Posts by MathMate

Total # Posts: 12,102

Principle of floatation: A floating object displaces its own weight of the fluid in which it floats. Volume of steel =Vs Mass of steel Ms = ρs*Vs Volume of mercury displaced, Vm = Ms / ρm Percentage of volume displaced =Vm / Vs If the steel block floats with bottom ...

Microsoft Excel
Excel is nothing but a tool to help us. It does not create a new rule for precedence, but follows what we learned in elementary school. In maths, the rules of precedence PEDMAS (or some variant) are: Parentheses Exponentiation Division/Multiplication Addition/Subtraction. They...

Start by drawing a diagram. If BC=BD, then ∠BDC=∠BCD=34° (angles opposite equal sides. Hence ∠CBD=180-(34+34)=112° ∠ABD=∠ABC+∠CBD=? Recall that ΔABC is equilateral.

See other post.

He saw penguins at his intermediate destination.

a) Total: 640 feet Two short sides: 2x long side 640-2x b) Since long side must be positive, we have 640-2x≥0 c) Area = short side * long side A(x)=x(640-2x) d) find x such that 30000≤A(x)≤40000 Make a table that gives x and A(x), Hint: A(50)=27000 <30000 A(86)=...

Stats Math 3
(1) The sample distribution taken from a binomial distribution is approximately normal because sample/population size < 0.05 ("small" sample). Also a binomial distribution approximates a normal distribution when np>K and np(1-p)>K, where K ranges between 5...

Stats Math 2
Population has binomial distribution. sample mean is 144/300. Check that sample satisfies normal approximation and proceed as in your next post. Do not forget to apply continuity correction when approximating a discrete distribution (such as binomial) by a continuous ...

Same as your other post:

CuCl2.2H2O See for example: for more details.

You're welcome!

If it is diprotic, then your equation in (2) is correct, and the molar ratio NaOH/C6H7O6 would be 2, and hence the answer in 4 would be halved, ... problem solved.

1. Numerically correct. You will have to get used to citing answers to the correct numnber of significant digits, depending on the given information. Here, the correct answer would be 0.001811 M. 2. The neutralization reaction is not correct. Ascorbic acid has only 1 H+, so it...

If the box rolls on a horizontal floor with a constant velocity, then it is in dynamic equilibrium, and no external (horizontal) force is acting on it. Thus the floor does zero work on the box.

Don't know. According to Google, the density of ethanol ("alcohol") is 789 kg/m³. So if the liquid has a density of 750 kg/m³, i.e. it is less than the density of ethanol, it must be something else. If ethanol is mixed with water, the density goes up, i...

Yes, Steve is right. Thanks Steve. Oversight on my part.

Thanks Steve. Oversight on my part.

Final total number of balls =10+6+112=128 Half of them would be 64. You will need 64 white and 64 yellow. I'll leave you to figure out how many of each colour to add.

Here, assume equal tails, then p̂=(0.045+0.133)/2=0.089 So the required form read: p̂-0.044≤p̂≤p̂+0.044

vectors( need answer asap)
The centroid of a triangle is located at 2/3 of the length of any median. Median=(OA+OB)/2=<5,1> 2/3 from vertex (origin)=<10/3,2/3>. Another way: It turns out that the coordinates of the centroid of a triangle is the mean of the x and y coordinates of the vertices...


To do this experiment, you need to collect data at your school, including number of pairs of shoes for each respondant. Number of men and number of women interviewed. The analysis can then begin with you have the data.

You need data before you can do the analysis.

Use Google translate if necessary.

[subordinate conjunction?] Mangyaring isulat ang iyong kumpletong tanong sa Ingles. Hindi namin na makipag-ugnay sa Filipino. (Please write your complete question in English. We are not able to communicate in Filipino.)

(a) "Given that it is not found in box 1" means that it is not in box 1, so probability of finding it in box 1 is zero. (b) Conditional probability: P(A|B)=P(A∩B)/P(B). Event A: defective in box 2 Event B: defective not in box 1 P(A)=1 box out of k = 1/k P(B)=not...

In case you have difficulties also with Q3, there is a good article that show you how to solve a similar problem step-by-step:

Question 3 requires the polynomial model, say P(x) where x is the month, 1 for January, 2 for February, and so P(7) is the value for July. So if you have already found the polynomial for question 3, it is a question of substituting the proper month (July) to find P(July) as ...

To obtain the acceleration of 6 m/s², a minimum force of 43.02 N is required. So the question is either incomplete, or contains typos. Please check.

use F=ma, and a=v²/r where m=981 kg, r=625 m, and F=2433 N (unit not given, Newton assumed). Solve for v.

Given L1: r= [4,-3,5] + t[2,0,3], t∈R L2: r= [4,-3,5] + s[5,1,-1], s∈R We need to find the plane that contains both L1 & L2. (changed to uppercase to avoid confusion with 1). Notice that P0=[4,-3,5] lies in the given plane, in fact, it is the intersection point of L1...

First, I suspect you are missing parentheses in your equations. It is very easy to forget them when working with typeset fractions which contain implied parentheses in the numerator and denominator. I assume the equations are: (x-1)/k = (y-2)/2 = (z+1)/(k-1).....(1) (x+3)/(-2...

Hint: Correlation studies do not reveal causal relationships.

Make a table and everything would be clear. stock totVol concentration 2 4 32 (2*64/4=32) 2 8 16 (2*64/8=16) 2 16 8 2 32 4 Now if 2 mL of water are added to each, then concentration would be: stock totVol concentration 2 6 32 (2*64/6=21.3) 2 10 16 (2*64/10=12.8) 2 18 8 ... 2 ...

Sorry, Reiny is right. What I calculated could be called "average rate of return". Effective rate is calculated for one year only. See:

Use compound interest formula: monthly interest, i = 0.06/12=0.005 period, n = 7*12=84 Principal, P=1000 (say) Future value =P(1+i)^84 =1000*(1.005)^84 =1520.370 Effective rate (= average interest per year) =((1520.370-1000)/7)/1000 =0.0743 p.a.

Conservation of Momentum: m1u1+m2u2=m1v1+m2v2 m=mass u=initial velocity v=velocity after impact 1,2 objects, people. Since the person catches the mass, the common velocity after "impact" is v1=v2=v. Solve for v, since all other variables are known.

See Reiny's answer :

now mr. damon, physics

now mr. damon, physics
See other post, modify constants to suit given values. Give final answer to 2 significant figures.

Breaking strength T=mg=33.8kg*9.8 N mass = 3.02 kg radius = 1.2 m velocity = v Tension on string S=mv²/r=3.02*v²/1.2 At breaking point, S=T 3.02*v²/1.2 = 33.8*9.8 Solve for v. I get 11.5 m/s

physics, please help
Please see other post, and check the heat capacity/other constants.

Calculate Tf=Ti+ΔT

use: ΣmcΔT=0 Silver: Ti=107, Tf=T, m=63.8kg, c=240 J/kg/°C Ice: mass=1 kg, Heat of fusion: 334000 J/kg (ΔT=0) 63.8*(240)*ΔT + 1*334000=0 ΔT = -334000/(63.8*240)=-21.8°C


math calculus
Writing in component notation, <1,0,0>=i <0,1,0>=j <0,0,1>=k and using rules ixj=k, jxk=i, kxi=j jxi=-k, kxj=-i, ixk=-j and the magnitude of all unit vectors is always one. Above reduces to <0,0,1>.<0,1,-3> + <1,0,-4>.<1,0,-4> - 8|ixk...

Both are correct! Good work!

Question says "using Earth data as a starting point" but does not give the radius of the earth. It could be 6371km (from Google) or any other value with different accuracies. So you will decide which value to use, you just have to state the source.

Assuming the mass distribution and average density of the super-Earth does not depart from our planet, then the radius will be increased by a factor of 10^(1/3)=2.154 approximately. Use whatever radius of Earth that is given to you or you can find.

I guess we all started at the same time, and I am the slowest of us all! :)

1. 4cos(x)-2=0 cos(x)=1/2 x=acos(x)=1/2 between 0 and 2π or π/3 or 5π/3 because cosine is positive in the first and fourth quadrants. 2. 3sec²(x)-4=0 3sec²(x)=4 cos²(x)=3/4 cos(x)=±(√3)/2 for cos(x)=+(√3)/2 x=π/6, 11π/6 cos(x...


It's not clear who received 9 pennies. Assuming Danni received 9 pennies, Carl got 9*3=27 pennies from Bev. Therefore Bev got 3*27=81 pennies from Al. Al had collected 81*3=243 pennies.

business math
I am not familiar with the rules of the contribution. My interpretation of the question tells me that the taxes are based on the total gross employee income, which comes to (14*640+3*720)*13 weeks (approx. unless leap year) = $ 144560 Based on the given tax rates, the taxes ...

Correct! Use sine rule to solve for the value of sin(B)=0.7825 which translates to 51.5 or 128.5°.

statistics - question incomplete
question incomplete

(a) use conservation of momentum, note that after collision, there is a common velocity v1=v2=v m1u1+m2u2=m1v1+m2v2=(m1+m2)v m1,m2=masses of bullet and block u1,u2=initial velocities of bullet & block v1,v2=(common) velocity of bullet and block after collision. substituting ...

ω(t)=t³+2t rad/s note that ω(0)=0 rad/s. (A) Angular displacement =∫ω(t)dt [0≤t≤T] =[t^4/4+t^2] from 0 to T =T^4/4 + T² (B) The angular acceleration is obtained by differentiation of ω(t) with respect to t.

physics please help
Start with the conservation of energy (when friction/air resistance are absent). Kinetic Energy, KE = (1/2)mv² Potential Energy, PE = mgh m=mass, v=velocity, h=change in height, g=acceleration due to gravity. Conservation of energy states that without external forces and ...

physics please help
Angle of ramp, θ=tan-1(2/12) Minimum force required (without friction), F = 65(9.8)sin(θ). Friction force, f= 50N Efficiency = useful force / total force = F/(F+f)

Draw a diagram to show the height of the tower (36m), angle of depression (from horizontal)=25°. So tan(25°)=36÷width Solve for wideth.

When μ and σ are known, the sample mean (x̄) has normal distribution so the statistic is Z=(x̄-μ)/(σ/sqrt(n)), where n=sample size=148. (a) Assuming a symmetrical confidence interval, we have α=0.003/2=0.0015. Looking up a normal probability...

If the three events are independent, then the probability of getting two given characteristics is the product of the probability of the individual events. Thus P(I∪N)=P(I)*P(N) (if I and N are independent) =(0.10*0.50)=0.05. Note: this probability may include those who are...

Momentum = mass*velocity Note that velocity is signed. Using subscript 1=before impact subscript 2=after impact. Here, mass=0.118 kg=m1=m2 v1=+3.14 m/s (towards bat) v2=-33.7 m/s (away from bat) Calculate the change in momentum, Δmomentum = m2v2-m1v1 and give answer in ...

As in your previous question, if we assume random arrival, all students have equal probability of arriving first. The probability of a female student arriving first is given by #of favourable outcomes ÷ total # of possible events.

Total number of students: 9+15+8+12=44 Total number of females: 15+12=27 The selection is random, so all students have equal probability of being selected. So the probability of selecting a female is 27/44. Convert to a fraction and round to the nearest hundredth (i.e. two ...

Let c=current speed, and b=boat speed in still water. Speed with current = 225/5=45 mph Speed against current = 225/9=25 mph, Set up equations: b+c=45 b-c=25 Solve for b and c. By the way, when you know the sum and difference of two variables, the variable with the larger ...

The equilibrium price is where the two lines meet, namely when the number of units the manufacturer is willing to sell equals the number of units the retailer is willing to buy, both at price p. So 20p-1500=x=-4p+900 Solve for p to get p=100 (and x=500)

2Al+Fe2O3 -> Al2O3 + 2Fe Since the coefficients of Al and Fe are both 2, so the amount of iron formed would be in the ratio of the atomic masses, namely 55.85/26.98 (approximatelyly).

The resultant velocity of two velocities at 90° (such as x and y) apart can be obtained by resultant=sqrt(x-component²+y-component²)

physics - insufficient information
There is not sufficient information to give a numerical answer.

This is a case of choosing without replacement, and order does not count. Number of ways = nCr = n!/(r!(n-r)!) =16!/(4!12!)

When two planes intersect (such as the edge of a rectangular box), the intersection is a line (not a point). When two planes do not intersect(such a the top and bottom faces of a rectangular box), then they don't intersect at exactly one point.

reference frames
Taking the difference is the right approach. However, they are heading in different directions, so the velocities have different signs. Hope that helps.

Math - correction
Correction: The equation given above σ²=(sum of (xi-μ)²)/N applies to a population. C is correct if we interpret the data as a sample of the given population, in which case the standard deviation is given as: σ²=(sum of (xi-μ)²)/(N-1) = ...

C is not correct. There is a choice which is close to the answer. The previous post shows how you can find the correct answer.

First find the mean, μ where μ = (sum of all numbers, Σxi)/(number of values, N) Standard deviation, σ, is given by σ²=(sum of (xi-μ)²)/N and finally σ=sqrt(σ²)

see other answer.

Linear Algebra
Your answer is correct. The fact that t2=0 means that t1 and t3 are linearly dependent, resulting in two independent variables in R3. This is still a linear dependent set.

To check whether a triangle is a right-triangle, add the square of the two shorter sides. If the sum equals the square of the longest side, then it is a right-triangle. Example: Triangle ABC has sides 5,12,13. 5²+12²=169 = 13² therefore the ABC is a right ...

A+P=25 P+B=19 B+A=16 Buy one from each deal and you will get 2 apples, 2 pears, and 2 bananas for (25+19+16)=60 pesos. How much would you spend if you buy only one of each?

Answer is correct! Q=mcΔT However, use of the equality sign is valid only when both sides of the sign are equivalent. You could write: Energy required =13g * 1.00 cal/g°C * 2 °C =26 cal

math - ratios
Given: Girls : Boys = 7 : 3 Girls+Boys:Girls-Boys = 10:4 = X:200 where X is the total number of children (Girls+Boys) or 10/4=X/200 Cross multiply to find X=200*10/4 = 500

math - correction
Since going around once reduces the width and length by 4', 9.26'/4'=2.315 Nala would need to mow around the lawn between 2 to 3 times to finish half the work.

Total area = 25*45 = 1125 sq.ft. Half of the area = 562.5 sq.ft What is needed is the size of the inside rectangle left, or (25-x)(45-x)=562.5 Solve for x to get x=9.26' and reject the other root which exceeds 25. Since 9.26'/2'=4.63 strips, so Nala has to go ...

Half life = 15h Activity A(t)=A(0)*2^(-t/15) Solve for t in A(t)=5000=80000(2^(-t/15)) to get t=60 (hours)

The position function for a free fall from rest is: x(t)=(1/2)gt² In metric units (x in metres, t in seconds), x(t)=(1/2)*(-9.8)t² =(1/2)(-9.8)6.7² =-220 m approx.

Horizontal component of velocity = 18 m/s Vertical component of velocity, Vf, is given by Vf²=Vi²+2*a*Δx Vi=initial vertical velocity=0 m/s a=acceleration due to gravity=-9.8 m/s² Δx=-41 m Vf=sqrt(0+2(-9.8)(-41))=28.4 m/s (downwards) angle with ...

Assuming the crate moves upwards. The applied force P is upwards whether the crate moves upwards or downwards at a constant velocity. coeff. of kinetic friction, μ = 0.75 angle of incline, θ = 46° (with horizontal) If crate moves upwards with a constant velocity, ...

Mechanism and Machines
It's surprising that your teacher did not mention any application when the subject was being taught. The linkage essentially converts rotational motion into a straight line movement. The rotational motion usually comes from a motor, and the straight line movement can be ...

math - fractions
Father does the work in x hours, or father does 1/x of the work in one hour. Son does 1/(2x) of the work in one hour. Together, they do 1/x+1/(2x)=1/6 of the work in one hour. 2/(2x)+1/(2x)=1/6 3/(2x)=1/6 Cross multiply 2x=18, x=9 So father does the wok in 9 hours.

Profit = 0 is break even. So solve for x in P(x)=-37x²+1073x-7548 = 0 to give x=12 or x=17 The profit is given by the maximum of the P(x) function, which is located at x=(12+17)/2=15.5, or the maximum profit is P(15.5). (substitute 15.5 for x and evaluate the profit).

Math - ratio
Use ratio / cross multiplication 18:162 ≡ 36:x x=162*36/18 = 324

Total (in fraction) = 1 Woodwinds = 1-2/5-1/3=(15-6-5)/15=4/15 half of woodwinds (4/15) are clarinets, so clarinets = (4/15)÷2= 2/15 One eighth of brass are tubas, so tubas = (2/5)÷8 = (2/40)=1/20 whole : 240 1/20 : x (number of tubas) x=240*(1/20)÷1 =240/...

Both Minnie and Amanda have 11 cds, so they have the same number of cds.

Physics - kinematics
Given Vi=36 m/s θ=30 Vix=36cos(30)=31.18 m/s Viy=36sin(30)=18 m/s Vy(t)=Viy*t+(1/2)gt² =18*1+(1/2)(-9.8)*1² =13.1 m/s velocity=sqrt(Vix²+Vi(1)²) =sqrt(31.18^2+13.1^2) =33.82 m/s

Math - compound interest
i=4% p.a. compounded quarterly = 1% per period Let R=(1+i), n= number of quarters/periods Future value FV=100(1+R+R²+R³....+R^(n-1) ) =100(R^n-1)/(R-1) =100(R^n-1)/i For FV=10000 we have 10000=100(R^n-1)/i R^n=(10000/100)*i-1 =2 n=log(2)/log(1.01)=69.66 It will take ...

You can also say (formally) "De quel pays êtes-vous venu/venus/venue/venues?" depending on the gender and number of persons to whom you're addressing.

Sorry, don't know if you have used Word or other word processors to write the equation, but they do not translate corectly. Here most HTML symbols are recognized, or you could use ^2 to mean square, and sqrt( ) to mean square-root, etc. Also please write the appropriate ...

Solubility is defined as the number of grams of solute that will saturate 100 grams of solvent at a given temperature. So at 20 degrees, we know that the solubility of CuSO4 is 25. Mass of water (solvent)=80 g Use ratios: 25:100 = x:80 Solve for x to get x=25*80/100=20g

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