Wednesday
April 16, 2014

Posts by MathMate


Total # Posts: 9,948

math
What you really want to do is to reduce the variables in simpler terms by dividing both sides by 20: v-c=120/20=6 ...(1a) v+c=120/10=12...(1b) This is a sum and difference form where the solution can be done mentally: v=(sum+difference)/2=9 c=(sum-difference)/2=3

math
Set-up: Let v=speed of boat c=speed of current Distance = speed*time Upstream: 120=(v-c)*20 ...(1) Downstream: 120=(v+c)*10 ...(2) Solve for v and c.

PHYSICS
Use KE=(1/2)mv² (irrespective of direction).

Trigonometry
Assuming angles α, β and γ are opposite to sides a, b and c respectively. β=29°, γ=61° => α=180-(29+61)=90° Since b and β are known, and both α and β are not obtuse, we can use the sine rule. a/sin(α)=b/sin...

Trigonometry
If θ is the inclination with the horizontal, ignoring friction, and assuming 2250 pounds is the working load, then the heaviest cargo it can pull is W=2250/sin(θ°)

Trigonometry
work done = weight*vertical distance (upwards) = 117 lbs *(18/12)' = 175.5 ft-lb (in gravitational units)

Math
Domain f : {a,b,c,d} Range f : {r,s,t} (note: elements are not duplicated in a set) Ordered pairs: f(x)={(a,t),(b,s),...(d,t)} fill-in the missing ordered pair.

Elementary Algebra
Please check your question for typos.

Trigonometry
Calculate the dot product of the three pairs of vectors. If the dot product is zero, the vectors are orthogonal. For example, (i)<18,-3>.<-1,-6>=-18+18=0 So pair (i) is orthogonal. Post your answer for checking if you wish.

finance
Present value=PV=2000 r=rate per period(6 periods/year)=(0.04/6) n=number of periods=6years*6periods/year=36 Use following formula to calculate future value FV=PV*(1+r)^n

math
If we assume that the river is at the same elevation of the base of the mountain, then Width of the river =distance of far shore - distance of near shore =1780/tan(θ2)-1780/tan(θ1)

math
The observer is 80-6.5=73.5 above the base of the tower and the base of the tree. An angle of depression to the base of the tree of 72-20-00 means that the distance between the tower and the tree is D=73.5/tan(72-20-00) the difference between the top of the tree and the observ...

Phystcs
Newton's law of gravitation stipulates that the attractive force F between two objects of masses M and m at a distance r apart is given by: F=GMm/r² where G is the gravitational constant. From the above relation, can you figure out the ratio of the new force after the...

Calculus
Flux = I = ∫∫F.n dS for S over the surface, g(x,y,z), where g(x,y,z) is the part of x=2y²+2z²+3 where x≤5, which translates to g(x,y,z)=x-2y²-2z²-3 and the region is the part of the paraboloid where y²+z²≤1 after substitution of x&le...

Heat Transfer
Devi, Guru and Rafeeq, Don't bother using different names. It is easier to address questions from the same person under the same name. Also, many of these questions are standard definitions which you can obtain from Wiki pages after a little reading. If you had read questi...

hyraullics
The answer lies in the definition of gauge pressure. See, for example: http://en.wikipedia.org/wiki/Pressure_measurement

Heat Transfer
Correct.

Heat Transfer
Dhilsath, I have some friendly advice for you. The pattern of your posts appears that you are downloading your homework assignments here. We do not see efforts on your part to solve the problems, not even to understand the material given the fact that multiple questions on the...

Discrete Math
Sorry, I came up with the same conclusion: when P=false, T=true, we cannot determine the truth value of neither Q nor S.

Discrete Math
A nice puzzle. The truth table for ~R is R ~R T F F T Since ~R=true, therefore R=false. Given R is false, and R v(P v T)=R ∨ P ∨ T is true, we conclude that P∨T is true, i.e. P=true ∨ T=true .... (1) Then we need the table for the conditional (->) A B A->B T ...

Math
The definition of inscribing a (regular) polygon in a circle is that all the vertices of the polygon lie on the circumference of the circle. Would that help?

math
Circumference = 2πr Distance travelled by wheel X =5*2π(5) =50π Distance travelled by wheel Y =4*2π(6) =48π What is the difference?

Trigonometry
You will need to draw a diagram of the objects, and be familiar with the trigonometric ratios. Measuring everything from the point 75' down, the height of the base of the building is B=75 sin(15°) The horizontal distance from the base is H=75cos(15°) The top of the...

physics
Volume divided by area of pool will give the height of water/pool. Volume of pool = 375 m³ Area of pool is 10m*5m=50m². Can you take it from here?

Math :)
You're welcome!

Math
xΩy = LCM(x,y) 10Ω32 = LCM(10,32)=160 6Ω20=LCM(6,20)=60 can you take it from here?

geometery
Circumference for 18" diameter is 18π, where π=3.14159... approx.

Math
The first three cards are irrelevant. For the second draw, the p=P(repeat at least once) = 1-P(no repeat at all) =1 - (37*36*35)/(40*39*38) =211/988 Odds: p : (1-p) = 211/988: 777/988 = 211 : 777

Math
No, you don't need to see the graph to give the correct answer. You have supplied sufficient information to calculate the class intervals. Class interval is the distance between classes. The distance can be calculated by taking the difference between class centres, class s...

Math
If we can assume random trials, and that probability remains constant (at 1/2). Use binomial distribution. N=5 (no. of trials), n=3 (no. of successes), p=1/2 (probability), q=(1-p)=1/2 P(3 out of 5) =C(5,3)p^3q^(5-3) =5!/(2!3!) (1/2)^3(1/2)^2 =10/32 =5/16

math
Post questions, one at a time, and try to learn from the responses in order to do the remainder. If you have more problems, post your questions together with your attempts. The best way to get questions unanswered is to post a number of similar questions of the same type. This...

math
$8.50 + 3*$1.00 = ??

Algebra 2 (again)
Multiply the second equation by 2 to get the system: |2x| |y + 7| |2x| = |14 - 6y| Equating the right-hand side gives us the TWO equations: 2*(7-3*x)=(x+7) which can be solved for x, and x=1 or 2*(7-3*x)=-(x+7) which gives x=21/5. Make an appropriate choice of the solutions.

Alebra 2
If we pre-multiply both sides of the equation by the inverse of the square matrix, m= 4 6 5 8 b= 24 40 m-inverse= 4 -3 -5/2 2 and m-inverse * B = -24 20 we get an identity matrix on the left, and the solution vector on the right, i.e. x=-24, y=20.

sat math :)
You're welcome!

sat math
There are 30 days in June, and 89 children born. Suppose 60 of the 89 were spread over 30 days evenly, so every day, there are two newborns, leaving 28 to be distributed over 29 days. If the remainder is spread out over the remaining days, so some have 3 and some have 2 newbor...

stats 101
Sort out the data in increasing order. If there are n pieces of data, calculate nc=√n to be the number of classes. Round up to the next integer if necessary. Find class width by dividing n by nc. Again round up to the next integer if necessary. Start the first class with...

qbasic
0. Set current sum as 0. 1. Set the current value as 2. 2. Set the current difference as 0. 3. Add current difference to current value. 4. Add current value to sum. 5. Print current value. 6. Increase current difference by 3. 7. As long as the current value does not exceed 200...

maths
I suspect you have not posted the part of the question which is general to many question, namely the unit cost of different items.

Pharmacy Math
It's inverse proportion: 95ml*7% = x ml * 5% x=95*(7/5)=133 ml.

statistics
Check for typo in your post. If there are no typos, here's how you would proceed. Standardize: P(X>100) =1-P(X≤100) =1-P(Z≤(100-690)/110) =1-P(Z≤-5.36) Look up a probability table for P(Z≤-5.36) and calculate the answer accordingly.

math
Correct.

Maths
f(x)=3x^3+ax^2+bx+4 f(1)=2 => 3+a+b+4 = 2 ....(1) f(-1)=0 => -3+a-b+4=0 ....(2) can you solve the system defined by (1) and (2) with a and b as unknowns? Hint: both a and b are negative.

math
An obvious solution would be 7*3+5*20=121 Consequently, change 5*7 for 7*5 gives 7*(3+5)+5*(20-7)=7*8+5*13=121 Similarly, 7*(8+5)+5*(13-7)=7*13+5*6=121 We cannot go further because number of baskets for groups of 5 will be negative. So possible values for baskets of 7 are: 3,8...

Math-one more
Use normal distribution, σ=1.4, μ=24.3 Look up z=Z-score for one-tail distribution for 0.75 Hours = μ+z*σ

statistics
76/1000 = 0.076 quite close to the theoretical of 1/13=0.0769230...

statistics
76/1000 = 0.076 quite close to the theoretical of 1/13=0.769230...

relative frequency
It is one of the ways to estimate/calculate probabilities by noting the frequencies of favourable events relative to all events. Post a particular example for more specific help.

math- finding zeros
It's a similar process as long division with numbers. Check out web resources such as: http://www.purplemath.com/modules/synthdiv2.htm or http://www.youtube.com/watch?v=bZoMz1Cy1T4

math- finding zeros
This is a trick question. We know that complex roots always come in pairs. If 1+i is a root, so is 1-i, its conjugate. The given root and its conjugate multiplied together become a real factor, namely (x-1-i)(x-1+i)=x^2-2*x+2. Repeat your synthetic division using the combined ...

use chebyshev's theorem to find what percent of th
With μ=295 σ=18²=324 k=(349-295)=295-241=54 Chebyshev's Theorem states: P(|X-μ|≥k)≤σ²/k² =P(|X-295|≥54)≤1/9 which means that P(|X-295|<54)≥1-1/9=8/9 In words, At most 8/9=88.9% of values will fall between 241 and 349.

Math
6+3+6+3=18 or 2(6+3)=18

Math
(x^2-3x)+(-6x+18) =x(x-3)-6(x-3) =(x-3)(x-6)

algebra**
A={1,3,5,7,9} B={5,10} A∩B={5} Assuming random sampling, P(B)=|B|/|S|=2/10=1/5 P(A)=|A|/|S|=5/10=1/2 P(A∩B)=1/10 Finally, P(B|A)=P(B∩A)/P(A) (by definition) I'll let you take it from here.

Statistics
This problem is similar to your other question, or your friend's question at: http://www.jiskha.com/display.cgi?id=1343087495

Statistics
From a normal distribution table, 97.5% probability corresponds to +1.96σ. Thus μ±1.96σ corresponds to 95% of all years. 1.96σ = 1.96*3.5=6.86" Therefore 95% of the years have precipitation between 72±6.86"

Math-Trigonometry
cosecant(θ) has the same sign as sin(θ). Use the CAST rule, which says that sin(θ) is positive in Q2.

College algebra
It is easier to tell which graph not a function. If there exists any vertical line x=k that intersects the graph at more than one point, the graph is not a function. This is call the vertical line test.

math advanced functions
I got dizzy watching the video of the ride. Never mind the ride! (a) average velocity - t∈(2,3) Average velocity = v(final)-v(initial) =(93-4.9(3²)) - (93-4.9(2²) =4.9(9-4) =24.5 m/s - t∈(2,2.1) similar to above. (b) h(t)=93-4.9t² instantaneous velocit...

satistics
Given X~Bin(n=18,p=0.75) and let C(n,r)=n!/(r!(n-r)!) P(X=14)=C(n,X)*p^X*(1-p)^(n-X) =(n!/X!(n-X)!)*p^X*(1-p)^(n-X)\ =(18!/(14!(4!)) * 0.75^14 * 0.25^4 =0.2 approx.

Math
Future value at 12% =30000*1.12^20 =$289388.79 Similarly for 18%, but almost 3 times as much.

Math
If the height remains the same, then the new volume will be (2²) times the original cylinder.

Finite Math
In the following, A' will be used in place of Ac for ease of typography. (1) since A and A' are partitions of A, we can apply the law of total probability P(B)=P(B|A)*P(A)+P(B|A')*P(A') (2) Use Bayes Theorem P(A|B) =P(A∩B)/P(B) ... def of cond. prob =P(B&ca...

Finite Math
Use conditional probability defined as: P(A|B)=P(A∩B)/P(B) Also, in general, P(A∩B)=P(A)*P(B) if and only if A and B are independent. You will have to assume independence of the outcomes or else there is not enough information to do the above calculations. Also, check ...

statistics
Binomial distribution: p=0.43 (probability of success) q=1-p=0.57 N=10 (sample size) Probability of r successes out of N: P(X=r)=C(N,r)p^r*q^(N-r) and C=combination=N!/(r!(N-r)!) a. r=4 P(X=4)=C(10,4)*0.43^4*0.57^(10-4)=0.24 b. r≥8 P(X≥8) =P(X=8)+P(X=9)+P(x=10) = similar...

chemistry help needed
Thank you.

Principle processes of flotation separation of Pol
Is there supposed to be a question that follows these descriptions?

math
Thank you all for the corrections. As Ms Sue said, I am glad you check the math. Remember that you should always check the tutor's math, not only for accuracy, but also to verify that you have understood how it is done. Sorry for the bad multiplication. It was a moment of ...

math
Multiply the total sale by 0.06 (=6%). Total sale = 5*12.95=64.92 Sales Tax = $64.92*0.06=$3.90

more math..
I do not know if there is a typo, notably on the RHS of the first equation. I assume the question reads as follows. If not, the same strategy can be used. |5x - 2y|= |18| ...(1) |x + 6y| = |10| ...(2) The use of absolute value on the right-hand side (RHS) of the equality sign ...

more math..
I do not know if there is a typo, notably on the RHS of the first equation. I assume the question reads as follows. If not, the same strategy can be used. |5x - 2y|= |18| ...(1) |x + 6y| = |10| ...(2) The use of absolute value on the right-hand side (RHS) of the equality sign ...

statistics
Please find response in original post which makes it for other readers to follow. http://www.jiskha.com/display.cgi?id=1342991495

ALGEBRA 2
A system of equations does not have a unique solution when the equations are not linearly independent. The equations are linearly independent if none of the left-hand side of the equations can be represented as a linear combination of the others. If we add equations (1) and (3...

John jay college
Sample mean from a sample of size n from a normal population with mean μ and σ has parameters N(μ,σ²/n) Since n=9, σ=9, σ²/n=9, so the sample mean ~ N(50, 3²). Z-score=((M-μ)/σ)=(59-50)/3=3

statistics
A little suggest for follow-ups to my responses. Start with a follow-up to the original post. If your patience runs out, then start a new post with or without the recipient's name under "school subject". Assuming you have no problem with parts (a) and (c), parts ...

statistics
Use binomial theorem with N=5, p=0.70 => q=1-p=0.3 Let C(n,r)=binomial coefficient=n!/(r!(n-r)!) (a) all five resolved P(X=5)=C(5,5)p^5q^0=1*0.7^5*1=0.17 (b) at least one not resolved i.e. not all five P(X≤4)=1-P(X=5) (c) none resolved P(X=0)=C(5,0)p^0q^5=1*1*0.3^5=0.002...

calculus
That rechneronline software is crisp and full of options! I'll definite keep that in the toolbox. Thanks Reiny!

Math
Sum the east (x-) and north (y-) components. x=∑D cos(θ) =25*cos(90°)+29 cos(90-300°) =0+29cos(-210) =-(29/2)√3 y=∑D sin(θ) =25*sin(90°)+29sin(90-300°) =25+29sin(-210°) =25+29sin(30°) =25+14.5 =39.5 Distance =sqrt(x^2+y^2) =...

MATH
Correct!

math
That's correct!

math
- and - give a +. So -2 is not correct. Please try again.

Finite Math
1. Probability of showing a head: Coins are chosen at random, so each coin has a probability of (1/3) of being selected. probability for a head: fair coin: (1/3)(1/2)=1/6 two heads: (1/3)(1)=1/3 unbalanced: (1/3)(0.6)=1/5 Add up the three probabilities to get 7/10. Conditional...

math grade 12
Arc length = rθ ...(1) where r is radius and θ is central angle in radians. To convert 225° to radians, multiply by (π/180) to get 225π/180=5π/4 Use formula (1) to calculate arc length, which should be in the same units as the radius.

Mat/116
Let x=fraction of funds invested with 6% return, then 3400x*0.06+3400(1-x)*0.03=144 Solve for x.

math
Distance between two points can be obtained using the distance formula based on the Pythagoras theorem. D=sqrt((x2-x1)^2+(y2-y1)^2) Here P1(6,32), P2(-8,-16), so x1=6, x2=-8, y1=32, y2=-16. Plug in the distance formula and calculate the result.

math
If you want the correct problem to be solved, you need to put parentheses around ALL numerators and denominators. For example, x+4/x-2 = x + (4/x) -2 because of the priority of division over addition and subtraction. x+4/x-2 does not mean at all (x+4)/(x-2) So can you confirm ...

algebra
If you multiply the first equation by 7, you will get exactly the second equation. So this system of equation has an infinite number of solutions. Geometrically, it means that two straight lines are coincident, so there are infinite points of intersection between the lines. Th...

math
The key to solving this kind of problems is to draw a diagram, and name the unknowns. After that, state the formulas that relate the unknown(s). Some times at the end, only one unknown is left, and you can therefore solve the problem. Let A be the end of the shadow, and C be t...

algebra 2
1. Sample space = 6*6 = 36 Number of successes (doubles) = |{11,22,33,44,55,66}| =6 Figure out the probability for doubles. 2. 8 choose 5 =C(8,5) where C(n,r) is defined as the combination of r items chosen from n. =n!/(r!(n-r)!)

algebra 2
Assume spinning of both spinners are random and independent of each other. Red spinner is labeled 1 to 6, consequently the event of spinning less than three is 1 or 2 (two outcomes) out of 6 possible outcomes for a probability of 2/6=1/3. Blue spinner has 4 sectors (4 possible...

algebra
We don't see the shading.

math help
1. Find f'(x)=-xe^((-x^2)/2) 2. plot f'(x) and find where f'(x) crosses the x-axis. Note that e^((-x^2)/2)>0 ∀ x∈R. Therefore the sign is determined by the factor (-x), which is >0 for x∈(-∞0) and negative for x∈ (0,+∞). 3. K...

Math
Use k<a,b>=<ka,kb> Post your answer for checking if you wish.

Statistics :)
You're most welcome. I am glad things are working out. Post if you have difficulties.

Statistics
Glad that you mentioned that an approximation is required. The question asks for exactly 90 seeds, which is discrete. Here's how I would proceed to approximate a discrete random variable from a continuous distribution. "Exactly 90" is approximately equal to the r...

Statistics
This is a binomial distribution with parameters N=130, p=0.6, r=90 so P(X=90)=C(N,r)p^r(1-p)^(N-r) =C(130,90)*0.6^90*0.4^40 =5.3347282074*10^33*1.0804695562359849*10^-20 * 1.2089258196146345*10^-16 =0.00697

Math
Vectors are usually represented by angle brackets, as shown below. u-v=<3,-4>-<-5,-2> =<3-(-5), -4-(-2)> =<8,-2>

Math
x"(t)=d²x/da²=a=4-t^2 Integrate two times and substitute the initial conditions to find the required equation: x'(t) =∫a dt =∫(4-t^2)dt =4t-(t^3/3)+C1 From x'(t)=2 mm-t^-1, we get 2 mm-t^-1 = 4(0)-(0^3/3)+C1 => C1=2mm-t^-1 x(t)=∫x'(t)d...

Calculus
In calculus terms, Profit=P(q)=42q-0.006q*q dP(q)/dq = 42-0.012q = 0 q=42/0.012=3500 cases.

Probability/Combinatorics
First card: any card (52/52) Second card: one of 12 remaining cards of the same suit (12/51) third card: one of 11 remaining cards of the same suit (11/50) fourth card: one of 39 cards of any other suit (39/49) Since all these are required events, use the multiplication rule t...

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