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Posts by MathMate

Total # Posts: 12,033

I find only one root at about x=2.7176022... a reasonable approximation to e.

you're welcome!

List price = £60 Discount = 15% discounted price = (1-15%)* £60 = $60(0.85)= £52 Amount tended = £100 Change = £100- £52 = £48.

Math - correction
Guess I misread the question. There was only one sum borrowed at an unknown rate of interest i, assumed compound interest compounded annually for 2 and 3.5 years respectively. Let P=sum borrowed i=interest rate P(1+i)^2=8320 P(1+i)^(3.5)=9685 => 9685/8320=P(1+i)^(3.5-2)=(1+...

I interpret the question as: Given: 1. future value (i.e. amount owing at maturity) of a two-year loan is Rs 8329 and that of 2. future value of a three-year loan is Rs 9685. Find the sum of the present value of the loans. P1=8320/(1+i)^2 P2=9685/(1+i)^3.5 sum=P1+P2 where i is...

Both solutions of the impersonator of MathMate and Henry give the same correct answer of 41.820°. By the way, for your information, impersonation is a serious offence at Jiskha, liable to be banned.

calculate the sines and cosines of the angles .... sintheta1=5/sqrt26 cosTheta1=1/sqrt26 sinTheta2=3/5 cosTheta2=4/5 check all those... Now, Sin(A-B)=sianAcosB - CosBsinA then compute aine (A B), and finally, the arcsin(A-B) which is the angle

Again, without the choices, we cannot know which one is the most likely. However, since we are talking about experimental probability, and that we cannot have an outcome of 7.5 times out of 150. Therefore the most likely result could be 7/150 or 8/150, whatever their decimal ...

weight = mg for a 98.17 kg mass and using g=9.81, then weight = 98.17 * 9.81 =963.0 N

Math - correction
Use hypergeometric distribution as Reiny showed you in your previous problem: C(12,2)*C(28,2)/C(40,4)=12474/45695 where we need to choose 2 out of 12 greens, 2 out of 28 non-greens, and in total, 4 out of 40 balls. For the second part, you can use what was given above, OR use ...

total, N = 40 Assume no replacement, P(G1)=12/40 P(G2)=11/39 P(G1∩G2) =12*11/(40*39) =11/130 35 balls are not yellow (X) So if all are not yellow, follow the same principle as above, P(X1)*P(X2)*P(X3)*P(X4) =(35/40)*(34/39)*(33/38)*(32/37) =...

use the distribute law, a(b+c)=ab+ac so 2(3a+4)=2*3a+2*4=6a+8

Length = 4 times width Area = length * width =(4w)w =4w² So 4w²=1024 cm² (given) w²=1024/4=256 w=√(256 cm²) =16 cm (reject negative value of square-root)

Let event G=seed grows into a healthy plant (success) ~G=seed does not grow (failure) We use the binomial distribution where N=6, p=0.70 (probability of success) n=5 (5 successes) C(N,n)=N!/((N-n)!n!) then by binomial theorem P(n=5)=C(6,5)p^5(1-p)^1 =6!/(1!5!)0.7^5(0.3^1) =.3025

From the data given, I cannot explain the difference. If you have a diagram, please post. Perhaps someone else can enlighten you on this.

Work due to frictional resistance = frictional force * Distance Here force = 10.0 N (due to friction) Distance = 2.5 m

maths for business Help!!!
Present worth of 600 monthly for 20 years at APR=24%: P=A*(P/A, 2%, 480) =600*(1.02^480-1)/[(.02)(1.02^480)] =29,997.766 Therefore down-payment =50000-P =50000-29,997.766 =20,002.23 Interest charged =future value - present value =29997.766*[(1.02^480)-1] =402,845.97 (no ...

Note: hyperbole is the French name for hyperbola.

A------m--M-----------B 0.75 M=25kg m=150kg Distance AM=2.0/2=1.0 m Take moments about A: (counter-clockwise positive) B*2-150*0.75-25*1.0=0 B=(150*0.75+25)/2=137.5/2=68.75 kg The reaction (thrust) at A can be found by summing vertical forces and equating to zero, or similarly...

Force = rate of change of momentum Propelling force=100N m (of propelling agent)=0.5 kg / s velocity=v 100 N=0.5 kg/s *v => v=100/0.5 m/s =200 m/s

Note: Above assumes the prize drawing order is first, second, third (third draw).

Hints: The average of the times is equal to the time to reach the maximum height, due the the symmetry of the parabola. So the sum of the times would be twice the time it takes to reach the maximum height, also equal to the time for the object to go up and fall back to the ...

Slope intercept form of a line that passes through point (x0,y0) with slope m is given by: y=m(x-x0)+y0 Substitute values to get equation. Post your answer for checking if you wish.

Note: When writing rational expressions (a polynomial divided by another), it is important to insert parentheses around each of numerator and denominator. The answers are ALL missing parentheses in the numerator and denominator. In the question, g(x)=x+3/x would mean (x)+(3/x...

Typo suspected, corrected version: 3/(x-3) - 5/(x-2) 1. find LCM of denominators (x-3)(x-2) 2. express both terms in terms of the LCM as denominator 3(x-2)/((x-3)(x-2))-5(x-3)/((x-3)(x-2)) (very similar to cross multiplication) =(3(x-2)-5(x-3))/((x-3)(x-2)) =(3x-6-5x+15)/((x-3...

Homeostasis is the system in the body to maintain the normal/healthy status of the body, such as temperature, concentration of nutrients (e.g. glucose), concentrations of Na+, K+, and Ca++, etc. When any vital equilibrium is disturbed, the body will suffer from serious health ...

Not sure what exactly the question wants to know, where, or what. In any case, Smooth muscles are involuntary, usually found in the linings of hollow organs such as intestines. Cardiac muscles are involuntary, responsible for the continual pumping actions of the heart. ...

mass=32 g volume = 200 mL concentration = mass by volume = 32 g /200 mL =32/200 g/mL Simplify or convert to decimals for the final answer.

For your information: Major minerals have RDA's (Recommended Daily Allowance) of hundreds of milligram (mg) per day. So Magnesium is a major mineral for the human body. Note: Iron is the trace mineral with the highest RDA at 10-15 mg/day. (a) mg=milligram = (1/1000) gram...

forensic science
The emitted wavelength is towards the IR range (from the visible range), relative to the exciting radiation. The difference in wavelength is called the Stoke's shift. Therefore wavelength of emitted light has a longer wavelength than the exciting radiation.

80 L of 60% acid contains (80*0.60)=48 L of 100% acid. To make 50% acid, it must be diluted to have a total volume of 48/(0.5)=96 L. Leave it to you to figure out how much distilled water to be added.

It is rare to adjust the position of the fulcrum of a seasaw to adapt to persons of different masses. Here we assume both Dad (D) and girl (G) are seated at the extremities of the 5m seasaw, and the centre of mass (M) of the 10 kg seasaw is in the middle. We assume the fulcrum...

I suppose the ray is BD and not AD. An angle bisector (ray BD) divides a given angle into two equal parts. You can take it from there. Hint: the answer will be apparent if you draw a diagram. This works for all geometry problems.

One or the other must occur means that the two events make up the sample space, like heads and tails in tossing of a coin. These events are then called complementary. In a Venn diagram, the universal set (&Omega) or sample space is divided into two parts, so that any outcome ...

Science , Biology
Both are passive movements, i.e. no energy (ATP) is required. Diffusion is basically a random movement of solute and water molecules in all directions. In a concentration gradient, area of higher concentration will contain more solute than that of low concentration. The net ...

See previously answered: Kms is a good pen name, no need to change.

This can be solved by sketching a Venn diagram. Given: a. 43% women b. 8% women art majors c. 15% art major d. 4% not chosen major 16. From (a) and (b), 15-8=7% are male art majors So P(art major∪woman) =43%+7%=50% 17. Assuming all students are either man or woman, P(male...

Algebra 2//read bottom
It's more perhaps you did not read the last response from a helper. Also, please show details of your previous answer, so we can better help you with your difficulties.

First step in evaluating limits: simplify the algebra and see what you get. If you get: (a number), then it is also the limit. (∞/(a number)), the limit is &infin. (0/(a number)), the limit is 0. (∞/∞), or (0/0), then you need other techniques/tools. Try the ...

So at 8 am, x had travelled 80*(1.25hours)=100 km. He was then 400-100=300 km away from y when the truck left y for x.

Hint: Meeting time for two travelling towards each other is the distance divided by the sum of the speeds.

Sorry, forgot the link. Will give two at different levels, just in case:

If you don't have a textbook, try the following link. After that, reread Ms.Sue's responses. The link explains how probability works, and with that knowledge, you will be able to solve other problems, without having to guess anymore, once and for all.

Chemistry, rate of reactions - help needed
Chemistry, rate of reactions - help needed

Use the formulas: Power (watts) = V^2/R V=voltage in V = 120 V R=reisistance in Ω => R=V^2/P............(1) R(30W)=120^2/30=480Ω R(90W)=120^2/90=160Ω Now using equation V=iR i=current in amps With three connected in parallel, i=4.5A R(equivalent)=V/i=120/4...

Write a 5 in the thousands place. Then fill in three more digits (0 to 9) to complete the number in a way that it is the smallest possible number.

math - aina
Aina, it would be nice to verify your earlier post before you repost. If you have objections to the response, you are free to explain your point of view.

Algebra 2 help please.
Can you explain exactly what you put in your calculator, including parentheses etc.? Can you reproduce the value? What do you get this time?

Algebra 2 help please.
Can you kindly explain the steps that led you to 6.616? It would help me understand your thinking process in order to help you solve the problem accordingly.

S=event of passing statistics M=event of passing mathematics P(S)=2/3 P(M∪S)=4/5 P(M∩S)=14/45 From the given information, we can apply the following relation, which is always valid, mutually exclusive or not. P(M∪S)=P(M)+P(S)-P(M∩S) in other words, P(M)=P(M&cup...

There isn't much we can do about it to simplify the expression, unless we are given the value of x, in which case we can evaluate it numerically. We can also transform it to (x-4)^(3/2) =(x-4)^(1+1/2) =(x-4)√(x-4) but that is not simpler. It all depends on which math...

Let original amount be A. A(1-0.1)(1-0.2)=?3600 Original amount =?3600/[(0.9)(0.8)] =?5000

Math - trigonometry
"Ferris wheel is elevated 1 metre above ground" means that the lowest point is 1 metre above ground. (Draw a sketch to show that). The highest point is 31 m. above ground, so the diameter is (31-1)=30m, and radius = 30m/2=15m. (Mark that on your sketch). The centre C...

I see π being properly displayed probably due to encoding. I also see that there is a removable discontinuity at x=π/2. Numerical integration (skipping x=π/2) gives identical results for both expressions, so hopefully no typo. Try translating limits to (-π/2, π/2).

A redox reaction would occur. Can you figure out the reaction?

A. dilation The dilation matrix is correctly done, except the original matrix (for KLM) should be in alphabetical order of the vertices, which is -2 1 -3 5 1 1 therefore you need to readjust the matrix of the dilated figure. It is normal practice to create matrices in ...

Physical science CHECK my answers
1. incorrect (review friction concepts) 2. correct 3. incorrect. (review concept of displacement) 4. correct. 5. incorrect. (Please explain justification of your choice) 6. incorrect. (review circular motion) 7. incorrect. (acceleration is not a force. review definition of a ...

hint: According to The solubility of ammonium chloride is 51.4 and 71.2 at temperatures 50°C and 90°C respectively. "Solubility" used in the above article is expressed in "grams per 100 milliliters of water...

Since you have learned about inscribed angles and intercepted arcs, it is safe to assume that you are familiar with what they are. Following is a summary of hints to help complete the proof. fact #1: the sum of the intercepted arcs of the sides of a cyclic quadrilateral (a ...


Again, see:

algebra - repost
If you are reposting within a short time, indicate repost in your subject box. It doesn't usually get faster response by reposting within a short time because tutors have to spend time answering in duplicate, thus reducing the response time of everyone. Read the following ...

fraction of income left: 1-(1/4+2/5+1/6).....[LCM=60] =1- (15/60+24/60+10/60) =1- (15+24+10)/60 =1- 49/60 =11/60 Total income/1=money left/(11/60) Cross multiply, total income=10000*60/11 =$54545.45 For faster response, enter the appropriate topic/subject in the subject box.

Assuming both are fair cubes. Any fair cube will give a "6" with theoretical probability of 1/6. (a) For case Red cube: P(6)=1/6, P(~6)=5/6 Blue cube: P(6)=1/6, P(~6)=5/6 Using the multiplication rule for the two step experiment (red, then blue), P(6R,~6B)=1/6*5/6 P...

algebra 1
Can you explain how you got 24? This permutation problem can be solved using the standard equation P(n,r)=n!/(n-r)! where n=8, (8 candidates) r=3 (three different positions out of n candidates) Use your calculator to help you find the right answer. Just in case, n!=1*2*3*4...

yes to " we can find the speed of the penny as instantaneous rate of change of height of penny when it hits ground. " Details: If you have been given the equation v²-u²=2aH then H=distance, and velocity=v (u=constant=0) If you express v as a function of H, ...

Chemistry - to Hina, Star, Rebecca,
Please use a single pen name when you post.

This is a two step experiment where each step is independent of the other. The probability of both succeed is the product of the probability of each step. [called the product rule] Step 1: P(even)=P({2,4,6} out of {1,2,3,4,5,6})=3/6 P(2)=P({2} out of {1,2,3,4,5,6})=1/6 Now use...

Algebra - to Tony
Tony, help is to give you hints or explanations to lead you to a solution. Giving answers could be help for someone who wants to understand, and detrimental for someone who does not. The help I gave above should help you eliminate two of the choices. If you need more ...

If it is a decrease, r is negative. In the proposed answers, the variable x is an exponent, so it should be written: A. f(x)=2000(0.94)^x,... and so on. Which do you think is the right answer?

"The sum of two rational numbers is always rational." - true, for example, 2+0.5=2.5 (decimals and fractions are rational) So statement is true. "The product of a nonzero rational number and an irrational number is always irrational." - true, 5*√2=5(&...

physic, please correct is am wrong
i. incorrect. The angle turned in radians? note (2π/360) is the conversion factor from degrees to radians. use 1 revolution = 2π radians For example, 5 revolutions equals (5*2π)=10π radians. ii. incorrect error inherited from (i) iii. incorrect error inherited from...

physics - to "question" and "carry on"
If you both have the above seemingly incomplete question (that finishes without a fullstop!), perhaps it is time to check with your teacher or tutor.

physics - please complete the question
It does not look like the question is complete.

Assuming the Y-shaped chords are symmetrical with respect to the vertical, and θ is angle of each chord with the vertical, then resolve forces along the y-axis (vertical), 2Fcos(θ)=mg F=tension on each chord,=force on anchor m=mass of climber Solve for F.

@ All Cheaters
Also, if you post 4-5 answers that do not make sense, one would be led to believe that they are chosen at random, and therefore do not represent your effort. However, if the answers are accompanied by your lines of thought or explanations, they will be more likely to be checked.

Algebra 2
Cos(x) is a sinusoidal function with a period of 2π and amplitude 1, i.e. it oscillates between +1 and -1. You're expected to know the basic graph of cos(x), sin(x) and tan(x). (see link below for details). Based on the basic graphs, we can graph the variants. From cos(...

"Distance" is the sum of distances travelled, irrespective of direction, just like the odometer on a car. "displacement" is the distance and angle of the final position relative to the initial position, irrespective of how and where intermediate stops are ...

Angles of elevation and depression
In geometry problems, we need to start drawing a sketch according to instructions. On the sketch, label the unknowns, and hence deduce the equations/formulas that may help to solve the problem. Start by sketching according to given information. Geometry will always be ...

Please double check your post before sending to make sure we're solving the right problem. This is what I suspect to be the correct version. Editorial changes have been indicated in italics. Also, I start a new sentence on a new line for easier reading and interpretation. ...

The monthly payment A over N=1 year(s) for a loan P=1300 at a nominal annual interest rate of i=0.10, compounded c=12 times annually is given by To simplify the formula, we write n=c*N=12*1=12=number of periods R=1+i/c=1+0.1/12=interest rate per period then monthly payment, A ...

Assuming fair coins. The "first" coin has a probability of 1/2 showing heads, and the "second" has a probability of 1/2 showing tails. Since the two events are independent, the joint probability (i.e. both are successful) is the product of the individual ...

The slope of a line Ax+By=C is given by -A/B. Therefore if A & B have different signs, the slope is positive. This will help you eliminate the third equation, since coefficients of x and y have the same sign, therefore negative slope. Now set x=0 in each of the equations and ...

The equation of a circle centred at (x0,y0) and radius r is given by (x-x0)²+(y-y0)²=r^2. The posted equation therefore represents a circle with radius=√81, centred at (-6,8). Continue with interpreting the results to complete the answer.

Physics - to adam
Congrats! What you did is valid, using strictly kinematics equations. Basically, you got H=29+14^2/(2g)=39 If you solved the energy equation above, where m (mass) cancels out on both sides of the equation, you will get H=(14^2/2+29g)/g=39 The two match exactly assuming no air ...

The air velocity is indeed still +90 m/s (due south). The velocity with reference to ground is Vg=+90+(-27)=63 m/s (due south). Think of the plane moving south for 90 m in one second, and head wind blows it back towards north by 27 m, also in one second, so the net/ground ...

Assuming the number is an integer. 45130 58269 97394 and many others, probably because question is incomplete.

Innovation - oops
It's Gay-Lussac's Law, not Charles' law (T vs V).

Charles' law, P1/T1=P2/T2, or P/T=constant, as long as volume is constant. T must be in °K. 24/(273.15+0)=P/(273.15+32) Solve for P P=24/(273.15)*(305.15) =26.8 lb/in²

Look for ordered pairs (x,y) with identical x-values. If the corresponding y-values are different, the ordered pairs do not form a function. This is the equivalent of the vertical line test (i.e. no vertical line cuts two points). However, in case where both x and y values are...

If a figure has rotational symmetry of order three, then it has either 0 or 3 lines of symmetry (one in each rotated position = 3). I would look forward to seeing a figure with rotational symmetry of order 3 and one single line of symmetry, if it exists.

Certainly, if you would post your attempt!

Math Help TIMED! -- a test?
Timed? Is it a test?

The rate i=8% is for 1 year (52 weeks). There are n=4 terms in a year. The value of the bill ($10) is not used in this problem. The effect interest rate (EAR) EAR=(1+i/n)^n - 1 =(1+0.08/4)^4 - 1 =1.08243 - 1 =0.08243 =8.24% (to hundredth %)

Exactly, we're looking for the change of sign which implies the presence of a root. It may be intuitive, but this fact is dependent on the Intermediate Value theorem, as stated above.

f(x)=x^3+5x-4 f(0)=-4 f(1)=2 Since f(x) is continuous (as are all polynomials), there exists a value c such that f(c)=0 (-4≤0≤2, and 0≤c≤1) by the Intermediate Value Theorem.

Calculus II - to Rosali
We must be careful to insert parentheses when they are needed. Expressions are evaluated according to the PEMDAS rule. For example, what you posted is mathematically equivalent 3x²+x +[9/(x²+5)]*(x-6) which is (probably...

Maths - vectors
Displacement is a vector obtained by the difference between final and initial positions, so displacement during t[1,3] =p(3)-p(1) You can leave the result in vector form <δx, δy>. Note: subtraction is done component by component, ex. <7,4>-<2,3>=&...

micro economices
First we need to understand "cardinalist", someone in favour of the cardinal utility theory, namely utility (happiness) is quantifiable, [ and can be mathematically represented by a curve, and diffentiable, most of the time. ]

trigonometry - to Jack
Drawing a diagram in geometry is a must. All we need to do is to follow instructions step by step. If you refrain from drawing diagrams, you will be handicapped in almost ALL geometry problems. This is how you could proceed: "the angle of elevation of a tower at place A ...

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