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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Word_Problems_With_Coins/235319: Penelope has several coins, all nickels and quarters in her piggy bank. The total amount of money that she has is \$15.65. If Penelope has 13 more nickels than quarters, how many quarters does she have? 1 solutions Answer 173381 by stanbon(57219)   on 2009-11-04 22:48:27 (Show Source): You can put this solution on YOUR website!Penelope has several coins, all nickels and quarters in her piggy bank. The total amount of money that she has is \$15.65. If Penelope has 13 more nickels than quarters, how many quarters does she have? ------------------- Quantity Eq:::: n = q + 13 Value Eq::::::: 5n + 25q = 1565 cents ---------------------------------------------- Substitute for n and solve for q: 5(q+13) + 25q = 1565 30q + 65 = 1565 30q = 1500 q = 50 (# of quarters) ================================ Cheers, Stan H.
 Percentage-and-ratio-word-problems/235320: Mrs. Smith needed 2 3/4 cups of sugar to make fudge and 2 3/8 cups to make ice cream. How much did she need all together?1 solutions Answer 173380 by stanbon(57219)   on 2009-11-04 22:41:59 (Show Source): You can put this solution on YOUR website!Mrs. Smith needed 2 3/4 cups of sugar to make fudge and 2 3/8 cups to make ice cream. How much did she need all together? ----------------------------------------- 2 3/4 + 2 3/8 = 11/4 + 19/8 = 22/8 + 19/8 = 41/8 = 5 1/8 cups =================== Cheers, Stan H.
 Probability-and-statistics/235316: An oil drilling company knows that it costs \$25,000 to sink a test well. If oil is hit, the income for the drilling company will bve \$425,000. If only natural gas is hit, the income will be \$125,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and the probability of hitting gas is 1/20, what is the expectation for the drilling company? Should the company sink the test well. 1 solutions Answer 173379 by stanbon(57219)   on 2009-11-04 22:39:52 (Show Source): You can put this solution on YOUR website!An oil drilling company knows that it costs \$25,000 to sink a test well. If oil is hit, the income for the drilling company will be \$425,000. If only natural gas is hit, the income will be \$125,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and the probability of hitting gas is 1/20, what is the expectation for the drilling company? Should the company sink the test well. ------------ Let the random variable, x, represent company profit. Values of "x": 400,000 , 100,000, -25000 Matched probabilities are (1/40) , 1/20, 37/40 ---------------------------------------------------- Expected profit = (1/40)*400,000 + (2/40)100,000 - (35/40)(25000) E(x) = [400,000+200,000-875000)/40 E(x) = -\$6875 They can expect to lose that amount every time they drill. ================================================================ Cheers, Stan H.
 Probability-and-statistics/235129: The pretzel pack company advertized that their pretzels weigh 2.5 ounces. The weights are normally distributed with mean 2.5 ounces and standard deviation 0.15 ounces. For a pretzel pack selected at random find the probabilty that it weighs less than 2.2 ounces and find the probability that it weighs more than 2.8 ounces.1 solutions Answer 173377 by stanbon(57219)   on 2009-11-04 22:30:46 (Show Source): You can put this solution on YOUR website!The pretzel pack company advertized that their pretzels weigh 2.5 ounces. The weights are normally distributed with mean 2.5 ounces and standard deviation 0.15 ounces. For a pretzel pack selected at random find the probabilty that it weighs less than 2.2 ounces and find the probability that it weighs more than 2.8 ounces. ----------------- z(2.2) = (2.2-2.5)/0.15 =-2 z(2.8) = (2.8-2.5)/0.15 = 2 ------------------------ P(2.2 < x < 2.8) = P(-2 < z < 2) = 0.9545 ============================================= Cheers, Stan H.
 Radicals/235274: Simplify and reduce to lowest terms 1/(√t-5)-3/(√t+5)1 solutions Answer 173362 by stanbon(57219)   on 2009-11-04 20:59:51 (Show Source): You can put this solution on YOUR website!Simplify and reduce to lowest terms 1/(√t-5)-3/(√t+5) ------------------ gcd = sqrt(t-5)*sqrt(t+5) = sqrt(t^2-5) --------------------------------- Rewrite each fraction with the gcd as its denominator: (sqrt(t+5))/gcd - 3(sqrt(t-5))/gcd -------------------------------------- Combine the numerators over the gcd: [sqrt(t+5) - 3sqrt(t-5)]/[sqrt(t^2-5)] ================================ Cheers, Stan H.
 Probability-and-statistics/235276: A factory worker places 86 newly created circuits on a shelf to be checked for quality. Of these, 6 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits she selects will be defective? Approximate the soulution to the nearest ten thousandth.1 solutions Answer 173361 by stanbon(57219)   on 2009-11-04 20:54:59 (Show Source): You can put this solution on YOUR website!A factory worker places 86 newly created circuits on a shelf to be checked for quality. Of these, 6 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits she selects will be defective? Approximate the soulution to the nearest ten thousandth. --- Number of ways to select two defective from 6: 6C2 = 15 Nomber of ways to select two with no restriction: 86C2 = (86*85)/(1*2) 43*85 = 3655 --------------------- Ans: 15/3655 = 0.0041 ============================ Cheers, Stan H.
 Percentage-and-ratio-word-problems/235277: What is the ratio of 20% of 40 to 4% of 201 solutions Answer 173359 by stanbon(57219)   on 2009-11-04 20:47:54 (Show Source): You can put this solution on YOUR website!What is the ratio of 20% of 40 to 4% of 20 --------------- [0.2*40]/[0.04*20] = 8/(8/10) = 10 ------------------------- Ratio is 10:1 ==================== Cheers, Stan H.
 Exponents/235278: what is the gcf of 5p and 20p to the second power:? 1 solutions Answer 173358 by stanbon(57219)   on 2009-11-04 20:45:03 (Show Source): You can put this solution on YOUR website!what is the gcf of 5p and 20p to the second power:? Greatest common factor = 5p ================================= Cheers, Stan H.
 Probability-and-statistics/235267: A bag contains 16 yellow marbles, 6 green marbles, and 7 red marbles. What is the chance of drawing a yellow marble? If a yellow marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a second yellow marble. Give solution in reduced fraction form, separated by a comma.1 solutions Answer 173357 by stanbon(57219)   on 2009-11-04 20:43:42 (Show Source): You can put this solution on YOUR website!A bag contains 16 yellow marbles, 6 green marbles, and 7 red marbles. What is the chance of drawing a yellow marble? Ans: P(yellow) = 16/29 ------------------------------------- If a yellow marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a second yellow marble. P(2nd yellow | 1st yellow) = 15/28 -------------------------------------------------- Cheers, Stan H.
 Volume/235253: If the edge of a cube is tripled,what change takes place in the volume and in the surface area?1 solutions Answer 173350 by stanbon(57219)   on 2009-11-04 20:26:07 (Show Source): You can put this solution on YOUR website!If the edge of a cube is tripled,what change takes place in the volume and in the surface area? -------------------- Volume Formula: V = s^3 ------------------------------- After tripling the side: V = (3s)^3 = 27s^3 ------------------------------- Surface Area S = 6s^2 --------------------- After tripling the side: S = 6(3s)^2 = 6*9s^2 = 54s^2 ================================= Cheers Stan H.
 Trigonometry-basics/235248: Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree. tanY=40/91 solutions Answer 173340 by stanbon(57219)   on 2009-11-04 19:58:07 (Show Source): You can put this solution on YOUR website!Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree. tanY=40/9 ----------------- arctan(40/9) = 77.32 degrees ==================================== Cheers, Stan H.
 Rectangles/235241: A rectangle has a perimeter of 80 centimeter. Its length is 10 centimeter greater than its width. What is the area, in square centimeter, of the rectangle? 1 solutions Answer 173335 by stanbon(57219)   on 2009-11-04 19:46:39 (Show Source): You can put this solution on YOUR website!A rectangle has a perimeter of 80 centimeter. Its length is 10 centimeter greater than its width. What is the area, in square centimeter, of the rectangle? ----------------------- P = 2(L + W) 80 = 2(W+10 + W) 40 = 2W+10 2W = 30 W = 15 L = 15+10 = 25 ------------------------- Area = 15*25 = 375 cm^2 =================================== Cheers, Stan H.
 Equations/235231: 7-2n=n-14 can you please explain how to solve1 solutions Answer 173329 by stanbon(57219)   on 2009-11-04 19:32:28 (Show Source): You can put this solution on YOUR website!7-2n=n-14 Add 2n to both sides to get: 7 = 3n - 14 Add 14 to both sides to get: 3n = 21 Divide both sides by 3 to get: n = 7 ==================== Cheers, Stan H.
 Probability-and-statistics/235035: What is the probability that a 89% foul shooter will make at least 2 shots in a basketball game? I know it is some sort of conditional probability, but I have now idea on what formula I need to use to solve it and my book is not very helpful.1 solutions Answer 173323 by stanbon(57219)   on 2009-11-04 19:18:11 (Show Source): You can put this solution on YOUR website!What is the probability that a 89% foul shooter will make at least 2 shots in a basketball game? -------------------------------------- P(2<= x <=89) = 1 - P(0<= x <= 1) = 1 - [2C0(0.89)^0(0.11)2 + 2C1(0.89)(0.11)] --- = 1 -[0.2079] --- = 0.7921 ==================== Cheers, Stan H.
 Inequalities/235182: How do you find the point of intersection between y=-1/2x+4 and y=2x+81 solutions Answer 173317 by stanbon(57219)   on 2009-11-04 18:45:59 (Show Source): You can put this solution on YOUR website!How do you find the point of intersection between y=-1/2x+4 and y=2x+8 -------------------------- Substitute for y and solve for "x": 1/2x+4 = 2x+8 --- (2x+4)(2x+8) = 1 4(x+2)(x+4) = 1 4(x^2+6x+8) = 1 x^2+6x+8-1/4 x^2+6x+7.75 = 0 --- x = [-6 +- sqrt(36 -4*7.75)]/2 --- x = [-6 +- sqrt(5))/2 --- x = -3 +- 1.118 --- x = -4.118 or x = -1.882 =========================== Cheers, Stan H.
 Probability-and-statistics/235126: Ed earned 88 on his math midterm and 84 on his english midterm. In his math class the mean score was 75 with standard deviation 8. In his english class the mean score was 73 with standard deviation 5. Convert each score to a standard score, then find which was the higher score relative to the rest of the class.1 solutions Answer 173312 by stanbon(57219)   on 2009-11-04 18:20:25 (Show Source): You can put this solution on YOUR website!Ed earned 88 on his math midterm and 84 on his english midterm. In his math class the mean score was 75 with standard deviation 8. In his english class the mean score was 73 with standard deviation 5. Convert each score to a standard score, then find which was the higher score relative to the rest of the class. --------------------------------- Math z-score: (88-75)/8 = 1.625 ----- English z-score: (84-73)/5 = 2.2 -------------------- His English score is further above average and is a higher relative score. ============================================================== Cheers, Stan H.
 real-numbers/235162: Can you simplify this problem? 1 solutions Answer 173302 by stanbon(57219)   on 2009-11-04 18:00:12 (Show Source): You can put this solution on YOUR website!simplify this problem? -2q^2+3(5+4q^2) --- -2q^2 + 15 + 8q^2 --- 6q^2 + 15 ================ Cheers, Stan H.
 Trigonometry-basics/235161: Express The Rule "Multiply By 6, Then Subtract 3" In Function Notation1 solutions Answer 173300 by stanbon(57219)   on 2009-11-04 17:54:36 (Show Source): You can put this solution on YOUR website!Express The Rule "Multiply By 6, Then Subtract 3" In Function Notation --------------- f(x) = 6x-3 ===================== Cheers, Stan H.
 Probability-and-statistics/235136: The life span of one species of a maple tree is normally distributed with mean 20 years and standard deviation 2.3 years. If one tree is choosen at random, what is the probability it will live 21 years or longer? What is the probability that the average lifetime of 9 such trees will be 21 years or more?1 solutions Answer 173298 by stanbon(57219)   on 2009-11-04 17:50:25 (Show Source): You can put this solution on YOUR website!The life span of one species of a maple tree is normally distributed with mean 20 years and standard deviation 2.3 years. If one tree is choosen at random, what is the probability it will live 21 years or longer? --- z(21) = (21-20)/2.3 = 0.4348 P(x >= 21) = P(z >= 0.4348) = 0.3319 ---------------------------------------------- What is the probability that the average lifetime of 9 such trees will be 21 years or more? --- z(21) = (21-20)/[2.3/Sqrt(9)] = 1/[2.3/3] = 3/2.3 = 1.305 P(x-bar >= 21) = P(z >= 1.305) = 0.09606 ============================================= Cheers, Stan H.
 logarithm/235064: write each of the following as a single logarithm a. 3In2+In (x^2)+2 answer 3In^2 b.1/2 loga 4-2 loga 5 answer loga4^1/2-log 5^2 can u please help me1 solutions Answer 173247 by stanbon(57219)   on 2009-11-04 14:39:14 (Show Source): You can put this solution on YOUR website!write each of the following as a single logarithm a. 3In2+In (x^2)+2 ln(9) + ln(x^2) + 2 ln[9x^2] + 2 Comment: 3ln^2 is not the answer to the problem you have posted. --- answer 3In^2 ------------------------------------------------ b.1/2 loga 4-2 loga 5 loga(4^1/2) - loga 5^2 ---------------------------- = loga [2/25] ========================= Cheers, Stan H.
 Permutations/235057: how can i figure out how many ways a group of 6 people can be arranged in a group of 30 people1 solutions Answer 173245 by stanbon(57219)   on 2009-11-04 14:30:57 (Show Source): You can put this solution on YOUR website!how can i figure out how many ways a group of 6 people can be arranged in a group of 30 people ----- Your statement in confusing. Counting groups is one process; counting arrangements is another. --------- # of groups = 30C6 = 593775 # of arrangement: = 30P6 = 427518000 ============================================ Cheers, Stan H.
 Linear-systems/235058: A total of 308 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold . How many adult tickets were sold?1 solutions Answer 173244 by stanbon(57219)   on 2009-11-04 14:26:55 (Show Source): You can put this solution on YOUR website!A total of 308 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold . How many adult tickets were sold? ---------------------------- Equations: s + a = 308 s = 3a ------------------ Substitute for "s" and solve for "a": 3a+a = 308 4a = 308 a = 77 (# of adult tickets sold) Since s = 3a, s = 3*77 = 231 (# Of students tickets sold) ========================================================== Cheers, Stan H.
 Equations/235061: Helping my daughter on Algebra. It's been 20 years. 1/2 x = 3 5/6 what is x, and how did you do it? also, 2/3 x = 24 don't understand equation to get to x. please help.1 solutions Answer 173242 by stanbon(57219)   on 2009-11-04 14:20:49 (Show Source): You can put this solution on YOUR website!1/2 x = 3 5/6 Change the mixed number to a fraction: (1/2)x = 23/6 --- Multiply both sides of the equality by 2 to get: x = 2(23/6) Cancel the common factor of 2 in the numerator and the denominator to get: x = 23/3 Change to a mixed number x = 7 2/3 ============================================================= 2/3 x = 24 Multiply both sides by 3/2 to get: x = (3/2)24 Cancel the common factor of 2 to get: x = 3*12 x = 36 =============== Cheers, Stan H.
 Radicals/235060: EEK! I need help in solving this equation. Simplify: a^1/2 . a^2/3 .a^-1/4. I know I need to simplify.Can someone explain the rule for mulitplying exponential expressions? Please1 solutions Answer 173241 by stanbon(57219)   on 2009-11-04 14:15:31 (Show Source): You can put this solution on YOUR website!Simplify: a^1/2 . a^2/3 .a^-1/4 ------------ Rule: If the bases are the same, add the exponents. ------------ (1/2 + 2/3 - 1/4) lcd = 12 = (6 + 8 - 3)/12 = l1/12 ------------- Answer for your problem: a^(11/12) ============== Cheers, Stan H.
 Probability-and-statistics/235055: 16! -------- (16-6)!1 solutions Answer 173239 by stanbon(57219)   on 2009-11-04 14:11:51 (Show Source): You can put this solution on YOUR website!16! -------- (16-6)! --- = 16!/(10!) ------------ = 16*15*...*11 --- = 5,765,769 ----------------- Cheers, Stan H.
 Quadratic_Equations/234991: Find the distance from Point A (2√3, 5√2) to Point B (-2√3, -√2) Whats the units? 1 solutions Answer 173197 by stanbon(57219)   on 2009-11-04 10:08:09 (Show Source): You can put this solution on YOUR website!Find the distance from Point A (2√3, 5√2) to Point B (-2√3, -√2) ---- d = sqrt[(change in x)^2 + (change in y)^2] --- d = sqrt[(2sqrt(3)+2sqrt(3))^2 + (5sqrt(2)+sqrt(2))^2] --- d = sqrt[16*3 + 36*2] --- d = sqrt[48+72] d = sqrt[120] d = 2sqrt(30) ================== Cheers, Stan H.
 Pythagorean-theorem/234990: Find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12. If necessary, round your answer to two decimal places.1 solutions Answer 173196 by stanbon(57219)   on 2009-11-04 10:03:37 (Show Source): You can put this solution on YOUR website!Find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12 --------------------- h^2 = 5^2 + 12^2 h = sqrt(25+144) h = sqrt(169) h = 13 ================= Cheers, Stan H.
 Quadratic_Equations/234992: 1 solutions Answer 173195 by stanbon(57219)   on 2009-11-04 10:01:22 (Show Source): You can put this solution on YOUR website!40x^2-8x-29 --------- Use the quadratic formula to find the factors: x = [8 +- sqrt(64 - 4*40*-29)]/80 --- x = [8 +- sqrt(4704)]/80 --- x = [8 +- 68.59]/80 --- x = -60.59/80 or x = 76.59/80 ------------- Factors: (x-(76.59)/80)(x+(60.59)/80) ================================ Cheers, Stan H.
 Rational-functions/234975: write rational in lowest terms? zw+4z-3w-12/zw+4z+5w+20 answer:z-3 /z+5 anyone know why the answer is z-3/z+5 with a full break down 1 solutions Answer 173194 by stanbon(57219)   on 2009-11-04 09:52:02 (Show Source): You can put this solution on YOUR website!write rational in lowest terms? zw+4z-3w-12/zw+4z+5w+20 ----------------- Factor numerator and denominator to get: ------------- [z(w+4)-3(w+4)] / [z(w+4)+5(w+4)] ----- = [(w+4)(z-3)] / [(w+4)/(z+5)] --- Cancel the common factor , (x+4) to get: =(z-3)/(z+5) =================== Cheers, Stan H.
 Probability-and-statistics/234981: Three coins are tossed in the air. what is the probability that exactly two of them turn up heads? 1 solutions Answer 173178 by stanbon(57219)   on 2009-11-04 08:45:33 (Show Source): You can put this solution on YOUR website!Three coins are tossed in the air. what is the probability that exactly two of them turn up heads? ------------------ P(x=2) = 3C2(1/2)^2*(1/2) = 3*(1/4)(1/2) = 3/8 ================================================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/234980: Two hundred trolls divided a block of gold evenly. What percent of the block of gold did each troll receive? a) 200% b) 1/200% c) c) 2% d) 0.5% e) 0.2%1 solutions Answer 173177 by stanbon(57219)   on 2009-11-04 08:43:38 (Show Source): You can put this solution on YOUR website!Two hundred trolls divided a block of gold evenly. What percent of the block of gold did each troll receive? ------------ Percent means per hundred. ------------ 1/200 = (1/2)/100 = (1/2)percent = 0.5% ============================================ Cheers, Stan H. a) 200% b) 1/200% c) c) 2% d) 0.5% e) 0.2%