# Posts by MathMate

Total # Posts: 12,086

Algebra 2
Use the rules of logarithm (any base): log(a)-log(b)= log(a/b) and the definition of log to the base a log_a(b)=x means a^x=b where a>0. So log_2(x^2-20)-log_2(x)=3 means log_2((x^2-20)/x)=3 now you can apply the definition of logarithm to solve for x.

Trigonometry (Logarithmic Function)
Rules of logarithm if log(a)=x, then log(a^2)=2x, ... log(a^n)=n×log(a) Similarly, if log(a)=x, then log(√a)=(1/2)x...

math
Correct! Well done.

Math
We have a problem with an integer solution. Use proportion/ratios, 2 boys to 3 girls means 2 boys to 5 total number of members. 2:5 = 4:10 = 6:15 .... try until the total number of members x is 20<x<30.

Algebra 2
Your steps are correct if the equation was: 8^(2x-1) = 16^(x+1) and assuming this is the case. Since 8=2^3, and 16=2^4, you can simplify further using the same rule of logarithms: log(a^b)=b×log(a)

Algebra 2
Grouping has to be done in such a way as to have a common factor. With cubics, the usual strategy is to find an obvious factor, then reduce the cubic to a quadratic by synthetic (or long) division. The first factor is to check for (x-1). If all the coefficients add to zero, ...

Algebra 2
I notice that the sum of all the coefficients is zero. Do you know how that would help?

Algebra 2
Have you done factoring of polynomials?

Algebra 2
x^2 - 3x^2-22x+24=0 is a quadratic with two like terms. Would you like to double check for typos?

math
Now you can take the time to reread and understand the question. What is the length if the width is x? Take the sentence "length is five less than two times the width" and replace the word "width" by x (that we defined above), and translate it to mathematics.

math
Put x = width of the garden then what would be the length in terms of x?

Math
It doe not look too clear what P and Q are, I am assuming the following. P=(4,3,0) Q=(0,6,6) PQ = Q-P = <4,-3,-6> by subtraction = 4i-3j-6k in unit vectors. Length of vector <x,y,z> = sqrt(x^2+y^2+z^2)

statistics
Let event A=pump A is working B=pump B is working Assume pumps A and B are independent. then A'=pump A is not working B'=pump B is not working, hence P(A')=0.1 (probability that pump A fails) P(A)=1-0.1=0.9 (probaility that pump A works) P(B')=0.2 P(B)=1-0.2=0....

Maths
Hmm, let me see. f(-2)=0, check f(1)=0, check f(2)=0, check when expanded, the leading coefficient is 2 (polynomial=2x³-2x²-8x+8) This checks too. Yes, your answer is correct.

Math
Hint: The factors of a number, say 12, are 1,2,3,4,6,12, or rearranged differently, 1,12, 2,6, 3,4 for a total of 6 (even). The factors of a prime number, say, 23, are 1,23 for a total of 2 (even). The factors of another composite, say, 36, are 1,2,3,4,6,9,12,18,36, or ...

physics
When the ball reaches the highest point, it means that its vertical velocty v1 is zero. With an initial velocity of v0 (upwards), and an acceleration due to gravity of -g (downwards), we use the relation v1=v0+at substituting v1=0, v0=16.5 and g=-9.81, you would be able to ...

Math

"solve" involves at least one equation and one unknown. I think you mean "simplify the expression". Also, according to PEMDAS, you need parentheses when dividing a polynomial by a binomial, and the division is written on a single line (as you do when you ...

Math
This is also the handshake problem. Use the logic of the answer to the previous post.

Math
This is the same as the hand-shake problem. N people talked to N-1 people. But each call involves two people, so the number of calls is N(N-1)/2.

physics
g is not required if the bike is on a horizontal road. velocity = 1.3*10^3 m / (14 min * 60 s/min) = (65/42) m/s Kinetic energy = (1/2)mv^2 = (1/2)(57.1)(65/42)^2 J

Algebra 2
f(x)=5x+3 g(x)=6x-2 fxg(x)= (5x+3)(6x-2) Expand and simplify. The domain of a polynomial is (-∞,∞)

Algebra 2
f(x)+g(x)=-5x-4 + 6x+7 You can simplify and make your answer choice from the list.

ALGEBRA
Please write in upper/lower case. It's easier to read. Here's an example to help you solve the given problems. Factorize (x+2)^2-5(x+2)-14. Keep the (x+2) as a single entity, say y=(x+2), then (x+2)^2-4(x+2)-12 =y^2-4y-12 =(y-6)(y+2) Now substitute y=x+2 =(x+2-6)(x+2+2...

Algebra
You can solve it like almost any equation, but replacing the equality sign with \≠. For example, solve for q in (4a+3)/5≠3 so we can continue 4a+3≠5*3 4a≠15-3 4a≠12 a≠3 is the answer. In set notation, a ∈ R\3, or a ∈ (-∞,3)∪(3,∞) (...

chemistry
The solubility of gases in water depend on the atmospheric pressure and the ambient temperature. Here's a link to the solubility of various gases (in g/1000g water). http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html

maths
Before 10:15, only car is on the road, by which time it has travelled 80*(15/60)=20 km towards B. So remaining distance as of 10:15 is 150-20=130 km. When lorry starts, they approach each other at a total speed of (80+40)=120 km/h. Elapsed time (since 10:15) when they meet is ...

java programming
Which sorting algorithm do you plan to use? For small number of items (less than 200), bubble sort is easy to understand and code using for-loops. For large number of random items, quick sort could be used, but requires the understanding of recursivity.

Medical billing/coding
Try http://www.findacode.com/ to help you look up the codes if you don't have access to any. Do remember that if you are coding for medical billing, you need the codes for acts performed, not the diagnoses.

Math/ Statistics
The null hypothesis is generally an equality, which makes it: H0: The average attendance at home games equals 3000. However, when the alternative hypothesis is one sided, which in this case is: H1: The average attendance at home games is less than 3000. It will be understood ...

math
Please check if what is needed is P(x1/x2<0.5) or is it P(xi/xj<0.5) because otherwise x3 is not playing any role.

math
It looks to me this is an incompatible mixture of the two previous problems. f(x)≠(x+1)/2 if X~N(6,4). Please explain or elaborate if I am mistaken.

math
See response to previous post: http://www.jiskha.com/display.cgi?id=1419789148

math
Look up normal probability table for X~N(6,4) for P(X<8)=0.69 (approx.), so P(X>8)=0.31. Since we have random samples which we assume to be independent, we can use binomial probability distribution to calculate P(max{x1,x2,x3}>8). Alternatively, we can calculate P(all...

math
Given f(x)=(x+1)/2, -1<x<1 and zero elsewhere. So for each individual sample, P(X>0)=∫f(x)dx from 0 to 1 =∫(1/2)(x+1)dx =(1/2)[x²/2+x] 0 to 1 =3/4 = p Assume x1...x5 are independent and random samples, binomial theorem is appropriate: P(four of 5 X >0...

programming
Programming is a subject learned by intuition (for geniuses) or by practice (most of us). If your teacher did not cover programming, then it must have been required as a prerequisite. The problem given is not even for a first course in c-programming, so you will have a lot of ...

programming
What course are you taking, and which topics have been covered? It looks like this is an assignment to help you understand and apply what you have learned. I believe you should be able to show us some code or at least some pseudocode and start getting help with difficulties ...

probability
Let's simplify the problem to having 7 red balls, 5 green balls, and 4 blue balls (for a total of 16). Find the probability of drawing 2 red balls, 2R 2 green balls, 2G 2 blue balls, 2B (total of 6 balls), then Below we will use the notation of (n,r)=combination (n,r) =n...

algebra
Here we have two samples from two populations and would like to determine if the means are the same, namely to accept or reject: H0: μ1-μ2=0 The sample size n=14 is not sufficient to justify normality using the central limit theorem. Either an assumption of normality has...

computers
One possible cause is that the remote server administration tools are not installed on Windows 8 or 8.1. By default, they are not. If that's the case, the Active directory utilities, users etc will not be available. The fact that it pings the file server means that it is ...

math
Correction to missing parentheses for above expression for Z Z=[(X̄1-X̄2)-(μ1-μ2)] / sqrt(σ1²/n1 + σ2²/n2)

math
We have two samples, n1=n2=25 both are normally distributed, and are independent. Under these given conditions, E(X̄1-X̄2)=E(X̄1)-E(X̄2)=μ1-μ2 VAR(X̄1-X̄2)=V(X̄1)+V(X̄2)=σ1²/n1 + σ2²/n2 Z=(X̄1-X...

Probability
the equation you need is P(X=r)=C(n,r)*p^r*(1-p)^(n-r) C(n,r)=n!/((n-r)!r!) and n!=n(n-1)(n-2)....(2)1=factorial n You have everything you need to calculate the required probability. It turns out that C(n,0)=1 for any positive value of n. The answer is less than 5%. You can ...

Math
The rule of 72 says that the time in years it takes to double your money is 72 divided by the interest rate in percent. However, it applies to compound interest, but it still gives an approximate number of 100=72/x or x=0.72%. To calculate accurately, we use Future amount =Pe...

Algebra
add: ...and the remaining 24 variables equal to zero.

Algebra
Because it is circularly symmetrical, all 26 variables cannot have the same value (otherwise the sum would be zero). To maximize the value of |a-n|, we need |a-n|=10 which in the integer domain gives ±(0,-10),±(1,-9),±(2,-8),...±(5,-5),

geometry
A hexagon consists of 6 equilateral triangles. Therefore the side of each triangle is 24/6=4 units which also equals the radius of the circumscribed circle.

geometry
AU+UQ=5*AU UQ=26 so 26+AU=5*AU solve for AU.

Statistics
Baye's theorem P(P|Q)=P(P∩Q)/P(Q)=P(Q∩P)/P(Q) =P(Q∩P)/P(P)*(P(P)/P(Q)) =P(Q|P)*(P(P)/P(Q)) or simply P(P|Q)=P(Q|P)*(P(P)/P(Q)) Here P=stereo came from company A Q=stereo is defective So P(P|Q) probability that the stereo came from company A given that it is ...

Physics
Connected in series means the resistances could be added. Equivalent resistor = 4+10=14Ω Voltage = 12 V Assuming battery has zero internal resistance, V=IR, or I=V/R = 12/14 A = 6/7 A.

Physics
Length L = 6m Angle with horiontal, θ = 50° Friction with wall = 0 Coefficient between ladder and floor, μ = 0.5 Mass of ladder = M Mass of man, m = 11M Let the man climbs up X m. from the bottom, Vertical reaction of floor, R = M+11M=12M (because wall is smooth) ...

Lat math question for some days. Can y'all help?
Didn't you get an answer last time: http://www.jiskha.com/display.cgi?id=1416267535

French
Sorry, the codes didn't show, hope it is better this time: Some hints: (skip the blank spaces after & and before ;) à write & agrave ; è write & egrave ; é write & eacute ; ô write & ocirc ;

French
Some hints: (skip the blank space before ;) à write à ; è write è ; é write é ; ô write ô ; etc. Most of the verbs used are conjugated with the verb être, which means that you need to match the form of the verb with the ...

French
Please post your work so we can give you help instead of doing it for you. If you have difficulty with a certain aspect, please explain.

How do you propose to do it, using a calculator, or by hand (there are algorithms to find square and cube roots)), or by factoring?

matha
Length of minute hand: 9m Angle moved in one hour = 360° Distance = (360/360)*2*π*9m=18π m Length of hour hand: 9m*2/3=6m Angle moved in one hour = 360/12=30° Distance = (30/360)*2*π*6 = π m Calculate the difference.

calc
This is a problem where the paraboloid projects a circle of radius 1 (represented by the region D) on the x-z plane. y=0 when x=z=0 y=1 when x²+z²=1 So let I=∫∫DydS It may be changed to cylindrical coordinates where dS=rdrdθ, and using y=x²+z²...

Chemestry
Density=mass/volume, so Volume = mass/density Check carefully units and number of significant figures.

Statistics
The "68-95-99.7 rule" represents the two-tail probability of data within ±1,2 and 3 standard deviations respectively. For example, the probability of picking a value X from a normal distribution within the range μ-σ<Xμ+σ is approximately 68%. ...

MATHS - ratios
use ratios: 60 km / 1.5 hours = 100 km /x hours x=1.5 hours * (100/60) = ?

subtract each number from the next number, and make your guess from there!

math
P=2πsqrt(L/g) dP/dL = 2π(1/2)L^(-1/2)/sqrt(g) =2πsqrt(L/g)/(2L) transpose appropriate terms: 2*[dP/(2πsqrt(L/g))] = [dL/(L)] Each term in square brackets is equal to the fractional form of percentage error, thus proved. (use Δ => differentials instead of ...

math help!
Add -2-2w to each side to get w=10. Put w=10 back into each side of the original equation to verify that you get the same value on each side (=32).

Ashworth college
I believe the "68-95-99.7 rule" means the percentage of observations within 1-2-3 standard deviations from the mean. Try to apply the rule to answer the given question.

physics
This problem is similar to the previous. Again, use conservation of energies.

physics
Since friction is negligible, use conservation of potential and kinetic energies. KE (at bottom) => PE (at top) mv²/2 = mg*Lsin(θ) v=2,g=9.81,sin(θ)=1/2 Solve for L. I get 0.82m

Physics
Ideas: Conservation of energies also means: - energies are transformed from one form to another. Some are easier to exploit/recuperate than others. - total energy in universe is constant, but could be out of reach.

Probability and Linear Math
40% of total investment = 40%*500000 = 200000 This puts a ceiling on B, and a lower bound on A.

physics
Let A=30 kg boy B=40 kg boy Force = 50 N For boy A: Static Friction = mgμs=30*9.8*0.15=44.1N < 50N => Boy A is set in motion. Net force after kinetic friction = 50N-30*9.8*0.1N=5.9N Acceleration = F/m = 5.9/30=0.69 m/s² (backwards) For B, the 40kg boy Static ...

Math
What you'll need to do is 1. find the 3 intersections of the lines, which are then the vertices, (xa,ya), (xb,yb), (xc,yc). 2. Find the mid-points of each side using Mab=((xa+xb)/2, (ya+yb)/2), ... 3. Find the perpendicular bisector of each side by passing a line ...

Chemistry Correction
Correct, you should get 1.974*10^(-29) instead. If you do not get the above value, it could be: 1. you did not use the correct value of pi (such as 3.14, 22/7,...) 2. Your expression is missing many parentheses. Remember PEDMAS or PEMDAS which your calculator sticks to, but it...

Here the population variance is not known, so use student-t distribution. A 95% (two-tail) confidence interval would include the limits. The value 1.96 comes from a T-value for 97.5% (half tail). x̄-Ts ≤ μ ≤ x̄+Ts where x̄=sample mean s=sample variance...

Statistics
Using Binomial probability function, we are looking for: P(280≤X≤300) =Σ C(300,r)p^r*(1-p)^(300-r) for r=280, 281, ...300, and C(300,r)=300!/((300-r)!r!) =0.00896+0.01530+0.02474+0.03777+0.05427+...+0.00004+0.0000 =0.98992 Using normal approximation with continuity...

chem
pKa=-log10Ka =-log10(6.3*10-8) =7.2

statistics
It all goes back to the definition and application of α and p-value. Read: http://www.statsdirect.com/help/default.htm#basics/p_values.htm for a detailed explanation.

Math
I=kS/d² where I=illumination, k=proportional constant >0 S=source strength >0 d=distance One light source is S, and the other is 4S. Let d=distance from weaker source, then 11-d =distance from stronger source. We have illumination as a function of d I(d) = kS/d²...

math
200 questions, 2 marks for good answer, -1/2 marks for wrong answer. Ajay answered all questions. If he didn't give any wrong answer, he would have got 400 marks. Each wrong answer will set him off 2.5 marks. If he got 360, he got (400-360)/2.5=16 wrong, therefore 184 ...

physics
v0=2.7 (package was rising) x0=11 x1=0 a=-9.8 x1=x0+v1*t+(1/2)at² 0=11+(2.7)t+(1/2)(-9.8)t² Solve for t to get t=1.8 sec.

algebra
First observation: People either liked the skin cream (x of them) or didn't like the skin cream (100-x of them). "80% of the people who liked the new skin cream also liked the new lip balm" that makes 0.8x liked new lip balm. "50% of the people who did not ...

Math
First factor the denominator: x^3+x^2+x=x(x^2+x+1) Then assume constants A, B and C as follows: (-5x^2-8x-3)/(x^3+x^2+x) = A/x + (Bx+C)/(x^2+x+1) The steps are to find constants A, B and C (the solution) by adding together the right hand side and comparing coefficients of each...

mathematics of investment
12% simple interest p.a. equals 0.12/365 simple interest per day. Principal=P10000 interest per day = P10000*0.12/365 =P3.28767 /day Time it takes to reach P700(=P10700-P10000) = P700/(P3.28767) = 212.9 days rounded up to = 213 days

chemistry
Not sure how you got 87! :) Start with PV/T=constant, where T is in °K. V1=1.75*10³L T1=(9.0+273.15)=282.15°K T2=(80+273.15)=353.15°K (ok to use excess significant digits for calculation, but reduce answer to appropriate number). since Pressure & amount of gas...

Physics
Principle of floatation: A floating object displaces its own weight of the fluid in which it floats. Volume of steel =Vs Mass of steel Ms = ρs*Vs Volume of mercury displaced, Vm = Ms / ρm Percentage of volume displaced =Vm / Vs If the steel block floats with bottom ...

Microsoft Excel
Excel is nothing but a tool to help us. It does not create a new rule for precedence, but follows what we learned in elementary school. In maths, the rules of precedence PEDMAS (or some variant) are: Parentheses Exponentiation Division/Multiplication Addition/Subtraction. They...

geometry
Start by drawing a diagram. If BC=BD, then ∠BDC=∠BCD=34° (angles opposite equal sides. Hence ∠CBD=180-(34+34)=112° ∠ABD=∠ABC+∠CBD=? Recall that ΔABC is equilateral.

Geometry
See other post.

physics
He saw penguins at his intermediate destination.

Algebra
a) Total: 640 feet Two short sides: 2x long side 640-2x b) Since long side must be positive, we have 640-2x≥0 c) Area = short side * long side A(x)=x(640-2x) d) find x such that 30000≤A(x)≤40000 Make a table that gives x and A(x), Hint: A(50)=27000 <30000 A(86)=...

Stats Math 3
(1) The sample distribution taken from a binomial distribution is approximately normal because sample/population size < 0.05 ("small" sample). Also a binomial distribution approximates a normal distribution when np>K and np(1-p)>K, where K ranges between 5...

Stats Math 2
Population has binomial distribution. sample mean is 144/300. Check that sample satisfies normal approximation and proceed as in your next post. Do not forget to apply continuity correction when approximating a discrete distribution (such as binomial) by a continuous ...

STATS Math
Same as your other post: http://www.jiskha.com/display.cgi?id=1417003909

Chemistry
CuCl2.2H2O See for example: http://en.wikipedia.org/wiki/Copper%28II%29_chloride for more details.

chem
You're welcome!

chem
If it is diprotic, then your equation in (2) is correct, and the molar ratio NaOH/C6H7O6 would be 2, and hence the answer in 4 would be halved, ... problem solved.

chem
1. Numerically correct. You will have to get used to citing answers to the correct numnber of significant digits, depending on the given information. Here, the correct answer would be 0.001811 M. 2. The neutralization reaction is not correct. Ascorbic acid has only 1 H+, so it...

phy101
If the box rolls on a horizontal floor with a constant velocity, then it is in dynamic equilibrium, and no external (horizontal) force is acting on it. Thus the floor does zero work on the box.

INTRODUCTION TO PHYSICS
Don't know. According to Google, the density of ethanol ("alcohol") is 789 kg/m³. So if the liquid has a density of 750 kg/m³, i.e. it is less than the density of ethanol, it must be something else. If ethanol is mixed with water, the density goes up, i...

Math
Yes, Steve is right. Thanks Steve. Oversight on my part.

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