Wednesday
April 23, 2014

Posts by MathMate


Total # Posts: 9,948

Algebra
The domain of all polynomials is real, i.e. (-∞,∞).

trig
The coefficients of sin(x) and -cos(x) are 1 and -1 respectively. We divide each term by the factor sqrt(1²+(-1)²)=sqrt(2) y=sinx-cosx => y=sqrt(2)[sin(x)*(1/sqrt(2)+cos(x)*(-1/sqrt(2)) Since cos(-π/4)=1/sqrt(2), and sin(-π/4)=-1/sqrt(2), we set a=3π/2, t...

math
Factorize using cos(x) as a variable: (2cos(x)+1)(3cos(x)-1)=0 Solve for cos(x).

Calculus
(a) 1. Find vectors AB and AC. 2. Calculate the cross product of ABxAC, which gives the normal vector to the required plane. 3. Form the equation of the plane. The components of the normal vector correspond to the coefficients of x, y and z of the equation of the plane. 4. Fin...

math
Multiply them out using the FOIL rule. When you get i², replace by -1. Using FOIL: F=1 O=-5i I=3i L=-15i²=15 Sum like terms: (1+3i)(1-5i) = 16-2i

math
Absolutely, thanks Reiny!

math
Probability of choosing 2 girls =(10/15) * (9/14) =3/7

algebra
Vertical asymptote is where the denominator of a rational function becomes zero. Assuming you made a typo and that you really mean: y = 4/(x-3) + 2 then the denominator becomes zero at x=3. The horizontal asymptote is what y becomes as x-> -∞ or x->+∞. Can yo...

math
If there is no typo, the solution is complex. (x-1)^2=-4 => (x-1)=±2i so x=1±2i

ALGEBRA
Assume upper case only, gives 26 letters. Add 10 digits, 1 space and 4 symbols. Total 26+10+1+4=41 possible symbols. Subtract the plate that has all spaces. This is a 7 part experiment each with 41 outcomes, so the total number of possible plates is N=41^7-1 =194754273880 I wi...

ALGEBRA
Try 7 times for the first, 7 times for the second 7 times for the third, the possibilities (3 independent trials each of 7 outcomes) is 7³=343.

math
3 red 5 yellow and 4 green. 1 red picked, leaves: 2 red 5 yellow and 4 green total 11 apples. What would be the probability of picking a yellow out of the remaining 11, of which 5 are yellow?

Math (need formula)
This is the same problem as a ball rolls down a board making an angle θ with the horizontal in t=2 seconds over a distance S of 1.3 m. We ignore the size of the ball, which can slow down the ball. Let g=acceleration due to gravity = 9.8 m/s² then a=acceleration down...

math
Set up the equations: 6H+7C=2500 1H+13C=2310 and solve for H (horce) and C (cow).

math
It could range from 730kg for a smart car to 2300 kg for a Cadillac de Ville. http://en.wikipedia.org/wiki/Smart_Fortwo http://en.wikipedia.org/wiki/Cadillac_Sedan_de_Ville

math
As posted, 14!/19*18*17*16*15=6402373705728000/19 but I think you mean 14!/(19*18*17*16*15) which equals 20180160/323 In any case, please check your problem for typo and parentheses. If you are posting a fraction, parentheses must be inserted BY YOU around the numerator and de...

math
Four people have different number of quarters and dimes. In order to make $1.85 without nickels, each must have an ODD number of quarters, namely 1,3,5 and 7, and the remainder made up of dimes. The total number of quarters is therefore 1+3+5+7=16

statistics
Normalize the variable for z=(X-μ)/σ=(67-65)/1.5=1.3333

algebra 2/help
10C2 = 10!/((10-2)!2!) x!=factorial x=x(x-1)(x-2)....(2)(1)

math 5th grade
$36 is the cost of pants, which accounts for (1-2/5)=3/5 of the total cost. So the total cost is 36÷(3/5)=60 If there are no sales taxes, he should get 100-60=$40 in change.

algebra
36x^2 + 60x +25 =(6x)^2+2*5*(6x)+5^2 Does that look familiar?

calculus
f'(x) should read: 16x^3-12x^2-70x+36 and f'(-2)=0 From there, you can find the other factors.

algebra
Try to start a new post for a new question. Sometimes these piggy-backed questions get forgotten. I will answer it this time. R is a function of x. So substitute 135 for x to get R=314.28*135 - 0.1*135²

algebra
Like terms are terms with the same variables raised to the same powers. 8x^5 - 7x^9-7x^5+ 8x^9 First groupe like terms and arrange in descending order = 8x^9-7x^9 + 8x^5-7x^5 Now the simplification =x^9 + x^5

geometry
Side of base = √64 = 8 cm Distance from centre to corner of base =8(√2)/2=4√2 Let h=height, h²=15²-(4√2)² =225-32=193 h=√193 = 13.89 cm approx. Volume =(64)h/3 =64*(√193)/3 =296.4 cm³ approx.

math
Can you please provide a definition of events A and B? Also, in (a) do you mean p(A|B) instead of P(A/B)? That is to say, probability of event A given B has happened?

Pre-Calc/Math
I think the parentheses are in the wrong place. It should probably read: (1-cos2x)/tan x = sin2x Again, split everything into sin and cos, and don't forget the identities: cos(2x)=cos²(x)-sin²(x) sin(2x)=2sin(x)cos(x) (1-cos(2x))/tan(x) =(1-(cos²(x)-sin²...

Pre-Calc/Math
One way to deal with identities is to convert every term to sin and cos: (sec x/csc x) + (sin x/cos x) =(1/cos (x))÷ (1/sin(x)) + sin(x)/cos(x) =sin(x)/cos(x)+sin(x)/cos(x) =2tan(x) =2/cot(x)

algebra 2
The reason you are not getting answers is probably because the question is not very clear. I assume the following: 1. The curved back wall is at the back of the auditorium, facing the stage. 2. There is no side wall, so the curved back wall joins the stage near the front at 40...

math
This is a hypergeometric distribution problem. Assuming that the tagged whales are subsequently randomly distributed in the whale population, we have population N, where N = (115/5)*100 = 2300 approximately. For more accurate estimations, use the hypergeomatric distribution an...

Algebra
Treat 11.443 as a fraction over 1: 11.443 -------- 1 Multiply both top and bottom by 1000: 11443 -------- 1000 which is then the required fraction.

Statistics
The .15% is the tail end of the probability distribution. Probability distributions are such that the total area is 1.0 from Z=-∞ to Z=+∞. For the normal distribution, Z=0 is at 0.5, which means that the probability of a variable falling above 0 is exactly that of ...

statistics
See your previous post with double answer: http://www.jiskha.com/display.cgi?id=1336949898

geometry
Yep, you got it, congrats! I hope you understand how it works. If not, feel free to post.

geometry
I guess you have not read this on Sunday: Standard equation of a circle with a radius of r and centre (x0,y0) is: (x-x0)²+(y-y0)²=r² Centre of circle: ((5-1)/2, (4+(-4))/2)=(2,0) Out of the four choices, there is only one that has a centre positioned at (2,0). (...

geometry
1. Centre is at (2,0) but (x+2)^2+y^2=5 has a centre at (-2,0) 2. radius is 5, so the right hand side should be 5^2=25.

geometry
Your answer is not correct. Please explain how you got (x+5)^2+(y+4)^2=100 as your answer. Hint: Centre of circle is at: ((5-1)/2, (4+(-4))/2)=(2,0)

geometry
I do not have the same answer as you. If AB is the diameter, the centre is located at the mid-point between A and B. The mid-point between A and B is ((Xa+Xb)/2, (Ya+Yb)/2)=(2,0) I do not know how you got -2 and 3 for the centre of the circle. Can you explain?

geometry
Standard equation of a circle with a radius of r and centre (x0,y0) is: (x-x0)²+(y-y0)²=r² Centre of circle: ((5-1)/2, (4+(-4))/2)=(2,0) Out of the four choices, there is only one that has a centre positioned at (2,0). (hint: refer to the standard equation of th...

MATH
p=probability of voting q=(1-p)=probability of not voting. Out of 5 adults randomly selected, the probability that exactly 2 voted is calculated according to the binomial expansion, C(5,2)p^2q^3 =(5!/(2!3!))*0.57^2*0.43^3 =0.258 (approx.)

math
Total number of marbles = 5+8+3 = 16 Marbles which are not green = 5+3 = 8 P(not green) = 8/16 = 1/2

math
55 mph= 55mph*5280 ft/mi * 12 in/ft /(60 min/h) = 58080 in/min Each revolution of the trailer tire travels a distance equal to the circumference of the tire =(13)*π inches Number of revolutions per minute =58080/13π =1422 rpm approx. Note: the answer is the same if the c...

math :)
You're welcome!

math
Volumes of pyramids above the cutting planes are proportional to the cube of the height. So the volume above the cutting plane at h/4 is V1=(3/4)^3*100=2700/64 in³ Volume above the 2h/3 cut is V2=(1/3)^3*100=100/27 in³ The volume between two cuts are therefore = V1-V...

Math
The volume of a sphere is (4π/3)r³ The shell thicknesses are: X=1", Y=2", Z=1" The proportions of volumes X, Y and Z are: X:Y:Z =(1³-0³):(3³-1³):(4³-3³) =1:8:55 Therefore weight of ball =(1*16+8*14+55*12)/(1+8+55) =788/64 =1...

Math
You're welcome!

Math
Out of the possible numbers (in the sample space), if you cannot represent both events (odd and even) by a single outcome, then the events are mutually exclusive. In this case, we cannot have a number which is both odd and even, so E and F are mutually exclusive. Events A and ...

algebra
Use P(1+r)^n Since interest is compounded quarterly, the interest rate has to be divided by 4 to get the quarterly rate. The number of periods (years) has to be multiplied by 4 to get quarters. P=500 R=(1+0.0425/4) n=12*4=48 So 500*(1+0.0425/4)^48 =830.41

statistics
Number of ways to choose 3 from each would be: n=11!/(8!3!) * 5!/(2!3!) out of total number of ways N=16!/(6!10!) Probability: n/N = 75/364

statistics
Among the 16, how many are from Atlantis and how many are from Zedonia?

factoring math
Use difference of two squares: -16sin^2a+81 =81-16sin^2a =9²-(4sin(a))² =(9+4sin(a))(9-4sin(a))

Math
Assuming 6-sided number cubes. Let the events A=throwing less than 6 B=one of them is a three Then P(A∩B) =|{(1,3),(2,3),(3,1),(3,2)}| / 36 = 1/9 P(B) =2/6 =1/3 Throwing less than six given one of them is a 3 is therefore the conditional probability of A given B, or P(A|B)...

Math 4
3 apples + 1 peach = 4 fruits. There are 10 fruits in the basket. What is the probability of picking (at random) one of 3 apples and 1 peach?

Calculus
f(x)=4x sqrt(1-x²) use substitution u=1-x^2 du=-2xdx ∫f(x)dx =∫(4xsqrt(u))du/(-2x) =-∫2sqrt(u)du =-(4/3)u^(3/2)+C =-(4/3)sqrt(1-x^2)^(3/2)+C

Algebra 2
9C9 =9!/(9!(9-9)!) =1

pre-calculus
f(x)=(1/3)x+5 g(x)=(1/3)x-2 can be interpreted as y=(1/3)x+5 y=(1/3)x-2 both of which are in slope-intercept form.

statistics
The same question was asked a few days ago and it appears in the "related questions" below. Here's a link to the question: http://www.jiskha.com/display.cgi?id=1336634629

ALGEBRA
We don't see the figure, so we don't know where to put the answers!

geometry
The area of a polygon of n sides with an apothem of a and side c is A=nac/2 For a hexagon, n=6, apothem=c*sqrt(3)/2 so Area=6*c*(sqrt(3)/2)*c/2 =3c²sqrt(3) In the given case, 96sqrt(3) = 3c²sqrt(3) Solve for c (length of side).

computers
Questions like this are generally not answered because we don't see any effort on the poster's part. If you are working on the problem and have a specific question, we'd be pleased to help.

statistics
What have you done so far?

Math
Assuming order of the toppings are not relevant, then you can order 7C4=7!/((7-4)!(4!)) Sundaes =35

math
Use conditional probability P(A|B)=P(A∩B)/P(B) P(B)=blue line = 0.6 P(N)=shot on net=0.3 P(N∩S)=on net & score = 0.01 P(B∩S)=blue line & score = 0.005 P(B∩S|B) =P(B∩S)/P(B) =0.005/0.6=0.0833 P(N∩S|N) =P(N∩S)/P(N) =0.01/0.3=0.0333

Programming with Eclipse
What have you done so far and what is your question?

Analytic Geometry
Given two planes: Π1 : Ax+By+Cz+D=0 and Π2 : ax+by+cz+d=0 The following uses the notation that <a,b,c> represents a vector with three components. The normal vectors are: N1 : <A,B,C> N2 : <a,b,c> If Π1 is perpendicular to Π2, then N1.N2=0 (dot-pro...

Math
Each minute, Lisa will shovel 1/45 of the driveway, while Bill will shovel 1/65 of the driveway. Together, each minute they will shovel (1/45+1/65) of the driveway. They will take 1/(1/45+1/65) minutes to shovel the whole driveway. Note: the answer is between 26 and 27 minutes.

math
"represents t, the time in seconds, as a function of l the number of laps" means that l is the independent variable, and t(time) is the dependent variable. Therefore you only have a choice between A and D. Choose the one with the correct relation.

Math
If you have not done the geometric distribution at school, you need to read up about it before. I agree that it is not obvious if you have not done the distribution before, or if you have not done summation of geometric series before. In my calculations above, P(1) is the prob...

Math
The geometric distribution gives the probability of getting a success at the xth trial: P(X=x)=Px(x)=(1-p)^(x-1)p The probability of getting the first success in n trials is therefore the sum of the above, or P(n)=Σ(1-p)^(n-1)p =pΣ(1-p)^(n-1) (geom seq.) =p(1-(1-p)...

geometry
Correct. I get P(C\T) (probability inside circle minus triangle) =(Ac-At)/Ac =81.92/113.1=72.4%

geometry
All right-triangles inscribe in a circle with a diameter equal to the hypotenuse. Therefore for the 30-60-90 triangle, the radius of the circle is 6 inches, and the short side is also 6 inches. The height is 6sqrt(3), so the area of the triangle is At=36sqrt(3)/2 = 18 sqrt(3) ...

math
If he takes out 8 marbles, they could be 4 blue and 4 green. So how many does he need to make sure there is one of each?

ALGEBRA
The question is best answered with a Venn diagram. Start with those that use all three. 14 use A & B, so 14-3=11 use A & B but not C. 8 use A & C, so 8-3=5 use A & C but not C. So those who use A only A only = 36-(11+3+5)=17

ALGEBRA
A & B but not C = A&B - all three = 19-9 =10

SQL
Many Access SQL tutorials are available online. Here's one of them: http://www.lynda.com/Access-training-tutorials/140-0.html?utm_source=google&utm_medium=cpc&utm_campaign=Search-Biz-Access&utm_content=PxYWfEX1&utm_term=%2Baccess%20%2Btutorials&gclid=CLbZy_HK9a8CFasBQAod8W...

algebra 2
y=x^2+2 -4x-y=10 y=-3x^2+x-2 y=-5x+3 Both systems have no real roots. If you graph the two curves, they do not intersect. If you are interested in complex roots, eliminate y by comparison and solve for x. Substitute x into the equations to find y.

Math
The two draws are independent. So the probability of getting a yellow in both bags is the product of the probability of getting a yellow in each bag. P1(Y)=3/12 P2(Y)=5/15 So P(Y,Y)=P1(Y)*P2(Y)

Math
Use the intersecting chord theorem: When two chords cut each other into p1,p2 and p3,p4, then p1*p2=p3*p4. In the given case (42/2)(42/2)=4.8(2R-4.8) Solve for R.

math
Try using the standard form: a^2-b^2=(a+b)(a-b) and noting that 9x^2-16 = (3x)^2 - 4^2

math-permutuation
First digit is even: 4 choices (assuming zero is excluded) Last digit is odd: 5 choices Eight digits remain for the second digit, and 7 for the third (no repetition). Total=product of all four numbers.

Math
Between 1 to 8: C: {4,6,8} composite. So P(C)=3/8 O: {1,3,5,7} odd. P(O)=4/8 P(C,O)=P(C)*P(O)=3/16

algebra
Put it in the form: y=ax^2+bx+c if a>0, then it's a happy parabola (opens up) if a<0, then it opens down (sad).

Calculus
If you notice that the Taylor's series expansion of e^(-x/4) = 1-x/4+x^2/32-x^3/384+x^4/6144-... is exactly the given series less the first term with x=1, so the given series is e^(-1/4)-1 = -0.2212 to four places. If you sum term by term, you just need to sum until the ne...

math
Do you just want the answer or you think you can work (or start to work) along the lines of your previous problem? http://www.jiskha.com/display.cgi?id=1336497331

math
Difference =($2.50 per basket)(125 baskets)(4 shifts per week)(4 weeks) =$2.50*125*4*4 =$5000

Calculus
From 4x + 5y – 3 = 0 Divide all coefficients by sqrt(4^2+5^2) to get 4x/sqrt(41) +5y/sqrt(41) - 3/sqrt(41) = 0 where 3/sqrt(41) = length of normal cos(θ)=4/sqrt(41), and sin(θ)=5/sqrt(41) Note: the normal form is given by: x cos(θ) + y sin(θ) - p =...

Maths
Answering by logic and mental calculations: Since the order of digits is not important (they will be reversed anyway), the only two-digit combinations that add up to 15 are (8,7) and (6,9). (8,7) does not work because 87-78=9. Now try 96-69=27, which is obviously the answer.

Maths(permutation)
As I indicated, this is a trick question. I have assumed that not all five books need to be distributed because the question says the teacher "prepares" 5 books, and any student can take "one or no book". It did not say he "distributes" 5 books. T...

Maths(permutation)
This is a tricky question. The teacher prepares 5 books for 7 students, but did not say that all five books HAVE to be distributed. So my interpretation is that 0 to 5 books could have been distributed. For the case of 0 book distributed, there is only one way: no one gets any...

Math
Normalize 515 and 585, namely z(515)=(515-550)/35=-1 z(585)=(585-550)/35=1 The percent is the difference of probabilities of one-tail z-values between -1 and +1. It should be a little less than 70%.

c programming
Here, we do not write complete programmes for you. We can give help in debugging, design, or answer specific questions. Here, you can create a 2-d array and work accordingly. Be sure to check for off-board indices to avoid memory errors. If you need help with your pseudocode o...

Geometry
A hexagon has six sides, so n=6. Use the formula given in: http://www.jiskha.com/display.cgi?id=1336457737

Geometry
Area of a polygon with n sides is given by Area = na/2 where n=number of sides of polygon a=apothem. For a triangle, n=3.

math probability
I assume you mean that it is a fair spinner (i.e. it stops at any position with equal probability) but the sectors of the spinner are of different sizes. In this case, the probability of it stopping on "a" is the sector angle of a (in degrees) divided by 360. If it i...

Calculus
F.PA=<5,10,10><6,5,1> =5*6+10*5+10*1 =30+50+1 =81

Calculus
Most books write vectors as <x,y,z> to differentiate from a point (x,y,z). You would separate the work done by P along the two lines (vectors) OP and PA. The force is 15N along <1,2,2>. Since <1,2,2> is not a unit vector, we need to normalize it as <1,2,2&...

Calculus
Work done by a force F along a vector P is F.P (dot product). So total work done is F.P + F.A where A=<1,-3,4>, P=<7-1, 2-(-3), 5-4> and F=15<1,2,2>/sqrt(1^2+2^2+2^2)=<5,10,10> The division by sqrt(...) is required to normalize the direction vector to a...

math
Work in tiers. If sales exceed the first tier: commission 30000*3%=$900 Subtract the first tier and calculate on the next: 130000-30000=100000 All of it goes on 7%, so 100000*5%=$5000 So he gets $5000+$900=$5900 in commission.

geomety
You're welcome!

geomety
Let x=east, y=north, x-component of velocity = 35 y-component of velocity = 8 Magnitude=sqrt(8^2+35^2)=sqrt(1289)=35.9 mph. approx. direction: θ=tan-1(35/8) direction=NθE

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