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Posts by MathMate

Total # Posts: 12,086

statistics
This problem is the same as putting 6 items in 4 bins. Different ways of solving this problem would be: 1. enumerate in a systematic way: 0006 0015 0024 0033 ... 6000 and count how many you've come up with. Note that since the children are of different ages, and the gifts ...

Computer Science
Explanation of the pattern follows: ^a specifies the string begins with "a" b\$ specifies that the string ends with "b" d* allows 0 or more embedded d's. (cd+)* requires a "c" to be followed by at least one "d". This can happen 0 or ...

Computer Science
Try my $pat="^ad*(cd+)*b\$" Use this pattern to match strings according to the rules specified. Note that $pat will match a qualifying string, but does not define a string. Hope someone else can answer the second part.

math
Outer perimeter: 4s=4*10'=40' Spacing = 6" = 0.5'/plant Number required = 40'/0.5'/plant = 80 plants Since the perimeter is a closed figure, there is no need to add one "at the end" as in the case of a linear row with two ends.

math urgent please
Don't know if you paraphrased the question, but the question is indeed confusing. First it gave the length of 320 cm and width of 320/2=160 cm. So there is no variable to optimized. Then it talks about maximizing 4 faces, and then jumped to optimizing 3 faces. Finally, it ...

calculus - insufficient information
Unfortunately we cannot see fig 2c unless you describe it or send a link.

math
Since it is not stated in the question, we assume that the unit of f(x) is in feet. There is inconsistency with the two expressions for f(x), namely f(x)=(1/2)x²+(4/5)x, and later f(x)=(1/12)x²+(4/5)x Solving the first. If the second expression is intended, you can ...

physics
Average acceleration =(0-30) m/s ÷ 5 s = -6 m/s² Force = ma = 80 kg * (-6 m/s²) = -480 N (resistive force)

math
correct!

Physics
Stress = force/area 1. stres= 6.5*10^5 dynes / (π(0.3)²/4 cm²) = 9195619 dynes/cm² = 919.6 kPa Young's modulus nor strain cannot be derived from the given information. 2. Stress = force /area 10 kg * 9.8 m/s² ÷ (π0.004²/4 m²) = 7....

Chemistry
Use C1*V1 = C2*V2 For example, to dilute 100 mL of 36M solution to 6M, we put 36M *100 mL = 6M * V2 Solve for V2 = 36M*100mL/6M = 600 mL This means that the 100 mL of 36M solution must be diluted to give a final volume of 600 mL.

math
1. -f is the reflection of f about the x-axis. 2. f(-x)=f(x) => f(x) is even 3. f(-x)=-f(x) => f(x) is odd Good job! :)

math
Sum of squares = p²+(p+5)² =625 Expand p²+p²+10p+25=625 2p²+10p=600 p²+5p-300=0 (p-15)(p+20)=0 p=15 or p=-20, reject negative root The sides of the squares are therefore: p=15 p+5=15+5=20

statistics
A five-number summary represents the following qualifiers: minimum Q1 median Q3 maximum the interval minimum/median represents 50% of the data in the lower half. the interval median/maximum represents 50% of the data in the upper half. the interval Q1/Q3 represents 50% of the ...

Precedence rules for the algebra community
Precedence of operators In simple algebra, there is a set of precedence (priority) of operations that should be respected in order that everyone evaluates mathematical expressions in the same way. Although these rules have been taught in elementary school or junior high school...

physics
Assuming the mass of the object is negligible compared to the mass of the person and the boat, then the speed of the object is 30km/h in addition to the speed of the boat. Using a terrestrial frame of reference, the apparent speed of the object by a stationary observer on the ...

proportions
35' : 0.28 kg x' : 7.2 kg Cross multiply and solve for x x=35' * 7.2 kg / 0.28 kg = 900'

college algebra
typo: N = (x+5)*x²/(x+3) =(x³+5x²)/(x+3)

college algebra
First, observe the rule of operator precedence, i.e. BEDMAS (brackets,exponents, division/multiplication, addition/subtration) in that order. Q1. I suspect the expression should have been written as (x+5)/(x+3) to be interpreted correctly. Based on that, we know that the new ...

mathzzz want answer in simple way
Let x=number of rows, and since number of rows = number of persons per row, we have x*x=3249, or x=sqrt(3249) take out your calculator and find x.

math
Sum of angles of a quadrilateral = 360° sum of the other two (C & D) = 360-150=210 If C : D = 2:3, then C+D=210, C: C+D = 2 : 5 = 84 : 210 C=84, D=210-84=126 The first two angles (A & B) add up to 150, which could be A=100, B=50, or A=75, B=75, etc. Without additional ...

Math
Correct! Well done! :)

isu
mass (m) = density (ρ) * volume (v) = 1.46 g/mL * 59.9 mL = 87.5 g

Business Math
Assuming the investment is placed for exactly one year, then the future value is FV=Principal*(1+i) =2989(1+0.03) = $3078.67

math
markdown: 12% : $1.20 sale price : 100% : X Cross multiply and get sale price, X = 1.2*100%/12%=$100

Math
Probability of getting the first white sock out of 30 socks is 24/30 Probability of getting the second white sock out of the remaining 29 socks is 23/29 Since he needs a pair of white socks, both of the above events (steps) must succeed, for which the probability is the ...

physics
Convert values to consistent units: 66 mi/h = 66 mi/h *5280 ft/mi ÷ 3600 s = 96.8 ft/s similarly 55 mi/h = 80.67 ft/s acceleration = -14 ft/s² Time required=(80.67-96.8)/(-14) = 1.15 s Do not forget to add the reaction time, which could exceed the mechanical ...

Statics
The angles are not precisely specified. It is not clear whether the a-axis makes an angle of -20 (340) with the x-axis, or -160 (200) with the x-axis. Same problem for the force F. Could you specify forces and axes using the following conventions: 1. All angles are measured ...

Statics
So you have three forces, the magnitude and angles of which two are known. You will need to first compile a table of known and unknown values. To avoid confusion, you need to follow these rules for describing forces: 1. All angles are to be measured counter-clockwise from the ...

Statics
A description of the accompanying figure is required. Minimally, the directions of F1 and the magnitude of F2 are required.

Statics
If Pa and Fb are both 305N, then angles aOF and FOb are equal to 38 ° See http://www.twiddla.com/1746657 Since F*cos(38)=305N, F=305N/cos(38). You can work out the orientation of b from the figure.

math
Please proof-read your question. ># is meant for which symbol? To take the limit, x-> ?

math
If you divide the second equation by 2 and transpose terms to the same form as the first equation, you will find that the two equations are identical. This is a situation where the two equations represent coincident lines, hence there is an infinitely many solutions.

Logic / Discrete Mathematics
You're welcome! :)

Logic / Discrete Mathematics
With simple expressions like these, the easiest proof is to make a truth table...unless it is specifically prohibited in the question. Also, there are precedence in the logical operators, just like + - * ÷. see http://en.wikipedia.org/wiki/Logical_connective The ¬ ...

science, physics
The heat of fusion of ice is 79.8 cal/deg C. Let T = final temperature, and sum heat change = 0 8 kg (T-20) + 2 kg ((T-0)+(79.8))=0 cal-kg Solve for T to get T=+0.04 deg. C.

3D Modling
One of the ways is to download the (free) software, and get familiar with it through tutorials. This way, the question (and many others) will be answered.

Business/Finance
June: 30-6=24 July: 31 August:31 September:30 October: 8 Total=24+31+31+30+8=124 days Discount period: The period of time between the date a bill of exchange is drawn and the date on which payment is due. So discount period = 200-124=76 days

physics
Kinetic energy, KE = (1/2)mv² resistive force = constant Retaining half the velocity means (1/2)^2=1/4 of the kinetic energy. Since 50% of the KE penetrates 25 cm, so 25% of the (remaining) KE penetrates 12.5 cm.

physics
p(t)=3t²-2t+1 W Δp =p(4)-p(2) =41-9 =32 W

physics
Power =mgh/Δt / efficiency =100kg*10m/s²*10m/5s / 60% = 2000/0.6 = 3333 W = 3.33 KW Thank you for posting the answers, but there are too many decimal points that I cannot make anything out of them. In addition, (C) and (D) seem identical to me.

Physics
585 zag/zoyear =585 *(1/0.18) zig/ (0.4 years) =(585/0.18) zig / (0.4*365*24 hours) = 0.928 zig/hour

Engineering
Try http://faculty.uoh.edu.sa/m.touahmia/CE353-CH3.pdf

math
The distance between two points with coordinates P1(x1,y1) and P2(x2,y2) is given by the distance formula: D(1,2)=sqrt((x2-x1)²+(y2-y1)²)

Math
36 students B:G = 3:1 = 27 : 9 Add x girls, 27/(9+x)=9/5 Solve for x by cross multiplication.

algebra 2
|x|-2≤-3 |x|≤-3+2 |x|≤-1 => x≤-1 or -x≤-1 => x≤-1 or x≥1 => on the number line: <------ -1.......0...... 1 ------>

Chemistry
The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

Chemistry
The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

algebra
* outcome 3 is "hit neither"

algebra
Calculate expected gain, E(X), of the venture. If E(X) is positive, it would probably be advantageous to sink a well. Expected value is the following sum: E(x)=Σ G(X)*P(X) where X is a possible outcome, G(X) is the net gain of the outcome, and P(X) is the probability of ...

computer science
Looks good to me!

algebra
To find the x-intercept, set y=0 and solve for x.

maths
You're welcome!

maths
Area of each triangular face = (1/2)base*height Surface area of tetrahedron = 4*area of each face.

Math
3768 grains mean 3768*1 second=3768 seconds. Convert to hours, minutes and seconds: 3768 seconds / 60 s/min. =62 minutes 48 seconds = 1 hour 2 minutes 48 seconds. The other rewards may be worked out in a similar way.

math
4C3(1/2)^3(1/2)^1 =4(1/16) =1/4

math
2=2^1 3=3^1 4=2^2 5=5^1 6=2*3 7=7^1 The least common multiple must have factors that satisfy all of the above: 2^2*3*5*7=420

math
Mid-point of (3,8) and (9,16) =((3+9)/2, (8+16)/2) =(6,12) Mid-point of (8,11) and (x,13) =((8+x)/2, (11+13)/2) =((8+x)/2, 12) To have the same mid-point, the x- and y-coordinates of the mid points must match. so (8+x)/2 = 6 Solve for x.

statistic
Total number of balls = 5+6+6=17 P(RR)=Probability of two reds =(5/17)*(4/16) P(WW)=(6/17)*(5/16) P(BB)=(6/17)*(5/16) Probability of two same coloured balls =P(RR)+P(WW)+P(BB)

math
You have assumed compound interest compounded monthly. Assuming these assumptions are correct, then we have total amount F, R=monthly installment deposited at the end of the month, i=monthly interest, n=48, I=1+i, F=R(I^(n-1)+I^(n-2)+...+I^(0)) =R(I^n-1)/(I-1) =500((301/300)^...

Basic Algebra
Also, note that factors must exceed 8, from the context of the question.

Basic Algebra
See http://www.jiskha.com/display.cgi?id=1408443950

Science
You're welcome! :)

Science
The independent variable is the amount of money offered, which in this case takes on only two values, $0 and $5. Evidently other experiments could be carried out to have varied incentives, assuming the teacher keeps the job long enough to do further experiments.

Applied Programming
Technically you do not need to ask for a 2D or 3D calculation because there is no overlap of the shape names. You will need a string of if-else-elseif-endif statements, or more conveniently a switch statement. Use the "default:" option in case the user feeds a wrong ...

chemistry calculations
It is given that the reaction at the given temperature is in equilibrium. Next check if the reaction is homogeneous: all gases, so homogeneous. Now denote the stoichiometric coefficients by a,b and c for the reactants and products respectively (all equal to 1 in this case). ...

Basic Algebra
This is more a riddle than math. In my opinion, it is hinged on the word "equally", which could mean equally to the dollar, or to the cent. Taking the first case: everyone has an equal number of dollars. Factoring 5130, we have as prime factors: 2,3³,5,19, which...

maths
If we assume that the ordered pairs (x,y) follow a linear rule y=ax+b, we will be able to solve for the rule using two of the ordered pairs, and use the third to check if the rule is appropriate. Thus, for the first ordered pair: y=ax+b => 14=180a+b .... (1) For the second ...

MAth
The question as it is has a large number of solutions. In general, optimization problems have an objective function, such as minimum cost, minimum surface area, etc. and subject to constraints, such as maximum number of fruits per box, or maximum sizes, etc. An example ...

Precal
Hint: look up triangle inequality. Basically, it says that the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the third side.

calculus
The diagonals are obtained by the sum and difference of the two vectors: a+b=<-2,5>+<3,2>=<1,7> a-b=<-2,5>-<3,2>=<-5,3>

Geometry
A plot of the three lines L1, L2 and L3 may be viewed here: https://imagizer.imageshack.us/v2/500x300q90/674/pUzIJX.png

Geometry
This problem is very interesting, and as Steve pointed out, there are 4 circles each of which is tangent to all three lines. This prompted me to look for a general solution for all four circles. If we first examine the condition of tangency of a circle C: (x-a)²+(y-b)&...

math
You're welcome! :)

math
When the perimeter of the triangle is doubled, it is 24. The perimeter before it is doubled is therefore half of 24=12. An equilateral triangle is a triangle with three equal sides. Perimeter = 12 Number of sides of an equilateral triangle = 3 Can you find the length of each ...

loyla
There is a black and a white ball left in the bag after pulling out the first. Can you find the probability of pulling out a black ball from a bag containing one black and one white ball?

physics
Use ratios, 15 g : 0.1 L 75 g : x L solve for x by cross multiplication.

physics
Let maximum velocity be x then x/α+x/β=t Solving, x=t/(1/α+1/β) =αβt/(α+β)

riddle?
Is this a question or a riddle?

Math: Equivalence Classes
To explain in more detail, we would investigate the relation: (a-2d)=(c-2b) Transposing terms, we get the same relation as (a+2b)=(c+2d) Hence all elements (a,b) in the equivalence class would have the same sum a+2b. For example, if the sum is 10, we can have 4 elements: (2,4...

Math: Equivalence Classes
If you haven't read the following link, you can read it before reading on: http://www.jiskha.com/display.cgi?id=1407879480 The idea of solving parts (a) and (b) of the linked question is to establish a methodical way to solve (c) and (d). The typical approach to solving ...

math
Area of a square = (length of each side)² If each side is measured in inches, the area is in square inches, or in².

statistics
Start with a table: R=rain (20%), ~R=no rain (80%) W=windy (30%), ~W=not windy (70%) If rain and wind are independent, the combined occurrence is the product of the respective probabilities. Example: (a)P(R∧W)=.2*.3=0.06 (b)P(~R∧~W=0.8*0.7=0.56 (c)... Will leave (c) ...

statistics
Total number of males =25+10+8=43 Total number of clients = 100 Selection is random. => Probability, P(M) = 43/100 = 0.43 You can proceed with the remaining questions in the same manner.

Math
As Reiny pointed out, the rings and chirps will occur at the same time every 6 seconds, or at 6, 12, 18, 24, 30, 36,.... seconds. So which of the 4 choices will be a moment where the two sounds will occur together?

math
Draw a diagram on paper according to the given information, and the answer will be on paper.

math
You don't have to solve each one, and you don't even need a calculator if you understand the following rules for integer calculations: Multiply: only odd*odd will give odd power: only odd to any power will give odd Add/subtract: only odd±even will give odd. Note...

phy
The few problems you have posted at the same time indicates that you are in the process of learning how to draw a free-body diagram (fbd). Follow your instructor's directions to draw a fbd and identify the triangle to be solved. You should end up with a right triangle in ...

Chemistry
Ammonia is NH3. The mass composition is the ratio of atomic masses (AM) within the molecule, i.e. mass composition of nitrogen =AM(N)/(AM(N)+3AM(H)) =14.0067/(14.0067+3*1.0079) =0.822 approximately.

ias question
If the question were "how do we write 13 aug 2014 in 5 letters without using numbers." then see http://www.jiskha.com/display.cgi?id=1400681438

math
The factor theorem helps us to say that the possible integral roots are in the form of (x±k), where k is a possible factor of the constant term (12) divided by a possible factor of the leading coefficient (1). Thus for the given problem, the possible integral zeroes are &pm...

Math
Hints: It can be shown by calculus that the maximum area of a polygon enclosed by a fixed length of perimeter is a regular polygon, i.e. a polygon with all sides and interior angles equal. It follows from the above that the maximum area enclosed by a fixed perimeter is a ...

Physics
1 HP = 745.6999 W 4 HP = 2982.7996 W 4t = 4000 kg Use mgh=PΔt h=PΔt/mg =2982.7996*10/(4000*10) =0.75m approximately

maths
Correct! Well done! :)

maths
use proportions/ratios: 1 7/8 : 2 1/2 ≡ x : 4 Simplify ratios: 15/8 : 5/2 ≡ x : 4 15 : 20 ≡ x : 4 3 : 4 ≡ x : 4 Solve for x.

math
Use ratio/proportions: 5.58 : 318.76 ≡ x% : 100 Product of means = product of extremes 318.76*x% = 5.58*100 x% = 5.58*100/318.76 = 1.75% approx.

fractions/math / Help!
With what Reiny showed, there should be sufficient information to work out 425 by yourself as an exercise. I will give you another example, 525: 525÷5=105 105÷5=21 21÷3=7 since 7 is a prime we cannot go further. so 525=5*5*3*7=3*5²*7 You're ...

collge sydney
Hints: Kinetic energy of a rotating object is given by: KE = Iω² I is moment of inertia in kg-m² and ω is angular velocity in rad/s. 1 RPM= 2πradians/60 s = π/30 rad/s.

Algebra
Correct! Well done! :)

math
one-to-one (injection): every element in the codomain is mapped by at most one element of the domain. onto (surjection): every element in the codomain is mapped by at least one element of the domain. We can see that f(x) is both one-to-one but not onto, since f(1)=4, f(2)=7, ...

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