Thursday

April 17, 2014

April 17, 2014

Total # Posts: 9,948

**Math**

Volume of each cube = 576/72 = 8 ml = 8 cubic centimetres. What would be the length of the cube's side?

**algr.2**

Since multiplications and divisions are not involved, we have y=b+a-x valid over Z or over R

**Calculus**

We'd be able to help if we see the figure!

**math**

It's a double application of the Pythagoras theorem: 3²+4²=5² and 5²+12²=13² Can you take it from here?

**calculus**

Try the substitution u=ln(3x) du= 3dx/(3x)=dx/x ...

**math statistics and probability**

a. 6 distinct digits available, each used once. Four digit numbers: first digit: 6 choices second digit: 5 choices third digit: 4 choices fourth digit: 3 choices. By the multiplication rule to multi-step experiments, the total number of possibilities is 6*5*4*3=360 b. Half of ...

**Math**

10 use A&C (may or may not use B) 2 use all three (A, B & C) So how many use A & C but not B?

**math**

The smallest vessel that can contain an exact number of times from each drum is the LCM of 600 and 800, which is 2400 litres. There is no limit for the largest.

**Math**

3 tbsp =3*15 ml = 45 ml. 250 ml base Total volume = 250+45 ml = 295 ml. Concentration =45 ml / 295 ml = 15% approx. (note: 1 tsp=5ml, 1 tbsp=15ml)

**math**

Given 3/4 tsp Po Bid First convert tsp to ml using 1 tsp = 5 ml. so 3/4 tsp = (3/4)*5 = 3.75 ml. So the prescription calls for 3.75 ml. of a suspension 125 mg/5ml 125 mg : 5 ml X mg : 3.75 ml By cross multiplication, we get X=3.75*125/5=93.75 mg (twice a day)

**math**

There may be other ones, but here's what I've got: √(8+8) + (8/8)

**Math**

The brackets [] are superfluous if the formula is entered into an algebraic calculator or if calculated by someone who follows the rules of algebraic priorities (x and ÷ before + and -), and from left to right for operators of the same priority. So a[(b-c)/d]-f is mathe...

**math**

The mathematical answer would be 4*8/50=0.64 sq.ft each One practical answer, if it is required to have each piece equal, would be to have each piece 0.8ft * 0.8 ft, so there will be 10 rows by 5 columns which fit exactly in a 4x8.

**Math**

To give an example, 17 can be thought of as (6+6+6+6)/4=6 or (17+17+17+17)/4=17 Since they are not all even, we can adjust by adding 1 to a number, and subtracting 1 from the next, such as: (18+16+18+16)/4=17 So work in a similar way for all the given choices until you find on...

**Math :)**

You're welcome! :)

**Math**

Correct! Well done!

**Math**

For a square to be a power of three, the original number itself must be a power of 3, namely 3, 9, 27, etc. Which of the squares of these numbers satisfies all of the above conditions?

**algebra**

The five posts are distinct (i.e. no duplicate posts). So the order of selection of these posts is important => solution is a permutation. Selecting r objects from n distinct objects, where order is important is given by P(n,r) where P(n,r)=n!/(n-r)! n! = n factorial For th...

**Algebra**

The absolute value actually represents two cases, the contents are positive (in which case the absolute value does not do much), or if the contents are negative, then the negative sign is dropped. Mathematically speaking, the above equation can be broken down to two: x+3 < ...

**Statistic**

It is not mentioned that the distribution is normal. We will assume that it is, either by assumption, or by an approximation using the central limit theorem (which preferably applies to samples of 30+). With the assumption, we can see that the variance is σ²/n=0.4&s...

**Math**

Think of the numberline. Can you find a number on the number line such that it is the same number on each side of 0?

**Math/Check**

The right answer should at least: be such that the coefficient of x² equal to 3*5 and the constant term equal to 7*(-2).

**statistics**

Find one-tail z-score from tables Z(0.96)=(12-μ)/0.05 Solve for μ

**math**

1. Note that 21*21=441 49*49=2401 Does that give you a hint? 2. The question looks for "The probability that its square root will not be an integer" so check your answer accordingly.

**math**

See response to: http://www.jiskha.com/display.cgi?id=1344678011 and post if you need more explanations or would like to post your attempt.

**Math**

a. A vertex adjacent to Y is one which is linked by an edge (∈E) to Y. An example from the set E above would be AY. The edge YY is a loop, i.e. it links back to itself, so Y is NOT considered adjacent to Y. b. question incomplete. If the question had been List all the edj...

**probability**

1. Find how many (initial) digits when squared gives one. Dividing that by 9 will give you the required probability. Also, it may be of interest to note that single digits that add up to 10 have the same last digits when squared. Example: 2²=4 8²=(10-2)²=64 also...

**math**

You're welcome!

**math**

Yes, you have done a fantastic job of setting up and solving the problem. If you reread the question carefully, you will probably discover a few traps. If you don't find the traps, here are a few hints to improve the solution: 1. Alcohol coming into the tank is 50%, so int...

**math**

Would it not be a similar to a previous problem? http://www.jiskha.com/display.cgi?id=1344476111 You can try the same approach and post your attempt for a check.

**math**

Typically for two numbers A and B for which we have found the LCM and HCF. The general formula is that A*B = LCM*HCF Can you find A and B such that LCM=HCF?

**Probality**

1. Union of Q and H (Q∪H) is the combined set of events of drawing one of the 4 queens or the event of drawing one of the 13 hearts. Note that P(Q∪H)=P(Q)+P(H)-P(Q∩H) The intersection of Q and H (Q∩H) is the event of drawing a Queen and a heart in the same draw...

**physics**

Assume no air resistance. For the object thrown downwards, t=4 s vi=-10 (+ve upwards) g=-9.8 m/s² S=vi*t+(1/2)gt² =-10*4+(1/2)(-9.8)(4²) =-118.4 m For the object thrown downwards, t=unknown vi=+10 (+ve upwards) g=-9.8 m/s² S=vi*t+(1/2)gt² -118.4=+10*t+...

**math**

To Roxann: when we have mixed addition and multiplications, the priority of operations dictate that multiplications and divisions take precedence over addition and multiplication. For example, 5*2+3*4 means (5*2)+(3*4) (* & ÷ before + & - =10+12 =22 (5*2+3)*4 would not ...

**math**

Find the total volume in cubic inches and divide by 144 cubic inches/board-foot. [4(1*8*(6*12))+3(1*6*(4*12)]/144 will be the answer. I will let you find that using your calculator.

**Math**

Let r=amount of money in dollars Mr. R has and x=cost of each orange We will set up the equations 15x=r+90 10x=r-60 You can then solve for r and x by the method of elimination, substitution, or comparison.

**math :)**

You're welcome!

**math**

You need to use the relation w=√12²-h²) to eliminate w from the function S. S(h)=k w h³ =k √12²-h²) h³ To find the maximum/minimum stiffness, you will proceed normally to equate S'(h) = 0 to solve for h.

**math**

You would use the relation of the circular cross-section of (w/2)²+(h/2)²=(12/2)² to relate h and w. After multiplying by 4 on both sides and rearranging, we have w=√(12²-h²). Now the stiffness has been defined as S=k(w)(h³) where k is a con...

**statistics**

I do not recommend doing the same thing both ways because this could cause confusion and consequent errors. I suggest you document clearly. For example, p=0.75=proportion of population infected n=sample size (6 patients per hour) so np=mean (expected value) of number of infect...

**statistics**

Conditions: 1. probability remains constant throughout (i.e. for every one of the six patients. 2. the outcome is of type Bernoulli, i.e. yes/no, 1/0, etc. In this case, infected or not. 3. The number of patients is constant at 6 per hour. 4. Sampling can be assumed to be rand...

**math**

With two given sides a and b, the biggest area of a triangle is when the two sides are at right angles, giving an area of ab/2. Can you figure out which of the 5 areas is not possible?

**Math**

CDE is a triangle has the same base b and the same height h as the rectangle. Its area is therefore bh/2. The area of the rectangle is bh=48. So what is the area of the triangle?

**Algebra II :) + note on √**

You're welcome! Note: the square-root sign can be represented using the character combination: & r a d i c ; but without the spaces in between. What you posted probably came directly from MS Word which does not use the same character codes. This will make the message intel...

**Algebra II**

Yes, √90 = √(3²*10) =3√10

**math :)**

You're welcome!

**math**

I assume you are familiar with integration or differential equations. y(t)=amount of air (in c.f.) in room at time t. Then dy/dt =y'(t) =rate of increase of fresh air per unit time (min) =fresh air in - fresh air out per minute =600 - 600(y/20000) =600*(20000-y)/20000 Sepa...

**Math Conversion**

Area = 33 1/3* (24/36) sq yd =22 2/9 sq yd Total cost = $4.95/sq yd * 22 2/9 = $110

**Solid Mechanics**

See: http://www.jiskha.com/display.cgi?id=1343987746

**Solid Mechanics**

See: http://www.jiskha.com/display.cgi?id=1343987746

**Solid Mechanics**

Hints: Axial stress is the same because the same load is distributed over the same area. However, buckling strength is widely different. Calculate the ratio of the area moments of inertia, and compare buckling their strengths using Euler's buckling formula: F=π²2EI...

**Math**

21 is correct. When in doubt, do one of the following: 1. Find GCF for two numbers at a time, the first time using two original numbers. The second time use the first GCF and the third number. 2. Divide each original number by the GCF found. If the numbers don't divide, th...

**Probability and Stats**

Out of six students, we need exactly 3 fit the criteria of being born in 3 months out of 12, i.e. with probability p=3/12=0.25. Since the probability is assumed constant throughout, and we know the total number of students, we can use the binomial distribution, where n=6 x=3 p...

**solid machanics**

Given: E=1.25*10^5 N/mm² ν=0.25 G=E/[2(1+ν)] K=E/[3(1-2ν)]

**Calculus :)**

You're both welcome!

**Calculus**

Your solution is almost good, just a change of the sign will fix it. y=-log(x^2/2+C) If it has to pass through P(1,2) substitute x=1, and y=2 and find C. 2=-log(1/2+C) log(1/2+C)=-2 take logs 1/2+C=e^(-2) C=e^(-2)-1/2 so y=-log(x²/2+e^(-2)-1/2)

**calculus**

raise both sides to the power of e e^(log(x))=e^(-0.123) since e^(log(a)=a, so x=e^(-0.123)

**Maths**

To ensure continuity, it is necessary that Q(1-) equals Q(1+), or The limit of Q(1) is the same when approached from the left or the right. In the given case, the limits are polynomials which can both be evaluated at x=1. Q(1-)=x^2=1 Q(1+)=a(1)+b Q(1-)=Q(1+) => a+b=1 Simila...

**Dynamics**

Assuming 1.4m/s^2 is the combined radial acceleration (ar) and tangential (at). Note that the two accelerations are orthogonal (perpendicular) so that the combined acceleration can be found using Pythagoras theorem. ar=v²/r=v²/45 at=1.2 where v=tangential velocity Wh...

**Math**

1) 5 choose 3 5C3=5!/(3!2!)=10 2) 3 out of 5 is green, so P(G)=3/5 3) check if "between 0 and 20" includes or excludes the two ends. 4) Number of people who play at least one of violin or cello =8+5-2=11 So four of the members do not play the violin nor the cello.

**Algebra 2**

∫-x^2-3x+7dx between -4 and 1 to evaluate [-x³/3-(3/2)x²+7x] between -4 and 1.

**Algebra 2**

-3 cos t = 1 cos(t)=-(1/3) Look at the plot of cos(t) between 0 and 2π, and note that there are two solutions between π/2 and 3π/2 where cos(t) is negative.

**math**

Here's visual way to calculate, which will let you do it mentally: given cream concentrations 1% ----- 4% ----- 6% ----3%--------2%---- Difference Then you take 2 parts of 1% and 3 parts of 6% to get 4%.

**math :)**

You're welcome!

**math**

Work out all dimensions in feet. r=7.5 inches = 7.5/12=0.625' h=25 inches = (25/12)' Volume = (1/3) π r² h and from the price of $50/ft², we get Cost=volume*price =(1/3) π r² h * 50 Round the answer to two decimal places (to the cent). I'll lea...

**physics**

Assuming acceleration is upwards. Tension=m(g+a)=2000kg(9.81+1.5)m/s²

**Calculus**

Use the substitution p=cos(4x) dp=-4sin(4x)dx I=∫sin(4x)cos²(4x)dx =∫(1/4)p²dp Can you take it from here?

**Calculus**

First make the substitution p=2x, dp=2dx dx=(1/2)dp I=∫cot 2x dx =∫cot(p)(1/2)dp =(1/2)∫(cos(p)/sin(p))dp =(1/2)∫d(sin(p))/sin(p) =(1/2)ln sin(p) + C Can you take it from here?

**MATH**

Let y=x² the equation can then be written as 4y²+15y-4=0 Solve for y using the quadratic formula (i.e. find y1 and y2). Since y=x², then x=±√(y1) or ±√(y2) giving a total of 4 solutions.

**Calculus**

V is a function of r(t) and h(t) so use the product rule and chain rule: V(t)=(1/3)πr(t)²h(t) V'(t)=(1/3)π[2r*r'(t)]h(t)+(1/3)πr(t)²h'(t) Can you take it from here?

**statics**

First, we do not see the loading diagram, but that does not stop me from giving a response. Also, for "f", you will need the properties of AISI 1040 cold drawn steel (yield stress). A cantilever is a statically determinate structure, so finding bending moments is a m...

**statics and strengths**

We don't see the loading diagram. See more detailed response at: http://www.jiskha.com/display.cgi?id=1344099068

**stats**

Here are some properties of the experiment: 1. Each trial is Bernoulli (i.e. yes/no) 2. Number of trials is fixed. 3. probability of success does not vary from trial to trial. 4. each trial is independent of the others (assumed random sample). All these point to the binomial d...

**Stats**

"Four people out of five have had cold pizza for breakfast" seems to imply that the probability for success (p)=0.8. After that, review the conditions for applicability of binomial distribution and apply accordingly. If some of the conditions are not specified, and i...

**Stats**

Here the distribution ~N(6,2²), i.e. mean=6, variance = 2²=4. Standardize the given variable to Z and look up probabilities from the normal distribution table.

**stats**

You need to assume that the age distribution is normal. Again, normalize the data which have a distribution of ~N(66,4²) and compute probabilities based on the looked up probabilities.

**algebra 117**

Let w=width length=w+4 Area, 77=(w+4)w Solve for w: w²+4w-77=0 (w+11)(w-7)=0 So w=7 or w=-11 (reject) => width = 7' check: 7*(7+4)=77, good.

**Trigonometry**

sin(2x)=2sin(x)cos(x) so sin(2x)+sin(x)=0 => 2sin(x)cos(x)+sin(x)=0 sin(x)[2cos(x)+1]=0 sin(x)=0 or cos(x)=-1/2 sin(x)=0 => x=0, x=π for 0≤x<2π cos(x)=-1/2 => x=2π/3 or x=4π/3 Combining, the solution set S={0,2π/3,π 4π/3} Add x=2π if the ...

**Ethics**

Marie, Cindy, and Cynthia. These are all very nice names, but you need to use only one of them. If you feel hesitant to post many questions of the same nature (using the same name) before getting replies, you're on the right track: try some of the problems first!

**Trigonometry**

Let y=tan(x) y²+y-1=0 use quadratic formula y=(-1±√(5))/2 or tan(x)=(-1±√(5))/2 find tan-1(-1±√(5))/2 using your calculator.

**pharmacy calculations**

500 ml of a 1:5 solution contains 500*(1/5)=100 ml. of the concentrate. So if x is the volume of 1:4, then 500-x is the volume of 1:10. Hence x(1/4)+(500-x)(1/10)=500*(1/5) Solve for x to get x=333.33 ml.

**physics**

There's probably a typo, you probably meant to post x(t)=5 sin (π + πt/3) The velocity is the derivative of x with respect to time, giving: velocity=x'(t)=5(π/3)cos(π+πt/3) Substitute t=1 in x'(t) to get the velocity at t=1.

**Solid Mechanics**

I'll give it a try. We have 50kN on 5cm², or 0.0005 m². So the axial stress σx = 105 kPa =100 MPa σy=0 So draw the Mohr's circle (in the σ/τ plane) with between (0,0) and (100,0) as a diameter. The centre is at (50,0). To find the stresse...

**math-law of sins**

I suggest you 1. verify if the triangles exist or not according to the two (different) conditions above. 2. try to draw the given triangle, if possible. If you have doubts, you are welcome to post your answers/results for a check.

**math-law of sins**

These problems are made up to show some cases where the triangle cannot exist. If A=61° (acute) and a=8, the longest side adjacent to A is a/sin(61°)=9.15. Since 21>>9.15, the triangle does not exist. If A is obtuse, then any adjacent side must be less than a. Ve...

**Trigonometry**

i^4=1 => i^44=(i^4)^11≡1 So what is i^45=(i^44)*i ?

**Math**

1. Solve for a a+2=6 a-2=2 2. Let x=initial number of friends. 0.4x = 0.25(x+6) Solve for x.

**Calculus AP**

Up to 1/2∫tcostdt, you're OK. After that, you need to integrate by parts. I=(1/2)∫t cos(t)dt =(1/2)[t sin(t) - ∫sin(t)] =(1/2)[t sin(t) + cos(t) To evaluate the definite integral, remember to adjust the limits accordingly, i.e. from x^2 to t sqrt(π/2)^2=&p...

**math**

This must be a problem from an older book. Printers today do not print a line at a time, but let's assume that's the case (for a "matrix" printer). 80 characters / second 2400 characters / page means 2400/80=30 seconds / page = 30/60= 1/2 minute / page If we ...

**calculus max area**

First take a piece of paper and draw the developed surface of the pyramid, namely a square base, with 4 isosceles triangles folded flat on each side. You will want the vertices of the four triangles (equivalent to the top of the pyramid) form a square, which is your paper. Dra...

**Calculus Max Profit**

"Assume the number sold is a linear function of the price" but no information is given on the price elasticity, so we will assume, in general, an increase in price of $1 will increase sales by m units. Under normal supply-demand curve, m is necessarily negative, of t...

**math**

Question incomplete. See completed question and answer at: http://www.jiskha.com/display.cgi?id=1343936302

**Statistics**

Given: μ=35000 σ=4500 X~N(35000,4500^2) Look for the two tail probability in the normal distribution table for 90% = 0.9, or Z=±1.645 So the range that contains 90% would be between μ±1.645*σ

**Dynamics**

The kinematics equations for the stone, ignoring air resistance, is as follows: vi=initial velocity = 15 (upwards) g=acceleration due to gravity=(-9.81) xi=initial position = 20 m (above ground) t=time in seconds from throwing stone upwards. (a) x(t)=vi*t+(1/2)gt² (rememb...

**Math**

See solution to the same problem at: http://www.jiskha.com/display.cgi?id=1343870485

**Math**

See solution to the same problem at: http://www.jiskha.com/display.cgi?id=1343870534 and http://www.jiskha.com/display.cgi?id=1343870950

**Math**

See solution to the same problem at: http://www.jiskha.com/display.cgi?id=1343870416

**number theory**

If you note that we only need to calculate 6 s=∑ i! n=1 or s=873 mod 21 = 12 Because all terms 7! and beyond are divisible by 21.

**number theory**

You can try the CRT (Chinese remainder theorem). Master sun proceeded as follows: Given N≡3 mod 7 N≡4 mod 9 N≡8 mod 11 We need to find the smallest positive N. First we find the unit remainders, 99≡1 mod 7 (99 is product of 9*11_ 154≡1 mod 9 (154 ...

**math**

"Solve each system graphically" You'll need to graph each equation and look for the intersection. If there is no intersection, the system has no solution. If the two lines coincide, the system has infinite solutions. If the two lines intersection at one point, th...

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