well done!

**Chemistry**

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.

**science**

Since the two vectors are equal, the parallelogram of vectors is a rhombus, and the length of diagonal becomes two times the component of each on the bisector, namely R=5m/s*cos(30°) along the bisector of the 60° angle. In other words, if we resolve the two vectors ...

**math**

Note: in Hindi-Urdu 1 croe = 1,00,00,000 = 10^7 1 lakh = 1,00,000 = 10^5 https://en.wikipedia.org/wiki/Indian_numbering_system 9*100,00,000 + 70*100,000 + 50,000 +358 = 9,00,00,000 + 70,00,000 + 50,358 = 9,70,50,358 (in Hindi-Urdu) = 97,050,358 (north American)

**Economics - price discrimination**

(a) if the monopolist discriminates Examine the price structures: more sales mean lower prices => there is an upper limit p1=15-q1 and p2=25-2q2 => (q1<15, q2<12.5) Examine the cost structure: c=5+3(q1+q2) => there is no discrimination of cost for each region. ...

**geometry**

As in all geometry problems, 1. start with drawing a diagram indicating all given information. 2. deduce from known theorems additional information, and mark any new information on the diagram. 3. repeat #2 above. I have done the first step for you, and the diagram is located ...

**Chemistry**

If you refer to the Liebig type of condenser, the water jacket is an integral part of the condenser. Without the water jacket vapour will not condense.

**Math**

Standard compound interest formula: F=P(1+i/k)^(kn) F=future value (in eight years) P=present value (amount of deposit) i=APR=nominal annual interest rate (0.03) k=number of compounding per year (2) n=number of years => P=F/(1+i/k)^(kn) =15000/(1+.03/2)^(2*8) =15000/(1.015^...

**Kinematics**

See previous solution (under related questions): http://www.jiskha.com/display.cgi?id=1337537113

**Computer Programming**

What help do you need? Would you like to post your own pseudocode as a start? We can take it from there.

**math**

The first step of any geometry problem is to draw a diagram from the given information. If you have not done that critical first step, it's time to do it now. Also, 1. point D has not been defined in this post. Is D on BC such that AD is perpendicular to BC? 2. would "...

**chemistry - types of reactions**

Hint: the four major types of chemical reactions are: decomposition synthesis substitution or single substitution methathesis or double substition For further hints, justifications and detailed explanations, review your class notes, or see: http://www2.ucdsb.on.ca/tiss/...

**Science**

Displacement is the distance and direction of the final position with respect to the initial position. Here δx=4 km δy=3 km Distance by Pythagoras, s=√(3²+4²)=5 km direction: atan(3/4)=?

**math**

Again, go through the same processes Let S=event that the first card drawn is a spade ~S=event that the first card drawn is not a spade s=event that the second card drawn is a spade ~s=event that the second card drawn is not a spade then probability of NOT drawing a spade in ...

**math**

Conceptually this is the same category of problems as the previous boomers problem. Let events w=a white ball was transferred b=a black ball was transferred now concentrate on urn B. W=a white ball was drawn B=a black ball was drawn then we know that probability of ...

**math**

Let events B=baby boomer ~B=pre-boomer (complement of B) A=answered in affirmative then by the law of total probability: P(A)=P(A∩B)+P(A∩~B) =P(A|B)*P(B)+P(A|~B)*P(~B) =232/400*(400/1000)+192/600*(600/1000) =0.424 using Bayes theorem, P(B|A)=P(A|B)P(B)/P(A) =(232/400)*...

**math**

Use the article for which you got a link (on your next question) and note that whole numbers belong to the set of rational numbers, for example, 5=5/1=10/2,etc, which are all rational numbers. I believe the question has a typo (parts missing).

**Math**

Since the edge lengths are integers, we start with the factors of 36: 36=2*2*3*3 and assemble take one or two factors to make a set of three numbers (out of 2,2,3,3) to represent edge lengths such that they are as close as possible. The cube so formed will have the minimum ...

**forensic science**

The following link contains your answer (scroll to bottom of page): http://www.se-source.com/gc.htm

**math**

As with all geometry problems, draw a diagram (plan). You will find that in right triangle ABD, we know AD=18 m ∠ADB=35° Solve this triangle to get mAB=AD tan(ADB) =18tan(35°) For right triangle CAB, mAB (known from above) mCA = 24m => ∠ACB=tan-1(mAB/mCA) =...

**maths**

As with all geometry and related problems, the first step is to draw a triangle of velocities. Wind is from south-west at 50 km/h. Draw a line from A to B with an arrow pointing north-east. From B, draw a line (approx. 5 times as long) towards north, ending at C which is ...

**math**

It depends on 1. what the bag contains (all quarters, quarters and dimes, only one quarter, etc.) 2. whether the quarters are indistinguishable. Assuming the bag contains a mix of coins of different denominations, and there are at least two quarters. Say there are 10 coins of ...