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 Numbers_Word_Problems/361522: Translate into equations and solve. 1.Six more than nine times a number is the same as two less than ten times the number.What is the number? 2.A pro shop in a bolwing alley drops the price of bowling balls 24% to a sale price of \$34.20.What was the former price? 3.An appliacne store drops the price of a certain type of tv 18% to a sale price of \$410.What was the former price? -please show as much work as you can to help me understand what you are doing. -Thank you1 solutions Answer 257740 by robertb(4012)   on 2010-10-25 18:04:42 (Show Source): You can put this solution on YOUR website!1.) 9x+6 = 10x-2. Then , . 2.) Let x = former price. Since there was a 24% discount, the sale price of \$34.20 is 76% of x, or , or x = \$45. 3.) This is similar to #2 above. Since there was a 18% discount, the sale price of \$410 is 82% of x, or , or x = \$500.
 Percentage-and-ratio-word-problems/361519: Jen and Heather went to lunch. When the bill came, Jen discovered that she had only \$8. Luckily, Heather had enough money to pay the other part, or 3/5 of the bill. How much did Heather pay? How much was the total bill?1 solutions Answer 257735 by robertb(4012)   on 2010-10-25 17:59:06 (Show Source): You can put this solution on YOUR website!Let x = total bill. Then , , . Total bill was \$20, and Heather paid \$12.
 test/361518: why does math suck !!!!!!!!!!!!!y do u make us do it...i hate math..............................................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 solutions Answer 257733 by robertb(4012)   on 2010-10-25 17:55:48 (Show Source): You can put this solution on YOUR website!Math is part of the cycle of life. Though I agree with you, it does suck...but not always :D
 Linear_Algebra/39572: Proof of a singular matrix: I need to show (in general) that either matrix A is "singular" or "A^2 = A^(-1)". A is an n*n square matrix such that A^4 = A. I want to know how to do this problem and what happens if the exponent values are different.(for example, odd number exponents?)1 solutions Answer 257611 by robertb(4012)   on 2010-10-25 03:33:51 (Show Source): You can put this solution on YOUR website!Let . Then . (The zero matrix!)Taking the determinants of both sides, , , ,or det(A) = 0, or . If A is nonsingular, then det(A)is NOT equal to zero, but ,(because ) so . Hence . If A is singular , then det(A) = 0 (since a square matrix is singular if and only if its determinant is 0). In which case the value of won't matter anymore.
 Matrices-and-determiminant/84358: Can someone help me with these two problems explaining them to me if someone has time please. Problem #1 If A is a 5 X 2 matrix and A + k = A, what do you know about K? Problem #2 Find the values of the variables in each equation. i don't know how to do the matrix box so i will separate them the first matrix is a 2 X 3 plus the second matrix that is a 2X 3 Equal the third matrix which is a 2 X 3. I try to separate the numbers inside the matrix with a forward slash. so a+2 is ontop of row that reads 4k and then the same for the second matrix and the last matrix [ a+ 2 / 3z+1 / 5m ] + [ 3a / 2z / 5m] = [ 10 / -14 / 80] [ 4k / 0 / 3 ] [ 2k/ 5 / 6] [ 10 / 5 / 9] 1 solutions Answer 257609 by robertb(4012)   on 2010-10-25 03:01:18 (Show Source): You can put this solution on YOUR website!Problem#1: K is the 5x2 zero matrix! Problem #2: , This means a+2+3a = 10, or 4a = 8, or a = 2. 3z+1+2z = -14, or 5z = -15, or z = -3, 5m+5m = 80, or 10m = 80, or m = 8, and 4k+2k = 10, or k = 10/6 = 5/3.
 Mixture_Word_Problems/361061: To make pickles, fresh cucumbers are soaked in a salt water solution called brine. How many liters of a 2% brine solution must be added to 30 liters of a 10% brine solution to dilute it to an 8% solution?1 solutions Answer 257586 by robertb(4012)   on 2010-10-24 22:55:26 (Show Source): You can put this solution on YOUR website!Let x = # liters of 2% brine to add. , , , , .
 Human-and-algebraic-language/361062: 14 less than three times a number is equal to the number. What is the number?1 solutions Answer 257585 by robertb(4012)   on 2010-10-24 22:51:02 (Show Source): You can put this solution on YOUR website!3x - 14 = x, 3x - x = 14, 2x = 14, x = 7.
 Geometry_Word_Problems/361068: The length of a rectangle is 2 less than 3 times the width. Find the dimensions if the area is 65 square meters1 solutions Answer 257584 by robertb(4012)   on 2010-10-24 22:43:53 (Show Source): You can put this solution on YOUR website!l = 3w - 2. Then A =lw, or (3w-2)w = 65. , , , , or . We eliminate the first value. Therefore, the width is 5 meters and length is 13 meters.
 Equations/361074: (y+3)(y+2)=01 solutions Answer 257583 by robertb(4012)   on 2010-10-24 22:36:31 (Show Source): You can put this solution on YOUR website!y + 3 = 0 or y+2 = 0. y = -3 or y = -2.
 Equations/361072: solve for x; y=bx-c1 solutions Answer 257582 by robertb(4012)   on 2010-10-24 22:33:19 (Show Source): You can put this solution on YOUR website!y+c = bx,
 Square-cubic-other-roots/361071: What is the simplest radical form of 1 solutions Answer 257581 by robertb(4012)   on 2010-10-24 22:32:20 (Show Source):
 Matrices-and-determiminant/361049: I have worked out Eigenvalues of the following matrix 1 -1 2 0 2 0 3 -3 2 They are = -1, 2, 4 I cant seem to work out the eigenvector for -1. Could someone show me step by step how this achieved. I can then use this to work out 2, and 4. 1 solutions Answer 257580 by robertb(4012)   on 2010-10-24 22:28:12 (Show Source): You can put this solution on YOUR website!For λ = -1, replacing -1 into the homogeneous system A - λI = O, we get the augmented homogeneous system . ~Divide r2 and r3 by 3. ~Add row2 to r3 ~-2*r3 + r1 ~Add r2 to r1 ~Interchange r1 and r3. Thus y = 0 and x + z = 0, or z = -x. hence, . The basis for eigenspace for λ = -1 is then , and this is its eigenvector.
 Expressions-with-variables/361051: 9s > -181 solutions Answer 257578 by robertb(4012)   on 2010-10-24 21:59:21 (Show Source): You can put this solution on YOUR website!s>-2, after dividing both sides by 9.
 Equations/361039: Simplify the algebraic equation 3x+(3y)+(12x)+10y Evaluate the expressions for a=5and b=4 5(a+4b)+3(2a-7b)1 solutions Answer 257577 by robertb(4012)   on 2010-10-24 21:58:18 (Show Source): You can put this solution on YOUR website!3x+(3y)+(12x)+10y = 15x + 13y. 5(a+4b)+3(2a-7b) = 5(5 +4*4)+3(2*5 - 7*4) = 5(21)+3(-18) = 51.
 Rectangles/361044: If a rectangle measures 4.00 inches by 5/6 inch, what is its area in square centimeters?1 solutions Answer 257576 by robertb(4012)   on 2010-10-24 21:53:15 (Show Source): You can put this solution on YOUR website!Think I've solved this already.
 Average/361048: Help Please: Determine a relationship between the x and y values in the relation {(1, 4), (2, 7), (3, 10), (4, 13)} write an equation1 solutions Answer 257575 by robertb(4012)   on 2010-10-24 21:51:50 (Show Source): You can put this solution on YOUR website!It seems like .
 Numbers_Word_Problems/361043: The sum of twice a first number and seven times a second number is 66. If the second number is subtracted seven times from the first number the result is 27. Find the numbers.1 solutions Answer 257574 by robertb(4012)   on 2010-10-24 21:49:39 (Show Source): You can put this solution on YOUR website!2f + 7s = 66 7f - s = 27. Multiply the bottom equation by 7, and then add corresponding sides with the top equation. We get 51f = 255, or f = 5. Then s = 7*5 - 27 = 35 - 27 = 8.
 Rectangles/361041: If a rectangle measures 4.00 inches by 5/6 inch, what is its area in square centimeters?1 solutions Answer 257571 by robertb(4012)   on 2010-10-24 21:43:58 (Show Source): You can put this solution on YOUR website!1 inch = 2.54 cm. Then 4 inches = 10.16 cm, and 5/6 inch = 2.117 cm . The area of the rectangle is then (10.16cm)*(2.117cm) = 21.51 sq.cm.
 Linear-equations/361040: what is x when 57.50=.05x+.06(1000-x) Show work1 solutions Answer 257570 by robertb(4012)   on 2010-10-24 21:40:44 (Show Source): You can put this solution on YOUR website!57.50=.05x+.06(1000-x), 57.50 = .05x + 60-0.06x, 57.50 - 60= -0.01x -2.5 = -0.01x, after transposing 60 from the left side to the right side. -2.5/-0.01 = x x = 250.
 Proofs/361025: prove: if t>0, there exists b such that if x>b then (1/(sqrt(x))) < t1 solutions Answer 257569 by robertb(4012)   on 2010-10-24 21:38:14 (Show Source): You can put this solution on YOUR website!Let . Proof: If, then because b < x, . , since t>0. , after transposition and factoring the quadratic expression on the right. , after dividing both sides by , which is surely positive. So ,and thus , since is positive.
 Matrices-and-determiminant/360408: how do you salve this problem z+2/3=5 z+2/3-2/3=5-2/3 z= 1 solutions Answer 257348 by robertb(4012)   on 2010-10-24 04:34:56 (Show Source):
 Probability-and-statistics/360451: The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results. Area A B C D E F G H before 14 7 4 5 17 12 8 9 after 2 7 3 6 8 13 3 5 Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.1 solutions Answer 257347 by robertb(4012)   on 2010-10-24 04:28:37 (Show Source): You can put this solution on YOUR website!Please see the solution I posted previously =)
 test/360412: What's the division to get tons from pounds1 solutions Answer 257346 by robertb(4012)   on 2010-10-24 04:27:17 (Show Source): You can put this solution on YOUR website!1 ton = 2000 pounds. For example, 450 pounds is the same as 450* = 0.225 tons.
 Probability-and-statistics/360511: The probability of contracting the kissing disease is .23 when one is exposed to a certain provocative environment. 60 people are exposed. What is the probability that no more than 10 are infected with this dreaded disease.1 solutions Answer 257345 by robertb(4012)   on 2010-10-24 04:24:10 (Show Source): You can put this solution on YOUR website!+...+
 Probability-and-statistics/360417: From surveys we know that 45% of dentists use nitrous oxide (laughing gas) in their practice. If we select many random samples of 10 dentists, on average how many of them would you expect to use laughing gas in their practice? A. 5. B. 4.5. C. Impossible to tell. D. 21 solutions Answer 257343 by robertb(4012)   on 2010-10-24 04:11:46 (Show Source): You can put this solution on YOUR website!B. 4(If we're going to follow rounding-off rules.)
 Rational-functions/360501: The cell phone plan is \$50 per month for 450 min. If you go over 450 min., they charge you an additional .20 per minute. Write a piecewise function to describe the plan. Let y represent the total monthly charge a x represent the number of minutes. 1 solutions Answer 257342 by robertb(4012)   on 2010-10-24 04:09:03 (Show Source): You can put this solution on YOUR website!y = 50, , y = 50+0.50x, .
 Probability-and-statistics/360460: The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results. Number of Crimes by Area A B C D E F G H before 14 7 4 5 17 12 8 9 after 2 7 3 6 8 13 3 5 Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value. 1 solutions Answer 257341 by robertb(4012)   on 2010-10-24 04:02:41 (Show Source): You can put this solution on YOUR website!The following are the values for the before-minus-after values: d = 12, 0, 1, -1, 9 , -1, 5 , 4 The average m of these values are 29/8 = 3.625. Now the following corresponding values for are 70.14,13.14,6.89,21.39,28.89,21.39,1.89,0.14. Their sum is 163.87. The standard deviation of the differences would be , and the standard error is . Now we use a one-tailed matched-pairs t-test. Null hypothesis: D = 0 Alternative hypothesis: D > 0 , under assumption of the null hypothesis. Now , so the p-value is 0.0359. Since 0.0359>0.01, we don't reject the null hypothesis. Hence the differences in the sample aren't significant to say that there is a drop in the number of crimes.
 Probability-and-statistics/360435: The first national bank of wilson has 650 (population) checking account customers. A recenter sample of 50 (sample) of these customers showed 26 to have a visa card with the bank. Construct the 99 percent confidence interval for the proportion of checking account customers who have a visa card with the bank.1 solutions Answer 257338 by robertb(4012)   on 2010-10-24 03:20:06 (Show Source): You can put this solution on YOUR website!*The first national bank of Wilson has 650 (population) checking account customers. A recent sample of 50 (sample) of these customers showed 26 to have a visa card with the bank. Construct the 99 percent confidence interval for the proportion of checking account customers who have a visa card with the bank.* The confidence interval for a proportion, , is p ± z σp, where p = 26/50 = 0.52, σp = (Note that this is just an estimate of the standard error of the proportion, since isn't given in the problem), and z = 2.575. Thus 0.52± (2.575)*(0.070654), or (0.338066, 0.701934)
 Rational-functions/360421: i need to write an equation of the line that passes through these points (2,3) and (4,11)1 solutions Answer 257336 by robertb(4012)   on 2010-10-24 02:55:03 (Show Source): You can put this solution on YOUR website!The slope m is , so by the point slope form: , , .