# Posts by MathMate

Total # Posts: 11,744

**statistics**

Yes, you can find the answers if the distribution curve is known. The standard normal distribution curve has an area of 1.0 under the curve. To convert a curve with mean 100 and SD=15 to the normal curve, we use Z(X)=(X-μ)/σ which means X=σZ(X)+μ where &sigma...

**Math**

I agree.

**PHYSICS answer check**

Please show equations or calculations used in obtaining your answer so that we can help you check your work.

**DISCRETE MATH**

The finite population has 100 devices, out of which 80 are non-defective. At each draw, both the total number devices and the number of non-defective device decrease, we have the running probabilities as: {80/100, 79/99, 78/98, 77/97, 76/96} the product of which give 0.31931, ...

**numerical methods**

Correction: V(h) should read: V(h)=π(3h²R-h³)/3 =πh²(R-h/3)

**numerical methods**

When the tank has 6.3 ft of oil, the dipstick will be wet by 6.3 feet if it is inserted vertically to the very bottom of the tank. The radius of the surface of water at height x in a sphere of radius R is given by r(x)=sqrt(R^2-(x-R)^2) By integrating r(x) with from 0 to ...

**chemistry**

molar mass of CH3COOH =(12+3+12+16+16+1) =60 mass of acetic acid in 250 mL of 0.26M =(250/1000) L * 0.26*60 = 3.9 g

**More math**

9C4=9!/((9-4)!4!) Use your calculator to work that out.

**Math**

nPr=n!/(n-r)! 6P2 =6!/((6-2)!) =?

**Simple math.**

n! = n(n-1)(n-2)...(3)(2)(1) for example, 3! = 3*2*1=6 You can use the ! or factorial function of your calculator to find the answer for 5!. You can also calculate the products long-hand.

**maths**

clarification: Hint: DC is not parallel to AB unless ∠DAB is 90°.

**maths**

It is an excellent exercise to follow instructions in order to draw a diagram. I would let you do just that, and at any step the statement is incorrect, it is the required answer. Hint: DC is not parallel to AB.

**physics - good catch!**

Haha! At least someone noticed that! Yes, in my days, slide-rules were not accurate enough, and survey calculations were done using 7-figure (log and trig) tables which were packed in a volume (I still have one!) thicker than today's calculus textbook. That taught me how ...

**basic trigonometry**

I hope you mean the ski track along the mountain is 235 m long. The mountain can be represented by a right triangle with the two legs horizontal and vertical, and where the angle of elevation is 35°. The ski track is the hypotenuse (C), and if the horizontal leg (B) and ...

**math-need figure**

To ollie: The question is meaningless without the accompanying diagram. You could post a link to the diagram, or you can describe what the diagram looks like. Sorry that we cannot go further without the rest of the required information.

**linear algebra**

Use the properties of linear transformations: 1. T(A+B)=T(A)+T(B) 2. T(kA)=kT(A) then let A=[1,1], B=[-1,1] and T(A+B)=T(0,2)=[-2,1]+[3,2]=[1,3] => T(0,1)=[1/2, 3/2]=P and T(A-B)=T(2,0)=[-2,1]-[3,2]=[-5,-1] => T(1,0)=[-5/2, -1/2]=Q So (a) L(-1,5)=-P+5Q =-[1/2,3/2]+5[-5/2...

**statistics**

7 choose 5 = 7C5 = 7!/((7-5)!5!) = ? ! means factorial.

**statistics**

probability is constant and independent of trials. trials are Bernouli, i.e. either success or failure. Number of trials is known. All this point to the binomial distribution where P(k successes out of n) =nCk p^k (1-p)^(n-k) p=probability of success of each independent trial=...

**physics**

Solve for n in PV=nRT 2.79*10^5(3.66)=n×8.314462175×(19.8+273.15) to get 419 moles (3 sig. figures) and similarly solve for P in P(7.20)=419.235(8.314462175)(28.5+273.15) to get 1.46*10^5 (3 sig. figures) Your approach is correct, but cannot tell where you got ...

**physics**

131 m. :)

**Mechanical Principles**

corrections. I forgot to multiply F(x) by x in the integral. So T should read less than 6 kN instead of 10.

**Mechanical Principles**

We have an increasing hydrostatic pressure varing from zero at water surface to the depth of the water, which exerts a varying force on the gate. The tension on the cable can be obtained by taking moments about the hinge of the gate (at the bottom). Let H=height of gate (where...

**CIRCUITS**

Resistance across resistors in series = R1+R2+R3 Voltage across each resistor is proportional to the fraction of each over the total. For example, resistors R1=2,R2=1,R3=3, ohms are connected in series and subject to a voltage of 12 volts, Resistance of resistors in series R=...

**Math**

For a rectangle, area = length × width perimeter = 2(length + width). Example: for a rectangle with length = 5 ft width = 3 ft area = 5×3 = 15 square feet perimeter = 2(5+3) = 16 feet

**maths**

Volume of a cube, Vc = (side length)³ Volume of a cylinder Vcy= πr²*h where h=length/height of cylinder r = radius of base = diameter of base /2 If their volumes are equal, then Vcy = Vc πr²*h = side³ Solve for h.

**geometry**

Height / distance = tangent so distance = height / tangent = 28 ft / tan(11°) = ...

**maths**

SI=simple interest formula is Interest = Principal * annual interest rate * number of years = 225 * 0.16 * 3.75 = 135 Add interest to principal to get final repayment amount.

**Combinations-Math**

74 is correct.

**physics. urgent answer please**

F1=10 N at 60° F2=15 N at 0° Use x- and y-components method: x-component Fx=F1*cos(60)+F2*cos(0) =20 N y-component Fy=F1*sin(60)+F2*sin(0) =8.660254 N Resultant, R= √(Fx²+Fy²) angle, θ = atan2(Fy, Fx) Hints for checking your answer: 20 N < R &...

**French**

The words are in the right places and the right form, except for #2 where the number does not agree with the definite article "le". It should be either l'assiette (sing., more probable) or les assiettes (plur.) Not knowing the instructions nor the purpose of the ...

**linear algebra urgent**

http://www.jiskha.com/display.cgi?id=1428173198 Also, remember that u3=u3-p(u1,w3)-p(u2,w3) where p(u1,w3) is the projection of w3 on u1, etc.

**linear algebra urgent**

see other post

**Math**

Assuming that strawberry on vanilla is considered the same flavour as vanilla on strawberry, i.e. order of the two scoops doesn't count, then there are 30C2 possible flavours, and 3 cones for a total of n=3(30C2) possible ice creams. For an order of 12 different ice-creams...

**math**

If you could post the question exactly as you were given, it would be possible for us to understand what you need. Especially in math, paraphrasing tends to lose important information.

**maths**

If the GP has its third term as 9 times its first term, then the sequence is a, ar, ar² where a is the first term, ar is the second term, etc. This means that ar²/a = r²=9, or r=3. Similarly, the fifth term divided by the second term should be a^4/a^1 = a^3, or ...

**Math**

The quadratic formula assume the equation to be: ax²+bx+c=0 (i.e. all terms are on the left-side of the equation). Rearrange the equation to be 3x²+4x-6=0 and try again. You do not need a graphing calculator to find the zeroes. Either by hand, or a regular calculator...

**Trigonometry (identities) (last help needed)**

Typically with simplification like these, you would convert all functions into sine and cosine, and simplify from there on. Use sin²x+cos²x=1 whenever appropriate.

**Trigonometry (identities ?)**

Trigonometric identities involve an equal sign with a different expressions on either side. So it's not clear what exactly you require in your questions. Do you need to simplify the expressions? I suggest you check for typos as well as I do not see what β has to do ...

**linear**

To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors. Define projection of v on u as p(u,v)=u*(u.v)/(u.u) we need to proceed and determine u1...u5 as: u1=w1 u2=w2-p(u1,w2) u3=w3-p(u1,w3)-p(u2,w3) u4=w4-...

**CALCULUS**

f(x)=9x³-4x^5 F(x)=∫f(x)dx=(9/4)x^4-(4/6)x^6+C Given F(1)=0, solve for C and hence find F(4) F(1)=(9/4)1^4-(4/6)1^6+C=0 => C=(4/6)-9/4=(8-27)/12=-19/12 => F(x)=(9/4)x^4-(4/6)x^6-19/12 Find F(4)

**Math (Help please)**

Rows are horizontal, numbered from top to bottom, columns are vertical, numbered from left to right. For example, element at row 1 column 3 is equal to 6, element at row 2 column 4 is equal to 0.

**physics - work, power**

We do not support LaTeX here, but you can use / for division, and unicode symbols for special characters. Power = work / time work = Force * distance speed = distance / time force * speed = force * distance / time I believe the four equivalences are sufficient for you to get ...

**READ - to Sarah**

Well said! Thank you!

**Physics**

Mass of water that escapes per unit time = m Since the mass of water drops in height by an equivalent of h=1.14 m, we can equate change in energy = 0, or mgh-(1/2)mv^2=0 Solve for v

**Physic**

Power for resistors in series = V²/(R1+R2) Power for resistors in parallel = V²/(1/(1/R1+1/R2)) = V²*(1/R1+1/R2) Solve for R2.

**Physic**

Power = V²/r watts so resistance for the 75W bulb R1 = 120²/75 Ω = 192 Ω Similarly calculate R2 for the 25W bulb. Net resistance of two resistors in parallel R = 1/(1/R1+1/R2)

**physics**

Without air resistance, time to drop to ground (irrespective of horizontal velocity) t = √(2gh) horizontal distance = horiz. velocity * t

**Mechnical principles**

Archimedes principle: Buoyant force on a submerged or floating object is equal to the weight of fluid displaced. Volume of metal = volume of fluid displaced = weight of fluid displaced / density of fluid = (buoyant force) / density of fluid = (500-446) g / 1000 g/L = 54 mL ...

**Math.**

1-4 are correct. For #5, interest = 1200*0.045*2=108 principal = 1200 Total to repay = 1200+108=1308.

**Math help**

Yes, B is correct, here's how: 3.36/6=(3+0.3+0.06)/6=3.00/6+0.30/6+0.06/6

**mat**

4.5% compounded monthly is i=0.045/12=0.00375 per month. n=38 months Present value, Pv=125 Future value, Fv = Pv(1+i)^n

**statistics**

4***5***6***7***8***9***10 If your studying time is a total of 6 hours between 4 and 10 pm. Time left after 8 pm is 2 hours. Assuming random checking, probability that study time after 8 would be the time period between 8 and 10 divided by the total possible time from 4 to 10.

**math-permutation**

The four digits are distinct, so there are 4! possible permutations of the digits.

**algebra**

I have not checked or proved, but believe (6,8,10) is the only triplet that is consecutive even. If you would like to search for more triplets, here's a reference to the work of Brahmagupta: "Pythagorean triples[edit] In chapter twelve of his Brahmasphutasiddhanta, ...

**Physics !**

A. you get the idea, but results can be simplified further Since the bulbs are identical each with resistance r, then in series, R=3r, in parallel, 1/R=(1/r+1/r+1/r)=3/r, in other words, R=r/3. B. Current = i, governed by V=iR. For light bulbs in household circuit, V is ...

**math**

Let x=number of mystery books on the shelf then 3x = total number of books on the shelf we are told that x/5<10<x/4 multiply by 20, 4x<200<5x which means that 40<x<50 So the number of mystery books can be any number between 41 and 49. In other words, the ...

**physics**

Energy = mgh h=difference in elevations between floors. The number of steps is irrelevant because it's the total difference in elevations that counts. If m is in kg, g in m/s², and h in metres, the result mgh is in joules.

**MATH PLZ SOMEONE HELP**

Bread costs $2 a loaf. How much would 1 loaf cost? How much would 2 loaves cost? How much would 10 loaves cost? etc. Similarly, Babysit earns $10 an hour. How much for 2 hours? How much for 5 hours? How much for 10 hours? How much for h hours?

**Physics - impressive**

Your posting speed is impressive, at less than 20 second interval for 7 posts. However, your efforts in solving problems is at the other extreme. The more effort you show, the more chance that help will be given in priority. In fact, you are encouraged to post a problem, study...

**Physics**

(a) Total tension = tension due to mass + tension due to acceleration = mg + ma (b) tension at uniform velocity = tension due to mass only = mg

**Astronomy**

It turns out that detecting planets around other stars is by the periodic dimming of the star, caused by the "eclipse" of the star by the planet. A smaller planet will dim the star to a lesser extent, hence either the periodic dimming phenomenon is more difficult to ...

**NEED HELP PHYSICS!!!**

Equate the centripetal force to 6.8g, i.e. mv²r = 6.8mg solve for r. Note that mass of aeroplane cancels out.

**NEED HELP PHYSICS!!!**

At the bottom of the swing, the vine is subject to two forces, gravity force = mg centripetal force = mv^sup2;/r m=mass of Tarzan (kg) g=acceleration due to gravity (9.81 m/s²) v=tangential velocity (m/s) r=radius of circular motion =length of vine (m) At point of rupture...

**NEED HELP PHYSICS!!!**

Centripetal force is the force that maintains an object in a circular motion. This is an external force that acts on the object in the direction of the centre of the circular motion, namely tension of the string in this case. Centripetal force may be calculated using the ...

**math**

By the pigeon hole principle (where each hole houses one car), it is impossible to have 23+34=57 repairs in 50 lifts (cars). So the surplus must go to cars that need both repairs. This is the least number of cars that need both repairs. Assuming that all cars need at least one...

**physics**

v²-u²=2aS v=0 u=-7.5 m/s S=-4.2 m Solve for a=acceleration in m/s² a=7.5²/(-2×4.2) =6.7 m/s²

**Math**

Median is the middle number of a sorted list of data such that there are as many numbers above it as there are below. For example, median of the set of numbers {3,5,7,10,14,18} is 8.5, which is the average of the two middle numbers. The median of {1,4,9,13,16} would be 9, ...

**French**

"adorer" is a transitive verb (meaning it requires a direct object). Based on Missy literal translation can you correct the sentence? Alternatively, you can say simply J'adore ... the warm days....

**French (if correct translation/grammar)**

Indeed, Ms Sue is right. To clarify, could you tell us if the objective of the exercise is to write a literary essay, or is it a translation exercise? In either case, it would be much easier if you would give the original English version, seeing that the text shows evidence of...

**Physics**

The second parachutist must open the parachute at the moment that she catches up with the first, i.e. has fallen the same distance as the first. 1. Establish the time/distance relation of first parachutist. For the first 3 seconds, distance = 0 + 9.8*(3²) = 44.1 m total ...

**physics**

1 revolution=2π radians 1 minute = 60 seconds (a) Angular acceleration = 180 rpm/8 s =22.5 rpm / s = 22.5*(2π) radians/60s /s =3π/4 rad/s² (b) No. of revolutions =average angular speed * time =(0+180)/2 rpm * (8/60) min = 12 revolutions

**physics**

Power = work done / time Work done =mgh =50*9.8*250 =122500 J Time =10*60 s =600 s Power = work done /time =122500/600 J/s = 204.2 W

**physics**

If car is accelerating uniformly, after 10 seconds, the velocity is 30/2=15 m/s. Distance travelled is time * average velocity =10 s × (0+15)/2 = 75 m Or calculate average acceleration a=30 m/s / 20 s =1.5 m/s² Distance =vi t + (1/2) a t² =0(10)+(1/2)(1.5)(10&...

**Telecommunication 2.**

Radio waves are electromagnetic waves and obey the relation v=fλ f=frequency (Hz) λ=wavelength (m.) v=velocity, m/s and in vacuum,equals the speed of light for electromagnetic waves c=3×108 m/s in air, v is slightly less than c. So solve for f in the above ...

**physics**

"KE 1= 1/2*0.002kg*300^2m/s=30 j KE2=0 work " should result in 90 J (and not 30 J), and assuming energy dissipation is uniform, then KE=W=F*d, F=KE/d=90/.05=1800 N which is exactly the answer you got for the second part. Note: units which are proper names (pascals, ...

**physics**

Correct, well-done! :)

**Chemistry - Stoichiometry**

From the equation, find the stoichiometric ratio of HCl and MnCl2 which equals 2. This means that 1 mol of MnCl2 will generate 2 mol of HCl. Using the fact that 1 mol of HCl occupies 22.4 L at STP, you will find how many mol of MnCl2 will be required to make 0.054 L of HCl.

**maths - cosine rule**

Use the cosine rule: c²=a²+b²-2ab cos(C) with a=7, b=15, and included angle C would vary from 0 to 180 degrees. Note that these limits themselves are not valid values, i.e. max>c>min. They represent the sum and difference of the two sides.

**Math**

An equation of a line must include an equal sign, and your answer does not have one. You probably meant y=-4x+10 Recall some properties of a dilation includes 1. conservation of parallelism, ------------------------------ i.e. lines before and after dilation should remain ...

**math**

Almost. It's 800 cubic feet. Units are important in the answers.

**math**

(2, 2 square root 2, and 2 square root 3) means (2, 2√2, 2√3) Square each number: (4, 2²×2, 2²×3) =(4,8,12) Do these numbers make a Pythagorean triplet?

**geometry**

See your later post.

**linear algebra check**

You have u1 and u2 correct. Don't know if you're expected to rationalize the denominator, in which case, u1 would read [(√3)/3,(√3)/3,(√3)/3]...etc. u3 should be [0,....] A good way to check your answer is to verify if u1.u2=0, u1.u3=0, u2.u3=0.

**Chemistry**

Keq can be obtained by substitution of the product concentrations and reactant concentrations in the definition of Keq. If in doubt, read: http://www.horton.ednet.ns.ca/staff/jeffrey/Chem%2012/answerkeysMJeffrey/kineticsandrates/Meaning%20of%20Keq%20page%201.pdf or examples in...

**accounting**

You can solve using the compound interest formula: Fv = Pv * (1+i)^n Fv=future value, to be calculated Pv=Present value ($8000) i=interest per period (6%/2=0.03) n=number of periods (2)

**chemistry ap**

Assuming zinc is in excess. 18 mL of 6.00 M H2SO4 equals 0.108 mol From Zn+H2SO4 -> ZnSO4 + H2 we deduce that 1 mol of H2SO4 produces 1 mol of ZnSO4. So mass of ZnSO4 produced is 0.108 mol, multiplied by the molecular mass of ZnSO4.

**accounting**

Use compound interest formula: Fv=Pv(1+i)^n here Fv=7500 Pv=present value to be calculated i=8%=0.08 (assume compounding annually) n=18 transposing, Pv=Fv/(1+i)^n

**math discrete**

Oops, I didn't do what the question asked. Go with Reiny's solution!

**math discrete**

f(x)=4x³ g(x)=2x h(x)=x² h◦(g◦f) =h◦(g(x²)) =h◦(2(x²)) =h◦(2x²) =4(2x²)³-5 =4(2²x²)³;-5 =4(2^6 x^6)-5 =256x^6-5

**PHYSICS**

You can read the response to the previous post and try to work out the answer.

**PHYSICS**

By the law of floatation, any floating object will displace a mass of fluid equal to its own mass. So a floating object of volume 1 m³ density 400 kg/m³ will displace 400 kg of water, i.e. fraction of immersed object is 0.4, equal to its specific gravity, and ...

**math - typo?**

A cubic foot of water weighs 62.4 pounds. An imperial gallon of water weighs 10 pounds. You used kg all over, so it is not clear whether there is one or more typos in the question. You will need to check the question and make appropriate corrections before your answer can be ...

**math**

First possibility: 10 B = 10 B After that, we can take advantage that 3B weighs as much as 2A, so you can progressive change every 3B for 2A, for example, 7B+2A = 10B 4B+4A = 10B there is one more that I will leave you to finish.

**Math**

All correct except the first: The square of the length ...

**math**

5•4•3 does not equal 40, you probably meant 5*4*2 you can add 5*8*1 If order does not count, I don't see other ways.

**calc**

A vector that is orthogonal to two given vectors is the cross product, namely |i j k| |x1 y1 z1| |x2 y2 z2| which in this case is |i j k| |1 6 1| |1 -9 1| Expanding the determinant, we get the following vector: <6*1+1*9, 1*1-1*1, 1*-9-6*1> <15, 0, -15> which can be...

**biology**

Some cons to think about: 1. Mandatory donation will no longer be a donation, it will be an obligation. 2. What do you think about the individual rights of citizens of Canada. 3. The need may be urgent, but will the organs of ALL Canadians be required?

**7TH MATH HELP**

A translation is defined as: T: (x,y) -> (x+p,y+q) where p and q are given constants. For example: (10,3) -> (10+p, 3+q) = (1,6) 10+p=1 => p=1-10=-9 3+q=6 => q=6-3=3 So we have established that the translation is T: (x,y) -> (x-9, y+3) (note: if p is positive, ...

**Algebra 2**

Expand sin2θ = 2sinθcosθ so sin2θ=-cosθ 2sinθcosθ + cosθ = 0 factoring out cosθ, cosθ(2sinθ+1)=0 cosθ(sinθ+1/2)=0 Using the zero product property, we deduce that cosθ =0 OR sin&theta=-1/2 Solve...

**Exponential Equations**

Direct substitution of equation: Pv=present value Fv=future value Fv=Pv*(1+i)n where i=interest rate per compounding period (assumed year here) n=number of compounding periods (assumed year here). note that 2.75% is equivalent to 0.0275 for i (interest rate). If both Pv and Fv...