Wednesday
April 16, 2014

Posts by MathMate


Total # Posts: 9,948

math
If you suspect that the rule is a straight line, y=mx+b then find the slope using m=(y2-y1)/(x2-x1) Substitute m and (x1,y1) into the equation to find b. Verify that the rule applies to all the points.

mathe
Not familiar with how bonds work. Here's a try. Assuming the bond is issued for 30 years, then, and the current yield is x*100%. 1000=78.5(1+x)^30 1+x=(1000/78.5)^(1/30)=1.08852, or current yield is 8.852%

algebra
You can use the same reasoning as the answer to your previous post.

math
The roots p,q, of the equation ax²+bx+c=0 have the properties that: p*q = c/a p+q =-b/a Check each of the solution sets above, c/a=-3.5 If p*q ≠ -3.5, then p and q are not solutions to the equation. If p*q = -3.5, then check if p+q = -b/a=2.5. If both conditions are sa...

solve the equation - typo
We will use a lemma that states: logax = loga²x² The proof of the lemma is left to you as an exercise, if it was not already covered in your course.

solve the equation
Given log14x+49 - log196x = 1 We will use a lemma that logax=loga²=x² Since 196=14², we write above as log14x+49 - log14²x = 1 Then log14²(x+49)² - log14²x = 1 Rewrite using laws of logarithm: log14²(x+49)²/x = 1 Using the alternate...

math
Let A be the top of the pyramid, B = centre of pyramid at ground level P=position of first observation (angle=20 deg) Q=position of second observation (angle=10 degrees) Then PQ=189 feet and APQ is a triangle where APQ=10° AQP=180-20=160° Consequently PAQ=10 deg by ang...

ap calculus
Assuming the function is x(t)=(ln(t))^2 then t has a vertical asymptote at x=0. which explains why the domain of x(t) is set at x>0. To find the maximum, we need to find x'(t)=0 where x'(t)=2ln(t)/t and x'(t)=0 at t=1. Check if maximum or minimum by finding x&qu...

Calc
To find the absolute maximum of a function within a finite domain, you can do: find f'(x) and equate to zero to find the relative maxima and minima. In this case, f'(x)=0 at x=1 and x=3. By checking with f"(x) or otherwise, you will find that x=1 is a minimum, and...

question still incomplete
Please complete "the table".

Trigonometry
I am curious how you find the probability of divisibility of palindromes by 4 using the sine law. Can you kindly show your work?

Trigonometry
What is the probability, i.e. a and b?

Trigonometry
What is your answer? Did you use the sine law?

Not trigonometry
There are 900 5-digit palindromes, from 10001, 10101 , 10201, 10301, ... to 99899, 99999. Out of these 900 palindromes, divisibility is determined by the last four digits, namely 00, 01, 02, ...99. The probability of divisibility by 4 for digits of 00 to 99 is 1/4. So a=1, b=4...

incomplete question
It seems that you have been copying the question in a rush. It says the probabilities are given in a given table which you have not posted.

algebra 2
The function does not have rational roots, as it does not factor. If you graph the function, you will find approximate values (3 of them) of the real roots. One of them is positive, and two are negative. To locate them without graphing, you can find f'(x) and equate to zer...

job related
If the slope is 9 inches per foot (run), then the roof is 15" per foot run. I suppose rake factor is the ratio of roof length to rise, which works out to 1.25 in this case. The roof area (for one sloping face) is therefore (15"/9")*10'*30' long = 500 sq....

Math - correction
Correction in an intermediate step (only): ... =M((1+i)^n-1)/(1+i-1) =M((1+i)^n-1)/i

Math
Use the compound interest formula: P=$3690 i=0.21/12=0.0175 n=17 M=amount of monthly payment Amount after 17 months (without payment) = A(1+i)^n Value of his payments at the same interest rate =M+M(1+i)+M(1+i)^2+...+M(1+i)^(n-1) =M((1+i)^n-1)/(1+i-1) =M(1+i)^n/i Equate the two...

Critical Points
Inflection point at (2,3) means f"(2)=0 => f"(x)=6x+2a = 0 at x=2, or a=-6(2)/2=-6 Since f(2)=3 (from given point (2,3) ), we conclude that: f(2)=c+2b-16=3 or 2b+c=19 ....(1) We also know that there is a critical point at (1,5), so f'(1)=0, or b=9 Substituting...

Minimum on a Closed Interval
Note: -3/2 is not in [1,2], so it cannot be the correction solution.

Minimum on a Closed Interval
On a closer look, the first equation f(x)=1/(x sin(πx)) is undefined at x=1 and x=2, so probably not what you want. For equation 2, f(x)=(1/x) sin(πx) you would find f'(x)= (%pi*cos(πx))/x - sin(πx)/x^2 equate f'(x) to zero to find the minimum, and solv...

Minimum on a Closed Interval
Is the function f(x)=1/(x sin(πx)) or f(x)=(1/x) sin(πx) [ as written ]?

Geometry
If centre has (6,8) and one end of the diameter has (4,2), add Δx and Δy to the centre to get the other end of the diameter, namely, (Δx,Δy) = (6-4, 8-2) = (2,6) So the other end of the diameter would be (6+2,8+6)=(8,14). Check: the mid-point of the dia...

math
It could be a rectangle (or any other shape). Use L and W to represent the length and width. Use the area and perimeter formula to construct 2 equations and consequently solve for L and W. The solution consists of integers.

geometrY!
Given: Let r=AE:EB Draw a diagram of the parallelogram ABCD. Insert E on AB. Extend DE to join CA at F. (The above is as given by the question). Examine the triangles FAE and DBE. Show that they are similar noting that FA is parallel to DB. Therefore the ration FE:ED = AE:EB S...

math
Correction: 4/52=1/13

math
Note: the above answer assumes no replacement of cards. If the question assumes with replacement, then drawing a queen from a full deck has a probability of 13/52=1/13. In a 4 step random experiment, the probability of getting a queen at each of the four steps is given by (1/1...

math
A standard deck of cards has 4 queens, one from each of the four suits (Spade, Heart, Diamond and Club). Therefore the event Q of drawing 5 queens does not exist in the sample space Ω. Therefore probability P(Q) of drawing 5 queens is zero.

Math
Assuming nobody shares the medals, 8 choices for the gold, 7 choices for the silver, 6 choices for the bronze. Use the multiplication rule.

Math
Use same method as the runners.

Math
1 inch = 25.4 mm (exactly) so 1/16" = (1/16)*25.4 = 1.5875 mm Can you round to the nearest 0.1 mm?

math
((x-12)÷ 7) + 23 = 32

math
Let the number be x. Difference of his number and x = (x-12) "divide the difference of his number and 12 by 7, and then add 23, the result is 32" (x-12)\÷ 7 + 23 = 32 Can you solve for x?

Computer
If you are using Windows 7, disk management is under: Control Panel -> Administrative Tools -> computer management -> storage -> disk management.

Allegbra
Use the quadratic formula to get a=-0.01 b=0.06 c=5.9 x=(-b±sqrt(b²-4ac))/(2a) 3±sqrt(599)

algebra 1
graphing tabulation substitution elimination comparison Cramer's rule Gauss methods inversion iterations (such as Gauss-Seidel method)

algebra
1. Expand expressions 9w+3=6w-12 2. Group like terms and isolate unknown on the left 9w-6w = -12-3 3w = -15 3. Solve for unknown. ... Can you take it from here?

Math
Fencing means putting up a fence around the perimeter. For a lot of 37.5 by 24.8, the perimeter would be 2(L+W)=2(37.5+24.8) linear metres. The height of the fence is not mentioned, so the answer should be in metres in length.

math
If you notice that numbers with the required property has two pairs of factors, for example, for 12, we have 2*6, 4*3. Which means that numbers divisible by 4 are more likely to have this property. Can you find them?

math
Check: Divide (-36) by 2 to see if you get back 18.

Math
Use the Gauss method: 60+61+62...+70+71...+80 80+79+78+..+70+69...+60 Add the two lines, you will get the sum 140 21 times. So half the sum is 70*21=1470.

calculus--please help!!
Hint: by definition H(x)=(fog)(x) = f(g(x)) what would be the appropriate functions f(x) and g(x) such that f(g(x))=(3x+2)^6?

FUNCTIONS 11
t(1)=-2 t(2)=5 t(3)=-10 ... Hint: compare 2,5,10,17,26 and 1,4,9,16,25.... The sign can be achieved by multiply by the factor (-1)^n

chemistry
Hint: again, start by balancing the "H".

chem
Hint: How many "H" is on the left side, and how many are on the right?

math
Hint: Can you find g if f(x)=x^6 ?

Information Technology (2 Qs)
Hints: 1. Cache is the fastest memory (aside from registers, which is not on the list). 2. By what data go from memory to the CPU and vice-versa? Does a human have access directly to the memory?

Math
Approximate a year to 50 weeks, with 12 miles each week, it would be 600 miles a year. 624 is within 10% of 600 miles, so it is reasonable that they job 624 miles a year.

statistics
There are 52 cards in a deck. There are 26 red suits, and 2 black kings for a total of 28 cards which are either red or a king. Can you find the probability?

math
4x^2-81 can be written as (2x)^2-9^2, then apply the identity a^2-b^2=(a+b)(a-b) to factorize the expression.

Math
The area of a square is the square of one side. So the length of a side is the square-root of the area, i.e. Side = sqrt(64x^2)=8sqrt(x^2)=8x.

design of rc structure
What kind of help do you need? Is the water tank in RC? Most water tanks in North America are in steel and supported over steel columns, which also gives resilliance when subject to earthquakes. 200kL is basically 200 m³. It could be a cylinder of 6.5m diameter by 6m high....

Probability
The problem satisfies the following conditions: -the experiment is a Bernoulli experiment (i.e. each trial has one of two outcomes) - the probability of each trial is known remains constant throughout the experiment - each trial is independent of the others. This indicates a b...

design of rc structure
Here are some ideas to investigate and comment. Working stress is generally more conservative. It does not take into account of the post-yield behaviour of the reinforcing steel. Ultimate stress caters to both strenth and serviceability requirements separately. If properly des...

Probability
I assume that each of the sixteen events has two outcomes of S, namely P(s1,s1), P(s1,s2).....P(s4,s4). By the multiplication rule, and assuming that the two outcomes are independent, we have P(s1,s1)=P(s1)P(s1)=0.5*0.5;=0.25 .... P(s4,s4)=P(s4)P(s4)=0.125*0.125=0.015625 Note:...

math
1. The closest is J, which should read (M-6)/3 2. a=b-2, then b-a=2 what should be (b-a)^4?

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.

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