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Posts by MathMate

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The future value FV can be calculated by summing payments and simplification using factorization: FV = S(1+(1+r)+(1+r)^2+...+(1+r)r^(n-1)) =S((1+r)^n-1)/((1+r)-1) =S((1+r)^n-1)/r FV=future value S=Semi-annual payment r=interest per period (6-months) n=number of periods (6-...

fourth term: ar^4 7th term: ar^7 Let common ratio = r then 7th term / 4th term = ar^7/ar^4 = r³ therefore r = cube root of r³ Fifth term = fourth term * r

The first step in evaluating a limit would be to substitute the limiting value into the expression. If it evaluates to a valid number, that is the limit. Example: limit x->1 x²/x =1²/1 = 1 Since sinx/tanx + tanx.sinx ≡ 1/cos(x) so the limit is 1/cos(0)=1.

Solve for x in 1500+0.04x=5000

Math - 7th grade (repost)
The number of CD's between Q1 and Q3 should be half of the total number of CD's. From the plot, you will not know how many cost less than $14.6, but since Q1 is 14.6, there are at most one quarter of the number of CD's cost less than $14.60. (One quarter of 12 CD&#...

Sum and Difference
Sum and difference problems are solved as follows: Larger number = (sum+difference)/2 Smaller number = (sum-difference)/2 So 1/p = (4+3/2)/2 = 11/4 p = 1/(11/4) = 4/11 I will leave it to you to do the smaller number (1/q).

We are given x²+y²=137 (x-y)=7 this means 49=(x-y)² =x²-2xy+y² =x²+y²-2xy =137-2xy From 49=137-2xy can you solve for xy? The longer way: equation 1: x-y=7 equation 2: x²+y²=137 Now solve the non-linear system in x and y.

Use law of exponents (ax)^b = a^b × x^b y=kx^3 y1=k(1.5x)³=k(1.5^3)x³=3.375kx³=...

There is an ambiguity in the question to be clarified about the interest rate. Generally annual interest is quoted. The wording of the question casts a doubt as to 7.2% is monthly or annual interest. Considering that 86.4% annual interest is illegal in some countries, 7.2% ...

Math - 7th grade
See later post

You're welcome. Also note a correction is required: 0.02/5 = 0.004/1 < 0.01=1%

Convert the given fraction to an equivalent fraction with either 1 or 100 as the denominator. We know that 1% = 1/100 = 0.01/1 So say, 0.2/5 = 0.004/1 < 0.01=1% 2/500 = 0.4/100 < 1/100 = 1% etc.

Repost, see previous discussions

French, foreign language
Yes, you need to correct the sentences where the verb and complements do not agree. "Ce sont" is followed by a noun in plural, and "C'est" is followed by a singular noun. Examples: Ce sont des carottes. (Ce sont....plural) C'est un hamburger. (C'...

Math Help Me Please
Ouch! question says "Determine which ordered pair is not a solution of "

Math Help Me Please
substitute x (first number in parentheses) into the right-hand side of the equation and check if the value equals y (second number in parentheses). For example, let's check (9,-48) which is not taken from the choices: -5(9)-4=-45-4=-49 but -49 does not equal -48, so (9,-48...

Question says: If not, then you lose your discount and you pay a 20% premium on the usage outside of that time. Check that you have calculated without the 15% discount.

Since usage is greater outside the prescribed period, there will be a 20% premium for those kW-h. Can you please show us how you got $51.08?

Yes, b is correct. Your method works well without having to memorize formulas. If the equations had been in the slope intercept form: y=-x+8 and y=-x then you could also calculate using distance = y-intercept difference / &radic(1²+(-1)²) =8/√2 =4√2

Actually, the expression is the expanded form of (x+2)(y-3)=0 which by the zero-product property means x+2=0 => x=-2, or y-3=0 => y=3, or both of the above. So yes, (a) is correct.

Algebra 2
If you are working on polynomials, then binomial is a polynomial with 2 terms, for example, (x+4) is a binomial, or (x³ - 2x²) is a binomial. The first example is a binomial with a degree of 1 (highest power of the variable), and the second is a binomial of degree 3...

The parallelogram of forces yields a triangle with vectors 10,15 and 20. where 20 is the resultant. The angle between the two vector is the supplement of the angle (between vectors 10 and 15) solved by the cosine rule. Draw the parallelogram of forces to understand why it is ...

If the quarter circle has the radii horizontal and vertical, the difference in height equals the radius=1.6m. Neglecting friction and other dissipative forces, then conservation of energy holds, and so KE+PE=0,or (1/2)mv^2 + mg(h-h0)=0 Solve for v where h=0, h0=1.6m and g=9.81...

Very often the phrase "of the" means multiply. So he packed 1/3. 1/2 "of the" 1/3 were shipped, this means (1/2)*(1/3) = 1/6 were shipped.

Do you have a diagram?
It is not clear to me how M1 and M2 are related, are they linked vertically by a string, are they released at the same time?

To Sara: I got 5/√2 as well. Perhaps it is time to check if there are typos in the question or the answer. Also, to print s∈R, you can write s & i s i n ; R, but skip the spaces.

Anne throws a ball horizontally... so the problem reduces to a free-fall over 50m. The equation Dy=-50m = V0t+(1/2)gt^2 will let you solve for the time to hit ground, and where v0=initial vertical velocity = 0, and g=acceleration due to gravity = -9.8 m/s² During this ...

calculus trigonometric substitution
You're ok so far. You only need to convert sin(u)cos(u)/54 back in terms of x, which should be x/(18x²+162). You can start by sin(u)cos(u)/54=cos^2(u)tan(u)/54 =3tan(u)/[162(sec²(u)) =...

Hint: think of what you find in the kitchen.

computer applications
It would be much easier for you to open a spread sheet and try it out. I suggest you do some practical work because it will help you understand how it works, and it will help you recall the procedure in the future.

Let's check: r1=(3,2,-1)+s<1,1,1> When s=0, r passes through the point (3,2,-1). Now check the product of the two direction vectors: <1,1,1> dot <1,1,-2> =1+1-2 =0 So the two lines are perpendicular and r1 satisfies the required conditions. Note: multiple...

Stress=σ=Force/Area Strain=ε=σ/E Change in length = ε*Length. Useful conversion factors 1 GPa = 10^9 Pa 1 kN = 10^3 N 1 m = 1000 mm Try to do calculations in standard units, namely kg, m, s.

You can work on the flow-chart based on a pseudocode such as: enter ID, ID enter number of policies sold, N if N > 25 print ID, N endif

1 pascal = 1 N/m² 1 MPa = 10^6 Pa Stress = Force /area, all in appropriate units. = 91*10^3 N / (π0.030²/4) m² Evaluate and convert to MPa.

1. find average acceleration, a Vi=0 S=(1/2)at^2 139 m =(1/2)a(8.7²) a=3.6729 m/s² 2. Find work done, W a. using F=ma, W = F*S = ma*S where m=1100 kg, S=139 m, a=3.6729 m/s² or b. using energy (neglect loss) final velocity, Vf = at where t=8.7 s final energy =(1...

If we select 6 out of 300 subjects, we can assume that the probability remains approximately constant, thus use of the binomial distribution is applicable, where n=6 p=0.58 bin(6,0.58, 3) =C(6,3)*0.58^3*0.42^3 =0.2891 approximately To be more precise, we calculate the ...

The question satisfies requirements for a binomial distribution, where n=10 p=1/2 Probability of r girls out of n =P(G=r) =(n, r)p^r (1-p)^(n-r) where (n,r)=combination n choose r = n!/(r!(n-r)!) For at least 2 girls out of 10, P(G>=2)=1-(P(G=0)+P(G=1)) 1-(1)(1)(1/1024)-(10...

Expected value is the sum of the product of all possible outcomes and the respective probability. Example of rolling one six-sided die: Payout equals the number appearing on top face. expected value = 1*1/6+2*1/6+3*1/6+4*1/6+581/6+6*1/6 =3.5

set sin²(x) = 1-cos²(x) 16(1-cos²(x))=16-8cos(x) and substitute c=cos(x) 16c²-8c=0 c(2c-1)=0 c=0 or c=1/2 Find all solutions for c=0 in [0,2π) and all solutions for c=1/2 in [0,2π). Substitute back the solution and check that they are valid.

Tia, You may or may not realize that here there are tutors who answer 50 to 100 posts a day on a voluntary basis just in order to help students. Any repeated post may get read 8 times by 8 different tutors, and worse, could also end up with a duplicate answer which you may not...

To get the first number right is 1 out of 31 choices. For the second number, there are only 30 choices (five different numbers)... So the probability of getting all five numbers right would be: (1/31)(1/30)...(1/27).

Calculus question: Let x=length remaining below winch. and ρ=mass density Work done winding up a length of dx is equivalent to bringing the length dx up by a distance of x, i.e. dW=ρg xdx Integrate W=ρg∫xdx from 0 to L =ρg L²/2 Physics question: ...

Initially, 49 out of 55 returns do not contain errors. So probability of selecting the first (first trial) correct return is 49/55. After this, there are 48 correct returns out of 54, so....48/54 For all three trials to succeed, we multiply the probabilities of all three ...

The probability for at least one correct answer, P(X>=1) is the same as probability of not getting ALL wrong answers or 1-P(X=0). P(X=0) is getting every one wrong, with a probability of (1/2)^n, where n is the number of questions guessed.

Note: 1L = 1000mL, so 100mL = 0.1L Use proportions: 3 mol are required to make 1 L of 3.0M solution. x mol are required to make 0.1 L of 3.0M solution. x=3 mol * 0.1L /(1L) =0.3 mol

Events: A=from store A B=from store B D=defective then probability of defective player given it is from store A: P(D|A)=P(D∩A)/P(A)=P(D∩A)/0.3=0.027 then probability of defective player given it is from store B: Solve for P(D∩A) P(D|B)=P(D∩B)/P(B)=P(D∩B)/0....

Physics (Tension and Springs)
          . T          .         .       . F-----       .     ...

Yes, Emily's approach will give the correct answer. You can also use another kinematics relation to solve for distance x: V1^2-V0^2=2ax where V1=final velocity = 0 V0=initial velocity = 12 m/s a=acceleration = -3 m/s² x=distance travelled in m.

Exponential distribution has mean = λ where λ is the number of occurrences in a unit time, say one hour. So λ=60/15=4 The exponential probability distribution function is given by: P(T=t)=λe-λt and the cumulative distribution function: P(T<...

Calculus check
You're asking for minimum value of f'(x) for 0≤x≤6 where f(x)=6x²-x³. First we need to know if f'(x) is increasing, decreasing, or there's a minimum within [0,6]. We can find out by first finding f'(x)=12x-3x² Find critical points for f...

Calculus check
First step, substitute x=1 to get (x^3-1)/(x^2-1)=0/0 need to do something. Then since both numerator and denominator are factorizable readily, we have Limit (x->1) (x^3-1)/(x^2-1) =Limit(x->1) (x-1)(x^2+x+1)/[(x-1)(x+1)] =Limit(x->1) (x^2+x+1)/(x+1) since x≠1 =...

perhaps you have confused the answer with that of a different problem, the answer is not 3/2. Since putting in x=1 gives 0/0, you can either use d'Hôpital's rule, or simply multiply by the conjugate (sqrt(x)+1) of the numerator to create the common factor (x-1). ...

f'(x)=sin(x) then by the derivative of trig functions, f(x)=-cos(x)+C Now solve for C in f(π)=-cos(π)+C=3

Please check my Calculus
It would help you if you say why you chose B. An inflection point is the point (x,f(x)) such that f"(x) [i.e. second derivative) equals zero. f(x)=x^n f'(x)=nx^(n-1) f"(x)=n(n-1)x^(n-2) So solve for f"(x)=0 when n is odd, say n=3, 5, 7... and solve for f&...

Calculus check
The slope is f'(x)=d/dx(tan2x)=2sec²(2x) so evaluate f'(pi/8) and make your choice again!

1. S=(-7,-4) 4(-7)= 28≠-10 =2(-4)-2 so S is incorrect. 2. S=(-1,4) (-1)+2(4)=7 = 7 3(-1)-2(4)=-11 = -11 Yes, S is correct 3. S=(4,12) 4(4)-3(12)=-20 =-20 5(4)-7(12)=-64 =-64 Yes, S is correct. 4. S=(2,1) 2(2)-5(1)=-3 ≠-1 So S is not correct.

Math - Equations
See your other post.

E=mass of earth M=mass of moon D=distance between centres of earth and moon. r=distance from centre of the earth m=mass of a certain object of the experiment Using Newton's law of gravitation, F=GMm/r^2 G=gravitational constant then force due to earth Fe=GEm/r^2 force due ...

Calculus check
Hmm... Mean value says that (f(x2)-f(x1))/(x2-x1) = f(x0) where x0∈[x1,x2] (f(x2)-f(x1))/(x2-x1) = (5-7)/2 = -1 f'(x)=-3/x^2 f'(sqrt(3))=-3/3=-1, Yes, C is correct.

Set up a contingency table and work from there: Contingency table of probability -------------------------------- case (treated) (not treated) outcome dies...(1/10)....(7/10) lives...(9/10)....(?/10)

Calculus check revised.
Yes, B is correct, again using chain rule.

Calculus check
Yes, B is correct. f'(x) d(sin^2(3-x))/dx Apply chain rule =2sin(3-x) dsin(3-x)/dx =2sin(3-x)cos(3-x)d(3-x)/dx =-2sin(3-x)cos(3-x) Then calculate f'(0) from above.

log(y-1)=-log(y-9) using the property of logarithms, log(x) = -log(1/x), then log(y-1)=log(1/(y-9)) take anti-log on both sides, y-1 = 1/(y-9) then solve for quadratic in y after cross-multiplication.

What do you do when you have the third object to be placed and supposed to place in a box already filled with two object? You would skip that case. How many of these cases do we have?

Assuming the 10 boxes are distinguishable or ordered. There are 10 ways to put the first item, 10 for the second, and 10 for the third. So by the multiplication rule, there are 10^3 ways to place the three objects.

If the y-coordinate of P is missing, you need to supply it. If it is not given, then use w to complete the problem. P(5,w),Q(-1,2), Mid-point: M((5-1)/2, (w+2)/2)=(Mx,My) Slope of PQ: m=(2-w)/(-1-5) slope of perpendicular: m'=-(-1-5)/(2-w)=6/(2-w) Perpendicular bisector ...

Rule for translation: (x,y)-> (x+h, y+k) Solve for h,k from (-2,3)->(10,10) (a) hence find the image Q' of Q. (b) if mp-nq=(-12,9), this means m(-2,3)-n(1,3)=(-12,9) Split into individual equations for x and y to get -2m-n = -12 3m-3n = 9 Solve for m,n.

Vf^2-Vi^2=2aS a=acceleration/deceleration Vf=final velocity = 0 Vi=initial velocity = 50 or 100 S=distance travelled. By proportion, double the initial velocity, will quadruple the stopping distance, with the same Vf and a.

Assume fine wire has zero mass Newton law of gravitation Weight=mg=GMm/r^2 where units are in m, kg, seconds R1=6400000 (at top of tower) R2=(6400000-20)=6399980 (at bottom) M=6*10^24 G=6.673*10^(-11) Difference in weight =GMm(1/R1^2-1/R2^2) Evaluate. Hint: the difference is ...

Hints: 1. Use basic laws of logarithm: log(a)+log(b)=log(ab) log(a)-log(b)=log(a/b) log(a^b)=b(log(a)) and use the fact that all the numeric values are powers of 2: 2^6=64 2^2=4 2^3=8 2^10=1024 2. I'll get you started: r^2s^2+3t^2+r^2t^2+3s^2 =(r^2s^2+r^2t^2)+(3t^2+3s^2 ) ...

Assuming the raft is navigating in fresh water with ρ=1. Archimedes principle of floatation says that the mass of a floating body equals the mass liquid displaced. So until the mass exceeds the mass of liquid (fresh water) displaced by the volume of the raft, it will float...

Total of (13+17+15+11)=56 balls, out of which 17 are orange and 11 are white. Assume no replacement of balls. The first orange: 17 out of 56 (17/56) The second orange: 16 out of 55 (16/55) The white: 11 out of 54 (11/54) The probability of pulling in the given order is the ...

You're welcome! :)

From the ratio of molar masses according to the equation, find the required mass of H2 for 45.9 g of CuO. If the required mass of H2 is greater than 2.57g, then the limiting reagent is H2. If the required mass of H2 is less than 2.56g, then the limiting reagent is CuO. MM for ...

Order is not important, so 5 ways to find a male, and 7 ways to find a female. Using the rule of multiplication, the number of ways to find a male and a female actor is 7*5=35 ways.

Since it is braking, the acceleration is negative. Use the standard equation Vf^2-Vi^2=2(a)S where Vf = final velocity (=0) Vi = initial velocity (90 km/h=90*1000/3600=25 m/s) a=acceleration required (m/s^2) S=distance = 1.3 km = 1300 m 0^2-25^2=2(a)1300 Solve for a (in m/s^2)

Molecular mass of CH4=12+4=16 Molecular mass of H2O=16+2=18 Use the combustion equation: CH4+2O2=CO2+2H2O or 16 grams of CH4 should produce 2*18=36 grams of H2O. If there are only 9g of H2O produced, use proportions to calculate the mass of CH4 that produced the H2O, and hence...

Algebra please explain!!!
Use depreciation formula: Future value = Present value (1-rate)^(number of years) rate is in % per annum = 0.15 number of years = 10 Present value = 92000

Use F=ma For top string, m=2*3.75=7.5 kg a=1.6 m/s62 T1=force in top string For staionary masses, T=mg If in addition, T1 casues upward acceleration, then (T1-mg)=ma or T1=m(a+g)=7.5(1.6+9.81)=85.75 N For the lower string (T2), use same argument, but with a different mass.

Probability =number of successful outcomes/number of possible outcomes. A standard deck has 4 kings and 52 cards. What constitutes a successful outcome is drawing a king. The number of possible outcomes is the number of cards in a deck. So use the definition given at the ...

programming in c++
Make a data structure (or simply a table) to store the pricing schemes. Use a pseudocode to plan the program flow. It should roughly look like the following: 1. Initialize pricing data 2. Prompt for input, e.g. number of persons, category/destination, etc. 3. Perform ...

(a) p=0.87, q=0.13, n=212 need P(X>=50) mean = np = 212*0.87 = 184.44 variance = npq = 23.9772 σ = sqrt(variance) = 4.8967 To find P(X>=50)=P(Z>(50-184.44)/4.8967) =P(Z>-27.45)=1.000 from Normal probability table. Do a similar calculation for (b) using p=0.13

The easiest way is to make a Venn diagram (which you probably know how to do). Draw a box containing 50 students. Draw a circle containing 22 skateboards Draw another circle, overlapping the first, with 18 roller shoes. The overlap represents 6 students with both. So the ...

statistics - can someone please Help me
You're welcome!

statistics - can someone please Help me
Note on log: At college and university level, log to the base 10 is rarely used, so often log stands for natural log, sometimes also written as ln. Log10 is used for log to the base 10. If you are not sure, check ln(0.5)=log(0.5)=-0.6931472 log10(0.5)=-0.3010300 To start, we ...

To find the ions, we need to know the properties of some metals. Since we added chloride and carbonate ions and obtained precipitates, we need to know the solubilities and colours of the following salts: (S=soluble, I=insoluble) Salt Solubility Colour AgCl I White CuCl2 S blue...

Check Answers (Math)
In a typical function y=ax²+k k will shift the graph up and down, so does not affect the width. a is the vertical stretching factor. The greater its absolute value, the narrower the graph gets. A negative value of a will flip the graph about the x-axis, but will not ...

finite math
The two dice are assumed distinct. How many ways are there to get the desired outcomes (success): Sum 4 1-3,2-2,3-1 so 3 5 1-4,2-3,3,2,4,1 so 4 6 1-5,2-4,3-3,4-2,5-1 so 5 7 1-6,2-5,3-4,4-3,5-2,6-1 so 6 ... Continue until 11 (less than 12) and add the total number of ways to ...

Foreign Language, French
For #3, you can also say: Le serveur a couvert la table d'une nappe.

Let N=event of picking a nickel (5 cents) D=event of picking a dime (10 cents) X()=value of outcome P()=probability of outcome Possible outcomes: NN : X(NN) = 10 P(NN)=(3/5)(2/4)=3/10 ND : X(ND) = 15 P(ND)=(3/5)(2/4)=3/10 DN : X(DN) = 15 P(DN)=(2/5)(3/4)=3/10 DD : X(DD) = 20 P...

Math help please!!!
"Min is 4 " I do not find a 4 in the data. Is there a typo in the answer or the question? Q1 is the median of the left half of data, which is 13,13|20,21 For the given data, Q1 equals the mean of 13 and 20, which makes 16.5. Good work!

dy/dx = 4y separate variables, dy/y = 4dx Integrate log(y)=4x+C or y=Ce^4x At x=7, y=6, so 6=Ce^(4*7) C=6/e^28 So y=6e^(4x-28) Check: y'(x)=dy/dx=24e^(4x-28) y'(2.5)=3.655*10^-7 y(2.5)=9.138*10^-8 y'(2.5)/y(2.5)=4.000 ok

Raptor flowchart software
zobon, Raptor is a visual software that does not quite express in words. It is quite visual and almost syntax-free, and you should have no problem working with it. You can also post your particular difficulty, if you have any. If you want your work checked, you can post an ...

Useful information for Kaytlin
Some selected ways to lower the priority of your question: 1. Multiple questions in the same post 2. Multiple questions in the same post of the same category 3. Multiple questions in the same post of the same category, and show no sign of any effort. 4. Multiple questions in ...

geography help needed
geography help needed

french (for Mya)
For French as in math, you cannot make a choice by guesses. You have to understand the rule/method to get the right answer, and then choose the correct one. These questions are based on the following: the noun which the pronouns replace must agree in gender and number. Gender ...

Math Help!
Range of a dataset is the highest data value minus the lowest data value. In light of this, would you change your answer, and why?

Hint: Domain of a set of ordered pairs is the set of all the "x-values", or the first value of each ordered pair. Range is the set of y-values of the ordered pairs.

In general, the line y=ax+b is in the slope intercept form, meaning that a=slope of the line, and b=y-intercept. For example, y=x+2 will have a line that has y-intercept =2 (i.e. the point (0,2)) and a slope of 1. So graph a point at (0,2), and draw the remaining line passing ...

We need to find a and b, so we will look for two equations. The first one is simply the point (1,1), which tells us that 1=y(1), or 1=a(1^3)+b(1)=a+b, or a+b=1............(1) The second one is the fact that the gradient (dy/dx) at (1,1)=-5. Since dy/dx = 3ax²+b, we have -...

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