Wednesday
July 23, 2014

Posts by MathMate


Total # Posts: 10,590

Math
Hint: cos(θ)=adjacent/hypothenuse (CAH)

Math
a number which is an easy multiple of 42 and less than 4452.

Math
4452-4200=252 (42*100=4200) 252/42=6 So the quotient is 100+6=106.

math
1.5*IQR=(49-28) IQR=21/1.5=14 So Q3=Q1+IQR=42 However, the median and Q1 should be recalculated after the outlier is removed.

Physics
For part c, you put average speed as 0.05 km/min, which is correct. Subsequently, as part 2 of (c), you did put average velocity as 0. Perhaps there was a confusion of the questions.

Physics :)
You're welcome! Yes, velocity is a vector, so it is described by the magnitude (speed) and direction. The same goes for displacement, which is also a vector, and therefore is described by the magnitude and direction. Keep up the good work!

Physics
(a) we usually express car speeds in km/hour (b) Displacement = 10.3 km in direction 25° S of east Time = 18 min = 0.3 hour So velocity = 34.3 km/hr in direction 25° S of E. (c)Correct.

math
2*5280 = ?

Physics
Use the equations: S=vi*t + (1/2)gt^2 For 1st ball: 20=0+(1/2)gt^2 => t=sqrt(40/g) For 2nd ball: 20 = vi*(t-1) + (1/2)g(t-1)^2 vi = [20-(1/2)g(t-1)^2]/(t-1) =(20-(9.81/2)*(t-1)^2)/(t-1) =14.62 m/s downwards

calc 3
Trouble-free way to get resultant: resolve into x- and y-components and add. Wind is FROM N45W, which means that its direction is S45E. Take East = x, and North = y, the wind vector is then <40sin(45),40cos(45)> The velocity vector of the plane is <200sin(60),200cos(6...

Math
Ratio of 40% and 25% solutions to form a 27% solution = 27-25 : 40-27 = 2 : 13 To make 54 litres, we need 54*(2/(2+13)) litres of 40% and 54*(13/(2+13)) litres of 25% solutions.

math
When you add (i.e. never need to borrow), you can calculate the integer and fractional parts separately, and carry if necessary. Integer part: 8+5-5=8 Fractional part: 9/10 + 3/4 find common denominator (=20) 18/20 + 15/20 =33/20 = 1 13/20 Carry the 1 to give 9 13/20

Algebra..
1. given slope, passes through origin: y=mx here m=3/2 2. given x-intercept=a, y-intercept=b y=-(b/a)x + b here a=4, b=-3 3. Given point (x0,y0) on line and slope m: y-y0=m(x-x0) (x0,y0)=(3,2) m=2 (coefficient of x in given line) 4. Given point (x0,y0) on line, and perpendicul...

math
Correction to one of the above lines: 12=a(0-24)(0+24)=-576a

math
x^2 means x squared, or x². If you just started with parabolas, it won't hurt to say what you've learned so far. Let's start over: We first assume the vertex of the parabola is at x=0. We know that y=0 at x=±24, or y=a(x-24)(x+24). We also know that y=1...

math
Take the vertex of the parabola at x=0. Then the equation of the parabola (opening downwards) is y=12-ax^2 where a is a constant to be found. We know that y=0 at x=±24 (half span), so 0=12-a(24^2) => a=12/576=1/48 The equation of the parabola is therefore y=12-x^2/48...

Calculus
a. The conditions that f(x) must satisfy to have an inverse is: 1. f(x) must be a function 2. f(x) must be onto, i.e. ∀x ∈ dom f(x), f(x)=f(x1) <=> x=x1 condition 2 implies that f(x) must be strictly increasing or strictly decreasing. This can be satisfied if...

math
"Nine parts of the first piece are equal in length to 3 parts of the second piece. " means that each part of the second ribbon is three times as long as each part of the first, which also means that the number of parts of the second ribbon is one-third of the number ...

Math
6 3/5 - 2 4/5 (Note: 3/5 is smaller than 4/5) =5 8/5 - 2 4/5 (borrow a whole) =3 4/5

Math :)
You're welcome!

Math
They are each 13 and 20 km from the starting point, at an angle of 44 degrees. Solve the triangle by the cosine rule which gives the distance between the two: c²=a²+b²-2ab cos(C) where c=distance between bikers a=13km b=20km C=44°

trig
My calculator says sin(70°)=0.93969262

Algebra 1 or 2
Assuming no parentheses are missing, i.e. the question actually means: ((5x)/4) + (1/2) = x - (1/2) x=2 is not correct. To solve: (5x/4) - x = -(1/2) - (1/2) x/4 = -1 can you finish the solution?

Math
(A) x=13/4 means that the equation is valid only at x=13/4, and is not valid elsewhere. Would that be an identity or a conditional equation? (B) There was an arithmetical error on the last line: -7x+21+4x = 21-3x +21-3x = 21- 3x So after cancelling, we get 21=21 Would that be ...

Computers
dptr = new double*[5]; // creates 5 rows for (int i = 0; i < 5; i++) dptr[i] = new double[3]; // creates 5 columns for each row. // use the free() function to release memory

math
Calculate $1500*14% =$1500*0.14 =$210

math
If there is no typo in the question, the number of females is 3000-70=2930. If the number 70 is meant to be 70%, then the number of females is 3000(1-0.7)=?

Math
If the requirements are complete, I also found 19 candidates. So supply the complete list as your answer as instructed.

Math
See: http://www.jiskha.com/display.cgi?id=1346396105

calc 3
Think of two points in space. The set of all points equidistant from the points is therefore a plane that separates the two points, right in the middle. Also the line joining the two points would be perpendicular to the plane. The mid-point between the two points would evident...

Adding & Subtracting Expressions
Distributive property: ac + bc = (a+b)c a=8.5 b=1.3 c=m Substitute.

math
Using system of equations: E=number of cartons of erasers P=number of cartons of pencils 5E+7P=85 E+P=15 Solve for E and P. Easier: We know E+P=15, so directly write 5E+7(15-E)=85 Solve for E and then find P=15-E. Even easier, do it mentally: 15 cartons of erasers cost 5*15=75...

statistics
This problem has the following characteristics: 1. Number of trials is fixed (25) and known. 2. The probability of success is constant (0.9) throughout the trials and known. 3. The tests are independent 4. Each test is Bernoulli (i.e. true/false, 0/1) These criteria indicate t...

algebra
See: http://www.jiskha.com/display.cgi?id=1346371677

Math
22n-1 = (2³)-n 22n-1 = (2)-3n By comparison, 2n-1 = -3n Solve for n.

algebra
It would be similar to the thermometer problem: http://www.jiskha.com/display.cgi?id=1346371286 Take the goal and add or subtract the variations to get the upper and lower limits. Try it and post your answer for a check if you wish.

algebra
If it reads 28°F, and it cannot be more than 1.2° from the ambient temperature, then the range is between (28-1.2)°F and (28+1.2)°F

statistics
μ=100; σ=15 What is μ+2σ?

statistics
Z-score = (X-μ)/σ =(75-60)/15 =1 Look up normal distribution tables to find P(Z≥1)=0.8413 So 15.87% of students have better scores than 75%.

Math
Just add as though they are decimal numbers. Remember to carry only when the digit sum exceeds 15 (when there are no more hex digits). Here are the hex digits Hex decimal value 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 A 10 B 11 C 12 D 13 E 14 F 15 (note: decimal digits can also...

Math
Hexadecimal numbers are not binary numbers. The digits are {0-9,A-F} while binary numbers have digits {0,1} only. To add two hex numbers, line up numbers and add digits just like decimal numbers, except that when the sum is below 16, use the hex digits. When the sum is above 1...

Math for liberal arts
How you add or multiply hex numbers have been explained in response http://www.jiskha.com/display.cgi?id=1346358289 If you need further explanations, post a follow-up to the response, explaining where you need more details.

math
You know that you expect to lose about 6% for any amount you played, assuming you played enough to be close to the expected value. How much is losing 6% of $130?

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)

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