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# Recent problems solved by 'Alan3354'

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 Permutations/574750: Four coins are tossed. In how many ways can they fall? 1 solutions Answer 369276 by Alan3354(30993)   on 2012-02-19 09:14:14 (Show Source): You can put this solution on YOUR website!Four coins are tossed. In how many ways can they fall?
 Expressions-with-variables/574688: -1/4(x-8)+1/2(x+2)=x+15 (-1/4*x)-(-1/4*8)+(1/2*x)+(1/2*2)=x+15 -1/4x-2+1/2x+1=x+15 3/4x-1=x+15 (3/4x-3/4)-1=(x-3/4)+15 x-1=1/4x+15 And now I'm completely lost. Thanks for any help you can give.1 solutions Answer 369226 by Alan3354(30993)   on 2012-02-18 21:50:13 (Show Source): You can put this solution on YOUR website!-1/4(x-8)+1/2(x+2)=x+15 (-1/4*x)-(-1/4*8)+(1/2*x)+(1/2*2)=x+15 -1/4x-2+1/2x+1=x+15 ************************-(-1/4*8) = +2 3/4x-1=x+15 ---------------- -1/4(x-8)+1/2(x+2)=x+15 (-1/4*x)-(-1/4*8)+(1/2*x)+(1/2*2)=x+15 -1/4x + 2 + 1/2x + 1 = x+15 (1/4)x + 3 = x+15 (1/4)x = x + 15 x = 4x + 60 -3x = 60 x = -20
 Money_Word_Problems/574653: a loan of 27,000 with a 6% rate paying 500 a month 1 solutions Answer 369211 by Alan3354(30993)   on 2012-02-18 20:25:33 (Show Source): You can put this solution on YOUR website!a loan of 27,000 with a 6% rate paying 500 a month ------------- What's your question?
 Rectangles/574647: The perimeter of a rectangle is 15 cm, and its dimensions are tripled. What is the perimeter of the larger rectangle?1 solutions Answer 369202 by Alan3354(30993)   on 2012-02-18 18:07:00 (Show Source): You can put this solution on YOUR website!3*15 = 45
 Circles/574652: What is the area of a circle whose diameter is 25cm1 solutions Answer 369201 by Alan3354(30993)   on 2012-02-18 18:06:21 (Show Source): You can put this solution on YOUR website!What is the area of a circle whose diameter is 25cm -------- r = 25/2 cm
 Travel_Word_Problems/574614: how many miles per hour would i need to run in order to finish 1 & 1/3 mile distance in 12 minutes1 solutions Answer 369175 by Alan3354(30993)   on 2012-02-18 14:27:39 (Show Source): You can put this solution on YOUR website!how many miles per hour would i need to run in order to finish 1 & 1/3 mile distance in 12 minutes -------------- d = r*t r = d/t = (4/3) miles/(1/5) hours
 t e s t/574615: What decimal is greater than 0.346 and less than 0.36?1 solutions Answer 369174 by Alan3354(30993)   on 2012-02-18 14:24:29 (Show Source): You can put this solution on YOUR website!What decimal is greater than 0.346 and less than 0.36? -------------- "What decimal..." makes no sense. If you mean what number in decimal format: There are an infinite # of them. 0.3460001 0.3460002 0.3460000000000007 etc
 Linear_Equations_And_Systems_Word_Problems/574608: Game rentals are \$5 each and movie rentals are \$2 each. Write an equation to represent the number of games, x, and the number of movies, y, that could be rented with \$150.1 solutions Answer 369171 by Alan3354(30993)   on 2012-02-18 14:00:57 (Show Source): You can put this solution on YOUR website!Game rentals are \$5 each and movie rentals are \$2 each. Write an equation to represent the number of games, x, and the number of movies, y, that could be rented with \$150. ----- 5x + 2y = 150
 Polynomials-and-rational-expressions/574517: what are the positive zeros of f(x)=2x^4-9x^3+2x^2+21x-10?1 solutions Answer 369169 by Alan3354(30993)   on 2012-02-18 13:33:47 (Show Source): You can put this solution on YOUR website!what are the positive zeros of f(x)=2x^4-9x^3+2x^2+21x-10? x = 1/2 & x = 2 -------------- Divide those out and solve the quadratic for the other 2, 1 is positive.
 Travel_Word_Problems/574601: You ride a motor scooter 8 km for 15 minutes. Your [average] speed is?1 solutions Answer 369166 by Alan3354(30993)   on 2012-02-18 13:17:42 (Show Source): You can put this solution on YOUR website!You ride a motor scooter 8 km for 15 minutes. Your [average] speed is? ---------- d = r*t r = d/t = 8 km/15 min r = 8/15 km/min
 Linear-equations/574559: 9. Write the equation of a line that passes through the given point and has the given slope. Then write the equation in slopeintercept form. Show all your work. Passes through (–5, 6) and has slope of 3 Passes through (4, 0) and has slope of 1/2 Passes through (3, –2) and has slope of –4 Take Note You can check your answer by first checking that the given slope and the slope in your equation are the same. Then substitute the ordered pair into your equation and show that it is a solution. 1 solutions Answer 369133 by Alan3354(30993)   on 2012-02-18 09:31:49 (Show Source): You can put this solution on YOUR website!Write the equation of a line that passes through the given point and has the given slope. Then write the equation in slopeintercept form. Show all your work. Passes through (–5, 6) and has slope of 3 Use y = mx + b and the point to find b 6 = 3*(-5) + b b = 21 --> y = 3x + 21 ======================== Do these the same way. Passes through (4, 0) and has slope of 1/2 Passes through (3, –2) and has slope of –4
 Money_Word_Problems/574565: I have tried, can you help please? Charles deposited 12,000 in the bank. He withdrew 5000 from his account after one year. If he reeives a total amount of 9350 after 3 years, fidn the rate of simeple interest. I tried i=prt but that is confusing - help please1 solutions Answer 369132 by Alan3354(30993)   on 2012-02-18 09:29:51 (Show Source): You can put this solution on YOUR website!Charles deposited 12,000 in the bank. He withdrew 5000 from his account after one year. If he reeives a total amount of 9350 after 3 years, fidn the rate of simeple interest. I tried i=prt but that is confusing - help please ================ i = prt is (sort of) the formula for continuous compounding, but this says simple interest. ---- If the interest was paid on 12000 the first year, then 7000 for 2 years: 9350 = r*12000 + 2r*7000 = 26000r r = 9350/26000 =~ 0.3596 --> 36% interest, a good rate. Is he a shylock?
 Rate-of-work-word-problems/574566: the time between a flash of lighting and the sound of thunder is 9 seconds. How far away is the lighting1 solutions Answer 369131 by Alan3354(30993)   on 2012-02-18 09:24:34 (Show Source): You can put this solution on YOUR website!the time between a flash of lighting and the sound of thunder is 9 seconds. How far away is the lighting ----------- 9 times the speed of sound (in feet or meters per second) The speed of sound varies with temperature, it's ~ 1000 to 1100 ft/second 9*1000 = 9000 feet
 Geometry_Word_Problems/574537: Billy likes to go cycling. His bike has wheels of diameter 85cm. He has invented a counter for his bike, which counts the number of revelations the wheel makes. One day the counter shows 240 revolutions. How far has billy cycled? give your answer to the nearest metre.1 solutions Answer 369130 by Alan3354(30993)   on 2012-02-18 09:23:22 (Show Source): You can put this solution on YOUR website!His bike has wheels of diameter 85cm. He has invented a counter for his bike, which counts the number of revelations the wheel makes. One day the counter shows 240 revolutions. How far has billy cycled? give your answer to the nearest metre. --------------- Circumference = pi*85 cm d = 240*85*pi = 20400*pi cm = 204*pi meters d =~ 641 meters ------------------ You can buy those for ~ \$20, they show speed and distance. No need to invent it. It works well on bicycles, but adapting it to rollerblades is not easy.
 Numeric_Fractions/574292: What is the answer and how do you solve: 5-3(5/8)1 solutions Answer 369128 by Alan3354(30993)   on 2012-02-18 09:18:14 (Show Source): You can put this solution on YOUR website!5-3(5/8) = 5 - (15/8) = 40/8 - 15/8 = 25/8
 Parallelograms/574564: What would be the square footage of a property with four unequal lenght sides? one 41.67 two 98.42 three 40.42 four 81.691 solutions Answer 369126 by Alan3354(30993)   on 2012-02-18 09:06:58 (Show Source): You can put this solution on YOUR website!What would be the square footage of a property with four unequal lenght sides? one 41.67 two 98.42 three 40.42 four 81.69 =========== Not enough info. Have to have angle data, or diagonal dimensions.
 Linear-equations/574557: Find an equation of the line in slope-intercept form that passes through each given set of points. Show all your work. (–2, 2) and (1, 5) (1, 7) and (3, 2) (–3, 1) and (8, 1) 1 solutions Answer 369125 by Alan3354(30993)   on 2012-02-18 08:38:23 (Show Source): You can put this solution on YOUR website!Find an equation of the line in slope-intercept form that passes through each given set of points. Show all your work. (–2, 2) and (1, 5) -------------- Find the slope, m m = diffy/diffx = (2-5)/(-2-1) m = 1 ------ Use y = mx + b and either point to find b 5 = 1*1 + b b = 4 ----- --> y = x + 4 -------------------- You can use determinants: |+x y 1| |-2 2 1| = 0 |+1 5 1| --------------------- x*(2-5) - y*(-2-1) + 1*(-10-2) = 0 -3x + 3y = 12 x - y = -4 ====================== Do these the same way. (1, 7) and (3, 2) (–3, 1) and (8, 1)
 Geometry_proofs/574390: how to solve the pythagorean theorem with the geometric men formulas1 solutions Answer 369080 by Alan3354(30993)   on 2012-02-17 18:43:27 (Show Source): You can put this solution on YOUR website!how to solve the pythagorean theorem with the geometric men formulas ------- Theorems are not solved. Equations are solved.
 Pythagorean-theorem/574421: A boat travels 30 miles east and then 40 miles north. How far is the boat from its point of origin ? (Hint:Use the Pythagorean Theorem)1 solutions Answer 369079 by Alan3354(30993)   on 2012-02-17 18:42:38 (Show Source): You can put this solution on YOUR website!A boat travels 30 miles east and then 40 miles north. How far is the boat from its point of origin ? (Hint:Use the Pythagorean Theorem) ------------ Hint: Use the Pythagorean Theorem ----------- East is perpendicular to North, so the 2 legs make a right angle. d = 50 miles
 Trigonometry-basics/574413: A highway sign warns that a section of a road ahead has a 7% grade. To the nearest degree, what angle does the road make with a horizontal line?1 solutions Answer 369078 by Alan3354(30993)   on 2012-02-17 18:21:16 (Show Source): You can put this solution on YOUR website!Angle = arctan(0.07) =~ 4 degs
 Travel_Word_Problems/574369: Flying to Moscow with a tailwind a plane averaged 142 km/h. On the return trip the plane only averaged 76 km/h while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind.1 solutions Answer 369070 by Alan3354(30993)   on 2012-02-17 17:40:36 (Show Source): You can put this solution on YOUR website!Flying to Moscow with a tailwind a plane averaged 142 km/h. On the return trip the plane only averaged 76 km/h while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind. ------------- The plane's airspeed is the average = (142 + 76)/2 = 109 km/hr The windspeed is the difference = 142 - 109 = 33 km/hr ---------------- That's a slow plane, cars would pass it on the road going upwind or downwind. 142 km/hr =~ 85 mi/hr ---------- Also, planes don't use km/hr, they use knots.
 Trigonometry-basics/574406: Given f(x)=cos5x+sin4x, find the exact value of f(pi sign/3).1 solutions Answer 369069 by Alan3354(30993)   on 2012-02-17 17:35:48 (Show Source): You can put this solution on YOUR website!Given f(x)=cos5x+sin4x, find the exact value of f(pi sign/3). ----------- If you mean f(pi/3) radians: = 0.5 + -sqrt(3)/2 =
 Functions/574388: 10x+41 solutions Answer 369068 by Alan3354(30993)   on 2012-02-17 17:33:03 (Show Source): You can put this solution on YOUR website!10x+4 -------- What about it?
 Proportions/574361: ONE NUMBER IS TWICE ANOTHER THE SUM OF THEIR RECIPROCALS IS 1.5 FIND THE NUMBERS1 solutions Answer 369067 by Alan3354(30993)   on 2012-02-17 17:28:23 (Show Source): You can put this solution on YOUR website!(1/n) + 1/(2n) = 1.5 Can you finish it?
 Trigonometry-basics/574405: if sin x= 0.0935, find the value of positive acute angle x to the nearest degree.1 solutions Answer 369066 by Alan3354(30993)   on 2012-02-17 17:25:26 (Show Source): You can put this solution on YOUR website!if sin x= 0.0935, find the value of positive acute angle x to the nearest degree. --------- =~ 5 degs Do you not have a calculator? Get one.
 Numbers_Word_Problems/574403: what is the average (arithmetic mean) of all the multiples of 5 from 1 to 9 9991 solutions Answer 369065 by Alan3354(30993)   on 2012-02-17 17:24:06 (Show Source):
 Numbers_Word_Problems/574396: What fraction would use to solve 33one-third% of 42 mentally 1 solutions Answer 369064 by Alan3354(30993)   on 2012-02-17 17:23:40 (Show Source): You can put this solution on YOUR website!1/3 Mentally, or otherwise.
 absolute-value/574359: what is the absolute value of -2+5-31 solutions Answer 369038 by Alan3354(30993)   on 2012-02-17 13:59:03 (Show Source): You can put this solution on YOUR website!Zero
 Travel_Word_Problems/574311: If I jog for 15 minutes, how far have I traveled?1 solutions Answer 369027 by Alan3354(30993)   on 2012-02-17 11:26:15 (Show Source): You can put this solution on YOUR website!If I jog for 15 minutes, how far have I traveled? ------------ It depends on your speed.
 Trigonometry-basics/574298: Prove that:~ cotB + tanB = cotB sec^2B1 solutions Answer 369023 by Alan3354(30993)   on 2012-02-17 10:37:32 (Show Source): You can put this solution on YOUR website!Prove that:~ cotB + tanB = cotB sec^2B --------------- Multiply thru by tan(B) ---------- 1 + tan^2 = sec^2 I'm convinced -------------- If you're not, multiply thru by cos^2 cos^2 + sin^2 = 1
 Linear-systems/574304: what is 3x+3y=27 1 solutions Answer 369022 by Alan3354(30993)   on 2012-02-17 10:34:53 (Show Source): You can put this solution on YOUR website!what is 3x+3y=27 ------------- It's an equation.