# Posts by MathMate

Total # Posts: 12,102

**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 ...

**Math**

Exactly, well done!

**Math**

In AP's difference between terms are equal, so a5+x=a6 a7-x=a6 Adding the two equations cancels x, and expresses a6 in terms of the sum of a5 and a7. Post your finding to check if you wish.

**Math**

Assuming question reads If y=1+X+X^2+X^3........, given |x|<1 then x=.....? then y=∑x^i for i=0 to ∞ y equals a known sum where y=(1-x^n)/(1-x) as n->&infin, then x^n->0 for |x|<1, and y=1/(1-x) solve for x: x=1-(1/y) Advice: Please do not paraphrase math...

**Calculus**

This is more a question to interpret the words: " integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx" which turns out to be: ∫cos(2x)dx/√(5-2sin(2x)) Check each case out by ...

**physics**

You will need the conversion factor between angular speed (usually in radians/second) and rpm (revolutions per minute). We know that one revolution equals 2π radians, and one minute equals 60 seconds, so 60 rpm = 60 * revolutions/minute = 60 * (revolutions*2πradians/...

**Thermodynamic**

If you would post briefly your findings about 1. the characteristics for each type of thermometer, 2. the perceived technical requirements of each of the three environments, we can take it from there to complete your project.

**Economics**

Yes, your answer is correct, as follows. P=A[P/A,0.03,30] =50000[P/A,0.03,30] =50000((1+0.03)^30-1)/(.03*(1+0.03)^30) =980022.067 As for the interest, there is no mention of the compounding rate, and 3% is qualified as "real" rate or return, or EAR (effective annual ...

**Maths**

Three significant digits means counting from the left, starting with the first non-zero digit. Do not add a decimal point unless it is buried in the three significant digits, so 5,000.080 becomes 5,000

**Physics**

Please post question with all original punctuation. Assuming the question is: A body is projected vertically up with a velocity 98m/s. After 2sec, if the acceleration disappears, what is the velocity of the body at the end of 3sec?? From the question, it is interpreted that ...

**Barretto national h.s.**

I agree with DrBob222's solution.

**Solubility**

mass percent is number of grams of solute dissolved in 100 g of solvent. 2.5 g of salt dissolved in 250 g of water. So 1 g of salt dissolved in 100 g of water (solvent) => so mass percent = 1%

**Math**

Wrong place for predictions of the future. Mathematically, any set is as good as your own choice.

**math**

Solve (N+1)(N-4)=36 Expand and simplify N^2-3N-40=0 (N-8)(N+5)=0 Solve N-8=0 or N+5=0 to give N=8 or N=-5.

**Maths - to Ash**

Kindly elaborate your question: Do you want to find tan(-3π/4), or do you want to prove tan(-3π/4)=1, or solve tan(x)=1 ???

**Maths**

Tanθ=sinθ/cosθ sin(-3π/4)=-(1/2)√2 cos(-3π/4)=-(1/2)√2 => Tan(-3π/4)=sin(-3π/4)/cos(-3π/4) =[-(1/2)√2]/[-(1/2)√2] =1

**math**

Start with ABCD. "my tens digit which is three more than zero, my ones digit" => AB30 "my thousand digit is an even number" (2,4,6,8)B30 "my thousand digit is an even number which is two more than my hundreds digit". (2,4,6,8)(2,4,6)30 "my...

**math**

Correct!

**Math**

I read the instructions wrong, the coded word should read: 3597206253997569964636384069705890201600000

**Math**

For practice: try decoding 14007996280973190758400000

**Accounting**

Company bonds usually have a nominal value (paid at maturity) of $1000, hence M=1000. It promises $80 per annum (at the end of the year). There are six years left. Present value of a series of A=$80, n=6, i=1.09 P=A*[P/A,.09,6) =A((1+.09)^6-1)/(.09*(1+.09)^6) =$358.87 Present ...

**Statistics**

Another way to look at it: Jar A has 8R and 2G, total=10 Jar B has 6R and 3G, total=9 We transfer 1 ball from A to B. 8 time out of 10, we transferred a red, so B contains 7R+3G, total=10 Probability of drawing a red = 7/10 (8 times out of 10) = 7/10 * (8/10) =0.56 2 times out...

**physics**

up one step: x=20cm, y=20cm, displacement=final position less initial =sqrt(20²+20²) =28.28 cm (approx.) So what is the displacement for 5 steps?

**math/statistics**

Assuming a ticket has four digits, would like to know if the last digit must match or not. In any case, matching each of the first three digits has a probability of 1/10. Matching all three is a three-step experiment, so multiplication rule applies, or P(123)=P(1)*P(2)*P(3)=1/...

**Math - correction**

Residue(t)=Initial*(1/2)^(t/L) [the negative sign removed]

**Math**

L=half-life in years, t=time lapse in years Residue(t)=Initial*(1/2)^(-t/L) Residue(10,000) =100%(1/2)^(10000/24000) =74.92%

**Economics**

The answer is grammatically correct, but not an adequate answer for an economics question. I suggest you get yourself familiar with the US (or other countries) dairy market and write a few descriptions in your own words. For US market, you can read up the following links, and ...

**math**

One idea: if you have 28 students in the class, how can you arrange the students in groups of equal size, example, 4 groups of 7, 7 groups of 4, 1 group of 28, 2 groups of 14, 14 groups of 2, or 28 groups of 1.

**Physics 2**

It depends on the density of air, which is about 1.225 g/L at sea level and 15°C (Wiki) Volume of room V=5.6*3.6*2.4 m³ =48.384 m³ =48.384 m³ *1000 L/m³ Multiply volume and density mass=volume*density =48.384*1000 L * 1.225 g/L =48.384*1000*1.225 g Use ...

**science**

In a lot of math and science problems, it is vital to first understand the meaning/definition of terms. Here "displacement" is used as: "final position less initial position". Use a blank piece of paper to help you figure out the final position with respect...

**Physics**

What you didn't do right are: 1. the reciprocal of 0.0694 is 14.4 2. the negative sign was ignored. To interpret the lens equation correctly, we need to agree on the sign convention. Following assumes the sign convention given here: https://apps.spokane.edu/InternetContent...

**Physics**

time = 30 minutes = 30/60 hour = 0.5 hour speed = 70 km/hour Use the equation Distance = time * speed to find distance, AFTER making sure the units used are consistent.

**Stats**

Whenever we work with an equation with given parameters, the first step is to define the equation in terms of the parameters. Here we have y_hat(x)=Ax+B where A=4.6 B is obtained from solving 530=4.6(258)+B from which B=-656.8 Hence y_hat(x)=4.6x-656.8 You have not posted the ...

**Economics**

What do you think when more firms enter the market, will there be more suppliers? Will the price go higher or lower? Draw the supply demand curve and predict the new price (in a competitive market).

**physics**

Assuming thermal energy is proportional to temperature in °K, then Initial energy =k*(-115+273.15) =158.15k Final energy =2(158.15k) =316.3k equivalent to a temperature of T=316.3°K =(316.3-273.15)°C =43.15°C >34°C Will the chocolate melt?

**math - to Lisa**

1220.79 is the future value of 1000 after 10 years, which is not the value of the annuity. The annuity formula is the sum of the future value of quarterly payments. The first quarterly payment (always deposited at the END of the first quarter) therefore earns 39 quarters of ...

**General Mathematics**

Yes, your answer is almost correct, but do take care of the case when d=4. I would put F(d)= {8.00 - if 0<d≤4 {(8+1.5[d]) - if d>4

**Calculus**

tan=sin(x)/cos(x) is a good start. How about putting lim x&rarrow;pi+ as x&rarrow; as (π/2+δ) as δ-> 0+. tan(x) =sin(x)/cos(x) =sin(π/2+δ)/cos(π/2+δ) =(sin(π/2)cos(δ)+cos(π/2)sin(δ))/ (cos(π/2)cos(δ)-sin(π/2)sin...

**math-plagiarism**

Erica, Lisa, James Smith, Mark Jackson. Please do not use multiple pen names. Also, just want you to know, taking an answer provided by someone else and claiming it your own is plagiarism. The answer was provided to James Smith who was requested to check the answer. If you ...

**Math**

Exactly. In fact, you borrowed $100, you pay back $100, so the interest is ... zero!

**Math**

Loan proceeds: Net amount disbursed by a lender to a borrower, under the terms of a loan agreement. from http://www.businessdictionary.com/definition/loan-proceeds.html So proceeds, P = amount disbursed by lender = $100 Discount = maturity value * rate * time (years) http://...

**math 106**

Number of periods, n = 4*10 = 40 interest per period (quarter), i= 0.02/4=0.005 Amount per period, A=1000 Future value =A((1+i)^n-1)/i =44158.85 (check my numbers)

**Math**

7 digit number ABCDEFG 1. A*G=A => G=1 2. D-G=C => D-1=C => D=C+1 3. A-F=D => D=A-F 4. Let x=A-B, G*x=D => 1*x=D => D=A-B 5. C+G=D => C+1 = D (same as hint 2) 6. C=A+B 7. E+G=F => E+1 = F 8. G+B=E => B+1 = E Now try to solve for A, B, C, D, E and F (...

**Physics**

"not required" is vague. For example, the heating effect of electric current along the wire feeding a domestic household is "not required", or ignored. In general, when the resistance of a conductor is very small, the heating effect is negligible. Along ...

**Physics**

You're welcome!

**Physics**

If you are using this convention: https://apps.spokane.edu/InternetContent/AutoWebs/AsaB/Phys103/MirrorsThinLens.pdf then your calculations are correct di=-18 do=+12 1/12-1/18=1/36 => f=36 cm

**Math - to Max**

To check answers, it would be necessary to post the questions correctly, i.e. use the correct symbols, e.g. type not= or ≠ (done by & ne; but skip the space between & and ;) Also, use parentheses appropriately, as in the first question. x/6x-x^2 means (x/6x) - (x²) ...

**Math**

It is convenient to use the Cartesian coordinates with x due east, and y due north. Then 040 (bearing) is N40°E, which in the Cartesian system is θ=90-40=50° counterclockwise from the x-axis. Then we apply the standard formulae: δx=rcos(θ) (due east ...

**physics**

g=9.8 (m/s) /s After two further seconds in a free-fall without air resistance, the increase in velocity is δv=g(2 s)=9.8*2 m/s =19.6 s which allows you to figure out the final velocity.

**Science**

The kinetic energy of a body of mass m=10kg moving at v=10m/s is E=(1/2)mv² After being stopped, the kinetic energy of the body has been transferred to work done (assuming no frictional loss), and has nothing left. So we can find Work done=loss/reduction in kinetic energy.

**physics**

Given T<(2/3)mg Tension of rope T+ma=mg => T ≤mg-ma =m(g-a) Solve for a in (2/3)mg=m(g-a)

**physics**

Figure is missing. Please either describe the figure completely, or post a link to an upload of the image.

**Quantitative methods**

Note: Ordinary interest method is based 360 days in a year. Exact interest method is based on 365 days in a year.

**math**

8(x²)-x+2=0 the formula is x=(-B±(b^2-4ac))/2a substitute a=8, b=-1, c=2 and use your calculator. Note: The given equation will yield complex roots.

**Math**

As solved previously: Total fence length = 100 m Total Length of each side perpendicular to river, W = X Length of side parallel to river, L = 100-2X Area, A(X)= length * width = L*W = (100-2X)X Simplify the right hand side to get the final solution.

**Physics**

r=distance from point to origin θ=CCW angle from positive x-axis = π/2 So polar notation = (r,θ)=(5, π/2)

**pen name conflict**

"MathMate", thank you for your help, but in the future please use a different pen name to avoid confusion with that of an existing tutor.

**Chemistry**

the colloids wont pass thru. Urea and glucose will as will the salt ions.

**math**

Total fence length = 100 m Total Length of each side perpendicular to river, W = X Length of side parallel to river, L = 100-2X Area, A(X)= length * width = L*W = (100-2X)X Simplify the right hand side to get the final solution.

**maths**

Sorry, above is the only (non-integer) solution I could find.

**maths**

x=y=z=1/2, n=0

**physics**

If the movement was in the direction of the force... workdone=change in KE + change in PE and workdone = force*distance=50*3=150Joules netforce=mass*acceleration 50-mg*sin30=m*A put mass m, and g in, solve for acceleration A

**maths**

Very true, x=-2000 solves the problem exactly. Please disregard solution x=2.7176022...

**maths**

I find only one root at about x=2.7176022... a reasonable approximation to e.

**Math**

you're welcome!

**Math**

List price = £60 Discount = 15% discounted price = (1-15%)* £60 = $60(0.85)= £52 Amount tended = £100 Change = £100- £52 = £48.

**Math - correction**

Guess I misread the question. There was only one sum borrowed at an unknown rate of interest i, assumed compound interest compounded annually for 2 and 3.5 years respectively. Let P=sum borrowed i=interest rate P(1+i)^2=8320 P(1+i)^(3.5)=9685 => 9685/8320=P(1+i)^(3.5-2)=(1+...

**Math**

I interpret the question as: Given: 1. future value (i.e. amount owing at maturity) of a two-year loan is Rs 8329 and that of 2. future value of a three-year loan is Rs 9685. Find the sum of the present value of the loans. P1=8320/(1+i)^2 P2=9685/(1+i)^3.5 sum=P1+P2 where i is...

**Physics**

Both solutions of the impersonator of MathMate and Henry give the same correct answer of 41.820°. By the way, for your information, impersonation is a serious offence at Jiskha, liable to be banned.

**Physics**

calculate the sines and cosines of the angles .... sintheta1=5/sqrt26 cosTheta1=1/sqrt26 sinTheta2=3/5 cosTheta2=4/5 check all those... Now, Sin(A-B)=sianAcosB - CosBsinA then compute aine (A B), and finally, the arcsin(A-B) which is the angle

**probability**

Again, without the choices, we cannot know which one is the most likely. However, since we are talking about experimental probability, and that we cannot have an outcome of 7.5 times out of 150. Therefore the most likely result could be 7/150 or 8/150, whatever their decimal ...

**Physics**

weight = mg for a 98.17 kg mass and using g=9.81, then weight = 98.17 * 9.81 =963.0 N

**Math - correction**

Use hypergeometric distribution as Reiny showed you in your previous problem: C(12,2)*C(28,2)/C(40,4)=12474/45695 where we need to choose 2 out of 12 greens, 2 out of 28 non-greens, and in total, 4 out of 40 balls. For the second part, you can use what was given above, OR use ...

**Math**

total, N = 40 Assume no replacement, P(G1)=12/40 P(G2)=11/39 P(G1∩G2) =12*11/(40*39) =11/130 35 balls are not yellow (X) So if all are not yellow, follow the same principle as above, P(X1)*P(X2)*P(X3)*P(X4) =(35/40)*(34/39)*(33/38)*(32/37) =...

**Maths**

use the distribute law, a(b+c)=ab+ac so 2(3a+4)=2*3a+2*4=6a+8

**maths**

Length = 4 times width Area = length * width =(4w)w =4w² So 4w²=1024 cm² (given) w²=1024/4=256 w=√(256 cm²) =16 cm (reject negative value of square-root)

**Statistics**

Let event G=seed grows into a healthy plant (success) ~G=seed does not grow (failure) We use the binomial distribution where N=6, p=0.70 (probability of success) n=5 (5 successes) C(N,n)=N!/((N-n)!n!) then by binomial theorem P(n=5)=C(6,5)p^5(1-p)^1 =6!/(1!5!)0.7^5(0.3^1) =.3025

**Physics**

From the data given, I cannot explain the difference. If you have a diagram, please post. Perhaps someone else can enlighten you on this.

**Physics**

Work due to frictional resistance = frictional force * Distance Here force = 10.0 N (due to friction) Distance = 2.5 m

**maths for business Help!!!**

Present worth of 600 monthly for 20 years at APR=24%: P=A*(P/A, 2%, 480) =600*(1.02^480-1)/[(.02)(1.02^480)] =29,997.766 Therefore down-payment =50000-P =50000-29,997.766 =20,002.23 Interest charged =future value - present value =29997.766*[(1.02^480)-1] =402,845.97 (no ...

**math**

Note: hyperbole is the French name for hyperbola.

**physics**

A------m--M-----------B 0.75 M=25kg m=150kg Distance AM=2.0/2=1.0 m Take moments about A: (counter-clockwise positive) B*2-150*0.75-25*1.0=0 B=(150*0.75+25)/2=137.5/2=68.75 kg The reaction (thrust) at A can be found by summing vertical forces and equating to zero, or similarly...

**physics**

Force = rate of change of momentum Propelling force=100N m (of propelling agent)=0.5 kg / s velocity=v 100 N=0.5 kg/s *v => v=100/0.5 m/s =200 m/s

**math-probability**

Note: Above assumes the prize drawing order is first, second, third (third draw).

**physics**

Hints: The average of the times is equal to the time to reach the maximum height, due the the symmetry of the parabola. So the sum of the times would be twice the time it takes to reach the maximum height, also equal to the time for the object to go up and fall back to the ...

**Algebra**

Slope intercept form of a line that passes through point (x0,y0) with slope m is given by: y=m(x-x0)+y0 Substitute values to get equation. Post your answer for checking if you wish.

**math**

Note: When writing rational expressions (a polynomial divided by another), it is important to insert parentheses around each of numerator and denominator. The answers are ALL missing parentheses in the numerator and denominator. In the question, g(x)=x+3/x would mean (x)+(3/x...

**math**

Typo suspected, corrected version: 3/(x-3) - 5/(x-2) 1. find LCM of denominators (x-3)(x-2) 2. express both terms in terms of the LCM as denominator 3(x-2)/((x-3)(x-2))-5(x-3)/((x-3)(x-2)) (very similar to cross multiplication) =(3(x-2)-5(x-3))/((x-3)(x-2)) =(3x-6-5x+15)/((x-3...

**Anatomy**

Homeostasis is the system in the body to maintain the normal/healthy status of the body, such as temperature, concentration of nutrients (e.g. glucose), concentrations of Na+, K+, and Ca++, etc. When any vital equilibrium is disturbed, the body will suffer from serious health ...

**Anatomy**

Not sure what exactly the question wants to know, where, or what. In any case, Smooth muscles are involuntary, usually found in the linings of hollow organs such as intestines. Cardiac muscles are involuntary, responsible for the continual pumping actions of the heart. ...

**science**

mass=32 g volume = 200 mL concentration = mass by volume = 32 g /200 mL =32/200 g/mL Simplify or convert to decimals for the final answer.

**Physics**

For your information: Major minerals have RDA's (Recommended Daily Allowance) of hundreds of milligram (mg) per day. So Magnesium is a major mineral for the human body. Note: Iron is the trace mineral with the highest RDA at 10-15 mg/day. (a) mg=milligram = (1/1000) gram...

**forensic science**

The emitted wavelength is towards the IR range (from the visible range), relative to the exciting radiation. The difference in wavelength is called the Stoke's shift. Therefore wavelength of emitted light has a longer wavelength than the exciting radiation.

**algebra**

80 L of 60% acid contains (80*0.60)=48 L of 100% acid. To make 50% acid, it must be diluted to have a total volume of 48/(0.5)=96 L. Leave it to you to figure out how much distilled water to be added.