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Posts by MathMate

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Assistance on whether numbers are correct? Financi
To check your answer, 523.23*4*25=52323 which is only about 6% of the final amount, which seems too low. So looking at your working: Future value = (payment)[((1+i)^n-1)/i] is basically correct, if we assume i=interest per period. rate 4.2% is annual interest (by normal ...

C=child ticket A=adult ticket 4C+8A=128 => C+2A=32...........(1) 6A=72 => A=12.................(2) Substitute (2) into (1) C+2(12)=32 solve for C.

Part 1: Use the amortization formula: P=(L)R^n(R-1)/(R^n-1) where P=Payment per period L=Loan amount R=1+interest rate per period n=number of periods For example, if monthly payment is required for a 100,000 loan over 30 years at 5% p.a., then L=100,000 R=(1+0.05/12) n=30*12=...

Bayes' Theorem
Agree with the first part, except that with probability calculations, I prefer to work with fractions. If a decimal answer is required, it will be rounded at the end. First Part: P(A)=1/200 P(+|A)=9/10 P(-|A')=1/10 P(+)=P(+|A)+P(+|A') =(1/200)(9/10)+(199/200)(1/10) =13...


A perpetuity payment is a payment received from an initial deposit and annuitized over an infinite period of time. In order for this to happen, each single payment must be equal to the interest generated from the initial deposit (assuming a constant rate of interest). The ...

Calculus Finals Review sheet!! Explanation needed
Next time please number your questions if you have multiple questions. In fact, it is preferable to make separate posts for different questions so that answers and questions will not be confused. If you are referring to the following question: "The altitude of a kite is ...

Stats: Counting Techniques Fundamental Theorems A
number of ways of choosing male employees N1=12C3=12!/(3!9!) number of ways of choosing female employees N2=10C3=10!/(3!9!) Number of possible teams =N1*N2

Check Answer!! Conditional Probability
The idea is sound, but You have the very first step incorrect. In probability problem, it is best to write out the assumptions, so that you AND others who read your text will be able to understand. You have assumed 10000 people in the population, which is ok, but 1/500 of ...

Assuming the question is actually: (n+7)! / (n!(n+6)(n+4))=9!/3 and n>0. First simplify the left-hand side by cancelling n!: (n+7)! / (n!(n+6)(n+4)) =(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)/((n+6)*(n+4) =(n+1)*(n+2)*(n+3)*(n+5)*(n+7) So the problem reduces to solving the ...

Since we don't have data that Tara has, perhaps a few thoughts will help direct us to the right answer: 1. Does the number of scratches always increase with time? Can it possibly decrease (without changing the windshield)? 2. Assuming the climatic conditions remain more or...

Isn't this the answer? "He needs to check the quality of 30% of the sweaters. "

Math - Coordinate Geometry
For the given figure of A(-2,3), B(5,4), C(4, -3) and D(-3, -4). we write it out as, repeating A at the end: A(-2,3), B(5,4), C(4,-3) D(-3,-4). A(-2,3), Find the four products: Ax*By-Bx*Ay=(-2*4)-(5*3)=-23 Bx*Cy-Cx*By=(5*-3)-(4*4)=-31 Cx*Dy-Dx*Cy=(4*-4)-(-3*-3)=-25 Dx*Ay-Ax*Dy...

Math - Coordinate Geometry
sorry, 24 is not correct. one diagonal is 6√2, and the other is 8√2. The product of the two diagonals/2=?

Math - Coordinate Geometry
1. A rhombus is a parallelogram with adjacent sides equal. 2. A rhombus is a quadrilateral with four equal sides. To prove that a figure is a rhombus, use either 1 or 2 above. In this case, proving that the four sides are equal is relatively easy even by visual inspection. The...

μ=np=10 σ²=npq=np(1-p)=9 Solve for n and p. Hint: substitute np in the second equation and solve for p. Hence solve for n.

compute the probability that a person who tests po
Solve using a probability tree: (sick)/0.003*0.9=0.00282 (positive) /0.003\0.003*0.06=0.00018 (false negative) 1 \0.997/0.997*0.02=0.01994 (false positive) (not \0.997*0.98=.97706 (negative) sick) check: .00282+.00018+0.01994+.97706=1.0000 √ "the probability that a ...

Conditional Probability
Note: The numbers in the contingency table can also be obtained by a tree diagram considering a sample of 4000 people. 400--A-->10--B-->9 -------------~B->1 ----~A-->3990--B-->399 --------------~B-->3591

Conditional Probability
Given: P(A)=1/400 P(B|A)=9/10 P(B|~A)=1/10 By the law of complements, P(~A)=1-P(A)=399/400 By the law of total probability, P(B)=P(B|A)*P(A)+P(B|A)*P(~A) =(9/10)*(1/400)+(1/10)*(399/400) =51/500 Note: get used to working in fraction when doing probability. (a) Find P(A|B): By ...

Take out your calculator, or do it by hand, 275/50=55/10=5 1/2

To understand the solution given below, you will need to know a few definitions or identities: 1. P(A)=probability of event A will happen. 2. definition of conditional probability: P(A|B)=P(A∧B)/P(B) i.e. Probability of event A happening GIVEN that B has already happened. ...

Use the annuity/compound interest formula: FV=A(R^n-1)/(R-1) where A=monthly deposit R=1+interest/period=1+0.02/12 FV=future value = 20000 n=number of periods = 7*12 Solve for A, where

Indeed, density of sand (and other soil related materials) depends on the moisture content. For dry sand, it is approximately 1.6 g/mL. Ref:

Use the annuity/compound interest formula. FV=Future value A=amount deposited each period = 3000 R=1+interest per period (year)=1.02 n=number years money was deposited FV=A(1+R+R^2+...+R^(n-1) =A(R^n-1)/(R-1) Take out your calculator and find FV. It should be around 150000.

The five cases of congruence of triangles are: ASA SAS SSS AAS and RHS If you can find which case this belongs, then the two triangles are congruent. If not, please post again for more information.

No problem! Yes, the best way to get more help is to post new questions, with a later time-stamp, and have more people looking at it.

Indeed it is! The theorem applied to the present situation tells us that AD/DB = AE/EC Fill in the values of the sides (three of them) and hence calculate the remaining side before making the choice.

"Another method to prepare MgI2 is mixing powdered elemental iodine and magnesium metal. In order to obtain anhydrous MgI2 the reaction should be conduct in a strictly anhydrous atmosphere and dry-diethyl ether can be used as a solvent." from

A contingency table helps. Complete the table Test . has . . doesn't have result disease disease + = 0.005*0.93 0.995*.02 - = 0.005*0.07 0.995*.98 tot. 0.005 0.995 The probability of a person who tests positive actually has the disease is in one of the cells.

Answers to questions of this kind are usually found readily by googling the key words. For example, googling "ammonium nitrate" will give you a whole lot of information about the salt, how it's formed, the manufacturing processes, its applications/uses, etc. You ...

Let x=number of cars he sells. $750 is his base salary. If he sells no cars, he gets paid $750. If he sells one car, he gets paid $750+300. If he sells two cars, he gets paid $750+300×2. If he sells three cars, he gets paid $750+300×3. If he sells x cars, he gets ...

Algebraic equations real life problems
"Widths are top--3b in. bottom--(2+a)in." ⇒ 3b=2+a "Lengths are left--(3a-b) in. And right--(2+a+2b) in." ⇒ 3a-b=2+a+2b Solve for a and b, hence perimeter. Hint: both a and b are positive, and are both integers.

Assuming money is deposited at the end of every month, and interest is compounded monthly, then the following annuity formula applies. FV=21000=A(1+R+R²+R³+...+Rn-1) =A(R^n-1)/(R-1) or A=FV*(R-1)/(R^n-1) where FV=future value=21000 A=monthly deposit (to be evaluated...

M W M W M W M W M This means that 5 men will have 5 different places to choose from, and women will have four. Men's choices = 5*4*3*2*1 Women's choices = 4*3*2*1 They can be arranged independently, so the product of the number of choices of each gender will give the ...

Conditional Probability
See similar problem here:

Math | Algebra
30% red means 70% white. Given 8 cups : 30%, then x cups : 70% Cross multiply and solve for x: x=8*70%÷30%=?

Find the z-score using Z(x)=(x-μ)/σ μ=mean, σ=standard deviation. Then use the normal distribution table to find the upper tail, i.e. probability of X greater than Z(x).

I think the problem says: f(x)=-4.7x+1 Very often checking your post before or after posting will save you time, and that of helpers. You need to know what is "domain" and "range". If you don't find the meaning of the words in your class notes or ...

math! again
3)The factors of 4 are: 1, 2, 4 The factors of 5 are: 1, 5 The factors of 6 are: 1, 2, 3, 6 Then the greatest common factor is ?.

Chemistry (Dr. Bob)
Quite right Dr.Bob. Thank you for the note. It just doesn't decompose like that. Carbon is required to reduce the oxide. Namely 2Al2O3+3C -> 4Al + 3CO2 The electrolysis part is more to help prevent the formation of CO. However, as you said, the ratio of Al and Al2O3 ...

Chemistry (PLZ HELP)
Aluminium oxide: Al2O3. Molecular mass (approx.)=27*2+3*16=102 Aluminium: Al Molecular mass=27. Write down the equation: 2Al2O3 -> 4Al + 3O2 (electrolysis) So 2 Al2O3 molecules -> 4 Al molecules. 2*102 Al2O3-> 4*27 Al 204 : 108 Use proportion to solve for the final ...

You will need to describe how the two pulleys are arranged, as well as the two blocks. Without that, it is not clear how the system is set up. You can also opt to post an image of the diagram/figure.

This might help you to learn about a.p. and g.p.:

Y-intercept is the point where x=0. From the given function, P=(6000-400x)*(x-2) we substitute x=0 to get P=(6000-400(0))*(0-2) =6000*(-2) =-12000 It also means the loss incurred when the manufacturer gives the paper away ("selling" at a price of x=$0 per ream).

Use Perimeter = 2(L+W) = 20 Substitute L (that you calculated) into the equation, and solve for W, hence L.

If you buy 10 apples with $2. How many apples would you get for $1?

Matrix application
"Substitute each pair of x,y values to produce 3 simultaneous equations with unknowns a, b and c" As instructed, x = 150m y = 190.650m a(150)^2+b(150)+c = 190.65 a(300)^2+b(300)+c = 611.450 a(450)^2+b(450)+c = 831.141 Form matrix, A= |150^2 150 1| |300^2 300 1| |450^...

Set up equations to solve for X=number of goats in farm x, Y=number of goats in farm y. "The ratio of the number of goats in farm x to the number of goats in farm y was 9:4." => X/Y=9/4 multiply by Y to get: X=9Y/4.....................(1) "After 35 goats were...

Fermat's little theorem says if p is prime, and p does not divide a, then a^(p-1)≡1 mod p. Here we put p=61, therefore 61 does not divide a=8. Hence 8^(61-1)≡1 (mod 61), or 8^(60)≡1 (mod 61). Recall the multiplication rule of modulus arithmetic, 8^120&...

Assuming ACD is a line segment, then by the rule of line segments, AD=AC+CD => CD=AD-AC=20-15=5 If ACD is not a line segment, then please supply additional information/description.

R=age of Rosa A=age of Amy then form two equations using information given: "Rosa is 14 years older than her sister Amy." => R-A=14 => R=A+14.................(1) "3 years ago, she was 3 times as old as Amy." Three years ago, both were 3 years younger...

Let long side = S (cm) then short side = S-10 (cm) A parallelogram has opposite sides of equal length, therefore the perimeter equals 2(S + (S-10))=4S-20 We were given the perimeter is 88 cm, therefore 4S-20=88 Solve for S (the long side) and S-10 (the short side).

First find out how many distinct letters are there in the word MATHEMATICS, call this number "n". For example, the word SAILING has the letters S,A,I,L,N,G, 6 out of 7 letters are distinct, while the letter I is repeated but not counted more than once. In the English...

Assuming the favourite and second favourite bands are distinct (different), then there are four choices for the favourite band, and (4-1)=3 choices for the second favourite band. Use the multiplication rule to find the number of possible votes.

1826.11 (1826.11019) is the correct monthly payment to obtain 100,000 at the end of four years. Note that your formula assumes that payments are made at the end of each month. The interest is the cumulative amount at the end of four years less the total amount paid, namely 4*...

Sue, You don't have to change the screen name. It will be easier for teachers to work with the same person. It would be similar to your previous question (in the name of Paige), except that to get every answer wrong, you only have three choices (and the student must know ...

We will assume that all the questions are independent of each other, and that each question requires exactly one choice. That is the instruction "indicate all that apply" will not be applicable. There are four ways to arrange the answers to the first question. There ...

Yes, the limiting reactant is CaCl2. Since it is a reactant, there is no new CaCl2 formed... unless you meant something else. The same idea extends to products. The overall molecular ratios are 1:1:1:2. So you can calculate amounts of products formed using the ratio.

Na2CO3 + CaCl2 = CaCO3 + 2NaCl Yes, the first step is to write a balanced equation of the reaction. The coefficients of the balanced equation tells us the relative number of moles of each reactants is required, as well as the relative number of moles of the products. In this ...

On an inclined plane, the forces acting on an object of mass can be resolved along the incline (+ up) as follows: Gravity force+Friction force =-mgsin(θ)+Ff The above sum equals zero if the object stays in equilibrium. Therefore Ff=mg sin(&theta) The above can be derived...

Since all numbers are known for m1,m2,g and θ, we can calculate that force pulling block up-plane = T = m2g=98.1 N Force pulling block down-plane = mg sin(&theta) =58.90 N The difference is due to friction, of the amount = 39.20 N I believe you answer is correct. Book ...

Math (calculus) (mean values)
Part (a) average rate of change is the difference between the end of last month to the beginning of the first month, divided by the number of months, so Average=(s(12)-s(0))/12 Part (b) Calculate the derivative of the function s(t), with respect to t: d s(t) / dt =d(1085-1395...

Civil engineering

Have you read the reply: ? If you have and it was not clear to you, would you consider posting a follow-up question instead of a new post?

How many of the dvrs are NOT defective? If selecting any item from the inventory has equal probability, what is the probability of selecting any NON-defective item from the 50 dvrs?

It all depends on the size of the units. If the mean of the y-values is, say, 100, then residuals not exceeding 0.6 is ok. If the mean of the y-values is 1, then it's not acceptable. Also, it is related to the number of data, and the sign of the residuals as well. For ...

Can someone help me please I've tired this problem
See similar problem here:

Data Probability
See similar problem here:

Factor x²-6x+9=64 x²-6x+9-64=0 x²-6x-55=0 the factors of 55 are 11 and 5 the difference of which is 6, so try (x-11)(x+5)=0, and it works. This the solutions of the equation are {11,-5} Check: (11^2-6*11+9=64, so 11 is good. Check the same for -5.

Given: radius=7cm Circumference=perimeter of rectangle Ratio of breadth:length = 4:7 Let b=breadth, then length=(7/4)b circumference=2π(7)=14π circumference=perimeter therefore 14π=2(b+(7/4)b) 14&;i;=2(1+7/4)b (11/2)b=14π b=14π(5/11)=7.997=8 cm approx. Check: ...

o 6 o o o 5 o 7 o o o 8 o The sum of the four angles equals 360°. ∠ 5= ∠ 7 (vertically opposite angles) Similarly ∠ 6= ∠ 8 (vertically opposite angles) Sum of the four angles ∠5+∠6+∠7+∠8=360° 2( 2x+15 + 3x) = 360° solve for x and ...

Math(Scale Factors and Scale Diagrams)
The game is 1/4 of the wanted size, so each of the dimensions of the wanted sized table is four times as big. For example, if he wanted a size twice as big (scale factor = 2), then the dimensions are 2*(9 1/4) × 2(4 15/16) = 18 1/2 × 9 7/8

Let f(x)=2x-tan(0.18x) the area required is given by integrating, ∫(2x-tan(0.18x))dx for x=1 to 5. How did you come up with a value of 9? Please show your work so we can help you correct the steps. As a rough estimate, we can see that f(1)=1.81 f(5)=8.74 And it is a ...

Algebra, please help
5x+3y=7 ...........(1) 3x-5y=-23 .........(2) We try to cancel/eliminate one of the variables. I choose to eliminate y. 25x+15y=35 ...........5*(1)....(1A) 9x-15y=-69 .........3*(2).....(2A) Add (1A)+(2A) 34x=-34 Solve for x. Substitute value of x into 1 and solve for y.

P=2950 (principal) i=0.081 per month (period=1 month) n=18 (periods) A=P(1+i)ni (accumulated value) Take out the calculator and calculate the value of A, value after 18 months.

We don't see the diagram, but assume that the cart is at the beginning of an uphill slope of angle θ with the horizontal. The problem comes to a matter of conservation of energy, since friction is neglected. Kinetic energy of the running boy KE= (1/2) mv²=(1/2)...

Algebra 1B Radical expressions & data analysis
I think you meant: #4 6/(√3 + 2) #5 y = 3√(6x + 42) #6 y = 2 √(3x + 4) - 5 #7 y = √(x+4) - 3 Note that a space does not imply parentheses, which are very important in mathematics. Read, for example:

Try reading carefully the following link:

See your other post.

Probability - marbles
8 black and 7 green in urn (15 in all) 5 drawn with replacement. Probability that first one is green: P(1)=7/15 Probability that second one is green P(2)=7/15 (ball is replaced) ... P(5)=7/15 For all 5 steps to succeed, multiply together the individual probabilities P(all five...

A number is rational when it can be expressed as a fraction of integers. For example, 24 is rational because 24=24/1=48/2... -3 is rational because -3 = -6/2 = -3/1 .... So see if you can figure out if -49 is rational.

height, h=135*16 cm = 21.6 m Time taken, t= 5 min 40 sec = 340 seconds mass, m= 63.9 kg g=9.81 m/s² (note that all values are in SI units) Work done, W = mgh J (joules) = 13540.2 J (multiply together m,g & h to get work done) Power = work done per second, so = W/t J/s =...

Cats have 4 legs. Budgies have 2 legs. Two ways to do it: 1. use algebra. C=no. of cats 3C=number of budgies total number of legs 4(C)+2(3C)=30 10C=30 C=30/10=3 So 3 cats and 9 budgies. Check: 3*4+9*2=30, checks. 2. by guessing We don't know how many of each, make a guess...

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Step 1 initially there are 20 students of which 6 have blue eyes. Probability of choosing the first with blue eyes is 6/20. Step 2 There are then 19 students left of which 9 have brown eyes. Then the probability of choosing a brown eyed student is 9/19. Since it is a two-step ...

computer science
pseudocode: x=input package name, x=1 for A, etc. n=input number of hours ... cost=0 if x=1 then cost=9.95+min(0,2*(n-10)) else if x=2 then cost=13.95+min(0,1*(n-20)) else if x=3 then cost=19.95 else print "incorrect package" endif print x, n, cost

Very cute problem. The answer is as cute! Look at the table shown in: f(x) and f'(x) are given on the third row! If you are in an exam, your teacher may not appreciate the "cute" answer. So let's work it out: f(x)=1/(1+(1/(1+(1/x)))) If ...

friction & centripetal force
Given: r=4.5 m angular velocity ω=2*π/7.2 rad/s =0.8727 rad/s When the cat is at position of 3 or 9 o'clock, the horizontal acceleration due to centripetal force is at its maximum. The centripetal acceleration is a=rω² The centrifugal force is F=ma=mr&...

The logical solution is to take away 3 from 27 and divide by two to give the smaller number. Then add 3 to get the bigger number. Check by adding the two results to see if they add up to 27. If you have to use system of 2 linear equations, then let x=smaller number y=larger ...

Oops! Good catch! Thanks. Elcia, please go with Reiny's answer.

Use the mortgage formula: Future value = FV = 1000000 payment per period = P (to be found) rate of interest (per period) = i (0.06/12=0.005 per month) R = 1+i = integrated rate = 1.005 n = number of periods = (55-28)*12=324 then FV=P(1+R+R²+R³+....+Rn-1) =P(R^n-1)/(R...

Math Help
Yes, they are correct! I didn't notice you gave answers, sorry.

Math Help
For question one, you need to look at each number (of eight digits) which represents 8 campers. Any digit 0 or 1 represents out-of-state campers. Count how many of the 20 numbers contain at least two of 0 or 1. For example, the first number is 69531217 which means that there ...

There are 360° in a whole turn (an hour). So 24 degrees is, by proportion, (24/360)=1/15 of an hour. Add this to 12:59 to get the time.

One Math Problem
See help above In fact, we are the ones to ask you for any thoughts!

P(diamond)=13/52 P(king)=4/52 To select a diamond and THEN a king (with replacement) is then the product of the two above probabilities.

Personal Finance
Front end loading is the commission of a given percentage to be deducted from the total amount invested. Here the percentage is 5.25%. The total amount invested is $20000. The product of the two is the commission (front-end load). See definition of front-end loading: http://...

This system can be solved readily by elimination. You can eliminate y by adding the first equation to twice the second equation. Show us what you get!

You need to find n^m where m is the sum of the digits of n. Step 1: Find the sum of digits of n. You could try the following algorithm, either inline or using a function (method): Let k=n m=0 do until k<=0 m+=k%10 k/=10 end do Step 2: Raise n to the mth power: result=1 k=m ...

Take moments about the fulcrum and equate to zero. Solve for F=effort. on the load side: force = 600N distance from fulcrum= 0.5 m On the effort side: force = F N distance from fulcrum= 1.5m - 0.5 m = 1 m. Moment equals force time distance from fulcrum, clockwise positive.

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