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Recent problems solved by 'richard1234'

richard1234 answered: 5385 problems
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Polynomials-and-rational-expressions/635535: Solve v^2=80 , where is a real number. Simplify your answer as much as possibl 1 solutions Answer 400412 by richard1234(5390)   on 2012-08-07 20:50:00 (Show Source): You can put this solution on YOUR website!

Proofs/632981: When you square any integer, the last digit of the number you get will never be an eight. Is this statement true, false, or sometimes true. Justify your result. to prove this i've tried... 1^2=1 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2 = 100 as you can see this is true for single digits i've tried double digits as well up till 30^2, and clearly enough the last digit is never an eight. from what i've got above im guessing that this statement is true! 1 solutions Answer 398623 by richard1234(5390)   on 2012-07-30 00:01:22 (Show Source): You can put this solution on YOUR website! You only need to check up to 10^2, because the last digit will repeat (because 12 is congruent to 2 mod 10, for example). I would brute force just like the other tutor did to check that a perfect square cannot end in 8.

Quadratic_Equations/632863: Proove: (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2 1 solutions Answer 398621 by richard1234(5390)   on 2012-07-29 23:56:20 (Show Source): You can put this solution on YOUR website! Expand both sides first.

test/632906: what is meant by absolute values? 1 solutions Answer 398619 by richard1234(5390)   on 2012-07-29 23:54:06 (Show Source): You can put this solution on YOUR website! The "distance" from that number and zero on a number line (which can be generalized to planes, spaces but you'll learn that later). For example, |5| = 5 and |-2.3| = 2.3.

Proportions/633043: the sum of three consecutive numbers is 63.find the product of extremes. 1 solutions Answer 398618 by richard1234(5390)   on 2012-07-29 23:52:23 (Show Source): You can put this solution on YOUR website! Let x-1, x, x+1 be the numbers. Then (x-1) + x + (x+1) = 63 3x = 63 x = 21 --> x-1 = 20 and x+1 = 22. Their product is 440.

Geometry_Word_Problems/631732: formula of a regular triangle and regular hexagon have the same perimeter, it is the lenght of one side of the hexagon is 14cm how long in each side of the triangle? 1 solutions Answer 398206 by richard1234(5390)   on 2012-07-27 03:18:42 (Show Source): You can put this solution on YOUR website! Perimeter of the hexagon is 14*6 = 84 cm Therefore the side length of the triangle is 28 cm, since 28*3 = 84.

Probability-and-statistics/631662: square of 6 cm,coin of 2cm radius,what is the probility of coin resting independently on 3 different squares(squares are side by side) 1 solutions Answer 397732 by richard1234(5390)   on 2012-07-25 01:23:04 (Show Source): You can put this solution on YOUR website! Assuming an infinite grid of 6x6 squares, and assuming "exactly" 3 different squares, the probability is zero. The corner of a square would have to lie directly on the edge of the coin.

Angles/631605: two pairs of complementary angles 1 solutions Answer 397731 by richard1234(5390)   on 2012-07-25 01:21:17 (Show Source): You can put this solution on YOUR website! x and 90-x (degrees). Replace x with any number.

�t�e�s�t/630843: Use the fact that cos(u+v) = cosucosv - sinusinv to calculate sin 75 degrees. 1 solutions Answer 397680 by richard1234(5390)   on 2012-07-24 19:38:57 (Show Source): You can put this solution on YOUR website! Easier method: Use the identity sin(u+v) = sin u cos v + sin v cos u, where u = 30, v = 45 (deg).

Quadratic_Equations/631381: In vertex form, how will a, h and k help us in graphing a quadratic function? 1 solutions Answer 397679 by richard1234(5390)   on 2012-07-24 19:35:15 (Show Source): You can put this solution on YOUR website! Need to specify what a, h, and k are.

Quadratic_Equations/631338: Suppose ax^2+bx+c=0 is a quadratic equation which has real complex roots. Why should it have complex conjugate roots? [Hint: Think of how roots of a quadratic equation are derived using the quadratic formula] (please help me with this) 1 solutions Answer 397678 by richard1234(5390)   on 2012-07-24 19:34:03 (Show Source): You can put this solution on YOUR website! Derive the quadratic formula by completing the square. Somewhere in there you'll see that if the roots are non-real, then they are complex conjugates.

Probability-and-statistics/629648: Estimate the probability of getting a baby girl in at least 8 of 15 births. 1 solutions Answer 397030 by richard1234(5390)   on 2012-07-21 16:41:45 (Show Source): You can put this solution on YOUR website! Assuming P(girl) = 1/2, note that the binomial distribution is symmetric. This means that The sum of and is 1, so .

Triangles/630359: 1. A triangle has the following three sides measured in feet: 26, 28, and 24. Calculate the perimeter of this triangle, the area enclosed by the triangle, and the angles made at the vertices of the sides. 1 solutions Answer 397028 by richard1234(5390)   on 2012-07-21 16:38:21 (Show Source): You can put this solution on YOUR website! Perimeter = 26+28+24 = 78 feet Area: use Heron's formula Angles: Either use law of cosines to find the cosine of each angle, or use where theta is the angle between sides a and b.

Probability-and-statistics/630594: A researcher wanted to see which candidate you would vote for. What level of significance would she use in testing? 1 solutions Answer 397027 by richard1234(5390)   on 2012-07-21 16:33:28 (Show Source): You can put this solution on YOUR website! Too little info. Also, significance tests are used for numerical data.

Linear-equations/630257: Find the range of function g(x)=3-5x. Given domain { -2, -1, 0, 1, 2 } 1 solutions Answer 397024 by richard1234(5390)   on 2012-07-21 16:29:09 (Show Source): You can put this solution on YOUR website! Replace x with -2, -1, 0, 1, 2. You should obtain five different values.

Quadratic_Equations/630519: If m and n are the roots of the equation then what is the equation whose roots are and ? 1 solutions Answer 397023 by richard1234(5390)   on 2012-07-21 16:27:14 (Show Source): You can put this solution on YOUR website! By Vieta's formulas, and . Also, the quadratic that we want can be written in the form . Note that -d is the sum of the roots and e is the product of the roots. Add/multiply the two given roots, write in terms of a,b,c and you're done.

Rational-functions/627798: how do i determine the number of real solutions of -2x^2 +5x-3=0 1 solutions Answer 395683 by richard1234(5390)   on 2012-07-15 01:34:31 (Show Source): You can put this solution on YOUR website! The discriminant is , so there are two real solutions.

Age_Word_Problems/627879: 12 is more than the sum of 23 and 14 is what 1 solutions Answer 395682 by richard1234(5390)   on 2012-07-15 01:33:28 (Show Source): You can put this solution on YOUR website! "12 is more than the sum of 23 and 14" is false. "12 more than the sum of 23 and 14" is what you should've asked.

Geometry_Word_Problems/628449: An equilateral triangle is ______________ an isosceles triangle. 1 solutions Answer 395681 by richard1234(5390)   on 2012-07-15 01:31:12 (Show Source): You can put this solution on YOUR website! An isosceles triangle is usually defined as a triangle with at least two sides of equal length, so I would say "always."

Percentage-and-ratio-word-problems/628211: Suppose that the National Weather Service states that there is a 50% chance of snow on Saturday and a 40% chance of snow on Sunday. What are the odds in favor of having snow on at least one of the two days? HINT: Assume that whether or not it snows on Saturday has absolutely no bearing on whether it snows or not on Sunday. 1 solutions Answer 395679 by richard1234(5390)   on 2012-07-15 01:29:45 (Show Source): You can put this solution on YOUR website! 1 minus the probability of having snow on neither day. What is that equal to?

Probability-and-statistics/628486: Determine the odds against the spinner landing on yellow: In a pie chart there are 5 yellow slices, 2 red slices, 1 blue slice 1 solutions Answer 395678 by richard1234(5390)   on 2012-07-15 01:28:21 (Show Source): You can put this solution on YOUR website! If they are of equal area then P(yellow) = 5/(5+2+1) = 5/8.

Quadratic_Equations/628517: 4. Take a number. Add 1. Square the result. Then subtract from it the product of the original number times two more than the original number. What did you get? I claim you will always get 1. Can you explain? I’m very confused on what to do here. 1 solutions Answer 395677 by richard1234(5390)   on 2012-07-15 01:24:06 (Show Source): You can put this solution on YOUR website! Suppose the number you think of is x. "Add 1." x+1. "Square the result." (x+1)^2 = x^2 + 2x + 1 Then you can take it from there.

Miscellaneous_Word_Problems/628212: Three cards are selected from a standard deck of playing cards. If both of the first two cards are spades, what is the probability that the third card is a spade? 1 solutions Answer 395539 by richard1234(5390)   on 2012-07-14 00:48:43 (Show Source): You can put this solution on YOUR website! 11 spades remain out of 52. 11/52

Geometry_Word_Problems/627558: A rectangle has a perimeter of 10. If the lengths of its sides are integers, enumerate all possible values for its length l and width w. 1 solutions Answer 395160 by richard1234(5390)   on 2012-07-12 01:25:54 (Show Source): You can put this solution on YOUR website! 2(l+w) = 10 --> l+w = 5 Therefore (l,w) = (4,1), (3,2), (2,3), (1,4).

Probability-and-statistics/627778: There are 2500 students in a school. If I am wearing color A shirt then what is the probability that one of the other 2499 students is wearing the same color shirt. I think the answer should be 1/2499 or maybe 1/7 raised to the power 2499 if we are talking about the seven primary colors. 1 solutions Answer 395159 by richard1234(5390)   on 2012-07-12 01:25:04 (Show Source): You can put this solution on YOUR website! There are only three primary colors. Anyway, assuming there are seven colors with equal probability, the probability that at least one of the other 2499 students is wearing color A is equal to 1 - P(none of them wearing color A). This is equal to , very close to 1. If you are looking for the probability that *exactly* one is wearing color A, you have to use the binomial distribution.

t e s t/627774: 1)at what point on the curve y=x^2+7x-8 is the gradient equal to 1? 2)at which point on the curve y=x^3+3x^2-5 is the gradient equal to 9 ? 1 solutions Answer 395158 by richard1234(5390)   on 2012-07-12 01:21:30 (Show Source): You can put this solution on YOUR website! 1) , solve for x. 2) Same thing, , solve for x.

Graphs/627219: If x+y<16 but x-y>6, where x and y are integers, what is the largest integral value of xy? 1 solutions Answer 395156 by richard1234(5390)   on 2012-07-12 01:02:59 (Show Source): You can put this solution on YOUR website! One problem with your question: answer is negative infinity. You could let x = -k, y = -k-7, where k is a positive integer. That will always satisfy both inequalities, but if the absolute value of k gets large, xy will also get large.

Pythagorean-theorem/627163: Which of the following sets could be the sides of a right triangle? {2,3,/10} {3,5,/34} {5,8,12} i dont know 1 solutions Answer 395155 by richard1234(5390)   on 2012-07-12 01:00:07 (Show Source): You can put this solution on YOUR website! Which one(s) satisfy the Pythagorean theorem?

Functions/627113: Let f(x)= ax+b, where a and b are positive numbers, and assume that the following equation holds for all values of x: f(f(x))= bx+a. Find a+b. 1 solutions Answer 395154 by richard1234(5390)   on 2012-07-12 00:57:35 (Show Source): You can put this solution on YOUR website! . Equate terms with "x" in it, as well as constants: and Substitute b with a^2 in the second equation: . Solving for a, (here, denotes the golden ratio) Since b = a^2, Therefore,

Geometry_proofs/627489: Hello, can you please help me prove that all four angles of a rectangle are right angles. Thank you :) 1 solutions Answer 395152 by richard1234(5390)   on 2012-07-12 00:46:33 (Show Source): You can put this solution on YOUR website! That's how a rectangle is defined, a quadrilateral with four right angles.

Quadratic-relations-and-conic-sections/627512: State whether a local maximum or a local minimum. (-1.5,-3.75) 1 solutions Answer 395150 by richard1234(5390)   on 2012-07-12 00:45:27 (Show Source): You can put this solution on YOUR website! Maximum or minimum of what function?