Saturday
April 19, 2014

Posts by MathMate


Total # Posts: 9,948

Statistics
Convert to z-score using (X-μ)/σ where X=89 or 121, σ=15, μ=105. Look up normal distribution table to find probability enclosed between these two z-scores.

geometry
The sum of exterior angles of all polygons (including triangles) is 360° Can you find the third exterior angle?

maths --plse help me..
L(ab): (0,-1,-1)+(4u,6u,2u) L(cd): (3,9,4)+(-7v,-5v,0) If they intersect at P, then corresponding x,y,z values match, hence 2u-1 = 0 => u=2.5 where P=(0+4*2.5, -1+6*2.5, -1+2*2.5)=(10,14,4) For line L(cd), we have P(3-7v, 9-5v, 4+0v) => 3-7v=10 => v=-1 or 9-5v=14 =>...

algebra
Andrea, which continent are you on? In USA, 1 billion = 10^9, and I think in UK and France, 1 billion = 10^12. This makes a big difference.

algebra
Formula for continuous interest: A=Pe^(rt) take log on both sides and solve for r: r=ln(A/P)/t where A=4300000000,P=0.93,t=1000 You should get around 2.2%, ASSUMING banks do not round interest deposits to the nearest cent. If they deposit interest every two months and round th...

maths --plse help me..
p/p=1

maths --plse help me..
By symmetry, we conclude at least one solution is x=y=z. Assume p=x=y=z, then 1/p^2=p/p+1=2 Can you solve for p?

math
We know that 3*3=9 4*4=16 so square-root of 11 is between 3 and 4. Can you now choose the piece from which to cut?

math
Let the smaller even integer be n. The larger is then n+2. The problem says "smaller added to five times the larger is 58" which translates to n+5(n+2)=58 Solve for n (smaller even integer)

Mathmatics
First simplify given expression 2a+6b-3(a+3b).... first remove parentheses =2a+6b-3a-9b .... group like terms =2a-3a +6b-9b .... sum like terms =-a-3b =-(a+3b) Square expression [-(a+3b)]^2 .... ^2 means raise to 2nd power =(-1)^2 (a+3b)^2 =(a+3b)^2 .... use identity (x+y)^2=x...

math
We have a cube of 6 cm broken into 216 cubes (of 1cm cubed), meaning each face is divided into 6x6=36 small squares. The interior cube that has no paint therefore has a size of 4 cm cubed, or 64 cubic cm. The cubes that have paint on two sides would be the middle four along ea...

annual interest
12000*0.05=600 12000*0.07=840 Proportion at 5% = (840-760)/(840-600)=1/3 Proportion at 7% = (760-600)/(840-600)= 2/3 (or 1-1/3=2/3) (1/3) of 12000 = 4000 at 5% (2/3) of 12000 = 8000 at 7%

math
For each large print, he sells small prints. For the three prints, he makes 45+2*20=85$. Rent = 510 He must sell 510/85=6 sets of three prints, or 6 large and 12 small prints to break even.

Discrete Mathematics
Think of the case of 4 people for 3 different posts, and if any one person can hold zero, one, two or three posts. There are 4 choices for the president, 4 choices for the secretary, and 4 choices for the treasurer. Invoking the multiplication rule, there is a total of 4×...

Physics
The package was released 82 m above ground. With no air resistance, and acceleration due to gravity = 9.81, time it takes is 82 = (1/2)gt² t=sqrt(2*82/9.81) = 4.089 s. During this time, the helicopter has travelled 96 m horizontally, therefore Velocity of helicopter = 96/...

Math
Normalize! Calculate Z=(X-μ)/σ where Z = Z score found in standard normal distribution tables X = value of random variable, the diameter of 5.45 inchs μ = mean diameter of population, 5.52 inches σ = standard deviation of population, 0.46 inch. Look up a stan...

algebra
First step: divide each equation by the common factors, i.e. first equation by 7, and second equation by 5. x + y = 11 4x- y = -7 Afterwards, use elimination to solve for x and y. Hint: there will be fractions in the answers.

math calc 2
Hint: Think of the difference in potential energies of the initial and final positions of the chain.

DBU
Z=(28-μ)/σ Look up the standard normal distribution table and look at the percentage for the left tail.

statistics/probability
Expected winning can be found by summing over all possible outcomes the product of winning and the respective probability. For outcome HH: winning=0.25 probability = 0.25 prodcut = 0.25*0.25=0.0625 Repeat for the 3 other outcomes, and add the 4 products together to get the exp...

calculus
"The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares." means that z=2y but since y=2sqrt(1-x^2) (on the circle), so z=2sqrt(1-x^2) For example, at x=0, z=1, at x=1, z=0. The volume of the solid is then ∫∫∫dx...

Geometry
It is a quadrilateral.

HELP A.S.A.P. PLEASE: linear programming-maths
The objective function in this case is to calculate the profit. s=number of squash rackets (made and) sold. t=number of tennis rackets (made and) sold. From "The profit on each tennis racket and squash racket is $7 and $9 respectively" we can say that the objective f...

Geodetic Survey
Unless you're very experienced in the area, it would simplify your thought process by drawing a diagram as described by the question. Here is more or less what you should have: http://imageshack.us/a/img441/9503/1347673609.jpg You will need to solve for the height H using ...

Help with Calculating Probabilities
You can review your teacher's class notes, and the textbook, which should be self-explanatory. You are probably stuck with notations, which are usually described at the beginning of the notes or textbook. Probabilites are numbers between 0 and 1, and represent the likeliho...

Linear Algebra :)
You're welcome!

Linear Algebra
The normal to this plane is normal to both lines, so the cross product of the direction vector of these lines will be the normal to the plane. Finally, find the equations of the plane passing through each of the given points. Both of them should give the same equation, otherwi...

STATISTICS
"a grade less than 58 and greater thAN 110 " No student will receive this grade! Seriously, you probably mean "a grade less than 58 or greater thAN 110 " What can be done is to calculate the percentage of students who receive X, where 58≤X≤110. Given ...

math
Hint: Since all the choices are independent, use the multiplication rule.

algebra 1 stat question
The maximum value is 70, which is (70-37.7)/14.01=2.3 standard deviations above the mean. You can calculate similarly for the smallest value of 15.

algebra 1
See response to: http://www.jiskha.com/display.cgi?id=1347171948

Linear Algebra :)
You're welcome!

Linear Algebra
To find the vector equation of M1, we need to find the direction along which it is moving, which is given by the difference of coordinates of B and A: BA=<7-(-3),10-(-10),-10-10> =<10,20,-20> We know that the speed (magnitude) is 3 m/s, so we normalize the directio...

Calculus
Hint: Rational functions (where the denominator is a polynomial) have discontinuities when the denominator vanishes (=0). This is where we find vertical asymptotes.

math
Assuming no loss in the cutting, how would I would cut 3 strips of 32 cm long, each subdivided into 8 pieces of 15 cm wide. This will take care of 24 pupils. For the remaining 4 students, we cut in the direction, giving an extra length of 30 cm. with some waste. The total leng...

math
The worst case is if you took out 34 brown, then 1 red, and 1 blue. After that, any colour goes! Can you work that out?

c/c++
Fun problem, a little different from most other standard ones. 11*24*23*22*21*20 12*25*26*27*28*19 13*14*15*16*17*18 Like that? You can iterate through with two variables, i,j so that if i=j, you switch directions. (note: C/C++ arrays are zero-based).

Math :)
You're welcome!

Math
We will assume that train A goes west at 72 km/h, and train B goes east at 54 km/h. We further assume that at time t=0, the two trains meat head to head, with the stationary observer at the head of train B, i.e. the engineer of train B. In 18 seconds, train B would have gone e...

Math
Hint: Distance = speed * time They have to have consistent units.

Math
The relative velocity between the two trains is 54+72=126 km/hr. The 18 seconds would be equivalent to the time it takes a train at 126 km/hr to pass a (stationary) lamp-post. Can you work out the length of the fast train? Hint: It's more than half a km long.

Programming in Python
Here's a tutorial with examples on Python input/output. http://docs.python.org/tutorial/inputoutput.html Study them and code accordingly. If you have difficulties, post your code for help.

Diff Eq
Differentiate y(t): y'(t)=3*2te^(t^2) = 6te^(t^2) Given y'(t)+p(t)y=0 => p(t)=y'(t)/y(t)=-2t The original DE becomes y'(t)-2ty(t)=0 If y(0)=y_0, then y'(0)-2(0)y_0=0 which is always true irrespective of the value of y_0, since y'(0)=6te^(t^2)≡0...

math
100 choose 4, or C(100,4) where C(n,r) is defined as C(n,r)=n!/[r!(n-r)!] Think of choosing the first number out of 100 choices. We can choose the next number from the remaining 99 numbers, then 98, then 97. By the rule of multiplication of a multi-step experiment, we have 100...

Computers
It appears there is a "write-lockout" command in the firmware. For more details, see: http://en.wikipedia.org/wiki/Floptical

math
Hint: Slope between two points = (Δy)/(Δx)

math
A vertical line has the form x=k, where k is the x-coordinate of all points on the line. The given point has an x-coordinate of 23, can you figure out the equation of the vertical line?

Maths
Looking from the side, the cylinder has an outline of a rectangle, of height 2x and width x. Since the cylinder is half-filled, at the point water touches the brim, there is as much water in the cylinder as there is air. So the water level divides the cylinder into two equal p...

Discrete Mathematics
a. C(n)=16+4n C(1)=16+4(1)=20 C(2)=16+4(2)=24 ... C(5)=16+4(5)=36 b. C(50)=16+4(50)=? c. 50 ∑ C(i) i=1 50 ∑ 16+4i i=1 16(50)+4sum(i) =800 + 4[ 50(1+50)/2 ] = 800+4(1275) = 5900

Math
Quadratic functions that have given x-intercepts x1 and x2 are given by the equation: y=a(x-x1)(x-x2) If a>0, the curve opens upwards, and if a<0, the curve opens downwards. |a| can be any value ≠0 depending on the location of the vertex or any other point on the curve.

Math
Standard quadratic function with given vertex (h,k) is given by: y=a(x-h)²+k where a can be found by substituting the values of any given point on the curve. Here, h=-2, k=5, so y=a(x+2)²+5 Now substitute x=0, y=9 and solve for a.

math
It is possible if we neglect the rounding of the cents. Ratio of prices is 1:2:4, and 1+2+4=7 So the prices are: $100*(1/7), $100*(2/7), $100*(4/7), or $14.29 $28.57 $57.14 Note that $14.29 has been rounded up half a cent, so $14.29>($28.57/2)

math
You're going to find the fifth root of 0.035? First, use the calculator. If you don't have one, calculate: Set x0=0.2 calculate x1=x0-(x0^5-0.035)/(5x0^4) Start with x0=0.55, and calcuate x1. Repeat by replacing x0 by x1 until the number stabilizes to the accuracy you ...

statistics
z-score = (X-μ)/σ μ=mean σ=standard deviation X=value of random variable (600)

physlcs
Acceleration has a unit of m/s². from 0 to 18m/s in 3 minutes</> is the same as 0 to 18 m/s in 180 seconds, which translates to 18m/s / 180 seconds or 0.1 m/s² A bicycle does better than that, haha!

Maths
Hint: Volume = area of base * height Knowing that 1 ml. of water occupies 1 cm³, then 400 cm³ = 40 cm² * height Solve for height.

Math
He needs to make 80%, so if he misses (100-80)=20%, he still passes. What is 20% of 35 items?

Math
Hint: cos(θ)=adjacent/hypothenuse (CAH)

Math
a number which is an easy multiple of 42 and less than 4452.

Math
4452-4200=252 (42*100=4200) 252/42=6 So the quotient is 100+6=106.

math
1.5*IQR=(49-28) IQR=21/1.5=14 So Q3=Q1+IQR=42 However, the median and Q1 should be recalculated after the outlier is removed.

Physics
For part c, you put average speed as 0.05 km/min, which is correct. Subsequently, as part 2 of (c), you did put average velocity as 0. Perhaps there was a confusion of the questions.

Physics :)
You're welcome! Yes, velocity is a vector, so it is described by the magnitude (speed) and direction. The same goes for displacement, which is also a vector, and therefore is described by the magnitude and direction. Keep up the good work!

Physics
(a) we usually express car speeds in km/hour (b) Displacement = 10.3 km in direction 25° S of east Time = 18 min = 0.3 hour So velocity = 34.3 km/hr in direction 25° S of E. (c)Correct.

math
2*5280 = ?

Physics
Use the equations: S=vi*t + (1/2)gt^2 For 1st ball: 20=0+(1/2)gt^2 => t=sqrt(40/g) For 2nd ball: 20 = vi*(t-1) + (1/2)g(t-1)^2 vi = [20-(1/2)g(t-1)^2]/(t-1) =(20-(9.81/2)*(t-1)^2)/(t-1) =14.62 m/s downwards

calc 3
Trouble-free way to get resultant: resolve into x- and y-components and add. Wind is FROM N45W, which means that its direction is S45E. Take East = x, and North = y, the wind vector is then <40sin(45),40cos(45)> The velocity vector of the plane is <200sin(60),200cos(6...

Math
Ratio of 40% and 25% solutions to form a 27% solution = 27-25 : 40-27 = 2 : 13 To make 54 litres, we need 54*(2/(2+13)) litres of 40% and 54*(13/(2+13)) litres of 25% solutions.

math
When you add (i.e. never need to borrow), you can calculate the integer and fractional parts separately, and carry if necessary. Integer part: 8+5-5=8 Fractional part: 9/10 + 3/4 find common denominator (=20) 18/20 + 15/20 =33/20 = 1 13/20 Carry the 1 to give 9 13/20

Algebra..
1. given slope, passes through origin: y=mx here m=3/2 2. given x-intercept=a, y-intercept=b y=-(b/a)x + b here a=4, b=-3 3. Given point (x0,y0) on line and slope m: y-y0=m(x-x0) (x0,y0)=(3,2) m=2 (coefficient of x in given line) 4. Given point (x0,y0) on line, and perpendicul...

math
Correction to one of the above lines: 12=a(0-24)(0+24)=-576a

math
x^2 means x squared, or x². If you just started with parabolas, it won't hurt to say what you've learned so far. Let's start over: We first assume the vertex of the parabola is at x=0. We know that y=0 at x=±24, or y=a(x-24)(x+24). We also know that y=1...

math
Take the vertex of the parabola at x=0. Then the equation of the parabola (opening downwards) is y=12-ax^2 where a is a constant to be found. We know that y=0 at x=±24 (half span), so 0=12-a(24^2) => a=12/576=1/48 The equation of the parabola is therefore y=12-x^2/48...

Calculus
a. The conditions that f(x) must satisfy to have an inverse is: 1. f(x) must be a function 2. f(x) must be onto, i.e. ∀x ∈ dom f(x), f(x)=f(x1) <=> x=x1 condition 2 implies that f(x) must be strictly increasing or strictly decreasing. This can be satisfied if...

math
"Nine parts of the first piece are equal in length to 3 parts of the second piece. " means that each part of the second ribbon is three times as long as each part of the first, which also means that the number of parts of the second ribbon is one-third of the number ...

Math
6 3/5 - 2 4/5 (Note: 3/5 is smaller than 4/5) =5 8/5 - 2 4/5 (borrow a whole) =3 4/5

Math :)
You're welcome!

Math
They are each 13 and 20 km from the starting point, at an angle of 44 degrees. Solve the triangle by the cosine rule which gives the distance between the two: c²=a²+b²-2ab cos(C) where c=distance between bikers a=13km b=20km C=44°

trig
My calculator says sin(70°)=0.93969262

Algebra 1 or 2
Assuming no parentheses are missing, i.e. the question actually means: ((5x)/4) + (1/2) = x - (1/2) x=2 is not correct. To solve: (5x/4) - x = -(1/2) - (1/2) x/4 = -1 can you finish the solution?

Math
(A) x=13/4 means that the equation is valid only at x=13/4, and is not valid elsewhere. Would that be an identity or a conditional equation? (B) There was an arithmetical error on the last line: -7x+21+4x = 21-3x +21-3x = 21- 3x So after cancelling, we get 21=21 Would that be ...

Computers
dptr = new double*[5]; // creates 5 rows for (int i = 0; i < 5; i++) dptr[i] = new double[3]; // creates 5 columns for each row. // use the free() function to release memory

math
Calculate $1500*14% =$1500*0.14 =$210

math
If there is no typo in the question, the number of females is 3000-70=2930. If the number 70 is meant to be 70%, then the number of females is 3000(1-0.7)=?

Math
If the requirements are complete, I also found 19 candidates. So supply the complete list as your answer as instructed.

Math
See: http://www.jiskha.com/display.cgi?id=1346396105

calc 3
Think of two points in space. The set of all points equidistant from the points is therefore a plane that separates the two points, right in the middle. Also the line joining the two points would be perpendicular to the plane. The mid-point between the two points would evident...

Adding & Subtracting Expressions
Distributive property: ac + bc = (a+b)c a=8.5 b=1.3 c=m Substitute.

math
Using system of equations: E=number of cartons of erasers P=number of cartons of pencils 5E+7P=85 E+P=15 Solve for E and P. Easier: We know E+P=15, so directly write 5E+7(15-E)=85 Solve for E and then find P=15-E. Even easier, do it mentally: 15 cartons of erasers cost 5*15=75...

statistics
This problem has the following characteristics: 1. Number of trials is fixed (25) and known. 2. The probability of success is constant (0.9) throughout the trials and known. 3. The tests are independent 4. Each test is Bernoulli (i.e. true/false, 0/1) These criteria indicate t...

algebra
See: http://www.jiskha.com/display.cgi?id=1346371677

Math
22n-1 = (2³)-n 22n-1 = (2)-3n By comparison, 2n-1 = -3n Solve for n.

algebra
It would be similar to the thermometer problem: http://www.jiskha.com/display.cgi?id=1346371286 Take the goal and add or subtract the variations to get the upper and lower limits. Try it and post your answer for a check if you wish.

algebra
If it reads 28°F, and it cannot be more than 1.2° from the ambient temperature, then the range is between (28-1.2)°F and (28+1.2)°F

statistics
μ=100; σ=15 What is μ+2σ?

statistics
Z-score = (X-μ)/σ =(75-60)/15 =1 Look up normal distribution tables to find P(Z≥1)=0.8413 So 15.87% of students have better scores than 75%.

Math
Just add as though they are decimal numbers. Remember to carry only when the digit sum exceeds 15 (when there are no more hex digits). Here are the hex digits Hex decimal value 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 A 10 B 11 C 12 D 13 E 14 F 15 (note: decimal digits can also...

Math
Hexadecimal numbers are not binary numbers. The digits are {0-9,A-F} while binary numbers have digits {0,1} only. To add two hex numbers, line up numbers and add digits just like decimal numbers, except that when the sum is below 16, use the hex digits. When the sum is above 1...

Math for liberal arts
How you add or multiply hex numbers have been explained in response http://www.jiskha.com/display.cgi?id=1346358289 If you need further explanations, post a follow-up to the response, explaining where you need more details.

math
You know that you expect to lose about 6% for any amount you played, assuming you played enough to be close to the expected value. How much is losing 6% of $130?

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