Friday
December 26, 2014

Posts by MathMate


Total # Posts: 10,867

st.paul
112,000,000,000
June 15, 2013

mATHS
Take away the legs of the 3 extra stools, which leaves us with 72-9=63 legs for equal number of stools and tables. Divide 63 by the total number of legs of one of one set (7 legs for 1 table and 1 stool), we have 63/7=9 sets. So he made 9 tables and 12 stools.
June 15, 2013

trig
Since (5,12,13) is a Pythagorean triplet, tan(θ)=5/12. Mathematically, we solve it by: Divide by the right hand side: (5/13)sin(θ)+(12/13)cos(θ)=1 Since (5/13)²+(12/13)²=1, we can put 5/13=sin(φ) 12/13=cos(φ) so sin(φ)sin(θ)+cos(&...
June 15, 2013

maths
common ratio = (1458/2)^(8-2)= ±3 So the g.p.s are 2/3,2,6,18,54,162,486,1458 or -2/3,2,-6, ....1458
June 15, 2013

physics
Acceleration phase: initial velocity, v0 = 0 m/s final velocity, v1 = at = 8*20 = 160 m/s distance, S = ut+(1/2)at² = 0 + (1/2)8(20²) =(1/2)8(400)=1600 m Free fall phase: v0 = 160 m/s acceleration,a = -9.8 m/s² v0 = 160 m/s v1 = 0 a = g =-9.8 m/s² use v1&...
June 15, 2013

math
I guess I did not interpret the question correctly the first time around. "At least 4 blocks" means that the 2nd, 3rd, 4th streets (north-south) are not accessible. Similarly, the 2nd to the 12th avenues (east-west) are not accessible. So near the starting point ...
June 15, 2013

math
All of them. Since there are 46x46 streets, there are 45x45 blocks. The dog has to run 4 blocks in a row in the horizontal direction, and 12 blocks in a row in the vertical direction, both of which are even numbers, it will never reach the food, in which direction it tries.
June 15, 2013

Calculus
f(x)=ax²+bx+c f'(x)=2ax+b f"(x)=2a f"(2)=3 => 2a=3 => a=3/2 f'(2)=2 => 2a(2)+b=2 => 3(2)+b=2 => b=-4 f(2)=6 => a(2)²+b(2)+c=6 => 4a+2b+c=6 => 6-8+c=6 => c=8 Therefore f(x)=(3/2)x²-4x+8 Using this final definition of f...
June 14, 2013

maths
Does an operation between two members of a group give you a unique value or multiple values?
June 14, 2013

math
When a problem requires "at least one", it is often easier to find the probability of getting none and subtracting the probability from 1 (complement). Here, probability of not getting a king at a draw is 48/52, or 12/13. Probability of getting no king at 4 ...
June 14, 2013

Calculus
f(x)=x+4/x f'(x)=1-4/x^2 f'(2)=1-1=0 Equation of tangent line: y=0(x-2)+4, or y=4
June 12, 2013

Geometru
A heptagon has 7 sides. The sum of exterior angles is 360. The six given angles have exterior angles equal to: 60,30,45,10,90 and 55 for a total of 290. The remaining exterior angle is therefore 360-290=70°. The largest exterior angle is 90°.
June 12, 2013

algebra
For √, type in & r a d i c ; but without the intervening spaces. I will solve the first one: Use the FOIL rule (2√5-√28)(√28+4√5) =(2√5-2√7)(2√7+4√5) =4(√5-√7)(√7+2√5) =4(10-7-√5√7) =12-4...
June 12, 2013

math check
Sorry, the second one is P(z<1.51), which makes 0.9354 the correct answer.
June 11, 2013

math check
Four decimal places for 0.409 should be 0.4090. The second one is correct.
June 11, 2013

math
These two lines are parallel and distinct, hence there are no solutions. Show that this is the case by dividing the first one by two to get 5x+5y=515 Since both equations have 5x+5y on the left, and different values on the right, it shows that the two lines are parallel and ...
June 11, 2013

math
What do you think, and why?
June 11, 2013

math
P=principal = $3000 i=interest=0.06 n=number of 6-month periods FV=future value =P(1+i/2)^(n)
June 11, 2013

ssm
acceleration = v²/r
June 11, 2013

math
The probability of a red pen on the first draw is 4/18. For the second draw, there are 3 red pens left out of 17 pens total. The probability of both happening is obtained by multiplying the two probabilities: P(RR)=(4/18)*(3/17)=2/51
June 11, 2013

math
There are 2^10 possible subsets, including Φ, the null set. Not sure what you mean by sum of the elements, do you mean the sum of the cardinalities of the 1024 subsets, or do you mean the sum of the numbers of each subset? In the case of the latter, the distinct sums would...
June 11, 2013

math problem
Assume that the "grid" means "grid of squares" is the collection of all the squares, then we consider one square: The "safe" area for the centre of the coin is a square of 1/2"x1/2" out of a total of 1.5"x1.5". Probability is ...
June 11, 2013

math
Rewrite the word as: "ceeeffitv" we see that it is a 9 letter word in which the letters e and f repeat 3 and 2 times respectively. The number of permutations is therefore 9!/(3!2!1!1!1!1!) =30240
June 11, 2013

math
Since "education" can be written as "acdeinotu" a nine letter word without repetition, the number of permutations is 9! = 362880
June 11, 2013

computer
There are many free C/C++ compilers available. Notable ones could be Microsoft's Visual Express C++, Dev-C, Borland C/C++ compilers. Cnet has a whole section for that purpose. Note that some of the compilers listed at the Cnet site are try and buy. Here are some links: ...
June 11, 2013

Probability
P(odd)=0.75 P(even)=0.25 P(3)=0.75/3=1/4 P(6)=0.25/3=1/12 Since 3 and 6 are mutually exclusive, P(3∪6)=P(3)+P(6)=1/4 + 1/12 = 1/3
June 10, 2013

Geometry
The radius is the distance between the centre and the given point, which is r=sqrt(15^2+4^2)=sqrt(241) The circle with centre (2,-5) is (x-2)^2+(y-(-5))^2=r^2 There is only one choice that fits these criteria.
June 10, 2013

Number Theory
Yes, it works! If we solve a,b,c in terms of d, we get, a=-(d+36)/6, b=d+11, c=-(11d-24)/6 from which we can define f(x)=x^4 -(d+36)x^3/6 +(d+11)x^2 -(11d-24)x/6 +d and based on this, f(1)=10 f(2)=20 f(3)=30 f(12)+f(-8)-19000 =-608(d+36)/3 +208(d+11)+2d+2(24-11*d)/3 +5832 =840
June 10, 2013

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 ...
June 10, 2013

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
June 10, 2013

maths
Use FOIL to expand (x+1)(x+2) =x²+2x+x+2 =x²+3x+2
June 10, 2013

maths
Does (x+1)3 stand for (x+1)³ or 3(x+1) ?
June 10, 2013

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
June 10, 2013

Hello? My math question was ignored?
See http://www.jiskha.com/display.cgi?id=1370816233
June 9, 2013

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 ...
June 9, 2013

Algebra II
There are infinitely many of them. Are you given a list of choices?
June 9, 2013

Math
Let ω=angular velocity (rad/s) To offset gravity, the centripetal force must offset gravity, g, or rω²=g Solve for ω.
June 9, 2013

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...
June 7, 2013

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)
June 6, 2013

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
June 6, 2013

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...
June 6, 2013

Calculus
Volume of pyramid =area of base * height /3 For a square base of side s, Volume =(s²h)/3
June 5, 2013

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
June 5, 2013

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...
June 5, 2013

maths
Do you agree with the following response? http://www.jiskha.com/display.cgi?id=1370323034
June 5, 2013

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.
June 4, 2013

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
June 4, 2013

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 ...
June 4, 2013

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 ...
June 4, 2013

math 7
experimental probability = (no. of successes) / (total number of trials) =8/20 =2/5
June 4, 2013

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 ...
June 4, 2013

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 ...
June 4, 2013

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 ...
June 4, 2013

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 ...
June 4, 2013

Math
Let O = centre of circle Γ, then ∠PAO=90°
June 4, 2013

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
June 4, 2013

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 ...
June 3, 2013

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
June 3, 2013

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
June 3, 2013

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 ...
June 3, 2013

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
June 3, 2013

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&...
June 3, 2013

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 ...
June 3, 2013

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....
June 2, 2013

To Sarah: please do not multiple post the same question
Sorry for having misspelled your name.
June 2, 2013

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 ...
June 2, 2013

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.
June 2, 2013

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)
June 2, 2013

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...
June 2, 2013

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
June 2, 2013

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
June 2, 2013

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) =...
June 2, 2013

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
June 2, 2013

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...
June 2, 2013

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
June 2, 2013

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.
June 2, 2013

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...
June 2, 2013

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.
June 2, 2013

check math
Correct!
June 2, 2013

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...
June 1, 2013

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.
June 1, 2013

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.
June 1, 2013

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
June 1, 2013

programming
What have you done so far, and how would you like us to help? Can you show us your pseudocode?
June 1, 2013

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(...
June 1, 2013

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 ...
June 1, 2013

probability
Create the probability distribution for the random variable X (see other post), and sum probabilities of all outcomes greater than 7.
June 1, 2013

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)
June 1, 2013

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!
June 1, 2013

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-...
June 1, 2013

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
June 1, 2013

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...
June 1, 2013

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
June 1, 2013

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...
June 1, 2013

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:...
June 1, 2013

Algebra
Hint:Use the compound interest formula Future=present*(1+i)^n Here Future=40000 n=30 i=0.06 (6%) Solve for Present.
June 1, 2013

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 ...
June 1, 2013

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 ...
June 1, 2013

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...
May 31, 2013

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. ...
May 31, 2013

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