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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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 Geometry_Word_Problems/272074: Find the equation for the line tangent to the circle x^2+y^2=58 at the points (-3,7) I dont even know where to begin this problem. thanks for the help.1 solutions Answer 199074 by stanbon(57424)   on 2010-02-20 16:47:28 (Show Source): You can put this solution on YOUR website!Find the equation for the line tangent to the circle x^2+y^2=58 at the points (-3,7) I dont even know where to begin this problem. thanks for the help. --------------------------------- The circle is the result of graphing two function: y = sqrt(58-x^2) and y = -sqrt(58-x^2) ==================== The 1st is in the 1st and 2nd quadrants. The 2nd is in the 3rd and 4th quadrants. --------------- The point (-3,7) is in the 2nd quadrant so the tangency point is with y = sqrt(58-x^2) ----- Take the derivative of y = sqrt(58 - x^2) y' = (1/2)(58-x^2)^(-1/2)[-2x] y'= (-x)/sqrt(58-x^2) ---- Find the slope when x = -3 y'(-3) = 3sqrt(49) = 21 -------------------------------- Find the equation of the line with m = 21 passing thru (-3,7) 7 = 21(-3)+b b = 70 ----- Tangent Equation: y = 21x + 70 ============================== Cheers, Stan H.
 Probability-and-statistics/272042: how many possible outcomes are there from tossing 2 number cubes labled 1 through 61 solutions Answer 199071 by stanbon(57424)   on 2010-02-20 16:34:32 (Show Source): You can put this solution on YOUR website!1st cube 6 ways 2nd cube 6 ways ---- # of pairs 6*6 = 36 ======================== Cheers, Stan H.
 Probability-and-statistics/271767: Given a normal distribution with a mean of 100 and a standard deviation of 10 what is the probability that a) x>75 b)x<70 c)x>80 or x>110 d) 80% of the data are between what two values(symmetrically distributed around the mean) 1 solutions Answer 199022 by stanbon(57424)   on 2010-02-20 09:50:07 (Show Source): You can put this solution on YOUR website!Given a normal distribution with a mean of 100 and a standard deviation of 10 what is the probability that a) x>75 Use a TI calculator to get: z(75) = (75-100)/10 = -25/10 = -2.5 P(x> 75) = P(z > -2.5) = normalcdf(-2.5,100) = 0.9938 ------------------------------------------------------------- b)x<70 Samee procedure: 1st: Find the z-value for 70. Find P(z < -3) = normalcdf(-100,-3) = 0.0013.. ------------------------------------------------------------- c)x>80 or x>110 x> 80 inclues all the x> 110 --- z for 80 is +1 P(z > 1) = normalcdf(1,100) = 0.1587 ----------------------------------------------------------- d) 80% of the data are between what two values(symmetrically distributed around the mean) Find the z-values that bracket 80% centered at the mean: That area leaves tails of 10% on the right and on the left under the normal curve. Find invNorm(0.1) = -2.3263 So z = -2.3263 and z=+2.3263 --------------------------------- Now find the x-value corresponding to those z-values x = zs + u x = -2.3263*10 + 100 = 76.74 and x = +2.3263*10 + 100 = 123.26 ============================================ Cheers, Stan H. ---------------------
 Probability-and-statistics/271895: If is a binomial random variable, compute for each of the following cases: (a) P(x>1), n=9, p=0.1 P(x)=1 solutions Answer 199019 by stanbon(57424)   on 2010-02-20 09:29:04 (Show Source): You can put this solution on YOUR website!answered
 Probability-and-statistics/271898: The results of the last test in Algebra 2/Trig. class were normally distributed and had an average of 75. If the variance (σ2) was 25, what percent of the students taking the exam scored above an 80? What are the step to solving a question like this using a TI-83 Plus graphing calculator? What exactly do you enter in the calculator?1 solutions Answer 199018 by stanbon(57424)   on 2010-02-20 09:27:45 (Show Source): You can put this solution on YOUR website!answered
 Matrices-and-determiminant/271955: Modular arithmetic ... Find all possible replacements for n for which each congruence is true. a. 6 + n ≡ 1 (mod 7) b. 3 - n ≡ 4 (mod 7) c. 2n ≡ 1 (mod 3) d. n/2 ≡ 2 (mod 3) (n/s is a fraction) 1 solutions Answer 199016 by stanbon(57424)   on 2010-02-20 09:08:58 (Show Source): You can put this solution on YOUR website!Modular arithmetic ... --- Comment: The fact to remember is (mod n) means n is zero. So 1 (mod 5) = 6 = 11 = 16 = -4 = - 9 5 in all these numbers is zero so 16 is just 1+3*zero = 1 ================================================================= Find all possible replacements for n for which each congruence is true. a. 6 + n ≡ 1 (mod 7) 7 is zero so add it to the 1 to get: 6 + n = 8 (7) n = 2+7k where k is any integer ---------------------------------- b. 3 - n = 4 (mod 7) Regular arithmetic applies so solve for "n": n = 3-4 = -1 (mod 7) n = -1+7 = 6 (mod 7) n = 6 + 7k where k is any integer c. 2n ≡ 1 (mod 3) 3 is zero so add it to the 1 to get: 2n = 4 (mod 3) Use regular arithmetic to get: n = 2 + 3k where k is any integer ----------------------------------------- d. n/2 ≡ 2 (mod 3) (n/s is a fraction) Use regular arithmetic to get: n = 4 (mod 3 n = 1 + 3k where k is any integer ===================================== Cheers, Stan H.
 Rectangles/271965: if the length of a golden rectangle is 10 meters then what is the width? here is the formula for the original rectangle l/w=w/l-w 1 solutions Answer 199011 by stanbon(57424)   on 2010-02-20 08:58:46 (Show Source): You can put this solution on YOUR website!if the length of a golden rectangle is 10 meters then what is the width? here is the formula for the original rectangle l/w=w/l-w --------------------- 10/w = w/(1-w) Cross-multiply: --- w^2 = 10 - 10w w^2 + 10w -10 = 0 ------ Quadratic Formula: w = [-10 +- sqrt(100 - 4*1*-10)]/2 --- w = [-10 +- sqrt(140)]/2 w = [-10 +- 11.83]/2 Positive solution: w = [-10+11.83]/2 w = [1.83]/2 w = 0.965 =================== Cheers, Stan H.
 Permutations/271956: Use binomial expansion to expand the following (2x-3y)^4 1 solutions Answer 199009 by stanbon(57424)   on 2010-02-20 08:50:52 (Show Source): You can put this solution on YOUR website!Use binomial expansion to expand the following (2x-3y)^4 ----- = (2x-3y)(2x-3y) = 2x(2x-3y)-3y(2x-3y = 4x^2 - 6xy -6xy + 9y^2 = 4x^2-12xy+9y^2 ======================= Cheers, Stan H.
 Quadratic_Equations/271959: A ball is dropped from a height of 64 feet. Its height above the earth in feet is given by h(t)=-16t^2+64, where t is the number of seconds after it is dropped. Find h(1). How long does it take the ball to fall to the earth?1 solutions Answer 199007 by stanbon(57424)   on 2010-02-20 08:48:02 (Show Source): You can put this solution on YOUR website!A ball is dropped from a height of 64 feet. Its height above the earth in feet is given by h(t)=-16t^2+64, where t is the number of seconds after it is dropped. Find h(1) = -16 + 64 = 48 ft ------------------------------------------- How long does it take the ball to fall to the earth? The height will be zero at that time. Solve -16t^2+64 = 0 -16t^2 = -64 t^2 = 4 Positive solution: t = 2 seconds ========================= Cheers, Stan H.
 Number-Line/271960: I have to write the slope-intercept form of the equation of the line described: through (-4,1) perpendicular to y = 5. y = 5 is a 0 slope so I'm not sure where to go from her. Can you help me through this please?1 solutions Answer 199005 by stanbon(57424)   on 2010-02-20 08:44:52 (Show Source): You can put this solution on YOUR website! I have to write the slope-intercept form of the equation of the line described: through (-4,1) perpendicular to y = 5. y = 5 is a 0 slope so I'm not sure where to go from her. -------------------------------- Right you are. Draw the line y=5. Plot the point (-4,1) Do this so you can see what the problem requires. ---- If the line if perpendicular to y = 5 it must be a vertical line. And that vertical line must pass thru (-4,1). --- So draw a vertical line that passes thru (-4,1) =============================== Now you have to notice that vertical line passes thru all the points where x = -4. THAT equation is the answer to your problem. ================================================= Cheers, Stan H.
 Rate-of-work-word-problems/271958: A can do a job in 9 days, A and B together can complete a job in 5 days. How long will it take B alone to complete it? 1 solutions Answer 198997 by stanbon(57424)   on 2010-02-20 08:16:40 (Show Source): You can put this solution on YOUR website!A Can do a job in 9 days, A and B together can complete a job in 5 days. How long will B Alone can complete it? -------- A rate: 1/9 job/day Together rate: 1/5 job/day B rate = 1/x job/day ----- Equation: rate + rate = together rate 1/9 + 1/x = 1/5 1/x = 1/5 - 1/9 1/x = 4/45 x = 45/4 x = 11 1/4 days (Time for B to do the job alone) ========================================================= Cheers, Stan H.
 Probability-and-statistics/271896: If is a binomial random variable, compute for each of the following cases: (a) P(x => 1), n=4, p=0.4 P(x)=1 solutions Answer 198975 by stanbon(57424)   on 2010-02-19 22:37:47 (Show Source): You can put this solution on YOUR website!If is a binomial random variable, compute for each of the following cases: (a) P(x => 1), n=4, p=0.4 P(x)= 1 - binompdf(4,0.4,0) = 1 - 0.1296 = 0.8704 ================ Cheers, Stan H.
 Travel_Word_Problems/271889: Joe can run twice as fast as Pete. They start at the same point and run in opposite directions for 40 minutes and the distance between them is then 16km. How fast does Joe run? Can you also show me how you worked it out1 solutions Answer 198974 by stanbon(57424)   on 2010-02-19 22:33:30 (Show Source): You can put this solution on YOUR website!Joe can run twice as fast as Pete. They start at the same point and run in opposite directions for 40 minutes and the distance between them is then 16km. How fast does Joe run? ---------------------------------- Joe DATA: time = 2/3 hr ; rate = 2x km/h ; distance = rt = (2/3)(2x) = (4/3)x km --------------------------------- Pete DATA: time = 2/3 hr ; rate = x km/h ; distance = rt = (2/3)x km ---------------------------------------- Equation: distance + distance = 16 km (4/3)x + (2/3)x = 16 2x = 16 x = 8 km/h (Pete's rate) --- 2x = 16 km/h (Joe's rate) ================================ Cheers, Stan H. ================================
 Probability-and-statistics/271891: The results of the last test in Algebra 2/Trig. class were normally distributed and had an average of 75. If the variance (σ2) was 25, what percent of the students taking the exam scored above an 80? What are the step to solving a question like this using a TI-83 Plus graphing calculator? What exactly do you enter in the calculator?1 solutions Answer 198973 by stanbon(57424)   on 2010-02-19 22:23:43 (Show Source): You can put this solution on YOUR website!The results of the last test in Algebra 2/Trig. class were normally distributed and had an average of 75. If the variance (σ2) was 25, what percent of the students taking the exam scored above an 80? What are the step to solving a question like this using a TI-83 Plus graphing calculator? What exactly do you enter in the calculator? ---- If sigma^2 = 25, sigma = 5 ------ 2nd; DIST normalcdf(80,100,75,5) Enter ------ Ans: 0.1587 = 15.87% ============================== Cheers, Stan H.
 Length-and-distance/271886: the 18 foot board cut into two parts. One of the parts is five times as long as the other. How long is each part.1 solutions Answer 198970 by stanbon(57424)   on 2010-02-19 22:11:27 (Show Source): You can put this solution on YOUR website!the 18 foot board cut into two parts. One of the parts is five times as long as the other. How long is each part. ----------------------------- Let the short piece be "x". Then the other piece is "5x". ----- Equation: x + 5x = 18 6x = 18 x = 3 ft (small piece) 5x = 15 ft (longer piece) ============================ Cheers, Stan H.
 Probability-and-statistics/271888: 1.A company recruits personnel for its sales department on the basis of special tests designed to judge the potential of the candidates. The following table gives test scores and the mean daily sales for 9 executives.1 solutions Answer 198969 by stanbon(57424)   on 2010-02-19 22:02:01 (Show Source): You can put this solution on YOUR website!Data did not show up in your post. Cheers, Stan H.
 Probability-and-statistics/271871: Use the normal distribution to approximate the desired probability. International Airlines reports that 74% of its planes are on time. A check of 60 randomly selected planes shows that 38 of them arrived on time. Find the probability that among the 60 planes, 38 or fewer arrive on time.1 solutions Answer 198964 by stanbon(57424)   on 2010-02-19 20:56:23 (Show Source): You can put this solution on YOUR website!Use the normal distribution to approximate the desired probability. International Airlines reports that 74% of its planes are on time. A check of 60 randomly selected planes shows that 38 of them arrived on time. Find the probability that among the 60 planes, 38 or fewer arrive on time. ---- If p = 0.74, the mean for all samples of size 60 is np = 60*0.74 = 44.4 and the standard deviation is sqrt(npq) = sqrt(60*0.74*0.26) = 3.3976 --- Then z(38) = (38-44.4)/3.3976 = -1.8837 ------------------------ P(x<=38) = P(z< -1.8837) = 0.0298 ===================================== Cheers, Stan H.
 Graphs/271843: graph the line passing though the points[-3,5]and[1,-7]1 solutions Answer 198945 by stanbon(57424)   on 2010-02-19 18:43:29 (Show Source): You can put this solution on YOUR website!graph the line passing though the points[-3,5]and[1,-7] ---------------- slope = (5--7)/(-3-1) = 12/-4 = -3 -------------------------- Solve for "b": 5 = -3*-3 + b b = -4 -------- Equation: y = -3x -4 ==================== Cheers, Stan H.
 Probability-and-statistics/271787: A quiz cosists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %1 solutions Answer 198944 by stanbon(57424)   on 2010-02-19 18:36:07 (Show Source): You can put this solution on YOUR website!A quiz cosists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 % ----- Binomial Problem with n = 20 ; p = 1/4 ------- 70% of 20 = 14 ---- P(x = 14) = 20C14(1/4)^14(3/4)^6 = 0.000025699... ----------------------- You could also find the probability that the person answered "at least" 14 questions correctly. P(14<= x <= 20) = 1 - binomialcdf(20,(1/4),13) = 0.000029512... =================================== Cheers, Stan H.
 Geometry_Word_Problems/271661: What is the largest possible area of a square cut out of a circle with radius 1 cm? A π cm^2 b square root 2cm^2 c 2cm^2 d 1cm^2 e π /2 cm^2 1 solutions Answer 198835 by stanbon(57424)   on 2010-02-19 07:18:08 (Show Source): You can put this solution on YOUR website!What is the largest possible area of a square cut out of a circle with radius 1 cm? ----------- Draw a circle Draw a square inside the circle. The diagonal of the square is the diameter of the circle = 2 cm --- Let the sides of the square be "x". Use Pythagoras to find "x": Equation: x^2 + x^2 = 2^2 2x^2 = 4 x^2 = 2 x = sqrt(2) ----------- Area of the square = (sqrt(2))^2 = 2 sq cm =============================================== Cheers, Stan H. =============================================== A π cm^2 b square root 2cm^2 c 2cm^2 d 1cm^2 e π /2 cm^2
 Radicals/271667: Premise: Television sets. What does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 10-in TV set also has a width of 8 inches. Question: What is the height? Please explain how you arrived at this answer. Thanks!1 solutions Answer 198834 by stanbon(57424)   on 2010-02-19 07:12:37 (Show Source): You can put this solution on YOUR website!What does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 10-in TV set also has a width of 8 inches. Question: What is the height? Draw a rectangle that has a width = 8" and a diagonal = 10" ----- Let the height be "x". Use Pythagoras to find "x": Equation: 10^2 = x^2 + 8^2 100 = x^2 + 64 x^2 = 36 x = 6" Ans: height = 6" ======================= Cheers, Stan H.
 Equations/271668: Find the variation constant and an equation of variation where Y varies directly as X and Y=60 when X=10. The variation constant is K=?? The equation of variation is Y=?? Please explain how you arrived at this answer. Thanks!1 solutions Answer 198833 by stanbon(57424)   on 2010-02-19 07:08:39 (Show Source): You can put this solution on YOUR website!Find the variation constant and an equation of variation where Y varies directly as X and Y=60 when X=10. ---------------- Direct Variation: y = kx Find k if y = 60 when x = 10: 60 = k*10 k = 60/10 = 6 --------------------- The variation constant is K=6 ------- The equation of variation is Y=6x ============== Cheers, Stan H.
 Miscellaneous_Word_Problems/271663: Every hour, Jennifer can sew 24dresses while her mother can sew only 20 dresses. how long will it take them to sew 110 dresses together ? A 1.5 hour b 1.8 hour c 2 hour d 2.2 hour e 2.5 hour 1 solutions Answer 198832 by stanbon(57424)   on 2010-02-19 07:05:28 (Show Source): You can put this solution on YOUR website!Every hour, Jennifer can sew 24dresses while her mother can sew only 20 dresses. how long will it take them to sew 110 dresses together ? ---- Let x be the time to sew 110 dresses Jennifer DATA: rate = 24 dph ; time = x hrs ; #of dresses = 24x ------------ Mother DATA: rate = 20 dph; time = x hrs ; # of dresses = 20x ---- Equation: # of d + # of d = 110 24x + 20x = 110 44x = 110 x = 2.5 hrs =============== Cheers, Stan H. ================ A 1.5 hour b 1.8 hour c 2 hour d 2.2 hour e 2.5 hour
 Probability-and-statistics/271204: To test the null hypothesis that the average lifetime for a particular brand of bulb is 750 hours versus the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used. If the standard deviation is 50 hours and a is equal to 0.01, what values for will result in rejection of the null hypothesis. Remember to determine whether this is a one- or two-tailed test. (Hint: This is similar to problem #4 but it is NOT a one-tailed test!)1 solutions Answer 198831 by stanbon(57424)   on 2010-02-19 06:51:58 (Show Source): You can put this solution on YOUR website!To test the null hypothesis that the average lifetime for a particular brand of bulb is 750 hours versus the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used. If the standard deviation is 50 hours and a is equal to 0.01, what values for will result in rejection of the null hypothesis. Remember to determine whether this is a one- or two-tailed test. ====== Ho: u = 750 Ha: u is not equal to 750 (2-tail test) ------------------------ Critical values for 2-tail, with alpha = 1% and df = 74: Using a TI-84 calculator I get invT(0.005,74) = +-2.6439 --- The rejection intervals are t<-2.6439 and t>2.6439 ============== Cheers, Stan H.
 Mixture_Word_Problems/271599: If you have 6 quarts of a 60% acid solution, how many quarts of water would you add to obtain a 40% acid solution?1 solutions Answer 198806 by stanbon(57424)   on 2010-02-18 22:54:58 (Show Source): You can put this solution on YOUR website!If you have 6 quarts of a 60% acid solution, how many quarts of water would you add to obtain a 40% acid solution? ----------------------------------------- Equation: acid + acid = acid 0.60*6 + 0*x = 0.40(6+x) Multiply thru by 100 to get: 60*6 + 0 = 40*6 + 40x 40x = 20*6 x = 3 quarts (amt. of water needed for the mixture) ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/271597: The total cost of 10 gallons of regular gasoline and 15 gallons of premium gasoline is \$32.75. Premium costs \$.20 more per gallon than regular. What is the cost of gallon of each type of gasoline?1 solutions Answer 198804 by stanbon(57424)   on 2010-02-18 22:48:13 (Show Source): You can put this solution on YOUR website!The total cost of 10 gallons of regular gasoline and 15 gallons of premium gasoline is \$32.75. Premium costs \$.20 more per gallon than regular. What is the cost of gallon of each type of gasoline? -------------------- Equations: 10r + 15p = 32.75 p = r + 0.20 ------------------- Substitute for "p" and solve for "r": 10r + 15(r+0.20) = 32.75 10r + 15r + 2 = 32.75 25r = 30.75 r = \$1.23 (price of regular) --- p = r+0.20 p = \$1.43 ================== Cheers, Stan H.
 Exponents/271596: If 450000 = 3 to the power of x, then how do you solve for x without using the graphing features on a graphing calculator?1 solutions Answer 198803 by stanbon(57424)   on 2010-02-18 22:42:10 (Show Source): You can put this solution on YOUR website!If 450000 = 3 to the power of x, then how do you solve for x without using the graphing features on a graphing calculator? ----- 450000 = 3^x ---- Use the log features. x(log3) = log(450000) x = log(450000)/log3 x = 11.8486.. ================== Cheers, Stan H.
 Probability-and-statistics/271587: order these events from most probable to the least probable. a) the first baby born next year is a girl. b) the sun will set today c) you will live to be 100 years old. d)a classmate will live to 90 years e)a class mate will live to 90 years1 solutions Answer 198801 by stanbon(57424)   on 2010-02-18 22:37:35 (Show Source): You can put this solution on YOUR website!order these events from most probable to the least probable. a) the first baby born next year is a girl. 1/2 ---- b) the sun will set today ::: 1 ---- c) you will live to be 100 years old.:: less than d and e d)a classmate will live to 90 years ::: greater than c e)a class mate will live to 90 years ::: same as e ========================== Cheers, Stan H.
 Linear-systems/271575: A steamboat went 8 miles upstream in 1 hour. The return trip took only 30 minutes. Assume that the speed of the current and the direction were constant during both parts of the trip. Find the speed of the boat in still water and the speed of the current. Please help me figure out what 2 equations I would use and then I believe I can get the answer. Thanks in advance for your help!1 solutions Answer 198794 by stanbon(57424)   on 2010-02-18 22:12:46 (Show Source): You can put this solution on YOUR website!A steamboat went 8 miles upstream in 1 hour. The return trip took only 30 minutes. Assume that the speed of the current and the direction were constant during both parts of the trip. Find the speed of the boat in still water and the speed of the current. ----------------------------- Upstream DATA: distance = 8 miles ; time = 1 hr. ; rate = d/t = 8 mph ------------------------------- Downstream DATA: distance = 8 miles ; time = 1/2 hr. ; rate = d/t = 16 mph ------------------------------- Equations: boat - current = 8 mph boat + current = 16 mph ----------------------------- 2*boat = 24 mph boat = 12 mph (rate in still water) -------------------------- Substitute into b + c = 16 to solve for current speed 12 + c = 16 c = 4 mph (current speed) ============================ Cheers, Stan H.
 Exponents/271578: Please help :) 1.Evaluate: a) (8/27)^(-4/3) b)[(3/5)^-1 - 4^0] ^-2 -- I got 9/4. 2.Which is equivalent to: a)[(25^x)]/[125^(x+1)(5)] Is it 5^x+2 ? b) [(9^x)]/[(27^2x)(3)] Is it 3^4x-1 ? c) (1/36)^x-2 Is it 6^-2x+4 ?1 solutions Answer 198791 by stanbon(57424)   on 2010-02-18 22:04:36 (Show Source): You can put this solution on YOUR website!1.Evaluate: a) (8/27)^(-4/3) Take the cube root of (8/27) to get: = (2/3)^-4 = (3/2)^4 = 81/16 --------------------------------------- b)[(3/5)^-1 - 4^0] ^-2 -- I got 9/4. = [(5/3) - 1]^-2 = [2/3]^-2 = [3/2)^2 = 9/4 You Got It. ------------------------------------- 2.Which is equivalent to: a)[(25^x)]/[125^(x+1)(5)] Is it 5^x+2 ? = [5^2x]/[5^(3x+3)*5] = [5^2x]/[5^(3x+4)] = 5^(-x-4) ------------------------------------- b) [(9^x)]/[(27^2x)(3)] Is it 3^4x-1 ? = [3^2x]/[3^6x*3] = [3^2x]/[3^(6x+1)] = 3^(-4x-1) -------------------------------------- c) (1/36)^(x-2) Is it 6^-2x+4 ? = (6^-2)^(x-2) = 6^(-2x+4) You Got It but be careful; use parentheses to avoid confusion. =================== Cheers, Stan H.
 absolute-value/271576: What is the domain of the square root of the absolute value of 4-x1 solutions Answer 198784 by stanbon(57424)   on 2010-02-18 21:50:19 (Show Source): You can put this solution on YOUR website!What is the domain of the square root of the absolute value of 4-x --------- Domain: All Real Numbers Cheers, Stan H.