Wednesday
July 30, 2014

Posts by MathMate


Total # Posts: 10,590

Probability
I get 1.89 also. Not sure if there is a typo or I made a mistake.

Math
Subtract one equation from the other to get: R=M/2. If there is no such option, decide which answer to choose.

statistics
Calculate the Z-score: Z=(10-5.7)/1.8=2.39 Look up the normal distribution table for the corresponding probability for LESS than 10 years, subtract this probability from 1.0 to get the probability of service of 10 years or more. Table link: http://www.math.unb.ca/~knight/utili...

algebra
First problem is correct. A direct variation will have the y-intercept as zero, so it is in the form y=kx, where k is a constant. In other words, a direct variation is a straight line that passes through the origin. Q2 and Q3 are not direct variations, because the y-intercepts...

algebra
See other response.

maths
Area of triangle = bh/2 Medians meet at one third from the base, so h'=h/3. Therefore triangles with the vertex at G is one third the area of the whole triangle, or 27/3=9 cm².

Functions 11: Series and Sequence 2
Let the four terms be a,b,c,d, and be the common ratio. b=ar c=ar² d=ar³ a+b=a(1+r)=3 c+d=ar²(1+r)=4/3 (c+d)/(a+b) = r² = (4/3)/3=4/9 => r=√(4/9)=±2/3, assume 2/3 a+b=a(1+r)=a(1+2/3)=5a/3=3 => a=9/5 b=ar=6/5 c=ar²=4/5 d=ar³=8/15

math
in an equation y=mx+b where m=slope, and b=intercept. Compare with the given equation y=(2-a)x + a we conclude that m=2-a, b=a Can you figure what the slope and intercept are?

math
Dilation means expansion. If it is not mentioned about which point dilation occurs, it is about (0,0). In such a case (also the present case), dilation by a factor of k means multiply all x and y coordinates by k. For example, a point originally at (2,1) will be at (4,2) after...

math
See http://www.jiskha.com/display.cgi?id=1356729021

maths
Hint: Find the intersection of the two perpendicular bisectors, which gives the circumcentre O. The distance AO=r is the radius of the circumscribed circle. The circle with radius r, and centred at O will intersect AB and AC at B and C respectively.

maths
Hint: Find the intersection of the two perpendicular bisectors, which gives the circumcentre O. The distance AO=r is the radius of the circumscribed circle. The circle with radius r, and centred at O will intersect AB and AC at B and C respectively.

Statistics
Any customer who comes in is equally likely to spend over or under $30 at the store, since $30 is the mean of a normally distributed random variable.

statistics
Sorry, it should be for 25-30 operating batteries, I get about P(25-30)=0.084

statistics
Recall that if the following conditions are met, we can use a binomial distribution to model the situation: 1. there are only two possible outcomes (operating or not operating, i.e. a bernoulli experiment) 2. probability applies to all units observed, and does not change. 3. r...

Statistics
Use the multiplication rule if the dial settings are independent of each other. For example, if we have 4 independent dials each with 5 numbers, then we have 5 choices for each, and multiplication rule gives 5*5*5*5=625 combinations.

Algebra 2 ..
Both problems require to graph the vertex. 1. we know that the parabola passes through the following points: (0,0), (50,125),(100,0). Using the standard formula, where (h,k) represent the coordinates of the vertex, we have h=50, k=125, and the parabola is: y=a(x-h)^2+k=a(x-50)...

Math 8
e. none of the above.

Business Math
LIFO: last in first out. Date qty unit price total inventory Jan1 10 9 $90 $90 Dec. 5 10 $50 $140 Sold 7: sold 5 10 $50 $90 sold 2 9 $18 $72 FIFO: first in first out Jan1 10 9 $90 $90 Dec. 5 10 $50 $140 Sold 7: sold 7 9 $63 $77

maths
(16+20+Moshina)/3=19 Solve for Moshina.

All d subjects except Sanskrit nd IT
Angle α (in radians) subtended at the centre of a circle of radius R by an arc of length A is α = A/R radians = 180A/πR degrees Example: Arc = π/2 m Radius = 3 m Angle = (π/2)/3 radian =π/6 radian

chemistr - correction
The molality is then M mol /(1000 g/kg /( m -10 g)

chemistr
In scientific calculations, it is important to know how accurate you'd like your answers. If you see a number like 0.9864g/ml, it means 4 significant figures are expected, so you have to carry your calculations to at least 5 significant digits, and then round off to 4 for ...

math
To calculate the percentage, you would - divide part by total - multiply fraction by 100% - simplify For example, if you have 14 sums correct out of 20, then 14 is the "part", 20 is the "total", so - divide 14/20 = 7/10 - multiply by 100% : 7/10*100% - simp...

math (incomplete)
"mike runs for 5 of an hour " Please clarify 5 (what) of an hour, it could be 5%, 5 minutes, or one-fifth, ...

math
tom, chris, charls, TIM, lorra, lindy: please do not use different aliases. A[]B = A^B-(A+B) for 3[]4, substitute A=3, B=4, rewrite the equation as: 3[]4=3^4-(3+4)=81-7=74 You can do the same for 7[]9. If you wish, you can post your answer for checking.

ctu
Calculate the present value of the investments using the compound interest formula over the past 10 years, or n=120 periods (t) at interest rate of i=0.0384/12=0.0032 per period. The monthly payment P=$625 per period, and therefore PV = present value FV = (i.e. future value fr...

maths
Should read: y"=0+2sec(x)*(-1/cos²(x))(-sin(x)) =2sec²(x)tan(x)

maths
y=x+tan(x) y'=1+sec(x)^2 y"=0+2sec(x)*(-1/cos²(x))(-sin(x)) =sec²(x)tan(x) => cos²(x)y"-2y+2x =2cos²(x)sec²(x)tan(x)-2(x+tan(x)+2x =2tan(x)-2x-2tan(x)+2x =0

maths
There is no diagram posted, and not enough description to give a defined question. I am adding the following guesses. Check if they are correct. If they are not, post the complete description. AMB is a straight line such that AM=MB. Semicircles are drawn with AB,AM and MB as d...

maths
From the familiar sin(A+B)=sin(A)cos(B)+cos(A)sin(B), and sin(A-B)=sin(A)cos(B)-cos(A)sin(B) Add both equations to get sin(A+B)+sin(A-B)=2sin(A)cos(B) .....(3) But 2x=3x-x 4x=3x+x, so substitute A=3x, B=x into equation (3) and simplify to get your answer.

Calculus
Roll's theorem applies to a continuous interval. So to answer the question, you will first need to look for discontinuities in the given rational function. You will get the hint by searching for at what point(s) the denominator vanishes (i.e. becomes zero).

Math
Let x=mAB then mBD=x+1 Since mAB=5, we apply Pythagoras Theorem to get (mBD)²=(mAB)²+(mAD)² All of the measures are either know or can be expressed in terms of x. Solve for x.

maths
See Derrick's post: http://www.jiskha.com/display.cgi?id=1356307353

math
Will be able to provide help when we see the figure, or when the figure is described in detail.

math
Without log, you only have to multiply 1.0 by 0.9 as many times as need to get a product of 0.05. I get 0.052 after multiplying 28 times and 0.047 after multiplying 29 times. So the answer is between 28 to 29 doses.

math
7*7=49 8*8=64 So the square root of 51 is between 7 and 8, in fact, approximately 7.14. What is the integral part of 7.14?

Stat
Look up a normal distribution table, such as: http://www.math.unb.ca/~knight/utility/NormTble.htm Look up P(Z<2.35), which gives you 0.9906. We now need to subtract P(Z<-1.5) to get P(-1.5<Z<2.35). For this, we need to make use of the fact that the normal distribut...

French
Un beau travail! Je n'ai pas terminé la lecture, mais je vous conseille de vérifier certains aspects: 1. Le genre, ex. un beau-père. 2. sujet et objet, ex. quelque chose qui changeait... 3. les virgules, ex. et mon beau-père qui s'appelle ...

calculus
all sides infinite! There are no constraints, so there is no limit to the length of the sides.

maths --plse help me..
Look at the coefficients as 1 -3 3 7 They add up to 8, so x=1 is NOT a factor. Now change the sign of the coefficients of the odd powers (x^3 and x): -1 -3 -3 7 They add up to zero, so x=-1 is a factor. We do a synthetic division, or a long division to get: (x^3-3x^2+3x+7)/(x+...

algebra
From the coefficients of the equation, you would have to figure out that x represents the number of quarters, and y=number of nickels. The x-intercept means the number of quarters required if y=0 (no nickels used.)

Algebra
Let x=weight of ground pork in kg then 8-x=weight of ground beef. total weight = 8 kg therefore 5.50x + 4.75(8-x) = 5.10 * 8 Solve for x.

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?

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