Sunday
April 20, 2014

Posts by MathMate


Total # Posts: 9,948

Geometry
It is a conditional probability problem where the distribution is binomial. The general expression for conditional probability for probability of event A given event B is P(A|B)=P(A∩B)/P(B) where A = P(exactly 2 heads) B=P(at least one head) P(A∩B)=P(A) since A is a su...

Algebra
If the length and width of the pool are L and W, and the width of the path is w, then perimeter of the pool = 2(W+L) perimeter of the outside = 2(W+2w + L+2w) Difference between outside perimeter and the pool =2(W+2w + L+2w) - 2(W+L) =8w So w=(74-50)/8=24/8=3 m

maths
Use FOIL to expand (x+1)(x+2) =x²+2x+x+2 =x²+3x+2

maths
Does (x+1)3 stand for (x+1)³ or 3(x+1) ?

maths
(x+1)3=2f(x+1) Transpose the two, and switch sides f(x+1)=(x+1)³/2 Since x+1 is the argument of the function, we replace y=x+1 and express the right-hand side in terms of y: f(y)=y³/2 Therefore: f(10)=10³/2

Hello? My math question was ignored?
See http://www.jiskha.com/display.cgi?id=1370816233

Math
(x+2)(x+1)=x²+3x+2 Multiply by 9: 9x²+27x+18 Now put it all together: 9x²+27x+18 -2x-2 -4x-4 = 0 group like terms: 9x²+21x+10=0 The next step is to factorize the expression by grouping: Find m, n such that m+n=21, m*n=90 so m=6, n=15 9x²+6x +15x+10 = 0 ...

Algebra II
There are infinitely many of them. Are you given a list of choices?

Math
Let ω=angular velocity (rad/s) To offset gravity, the centripetal force must offset gravity, g, or rω²=g Solve for ω.

French
The difference between the two sentences is the adjective "vert", which varies according to gender and number vert (masc. sing.) verte (fem. sing.) verts (masc. plur.) vertes (fem. plur.) Since herbe is a feminine noun in singular, you will choose the adjective , and...

Math check and question
What did you do for #a? P(n=1, x=0, p=0.15) =nPx 0.15^0((1-0.15)^(1-0) =1!/(0!1!)(0.15^0)(0.85)^1 =1*1*0.85 =0.85 For #b, P(n=3,x=3,p=0.15) =3P3 (0.15^3)(1-0.15)^(3-3) =1*(0.003375)(0.85^0) =0.003375 Check out the other numbers using P(n,x,p) =nPx (p^x)(q^(n-x)) where q=(1-p)

Algebra
Solve the equation -16t^2+20t+6 = 0 will give you the times that the ball is on the ground. The negative root accounts for the fact that the ball is 6 feet above ground at t=0. I get t=3/2 and t=-1/4

C++
C++ is just another programming language. If you have already programmmed in other languages, switching to C++ will not be difficult. On the other hand, if you are programming for the first time, you will be learning two things at the same time: programming concepts, and the C...

Calculus
Volume of pyramid =area of base * height /3 For a square base of side s, Volume =(s²h)/3

Calculus
e^x is non-negative, so the volume is the definite integral from 0 to 10 of I=∫A(x)dx =0.01*10e^0.01x =0.1*e^0.01x evaluated from 0 to 10

maths
f(208)=208/207+208/207×206/205+208/207×206/205×204/203+… =208 This can be obtained by induction: Let f(n) be the function such that: f(n)=n/(n-1) + n/(n-1)*(n-2)/(n-3) + … n/(n-1)*(n-2)/(n-3)…(2/1) where n is even. Then f(2)=2/1=2 f(4)=4/3+(4/3...

maths
Do you agree with the following response? http://www.jiskha.com/display.cgi?id=1370323034

probability statistics
Assume population height follows a normal distribution N(μ,σ), then the top 4% falls above μ+1.75σ (approximately) as read from the normal distribution table.

Math
3/5-2/5=1/5 So proportion is 1/5 of the class equals 12 students So the whole class is 5*12=60 students. # of Girls = 60*2/5=24

math
Volume = 256 m³ Let base = x by x m height = 256/x² Surface area = x²+4(x)(256/x²) =x²+1024/x differentiate with respect to x and equate to zero for extremum: 2x-1024/x²=0 x=8 So the box size is 8x8x4 high Note: I have assumed that the base area i...

algebra1
Remove the first set of parentheses with no change of the contents. Remove the second set of parentheses but change the sign of each term in the parentheses, since the parentheses are preceded by a negative sign. (3x^2-2x-1)-(5x^2-4x-2) =3x^2-2x-1-5x^2+4x+2 Now group like term...

math 7
experimental probability = (no. of successes) / (total number of trials) =8/20 =2/5

comptuer programming
There are quite a few things to note. I believe your hour rate is multiplied by 1.5 only for those hours exceeding 40 hours. The way you're doing it, it will never get changed because the hour rate is changed AFTER you calculated the total. Don't know what you want to ...

maths - typo
Please check you post. I think 4.2 m is not the right length because if you add any two sides of a triangle, it should be greater than the third side. Here 4.2+(hypotenuse-14)=hypotenuse-9.8 which is shorter than the hypotenuse. It probably reads 42. Let x=length of the other ...

Maths
I have a winning strategy, but perhaps there are others. Draw a line of symmetry to split the game into two identical games. Whatever the next player does, you would do the mirror image. Therefore you will end-up splitting the last rectangle. Based on this, there are only two ...

Math
Let O = centre of circle Γ, then ∠PAO=90° Consider ΔPAC, use sine rule to find ∠PAC, which equals 13° (approx.). ∠CAO is therefore 90-∠PAC and equals 77° approx. Since Δ CAO is isosceles, with congruent legs equal to the radius r o...

Math
Let O = centre of circle Γ, then ∠PAO=90°

Math
I have one feasible solution, not sure if it is optimal. You can find others for a check along the same lines. C=4, 3 factors: 1,2,4 B=6, 4 factors: 1,2,3,6 A=12,6 factors: 1,2,3,4,6,12 N=72,12 factors: 1,2,3,4,6,8,9,12,18,24,36,72

Math
brake. Use the kinematics equation v2²-v1²=2aS v2=final velocity v1=initial velocity S=distance travelled a=uniform acceleration. I get approximately 20 m/s if I assume you mean deceleration of 4.5m/s or acceleration of -4.5 m/s. Deceleration of -4.5 m/s will actuall...

Velocity
v^2 = 11m/s + 2 * 9.81m/s^2 * 60 should read: v =sqrt( 11m/s ² + 2 * 9.81m/s^2 * 60 ) I get about 36 m/s

math
x=Bessy y=Bob x=6y (Bessy has 6 times as much as Bob) x+6=3(y+6) (when each earns $6, Bessy will have 3 times as much money as Bob) Solve for x and y

math
The only right triangle that I know of which has the side lengths form an arithmetic sequence is (3,4,5) or multiples thereof. If the 8 cm leg is the shortest side, then we can find the remaining sides by proportions, namely 8 cm, 8*4/3=32/3, 8*5/3 = 40/3 If the 8 cm side is t...

Math
A=cost of adult ticket C=cost of child ticket 9A+2C = 252 A=C+6 Use substitution 9(C+6)+2C = 252 9C+2C = 252-54 11C = 198 C=18 A=C+6=24 Check: 9A+2C=9*24+2*18=216+36=252 OK

pcm
I assume you mean what is the minimum possible value of f(75p²). Is it known if p is greater than 5? If it is, would it be the number of distinct factors of 75 multiplied by 3 (6*3)=18, namely 1,3,5,15,25,75, then multiply each one by p, and then multiply each one by p&su...

tech III math ( ACT Prep)
You need the LCM (lowest common multiple) of the two numbers. Here's a systematic way to find the LCM between two numbers. In the following calculation, the number on the right is a common factor. Extract a common factor on each line (write on the right). Then divide each ...

Statistics
Binomial distribution, n=10 p=0.28 q=1-0.28=0.72 mean=np variance=npq std dev=sqrt(npq) Exactly r successes =P(r) =nCr p^r q^(n-r) Work out each of the above problems and you will find a match. For example, the first one: P(no more than 3 tails) =P(0)+P(1)+P(2)+P(3) =0.037+0.1...

To Sarah: please do not multiple post the same question
Sorry for having misspelled your name.

To Sara: please do not multiple post the same question
There are people on earth who work with 56kb Internet connections, which means that the 3 seconds that you take to make each of the quintuple posts, it could take up to 3-4 minutes for others to just to display it. The Air America problem is a multi-step experiment, where succ...

algebra
xy=36 x+y=26/2=13 Since 4*9=36 and 4+9=13 we have the sides of the rectangle as 4 and 9 yards.

algebra 2
Use the given formula i=500 mg r=(1-0.25)=0.75 (fraction of what remains) t=6 hours e=base of natural log a(t)=amount left after t hours in mg. a(t)=i e^(rt)

algebra
By proportion, you get 2.5%-1%=1.5 1%-0.25%=0.75 Ratio=1.5:0.75=2:1 To make the mixture, we use the inverse of the ratio, therefore Mixture=1:2, or 120g of 2.5% and 240g of 0.25% make 360g of 1% (assuming both have same density). Check: (120*.025+240*.0025)/360=1% You can also...

physics
Hint: Calculate the time it takes to reach the lower roof, say t (in seconds), by solving for t in: (100-25)=(1/2)gt² The minimum horizontal velocity will be 20/t m/s

Math check
Check your calculations! Did you get standard deviation or σ² as 2.88? Don't understand how you got 2.88 and 10.58. Can you post what you did? For the variance, I have 1.49+0.09+0.00+0.14+1.39=3.1

Math check
First step: Check to see if it is a discrete probability distribution by summing all probabilities. If it does not equal one, either the given distribution is incomplete, or it is not a discrete distribution. Second step: Mean (expected value of X, E(X), μ) =ΣX*P(X) =...

statistics
Let D=event that a television selected is defective and ~D=event that a television selected is NOT defective Then probability that both are not defective: P(~D~D)=(5/9)(4/8)=5/18 Therefore at least one defective is its complement P( (~D~D)') = 1-5/18 = 13/18

Math
Follow the same strategy as the previous problem, we make use of given information and deduce values by expansion. Let f(x)=x^2+(a+6i)x+b+12i=0 and given that f(x) has a repeated root, we deduce that the discriminant is zero, i.e. (a+6i)²-48i=0 which expands to a²-4b...

Math
Let z=a+bi where i²=-1 then z²-26z =-b²-26a + (2a-26)bi Since is real, and z is non-real, therefore b≠0, and consequently (2a-26)bi = 0 => 2a-26=0, => a=13 Thus z=13+bi, z(conjugate) = 13-bi so z+z(conjugate)=13+bi+13-bi=26

Math
Overall loss, neglecting benefit from use of the car, is loss = $20,000 - $18,200 = $1800 It is a loss because he ended up with less money than the start.

Calculus
Define the surface as: f(x,y,z)=xy^2+zy^2+4y-xz^2-18=0 Then check that P0(-2,0,3) is on the surface by evaluating f(-2,0,3) and confirm that it is zero. Let fx,fy,fz be the partial derivatives of f(x,y,z) with respect to x,y and z respectively, and evaluated at P0(-2,0,3). The...

math check
Your answer corresponds to P(-0.25<z<0). Look up a probability table (or use your calculator) for +1.32. Many normal probability tables are one-tail from -∞ so you need to subtract 0.5 from the result, taking advantage of symmetry of the normal distribution.

check math
Correct!

check math
Your answer corresponds to at least one boy in a family of 6. Retrace what you did and work it out for a family of 8. "At least one boy" corresponds to "NOT all girls". So calculate the probability of having all girls in the family, and subtract from 1.0 to...

math
Sale price = normal price *(1-markdown) =$2.77(1-0.22)=$2.16 It must have been a while back since Macy's sold a designer jacket for $2.77.

Math check my answer
Since we are talking about costs, a better deal is a lower cost, so the inequality should read: .80x + 29 < 1.19x + 17 The answer is almost perfect... 30.769 rounds to 30.8, although in this case, it does not count because we are talking about integers.

math
Work with the "weighted mean". For each pound, cost of meat powder = 0.4*1.20 = 0.48 cost of grain = 0.6*0.80 = 0.48 Total cost per pound = 0.48+0.48 = $0.96

programming
What have you done so far, and how would you like us to help? Can you show us your pseudocode?

arithmetic
Set up a table of outcomes and the corresponding probabilities to create the probability distribution. For example, the lowest outcome is X=2 (=1+1) with probability 1/36. then X=3 (1+2 or 2+1) with probability 2/36 ... X=12 (=6+6) with probability 1/36. Find the mean using E(...

arithmetic
Did you read your other post? http://www.jiskha.com/display.cgi?id=1370132243 Set up a table of outcomes and the corresponding probabilities to create the probability distribution. For example, the lowest outcome is X=2 (=1+1) with probability 1/36. then X=3 (1+2 or 2+1) with ...

probability
Create the probability distribution for the random variable X (see other post), and sum probabilities of all outcomes greater than 7.

Math
For 23)(ii) I have σ=√(npq)=√(379*0.15*0.85)=6.95 For 24(ii) p=0.89, q=1-0.89=0.11 σ=√(npq)

Math
17% are left-handed means P(left-handed)=0.17 (remember 17%=17/100=0.17) so N=59, p=0.17, q=1-0.17=0.83 you can take it from here!

Math
For a binomial distribution with N bernoulli trials with probability of success p (i.e. failure q = 1-p), the following properties can be proved: mean = Np variance = Npq Take the square-root of variance to get standard deviation. In 15 tosses of a fair dime, N=15, p=0.5, q=1-...

math answer check
I don't know to which question 0.0675 referred. Note that: nCr = n!/[(n-r)!(r!)] For (e), we have P(n=3,x=1,p=0.45) =3C1*0.45^1*(1-0.45)^(3-1) =3*0.45*0.55^2 =0.408375 (f) probabilities never exceed 1! P(n=6,x=6,p=0.25) =6C6*0.25^6*(1-0.25)^(6-6) =1*0.25^6 =0.000244

math answer check
For a binomial distribution, the outcomes are either 1 (success) or zero (failure). The probability of success (outcome =1)of EACH step (out of n steps) is p and remains unchanged over the duration of the experiment. The probability of failure (outcome =0) of EACH step (out of...

Math
Hint: cot^2(x)=cos^2(x)/sin^2(x) =(1-sin^2(x))/sin^2(x) =1/sin^2(x) - 1 cos(x)dx = d(sin(x)) so use the substitution u=sin(x), then du=cos(x)dx cot^2(x) cos(x)dx =(1/u^2 -1)du =(-1/u - u) + C backsubstitute u=sin(x) I=-1/sin(x)-sin(x)+C

math-probaility
Use complementarity. Calculate the probability of getting no lemon, and subtract from 1. Two-step experiment, second step dependent on the first: Total number of candies at start=5 Step 1: Number of grapes=2 Probability(No lemon)= 2/5 Step 2: Number of candies left=4 Number of...

Probability
Expectation = ΣxP(x) where x represents the gain from each of the outcomes in the sample space. Here the gains and probabilities are: outcome=oil gain=375000-25000=350000 P(oil)=1/40 xP(oil)=8750 outcome:gas gain=130000-25000=105000 P(gas)=1/20 xP(gas)=5250 outcome:nothi...

Algebra
Hint:Use the compound interest formula Future=present*(1+i)^n Here Future=40000 n=30 i=0.06 (6%) Solve for Present.

heeeeeeeeeeeeelp math
You were quite right, Andrew. The answer should have been (4!)^4/(4!)² 4! is the number of ways to assemble a single body part. Since there are 4 body parts to assemble, we have (4!)^4 ways to assemble the 4 people where order counts. Since there are 4! permutations of th...

Algebra
There is a rule for this class of problems of finding proportions of mixtures. Most of the time this can be done mentally, for example by chemists or nurses. We have one ingredient A at 20%, and B at 60%. The required mixture is 30% (must be between those of A & B). Take the d...

math
There has been quite a few problems solved on markup based on selling price. This should give you (or others) another example to work on your other problems. retail price = selling price. If there is a 55% markup based on selling price, then the cost price is 100-55=45% So the...

Algebra 1
1. Use the distance formula: distance = (4-1)²+(a-1)²=5² Solve for a (a quadratic equation) 2. Use Pythagorean formula: 8²+b²=14² Solve for b. 3(a) 7²+9²=49+81 = 130 ≠ 12² Therefore the three sides do not form a right triangle. T...

Math :)
You're welcome!

Math
This is a discrete probability function which has the following characteristics: 1. The function is non-negative throughout its domain. 2. ΣR(i)=1 for i∈ domain From the given data, R(0)=0.2 R(1)=0.2 ... R(4)=0.2 for a sum of 1.0.

Geometry
The largest area a given perimeter can enclose is a circle. The largest area of a rectangle for a given perimeter is a square. The question did not specify that the area be a polygon, so the circle gives the largest area. 2πr=18 r=18/2π=9/π Therefore largest area =&pi...

math
Selling price = cost + markup = 47.5 + 34 = $81.50 Mark-up base on cost = mark-up/cost = 34 / 47.5 = 71.6%

Math :)
You're welcome!

Math
Therefore 120 more workers are needed.

Math
Each person accomplishes 1/3÷(60*18) of the project, 1/3240 per person per day. To finish 2/3 of the project in 12 days, Total number of workers need =2/3 ÷ (12*(1/54) =(2/3)*(3240/12) =180 Therefore 120 more workers are needed.

maths
If the original question has a unit of 8m/min., I prefer to give the answer in minutes. The question did not say to answer in hours, and did not say you have to round to the nearest hour. But it is up to you.

maths
Distance travelled =8-(-475) =483 m Speed = 8 m / min. Time = Distance ÷ speed =483÷8 =60.375 minutes

Aviation
See if this link helps answer your question: http://en.wikipedia.org/wiki/Cessna_162_Skycatcher#Specifications

Math
Hints: P(A∪B)=P(A)+P(B)-P(A∩B) If A and B are mutually exclusive (ME), then P(A∩B)=0. This should take care of (d)

math
Nora 4: Hint for you. If you provide attempted answers to the question, do add "(answer check)" to the end of "school subject", especially if you have a whole series of questions which makes it look it homework dumping.

math
Hints: Work out the following: - equal numbers of red marbles and yellow marbles (call x=number of red x=number of yellow - twice as many green marbles as red marbles 2x=number of green Now work out the sample space and the corresponding probabilities.

Math
142=58-7x Add 7x to each side 7x+142=58-7x+7x 7x+142=58 Now subtract 142 from each side to isolate x 7x+142-142=58-142 7x=-84 Divide by 7 to find x 7x/7 = -84/7 x = -12 Now you should be able to try the remaining problems the same way as above and post your answers for checking.

Math
1711 sales out of 1950 calls. The success rate is quite impressive: 1711/1950=87.7%

Algebra1study helps
Multiply both sides by the LCM of the denominators: 3(x+3) to get 1-2*3=2*3(x+3) x+3=(-5)/6 x=-5/6-3 =-23/6

algebra
Let x = number of calculators she can buy, 80x=60*24 x=60*24/80 = 18 Mrs Hopkins can buy 18 calculators at $80 each.

math
39% of selling price is mark-up, so 61% is the cost. Therefore retail selling price =24.30÷0.61 =$39.84 Check: $39.84*0.39=15.54 39.84-15.54=24.3=cost ok.

heeeeeeelp math
Assembling the head, there are 4! ways. Same for each of the three other parts. Total number of ways = 4!4!4!4! But we can arrange the 4 people in 4! different orders, so total number of sets of 4 people = (4!)^4/(4!) =(4!)³

Exponential
Hints: The base is (x^2-17x+71) which does not have rational factors, because 71 has only two factors, 71 and 1, each of which is not a factor to the expression. This means that all integer values of x will make the base non-zero. The exponent, (x^2-34x+240), has two integral ...

Maths Please Help - incomplete
and then...

Math/Statistics
See hints here: http://www.jiskha.com/display.cgi?id=1369881705

Math/Statistics
Hints: P(A∪B)=P(A)+P(B)+P(A∩B) So if any three of the four probabilities are known, we can find the fourth one. Note: Events A and B are mutually exclusive if and only if P(A∩B)=0.

Math/Statistics
(a) P(A|B) conditional probability of A given B =P(A∩B)/P(B) [∩ written as & c a p ; omit the spaces] (b) P(B|A) =P(B∩A)/P(A) (c) A and B are independent if and only if P(A∩B)=P(A)*P(B)

Physics
I assume "linear velocity" means tangential velocity. F=mv²/r =0.25(10²)/3 =25/3 N

Math
#2 is correct.

Math
#2: question incomplete, cannot check. #3: correct You can check: $3*5+$6*6=15+36=$51 #6: correct Check by multiplication 2*5*5*11=550 #7: correct 12-6x2/4+1=12-3+1=10

Mathematics
Assuming "thickness" means height in the usual sense of a cylinder, then volume = πr²h =π(17.1/2)²1.2 =275 cm³ approximately. (π=3.14)

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