# Posts by MathMate

Total # Posts: 12,095

maths
Use the point of division formula. Let the divided segment be PABCQ Then r1=PA/PQ=1/4 r2=PB/PQ=2/4 r3=PC/PQ=3/4 Applying the point of division formula to points A, B and C: A(a+r1(c-a), b+r2(d-b)) B(a+r2(c-a), b+r2(d-b)) C(a+r3(c-a), b+r3(d-b)) For more explanations and ...

math
"Will paid 1/3 of the dinner bill." means Micah and Sue paid (1-1/3)=2/3 of the bill. If Micah and Sue paid in the ratio 2:5, that means Sue paid 5/(2+5)=5/7 of their portion. \$6÷5/7=\$8.40 which is 2/3 of the cost of dinner. Proceeding the same way, 8.40&...

The question is not clear when out of context. Are you working with arithmetic or geometric progression? "rate of growth" could be an amount (arithmetic) or a ratio (geometric). Your answer is (almost) correct for linear growth (arithmetic). You only have to put the ...

Maths
We have AD perpendicular to BC. So triangle ABD is right-angled at D. AB=7, BD=3, therefore by Pythagoras theorem, AD=√(AB²-BD²) =√(7²-3²) =√40 Construct triangle ABD with the given dimensions. Extend BD to C such that BC=13. Join A and C ...

Transformations (to Keith)
Keith, please refrain from using different screen names. Also, please mention that you are reposting the question, and reposting within a short time could mean duplicate efforts by tutors, and hence slow the answering process. Your previous question has also been answered here...

Sorry, more details required. The following details seem to be subject to interpretation. Please give your comments. 1. the advance payment in December is a prepayment for the next two months. Does that practice continue for the rest of the loan repayment? 2. Is the 13th month...

Is the interest rate given? When was the 13th month advance payment paid, Dec.15 or January 15?

Transformations - Maths
The general transformation equation is: g(x)=a*f(b(x-h))+k where h=horizontal translation (right if h>0) b=horizontal scaling (stretch if 1/b>1) a=vertical scaling (stretch if a>1) k= vertical translation (up if k>0) applied in the above order, i.e. according to ...

Probability
similar to the APGAR test for newborns. Give it a try and post what you get.

Probability
Interesting problem. Check if binomial theorem applies. 1. Is each trial a Bernoulli trial (either success or failure)? Yes 2. Is probability of success (Apgar><6) known and remain constant throughout experiment (audit)? Yes 3. Are trials (result of each birth) ...

Geometry

data management gr.12
You're welcome!

data management gr.12 (to Jenna)
A tree diagram includes the related probabilities, which is the real purpose of the tree diagram, because it then enables us to get the probability of each situation.             /positive(0.98*0.02=0.0196)  &...

algebra 2
For the point (x0,y0), error=y0-f(x0) SSE=Σerror² =Σ (y0-f(x0)² point error error² (3,6) 2 4 (6,2) -4 16 (9,10) 2 4 --------------- total = (4+16+4)=24

math
"What is 3 times the quotient of n divided by 5?" "...the quotient of n divided by 5"=n/5 "...3 times..." = 3* So put it all together: "3 times the quotient of n divided by 5" =3*(n/5)=3n/5

data management gr.12
This is a typical case of application of the binomial distribution, which requires: 1. probability of success (0.3) is known and remains constant throughout the experiment. 2. each trial is independent of the others. 3. there are exactly two possible outcomes, success or ...

data management gr.12
Contrary to probability calculations, we do not need to divide by XC9 when finding the number of arrangements. C(2,1)*C(3,1) is correct for the first two items. For the toppings, since we are allowed 0 to 4 toppings, the number of choice available equals the power set, or 2^4...

data management gr.12
ok, that sounds reasonable. If you like, you can continue with your method, which is (7C3*9C5)+(7C4*9C4)+(7C5*9C3)+(7C6*9C2)+(7C7*9C1) or, equivalently, 16C8-(7C0*9C8+7C1*9C7+7C2*9C6) which gives (or should give) the same result above. In doing counting problems, it is always ...

data management gr.12
I would like to see, in your interpretation, what each of the expressions mean. (7C3 x 4C2) (7C4 x 4C1) (7C5 x9C0)

data management gr.12
It would depend on the denominations. If the denominations are coprime with each other, then the number of different sums would equal to the power set of the coins. If |A|=3, |Power set (A)|=2^3. That includes the amount \$0, i.e. no coin used. A notable example would be for ...

Chemistry
Here it is: H2SO4: 500 g 35% w/w H2SO4 contains 500*0.37 g pure H2SO4, or 500*0.37/0.96 g of 96% (w/w) H2SO4 =192.71 g of 96% H2SO4 =192.71/1.840 mL of 96% H2SO4 =104.73 mL. of 96% H2SO4 H2O: Volume of diluting water = 500-192.71 g =307.29 g = 307.29 mL. Summary: use 104.73 mL...

Chemistry
If you do not have the means to weigh the chemical, and if an approximate concentration is needed, than use the approximate value of density=1.840 g/mL to estimate the weight from given volumes. If you need a modified version without weighing, please let us know. It is ironic ...

math
If you want just numerical value, then a+b=atan(2/3)=33.69° a-b=atan(2/5)=21.80° 2b=atan(2/3)-atan(2/5) tan(2b)=tan(atan(2/3)-atan(2/5)) =0.210526

Maths
75cm

Maths
In a rectangle, the perimeter is given by perimeter=2(length+breadth) 250=2(length+50) Solve the above equation for length.

Math
Hint: The three sides cannot even form a triangle, because 20>5+10. Let X=length of fourth side, then Since 20-(5+10)=5, the fourth side must be greater than 5, or X>5 Similarly, the fourth side cannot be longer than the sum of the other three sides, otherwise the ...

Maths
Let N="a number" "When 100 is added to a number the result is 50 more than 3 times the number" translates to 100+N=50+3N Solve for N.

data management gr.12
Expected value, E[x]=Σpixi Now complete the table below sum P(sum) X(sum) 1 1/6 \$10 2 1/6 \$9 3 1/6 \$8 4 1/6 \$7 5 1/6 \$6 6 1/6 \$5 E[X]=ΣP(sum)X(sum) =(10+9+8+7+6+5)/6 =45/6 =7.5 Cost to play the game = 7.0 Expected winning = 7.5-7.0=0.50 I leave it to you to find ...

data management gr.12
The available options would therefore be to say that P(Z)=1 for Z>2.9, and P(Z)=0 for Z<-2.9.

data management gr.12
n=270 (>40) p=0.2 q=1-0.2=0.8 np=270*0.2=54 (>10) nq=270*0.8=216 (>10) All prequisites for normal approximation are satisfied. μ=np=54 s=std dev=√(npq)=sqrt(43.2) a) P(X≥100) apply continuity adjustment Z=(99.5-μ)/s=6.92 P(Z≥6.92)~1-2.26*10^(-12) =1 ...

data management gr.12
In a large population, a sample of 40 will not appreciably affect the probability of the population, hence the binomial distribution is applicable, namely P(x)=C(n,x)p^x*(1-p)^(n-x) p=0.35, n=40 a) E(x)=np b) P(0)=C(n,x)p^(x)*(1-p)^(n-x) =C(40,0)(0.35^0)(0.65^40) c)P(x>=3...

math
You're welcome!

math
You get the idea, but there is something missing. You have A(0)=125 A(1)=118.01 A(2)=111.02 ... A(n)=125-6.99n So when the card is used up, A(n)=0, or 125-6.99n=0 Solve for n=125/6.99=17.88 Drop the fraction to get 17 as the maximum number of apps he can download.

MATH
1. get familiar with finding the equation of the line using the Point-Slope form: (y-y0)=m(x-x0) m=-4/3 (x0,y0)=(12,6) Line L : (y-6)=-4/3(x-12) Simplify y=-4x/3 + 16+6 or y=-4x/3+22 To find other points on the line, substitute 3 different values of x and evaluate the ...

Math
See response at: http://www.jiskha.com/display.cgi?id=1482369962

math
See response at: http://www.jiskha.com/display.cgi?id=1482373766 Preferably do not change your screen name, and for repost, you could mention the link to the previous post that was not answered so there will not be duplicate efforts by different tutors. Thank you for your ...

Math
remaining area = 80*50-4*(5*5) =400-100 = 300 sq cm Mass = density*volume Density of metal = 2.5 g/cm³ Volume=300 sq cm *2mm =300*0.2 cm³ =60 cm³ So mass of open box?

math
Here's the table of P(Z') for Z=3.0 to 7.9 in steps of 0.1 3 1.3498E-3 9.676E-4 6.8713E-4 4.8342E-4 3.3692E-4 2.3262E-4 1.591E-4 1.0779E-4 7.2348E-5 4.8096E-5 4 3.1671E-5 2.0657E-5 1.3345E-5 8.5399E-6 5.4125E-6 3.3976E-6 2.1124E-6 1.3008E-6 7.9332E-7 4.7918E-7 5 2....

math
Quite true. If you do not have access to software nor calculator, this might be a problem using paper tables. You can try the following: 1. following link gives probabilities for z=0,1,2...50 but does not give fractional z values. 2. if possible, find a calculator that gives ...

math
The proper way to calculate P(x≥90) is to sum the binomial probabilities from 90 to 270. Using the computer, it should not be a problem. Using a calculator will need a little patience. For P(x≥90), np>10, npq>10 and with a sample of 270 people (n>>40), you ...

Chemistry
You need w/w solution, so we assume 1. 96% is w/w to start, 2. density of water = 1 g/mL 3. volume of mixture equals sum of volumes (=> approximation). We know that 500 mL of 37% w/w H2SO4 contains 500*0.37=185 g by weight of pure H2SO4. Concentrated H2SO4 has a density of ...

math
Kamil Soliciting an answer from a forum and using it as your answer is considered cheating by most educational institutions. Do you realize that teachers of your school check various forums for students who cheat? Here's an example to a similar question: 20% of 35 apples ...

math
You're welcome!

math
Yes, your answer is correct. To check, compare 75/200=0.375 500/1333.333=0.375 However, biologists use a more elaborate method to calculate. The proportional method used above assumes replacement of the sample after each recapture, which is not (usually) the case. When the ...

Math
The sum of the other two angles is 180-110=70 °. The sum of half of the other two angles is 70/2=35°. Therefore the angle between the bisectors of the other two angles = 180-35 = 145°.

Structural Steelwork
Take a piece of paper, and sketch the geometry as describe below to make a sketch that you can follow the steps. 1. Sit the triangle on the x-axis, with the left vertex A at origin, so that (0,900) is the other vertex B. The third vertex C has coordinates (450, 450√3) 2...

data management gr.12
Actually, the probability table should include the case P(0) as well. Do you know how to make a tree diagram? This is a foolproof way to make a distribution table, as long as it is not too complicated. In this case, you will have 2^4=16 "leaves", i.e. where the ...

data management gr.12
For (a), you may have double counted some cases, since the total is 1381/1050 >1, whichis impossible.

math
It's almost the same as the silt/soil problem. Let x be the volume of metal in oz needed, then (0.9x+3)/(x+3)=0.92 Solve for x. Do not forget to distribute when you cross multiply.

math
4 cubic ft (cf) of soil contains 4*10%=0.4 cf of silt If we add x cf of silt, total volume = 4+x volume of silt = 0.4+x Given the new percentage is 60%, we have (0.4+x)/(4+x)=0.6 Solve for x by cross multiplication: 0.4+x = 0.6(4+x)=2.4+0.6x transpose and solve for x x-0.6x=2....

math
Let h=height of the box. Then width=120/h length=168/h We know the area of the base is Ab=316 so Ab=width*length, or 316=(120/h)*(168/h)=(120*168)/h². Solve for h h=√(316/(120*168) =12√35/√79. Use the above equations above to find length and width.

algebra
Method 1: Use calculator, and do not forget to surround the numerator and denominator by parentheses, i.e. type in: (9.6*10^2)/(3.2*10^5) Method 2: (easier way) (9.6*10^2) ------------ (3.2*10^5) Note that 9.6/3.2=3, and 10^2/10^5=10^(2-5) =10^(-3) so the answer is 3.0*10^(-3...

Alebra
Example similar to the first one: solve 7x-9>61 Add 9 to both sides 7x-9+9 > 61 + 9 7x > 70 Divide by 7 (on both sides) 7x/7 > 70/7 x > 10 [answer]

HELP ME PLZ MATH
Great!

HELP ME PLZ MATH (to savepuppy)
When we go to the supermarket, with four similar items at different prices and packaging, we need to find the unit price of EACH of the four items in order to determine the best (lowest) unit price. Unit price can be found by the formula unit price = price / number of units or...

Math
1. find Z-score = (X-mean)/stdev =(67-65.5)/(2.5) =(1.5)/2.5 =0.6 2. Look up standard normal distribution tables for one-tail where Z-score = 0.6 P(x<X=67)=0.7257469 [from tables for Z=0.6] For part b, find similarly P(x<X=64) then P(64<x<67) =P(x<67)-P(x<64)

math
ME=Z√(0.25/n) For 90% confidence level, and ME=1% Z=1.644854 [ from tables for two tale at 95%] => 0.01=1.644854√(0.25/n) => n=(1.644854/0.01)^2*0.5 =6763.86 ~ 6764 persons

Algebra
M' means the complement of M. M' will encompass all the elements in the universal set but NOT in the set M. So please give it another try.

Math (1 Question)

Algebra 9th
In problems of this type, it is easier if you could make a scatter plot (or dot-plot) of the data before starting the calculations. In case you spot an outlier, you will have to occasion of excluding it before you do the calculations. In the given data, I suspect there is an ...

Financial mathematics
Is this a continuation of the post http://www.jiskha.com/display.cgi?id=1482086783 ? If it is, it would be another advantage to keep your pen name the same (except using anonymous), because otherwise tutors cannot assume continuation and have to ask for details. Is \$800,000 ...

Chemistry (to Alice Keign)
morality ≠ molarity lol molarity is the fraction mass of substance contained in 1 L of solution ÷ molecular mass of the substance. Note: atomic mass of Na ~ 23 atomic mass of Cl ~ 35.5 so molecular mass of NaCl ~ 58.5 But you need to look up exact masses from ...

chemistry (To Yasine)
Your effort has a good start, shows you have an idea what's needed, but, to balance equations, you have to know what the possible products are. For example, HO and ZnCl are not known products to me. If you lookup/Google Zinc Chloride, and Hydrogen Oxide, you will find the ...

math(geometric series)
1. find the common ratio: r=T(n)/T(n-1)=12/18=2/3 2. form the general sequence (considering 18 as first term, or n=1) T(n)=ar^(n-1)=18(2/3)^(n-1) 3. solve for T(n)=18(2/3)^(n-1)=512/729 or even simpler, (2/3)^(n-1)=256/6561=(2/3)^8 Solve for n.

math(geometric series)
Sum of a geometric series to n terms with common ratio r is given by S(n)=a(r^n-1)/(r-1). 1. Form the equation: S(20)/S(10)=244 (given condition) 2. Cancel out the common factor a and (r-1). 3. set u=r^10, then r^20=r^2. 4. solve the resulting quadratic in u. 5. Back-...

tangent help me maths
To prove that L1 : 2x+5y+11=0 is a tangent to the circle C : x²+y²+2x-8y-12=0 it is sufficient to prove that the distance of the centre O of the circle C to the line L1 equals the radius of the circle. To find the centre and radius of the circle C, we complete ...

physics (science)
There is a standard formula for this: "from rest" means initial velocity = 0 or V0=0 m/s Given acceleration, a = 8 m/s² S = distance travelled = 100 m Let V1=final velocity, then the given formula is: V1²=V0²+2aS Substitute values of V0, a and S into ...

Chemistry
I do believe that the skill of transforming an actual problem to numbers is part of your training. However, I will work on this for this time. The problem can be solved by proportions. Using: "Therefore 24 g of Mg produces 2 g of H2. How many grams of H2 will be produced ...

Chemistry
The atomic mass of magnesium is 24, which means 24 grams of magnesium makes 1 mole. On the other hand, the atomic mass of hydrogen is 1, so H2 will weigh 2 grams per mole. From part A, which you correctly answered (except for the missing + sign), we conclude that 1 mole of Mg ...

chemistry
Molecular mass of propane (C3H8) = 3*12+8*1 = 44 Molecular mass of water (H2O) = 2*1+1*16 = 18 using the balanced equation, we find that the ratio mass of propane : mass of water = 1*44 : 4 * 18 = 44 : 72 Hence the mass of water can be calculated. Note: replace the above ...

math (to Jose)
hint: 5(S+15)=5*S+5*15 (distribution) =5S+75

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 ...

Math
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.

SUMMARY OF FINANCIAL TIME VALUE OF MONEY
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...

MATH
6

MATH
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

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 ...

Math
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 ...

math
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...

math
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...

Math
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 ...

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

CAN A TUTOR HELP ME WITH THIS PROBLEM PLEASE!
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. ...

Math
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

chemistry
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: http://www.rfcafe.com/references/general/density-building-materials.htm

Deposit
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.

Math
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.

Geometry
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.

Geometry
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.

Chemistry
"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 https://en.wikipedia.org...

MATH
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.