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# Recent problems solved by 'stanbon'

 Travel_Word_Problems/857518: First car traveling at 70 mph and a second car 5miles behind the first how fast would the second car have to travel to catch the first car? 1 solutions Answer 516639 by stanbon(69061)   on 2014-03-27 18:16:58 (Show Source): You can put this solution on YOUR website! You need to post either the time or the distance. Cheers, Stan H.
 Rectangles/857521: A rectangle has a diagonal of length 10 and one side of length 6. What is the perimeter of the rectangle? 1 solutions Answer 516638 by stanbon(69061)   on 2014-03-27 18:14:00 (Show Source): You can put this solution on YOUR website! A rectangle has a diagonal of length 10 and one side of length 6. What is the perimeter of the rectangle? ------ other unequal side = sqrt[10^2-6^2] = sqrt(64) = 8 ----- Perimeter = 2(6+8) = 2(14) = 28 ---------------------------------- Cheers, Stan H.
 Travel_Word_Problems/857519: What is the distance traveled at a speed of 60kilometers per hour, for 2 hours? I've tried everything but can't find the right answer. 1 solutions Answer 516637 by stanbon(69061)   on 2014-03-27 18:08:52 (Show Source): You can put this solution on YOUR website! What is the distance traveled at a speed of 60kilometers per hour, for 2 hours? ------ distance = rate*time distance = 60(km/hr)*2hr = 120 km ------------------------------------ Cheers, Stan H. =============
 Angles/857356: Complementary angle for 53 degrees 12' Supplementary angle for 121 degrees 47'38" 1 solutions Answer 516530 by stanbon(69061)   on 2014-03-27 10:05:08 (Show Source): You can put this solution on YOUR website! Complementary angle for 53 degrees 12' :: 90-53 12' = 89 60' - 53 12' = 36 48' ----------------------------------------------------------- Supplementary angle for 121 degrees 47'38":: 180-47' 38" = 179 59' 60" -47' 38" = 179 12' 22" ======================= Cheers, Stan H.
 Permutations/857352: how many ways select a captain and a vice captain from 20 member football team. 1 solutions Answer 516527 by stanbon(69061)   on 2014-03-27 09:59:06 (Show Source): You can put this solution on YOUR website! how many ways select a captain and a vice captain from 20 member football team. ----- select a captain: 20 ways select a vice cap:: 19 ways ---- Answer: 20*19 = 380 ====================== Cheers, Stan H. -----------------------
 Human-and-algebraic-language/857354: The Cornelius institute increases their enrollments by 15 students each year. The Plato institute decreaes their enrollments by 12 students each year. Knowing that in Year 0, the enrolled students in the Cornelius insitute were 957, while the enrolled students in the Plato institue were 1200. In which year will the cornelius institute have more enrolled students than the Plato institute? Please help me out. Ifeel that this is quite a easy question yet i can't get my head around it! Please help me out thanksss!!!!!!!!!!! 1 solutions Answer 516524 by stanbon(69061)   on 2014-03-27 09:55:29 (Show Source): You can put this solution on YOUR website! The Cornelius institute increases their enrollments by 15 students each year. The Plato institute decreaes their enrollments by 12 students each year. Knowing that in Year 0, the enrolled students in the Cornelius insitute were 957, while the enrolled students in the Plato institue were 1200. ----------------------- In which year will the cornelius institute have more enrolled students than the Plato institute? Cornelius:: c(x) = 957+15x Plato:::::: p(x) = 1200-12x ---- Solve: c(x) > p(x) 957+15x > 1200-12x ----- 27x > 243 x > 9 Ans: year 10 -------------------- Cheers, Stan H. -------------------
 Probability-and-statistics/857256: When treated with antibiotics. 98% of dolphins are cured of an ear infection. if 5 dolphins are treated, find the probability that exactly 3 are cured 1 solutions Answer 516512 by stanbon(69061)   on 2014-03-27 09:14:44 (Show Source): You can put this solution on YOUR website! When treated with antibiotics. 98% of dolphins are cured of an ear infection. if 5 dolphins are treated, find the probability that exactly 3 are cured ------- Binomial Problem with n = 5 ; p(cure) = 0.98 ; p(not) = 0.02 ------------------- P(x = 3) = 5C3*0.98^3*0.02^2 = binompdf(5,0.98,3) = 0.0038 ----------------- Cheers, Stan H. ================
 Probability-and-statistics/857313: n is the sample size p is the population proportion p-hat is the sample proportion Use the Central Limit Theorem to find the Proportion probability. n = 101, p = 0.86, P (p-hat < 0.80) 1 solutions Answer 516511 by stanbon(69061)   on 2014-03-27 09:06:18 (Show Source): You can put this solution on YOUR website! n is the sample size p is the population proportion p-hat is the sample proportion Use the Central Limit Theorem to find the Proportion probability. n = 101, p = 0.86, P (p-hat < 0.80) ------ z(0.80) = (0.80-0.86)/sqrt[0.86*0.14/101] = -1.7378 ---- P(p-hat < 0.8) = P(z < -1.7378) = normalcof(-100,-1.7378) = 0.0411 ======================== Cheers, Stan H. --------------------
 Probability-and-statistics/857315: 75% of freshman entering public school graduate with their class. A random sample of 135 freshmen is chosen. Find the mean of the binomial probability. Find the standard deviation of the binomial probability. Find the binomial probability that less than 80% of the freshmen in the sample graduated. 1 solutions Answer 516509 by stanbon(69061)   on 2014-03-27 09:01:56 (Show Source): You can put this solution on YOUR website! 75% of freshman entering public school graduate with their class. A random sample of 135 freshmen is chosen. Find the mean of the binomial probability:: np = 135*0.75 = 101.25 ------------------------------------------------------------ Find the standard deviation of the binomial probability:: sqrt(npq) = 5.031 ---------------------------------------------- Find the binomial probability that less than 80% of the freshmen in the sample graduated. 0.8*135 = 108 P(x < 108) = binomcdf(135,0.75,107) = 0.8949 ----- Cheers, Stan H. =========================
 Probability-and-statistics/857316: n is the sample size p is the population proportion of successes X is the number of successes in the sample Use the Normal approximation to find the Binomial probability. n = 538, p = 0.86, P (X< 450) 1 solutions Answer 516506 by stanbon(69061)   on 2014-03-27 08:55:23 (Show Source): You can put this solution on YOUR website! Use the Normal approximation to find the Binomial probability. n = 538, p = 0.86, P (X< 450) --- mean = np = 538*0.86 = 462.68 std = sqrt(npq) = sqrt[462.68*0.14] = 8.05 ------------------- z(450.5) = (450.5-462.68)/8.05 = -1.5130 ------------------------------- P(X < 450) = P(z < 0-1.5130) = normalcdf(-100,-1.5130) = 0.0651 ------------------------ Cheers, Stan H. ------------------------
 Probability-and-statistics/857330: IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that iq score is less than 88 1 solutions Answer 516504 by stanbon(69061)   on 2014-03-27 08:48:40 (Show Source): You can put this solution on YOUR website! IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that iq score is less than 88 ---------------- z(88) = (88-100)/15 = -12/15 = -4/5 --- P(x< 88) = P(z < -4.5) = binomcdf(-100,-4/5) = 0.2119 =================== Cheers, Stan H. ------------------
 Probability-and-statistics/857332: from a lot of products having fraction defective (p=.5) ,you draw 16 items one by one. what is the probability that out of 16 times 5 times you will get no defective item ? (answer using distribution method) 1 solutions Answer 516499 by stanbon(69061)   on 2014-03-27 08:45:13 (Show Source): You can put this solution on YOUR website! from a lot of products having fraction defective (p=.5) ,you draw 16 items one by one. what is the probability that out of 16 times 5 times you will get no defective item ? ----------------- Binomial Problem with n = 16; p(defective) = 0.5 ; p(no defect) = 0.5 ------------------------------- P(x = 5) = 16C5*(0.5)^5 * (0.5)^11 = 16C5*(0.5)^16 = 0.0667 -------------------- Cheers, Stan H. -----------------
 Miscellaneous_Word_Problems/857252: The gasoline gauge on a van initially read ¼ full. When 14 gallons were added to the tank, the gauge read ¾ full. How many more gallons are needed to fill the tank? 1 solutions Answer 516448 by stanbon(69061)   on 2014-03-26 23:18:21 (Show Source): You can put this solution on YOUR website! The gasoline gauge on a van initially read ¼ full. When 14 gallons were added to the tank, the gauge read ¾ full. How many more gallons are needed to fill the tank? ------- Let x be the # of gallons in a full tank ----- (1/4)x + 14 = (3/4)x ---- 14 = (2/4)x x = 28 gallons ------ Gallons needed:: 28-14-(1/4)28 = 28-14-7 = 7 gallons ---------------------------------------------------- Cheers, Stan H.
 Triangles/857257: What is a triangle that is A= 3m , B = 4m, what is C= ____ This is a right sided triangle 1 solutions Answer 516444 by stanbon(69061)   on 2014-03-26 23:12:35 (Show Source): You can put this solution on YOUR website! What is a triangle that is A= 3m , B = 4m, what is C= ____ This is a right sided triangle ------- C = sqrt[A^2 + B^2] ------- C = sqrt[(3m)^2+(4m)^2] ------- C = sqrt[9m^2+16m^2] ------- C = sqrt(25m^2) ------ C = 5m ------------------ Cheers, Stan H. -------------------
 Trigonometry-basics/857178: find the angle between the given vectors to the nearest tenth of a degree. u=sq.root5i-8j, v=sq.root5i+j 1 solutions Answer 516439 by stanbon(69061)   on 2014-03-26 22:59:14 (Show Source): You can put this solution on YOUR website! find the angle between the given vectors to the nearest tenth of a degree. u=sq.root5i-8j, v=sq.root5i+j -------------------- standard angle with terminal side thru (sqrt(5),-8) is arctan(-8/sqrt(5)) = 285.62 degrees ----- standard angle with terminal side thru (sqrt(5,1) is arctan(1/sqrt(5) = 65.91 degrees ---- Angle between = 285.62-65.91 = 219.71 degrees ------------------------------------------------ Cheers, Stan H. ------------------------------------
 Trigonometry-basics/857251: The point P is on the unit circle. Find P(x,y) from the given information. The x coordinate of P is 4/5 and P is in Quadrant I. It's been a while since I had to remember to do this. Can someone please help remind me what they are asking here. Thank you 1 solutions Answer 516435 by stanbon(69061)   on 2014-03-26 22:45:21 (Show Source): You can put this solution on YOUR website! The point P is on the unit circle. Find P(x,y) from the given information. The x coordinate of P is 4/5 and P is in Quadrant I. ------- Since the point is on the circumference of a unit circle, x^2 + y^2 = 1 --------------------------- Your point is ((4/5),y) and y is positive (4/5)^2 + y^2 = 1 y^2 = (25/25)-(16/25) y^2 = 9/25 y = 3/5 ------------------- Cheers, Stan H. ===================
 Quadratic_Equations/857249: what is f(x)=96+12x+8x+x^2 in vertex form 1 solutions Answer 516434 by stanbon(69061)   on 2014-03-26 22:40:15 (Show Source): You can put this solution on YOUR website! f(x)=96+12x+8x+x^2 in vertex form -------------- x^2 + 20x = y-96 --------- x^2 + 20x+100 = y-96+100 ---- (x+10)^2 = y+4 ======================== Cheers, Stan H. ========================
 Radicals/857245: Square root/ 16a^8b^4 Please I want to now if I can square root the exponent 8 1 solutions Answer 516431 by stanbon(69061)   on 2014-03-26 22:36:08 (Show Source): You can put this solution on YOUR website! Square root/ 16a^8b^4 ------ = 4a^4b^2 ================ Cheers, Stan H. ================
 Trigonometry-basics/856922: what is the value of x in cot (90° − x) = 1 in degrees 1 solutions Answer 516352 by stanbon(69061)   on 2014-03-26 15:43:24 (Show Source): You can put this solution on YOUR website! what is the value of x in cot (90° − x) = 1 in degrees Note: cot(t) = 1 when t = 45 degrees or t = 225 degrees -------- Your Equation: 90-x = 45 or 90-x = 225 x = 45 degrees or x = -135 = +225 degrees ============================= Cheers, Stan H. =============================
 Mixture_Word_Problems/857057: How much of a 50% salt solution should be added to 80L of a 5% salt solution to obtain a 30% salt solution? 1 solutions Answer 516350 by stanbon(69061)   on 2014-03-26 15:37:04 (Show Source): You can put this solution on YOUR website! How much of a 50% salt solution should be added to 80L of a 5% salt solution to obtain a 30% salt solution? ---------- Equation: salt + salt = salt 0.50x + 0.05*80 = 0.30(x+80) ------- 50x + 5*80 = 30x + 30*80 20x = 25*80 x = 100 L (amt. of 50% solution needed) ------------------- Cheers, Stan H. -------------------
 Geometry_Word_Problems/857060: Please can you help me with this question Explain the meaning of the ordered pair (3,18)? 1 solutions Answer 516349 by stanbon(69061)   on 2014-03-26 15:32:43 (Show Source): You can put this solution on YOUR website! Please can you help me with this question Explain the meaning of the ordered pair (3,18)? ----- It has meaning in graphing; tells you a point is 3 to the right of the vertical axis and 18 above the horizontal axis, or it is the intersection point of two linear equations, such as: x = 3; y = 18 Therefor 2x = 6 and 3y = 54 OR 3x = 9 ; 5y = 90 Equation 1:: 2x + 3y = 60 Equation 2:: 3x + 5y = 99 (3,18) is the solution for this system (2 or more) of equations. ====================== Cheers, Stan H. ----------------------
 Permutations/857059: Determine the number of arrangements for the letters of the word REMEMBER. 1 solutions Answer 516347 by stanbon(69061)   on 2014-03-26 15:27:20 (Show Source): You can put this solution on YOUR website! number of arrangements for the letters of the word REMEMBER. ----- 2 R's are indistinguishable 3 E's are indistinguishable 2 M's are indistinguishable B is unique ----- Ans: 8!/(2!*3!*2!) = 8!/24 = 1680 ------------------------------------ Cheers, Stan H. ------------------------------------
 Reduction-of-unit-multipliers/857042: How do you use two unit multipliers to convert 125 square miles into square feet 1 solutions Answer 516346 by stanbon(69061)   on 2014-03-26 15:23:30 (Show Source): You can put this solution on YOUR website! use two unit multipliers to convert 125 square miles into square feet -------- `125 miles^2(5280 ft/1 mile)(5280 ft/1 mile) = 125*5280^2 = 660,000 ft^2 ------------------------------- Cheers, Stan H. -----------------
 Polynomials-and-rational-expressions/857041: 42x^7(a+10)+60x^5(a+10)-24x^2(a+10) I'm completely stuck can someone do step by step how to factor this fully. You would be my life savior. 1 solutions Answer 516339 by stanbon(69061)   on 2014-03-26 14:47:30 (Show Source): You can put this solution on YOUR website! 42x^7(a+10)+60x^5(a+10)-24x^2(a+10) ---------------------- = 6x^2(a+10)[7x^5 + 10x^3 - 4] ================================== Cheers, Stan H. =============
 Graphs/857038: A line passes through the points (-10,-4) and (-1,2). What is the slope of the line that passes through the two points? 1 solutions Answer 516337 by stanbon(69061)   on 2014-03-26 14:43:51 (Show Source): You can put this solution on YOUR website! A line passes through the points (-10,-4) and (-1,2). What is the slope of the line that passes through the two points? ------ slope = (change in y)/(corresponding change in x) -------------- slope = (2--4)/(-1--10) = 6/9 = 2/3 ----------------------- Cheers, Stan H. --------------------
 Trigonometry-basics/856940: find sin(x/2)by using half angle formulas when tanx=-5/12 and 3pi/2 1 solutions Answer 516250 by stanbon(69061)   on 2014-03-26 10:59:42 (Show Source): You can put this solution on YOUR website! find sin(x/2)by using half angle formulas when tanx=-5/12 and 3pi/2 ------ sin(x/2) = sqrt[(1-cos(x))/2] ----- Since tan(x) = -5/12, y = -5 and x = 12 ---- Then r = sqrt(25+144) = 13 ---------------------------------- So, sin(x/2) = sqrt[(1-(12/13))/2] = sqrt[1/26] Cheers, Stan H. ==================
 Permutations/856928: How many permutations can be made out of the letters of the word 'BUSINESS'? How many of these begin with B and end with N ? 1 solutions Answer 516249 by stanbon(69061)   on 2014-03-26 10:54:50 (Show Source): You can put this solution on YOUR website! How many permutations can be made out of the letters of the word 'BUSINESS'? Ans: 8!/(3!) = 8*7*6*5*4 = 6720 ----------------------------- How many of these begin with B and end with N ? ----- Ans: 1*(6!/2!)*1 = 360 ------------------------------- Cheers, Stan H.
 Angles/856937: Find the value of x for which p is parallel to q, if m<1 = (9x) and m<3 = 117 1 solutions Answer 516247 by stanbon(69061)   on 2014-03-26 10:48:51 (Show Source): You can put this solution on YOUR website! What p and q?
 Rate-of-work-word-problems/856939: The speed of a boat in still water is 10 mph. If the boat travels 108 miles upstream in the same time it takes to travel 132 miles downstream, find the speed of the current. 1 solutions Answer 516244 by stanbon(69061)   on 2014-03-26 10:46:35 (Show Source): You can put this solution on YOUR website! The speed of a boat in still water is 10 mph. If the boat travels 108 miles upstream in the same time it takes to travel 132 miles downstream, find the speed of the current. ---------- Upstream DATA: dist = 108 miles ; rate = c-10 mph ; time = d/r = 108/(c-10) ------- Downstream DATA: dist = 132 miles ; rate = c+10 mph ; time = 132/(c+10) --------- Equation: 108/(c-10) = 132/(c+10) ------- 108c + 1080 = 132c - 1320 ------- 24c = 2400 c = 100 mph (rate of the current-----unbelievable) ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/856938: find an equation for the line with the given properties express in slope intercept form p=(-1,3) q=(1,0) 1 solutions Answer 516241 by stanbon(69061)   on 2014-03-26 10:38:54 (Show Source): You can put this solution on YOUR website! find an equation for the line with the given properties express in slope intercept form p=(-1,3) q=(1,0) ------ Form: y = mx + b Solve for "m" and "b":: m = (3-0)/(-1-1) = -3/2 ------ Solve for "b": 0 = (-3/2)(1) + b b = 3/2 --------- Equation: y = (-3/2)x + (3/2) ---------------------- Cheers, Stan H. ----------------