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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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 test/473709: If we roll 4 dice once, what is the chance the sum will be 12?1 solutions Answer 324922 by stanbon(60771)   on 2011-07-24 13:29:07 (Show Source): You can put this solution on YOUR website!If we roll 4 dice once, what is the chance the sum will be 12? --- Sums range from 4 to 24 --- Count the # of ways to get a sum of 12. --- The probability you want is that # divided by 24 =============== Cheers, Stan H. ==============
 Miscellaneous_Word_Problems/473677: Determine if this is an example of probability or statistics: Of 120 dice throws, 20 are likely to be “two”. and why. Thank you 1 solutions Answer 324919 by stanbon(60771)   on 2011-07-24 13:22:11 (Show Source): You can put this solution on YOUR website!Determine if this is an example of probability or statistics: Of 120 dice throws, 20 are likely to be “two”. and why. --- With one die the probability of a "two" = 1/6. --- The dies act independently (they have no effect on one-another). --- The expected # of "two's" when you throw 120 die = (1/6)120 = 20 ================= Cheers, Stan H. =================
 Graphs/473704: By 3:00 PM, John had plowed 7 driveways and by 5:30 PM he had completed 13. a) Find John’s plowing rate in number of driveways per hour. b) Find John’s plowing rate in minutes per driveway 1 solutions Answer 324918 by stanbon(60771)   on 2011-07-24 13:18:13 (Show Source): You can put this solution on YOUR website!By 3:00 PM, John had plowed 7 driveways and by 5:30 PM he had completed 13. a) Find John’s plowing rate in number of driveways per hour. --- rate = (# of driveways)/(# of hours) = 6/2.5 = 2.4 driveways/hour ---------------------------------------------------------- b) Find John’s plowing rate in minutes per driveway (2.4)(driveways/hour)(1 hr/60 minutes) --- = (2.4*1)/(1*60)(driveways/minute) --- = 0.04 driveways/minute ============================ cheers, Stan H.
 Subset/473711: Find the number of subsets the set has. {1, 2, 3, 4, 5, 6, 7, 8, 9}1 solutions Answer 324915 by stanbon(60771)   on 2011-07-24 13:14:02 (Show Source): You can put this solution on YOUR website!Find the number of subsets the set has. {1, 2, 3, 4, 5, 6, 7, 8, 9} ---- Each of the elements is either in or not in a subset: --- # of subsets = 2^9 = 512 ============================ Cheers, Stan H.
 Equations/473715: Change the equation to slope-intercept form and determine the slope and y intercept of the line. 6x+y=9 y= slope= y intercept (x,y)=1 solutions Answer 324914 by stanbon(60771)   on 2011-07-24 13:12:10 (Show Source): You can put this solution on YOUR website!Change the equation to slope-intercept form and determine the slope and y intercept of the line. 6x+y=9 y = -6x + 9 slope = -6 y intercept (x,y)= (0,9) =============================== cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/473706: The gas mileage, M, of a compact car is a linear function of the speed,s, at which the car is driven, for 40 <-s90<-(not sure how to get the line under the <). From the graph we see that the gas mileage for the compact car is 45 miles per gallwon if the car is driven at a speed of 40 mph and the gas mileage for the compact car is 20 miles per gallon if the car is friven at a speed of 90 mph. find the linear function M(s) in sleop intercept form. Interpret the slope found in a. Find and interpret M(60).1 solutions Answer 324912 by stanbon(60771)   on 2011-07-24 13:10:14 (Show Source): You can put this solution on YOUR website!The gas mileage, M, of a compact car is a linear function of the speed,s, at which the car is driven, for 40 <-s90<-(not sure how to get the line under the <). From the graph we see that the gas mileage for the compact car is 45 miles per gallon if the car is driven at a speed of 40 mph and the gas mileage for the compact car is 20 miles per gallon if the car is driven at a speed of 90 mph. find the linear function M(s) in slope-intercept form. Interpret the slope found in a. Find and interpret M(60). ---- You have 2 points relating mileage and speed: (40,45) and (90,20) --- slope = (20-45)/(90-40) = -25/50 = -1/2 --- M = (slope)s + b Solve for "b": 20 = (1/2)90 + b 20 = -45 + b b = 65 ----- Equation: M(s) = (-1/2)s + 65 ---- M(60) = (-1/2)*60 + 65 M(60) = -30 + 65 M960) = 35 mpg ====================== Cheers, stan H.
 Linear_Algebra/473696: x+y+z=9 2x+5y+2z=30 -x+6y-3z=15 What are the solutions?1 solutions Answer 324898 by stanbon(60771)   on 2011-07-24 11:56:14 (Show Source): You can put this solution on YOUR website!x+y+z=9 2x+5y+2z=30 -x+6y-3z=15 --- x = 3 y = 4 z = 2 ============ Cheers, Stan H. ============
 Linear_Algebra/473698: x+y+z=-8 2x+4y+2z=-28 -x+6y-3z=-24 What are the solutions?1 solutions Answer 324897 by stanbon(60771)   on 2011-07-24 11:51:33 (Show Source): You can put this solution on YOUR website!x+y+z=-8 2x+4y+2z=-28 -x+6y-3z=-24 ----------------- x = 3 y = -6 z = -5 =========== Cheers, Stan H.
 Probability-and-statistics/473697: The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.6, what is P(A and B)?1 solutions Answer 324896 by stanbon(60771)   on 2011-07-24 11:48:36 (Show Source): You can put this solution on YOUR website!The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.6, what is P(A and B)? --- If A and M are mutually exclusive, P(A and B) = P(A) + P(B) = 0.2 + 0.6 --- = 0.8 =========== cheers, Stan H.
 Exponents-negative-and-fractional/473692: Subtract and simplify, if possible: 1-v/v-6 - 3v-2/6-v Divide: 8/x divided by 64/x1 solutions Answer 324894 by stanbon(60771)   on 2011-07-24 11:47:00 (Show Source): You can put this solution on YOUR website!Subtract and simplify, if possible: 1-v/v-6 - 3v-2/6-v --- Modify the 2nd fraction to get: = (1-v)/(v-6) + (3v-2)/(v-6) ---- Combine the numerators over the common denominator = [1-v+3v-2]/(v-6) ---- Simplify to get = (2v-1)/(v-6) ======================= Divide: 8/x divided by 64/x --- Invert and multiply to get: (8/x)*(x/64) = 1/8 ================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/473694: how do you write a linear equation in two variables for this situation. Cost of cell phone is \$34.99/month plus \$.09/long distance minute used?1 solutions Answer 324892 by stanbon(60771)   on 2011-07-24 11:42:55 (Show Source): You can put this solution on YOUR website!write a linear equation in two variables for this situation. Cost of cell phone is \$34.99/month plus \$.09/long distance minute used? ---- Cost = 34.99(month) + 0.09(# of minutes) --- C = 34.99m + 0.09t where m is # of months and t is # of minutes =============================================================== Cheers, Stan H.
 test/473683: if p+q=4 and p^2+q^2=7,then the value of p/q is1 solutions Answer 324891 by stanbon(60771)   on 2011-07-24 11:40:35 (Show Source): You can put this solution on YOUR website!if p+q=4 and p^2+q^2=7,then the value of p/q is ------------------- p = 4-q --- Substitute for "p" and solve for "q": (4-q)^2 + q^2 = 7 16-8q+2q^2 = 7 --- 2q^2-8q - 23 = 0 ---------------------- q = [8 +- sqrt(64 - 4*2*-23)]/4 --- q = [8 +- sqrt(248]]4 --- q = [8 +- 2sqrt(62)]/4 -- q = [2 + (1/2)sqrt(62)] or q = [2 - (1/2)sqrt(62)] =========================== p/q = (4-q)/[2 + (1/2)sqrt(62)] or p/q = (4-q)/[2 - (1/2)sqrt(62)] ============ Cheers, Stan H.
 Rational-functions/473690: I can not seem to figure out thie problem. Can you please help by showing the steps. Thank you (3)^(1/4)(2)^(1/3) use rational exponents to write as a single radical expression.1 solutions Answer 324888 by stanbon(60771)   on 2011-07-24 11:32:12 (Show Source): You can put this solution on YOUR website!(3)^(1/4)(2)^(1/3) use rational exponents to write as a single radical expression. ------- = 3^(3/12)*2^(4/12) --- = [3^3*2^4]^(1/12) ----- = [27*16]^(1/12) ----------------- = 432^(1/12) ======================= Cheers, Stan H.
 Linear_Algebra/473688: x-y=2 (1) 3x-4z=15 (2) 3y+z=9 (3) Is there a solution and if there is what are the solutions?1 solutions Answer 324886 by stanbon(60771)   on 2011-07-24 11:29:09 (Show Source): You can put this solution on YOUR website!x-y=2 3x-4z=15 3y+z=9 --------------- x - y + 0 = 2 3x + 0 -4z = 15 0 +3y + z = 9 ------------------------- Use any method you know to get: x = 5 y = 3 z = 0 =============== Cheers, Stan H. ==============
 test/473685: If a/b=6/7 and a/c=2/5,what is the value of 3b+c in terms of a? (A)12a (B)9a (C)8a (D)6a (E)4a Thank you so much!1 solutions Answer 324884 by stanbon(60771)   on 2011-07-24 11:23:22 (Show Source): You can put this solution on YOUR website!If a/b=6/7 and a/c=2/5,what is the value of 3b+c in terms of a? --- b = 7a/6 ; c = 5a/2 --- 3b + c = 3[7a/6] + 5a/2 --- 3b + c = 7a/2 = 5a/2 --- 3b + c = 12a/2 -- 3b + c = 6a ==================== Cheers, Stan H. (A)12a (B)9a (C)8a (D)6a (E)4a
 Numbers_Word_Problems/473642: can you find the second of four consecutive even integers such that the product of the first and fourth integer will be the square of the second integer?1 solutions Answer 324870 by stanbon(60771)   on 2011-07-24 10:00:48 (Show Source): You can put this solution on YOUR website!find the second of four consecutive even integers such that the product of the first and fourth integer will be the square of the second integer? --- 1st: 2x-2 2nd: 2x 3rd: 2x+2 4th: 2x+4 =============== Equation: (2x-2)(2x+4) = (2x)^2 ---- 4x^2+4x-8 = 4x^2 4x-8 = 0 x = 2 --- 2nd: 2x = 4 =================== cheers, Stan H.
 Probability-and-statistics/473649: A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting • a three given the card is a not a face card. • a four, given that the card is not a diamond. • a Jack given the card is not a face card. CAN SOME ONE HELP ME PLZZ1 solutions Answer 324868 by stanbon(60771)   on 2011-07-24 09:57:51 (Show Source): You can put this solution on YOUR website!A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting • a three given the card is a not a face card. Comment: When the condition is "not a face card" your universe has only 40 cards in it. Four of those 40 are 3's. So the probability is 3/40 ----------------------------------------------------- • a four, given that the card is not a diamond. "Not a diamond" has 39 cards including one of the 4's. Ans: 3/38 ---------------------------------------------------- • a Jack given the card is not a face card. "Not a face card" has 40 cards, but none of them is a jack. Ans: 0/40 = 0 =================== Cheers, Stan H.
 Quadratic_Equations/473656: In a milling operation, the thickness of the formica sheets that can be produced satisfies the inequality Ix-1.74I < or = to 1.16. What range of thicknesses corresponds to this inequality?1 solutions Answer 324866 by stanbon(60771)   on 2011-07-24 09:50:56 (Show Source): You can put this solution on YOUR website!In a milling operation, the thickness of the formica sheets that can be produced satisfies the inequality Ix-1.74I < or = to 1.16. What range of thicknesses corresponds to this inequality? ------------- Solve: -1.16 <= x-1.74 <= 1.16 --- 0.58 <= x <= 2.90 ================== Cheers, Stan H.
 Trigonometry-basics/473660: 7. The shadow of a flagpole measures 15 feet. At the same day, the shadow of a 2-foot stake measures ¾ foot. How tall is the flagpole? 1 solutions Answer 324865 by stanbon(60771)   on 2011-07-24 09:47:51 (Show Source): You can put this solution on YOUR website!The shadow of a flagpole measures 15 feet. At the same day, the shadow of a 2-foot stake measures ¾ foot. How tall is the flagpole? --- Use proportion: object/shadow = object/shadow ----- f/15' = 2'/(3/4)' --- (3/4)f = 30 --- flagpole = 40' ==================== Cheers, Stan H. ================
 Trigonometry-basics/473662: 4. When the moon is exactly half full, the earth, moon, and sun form a right angle (see the figure). At that time the angle formed by the sun, earth, and moon is measured to be 89.85°. If the distance from the earth to the moon is 240,000 mi, estimate the distance from the earth to the sun.1 solutions Answer 324864 by stanbon(60771)   on 2011-07-24 09:44:44 (Show Source): You can put this solution on YOUR website!When the moon is exactly half full, the earth, moon, and sun form a right angle (see the figure). At that time the angle formed by the sun, earth, and moon is measured to be 89.85°. If the distance from the earth to the moon is 240,000 mi, estimate the distance from the earth to the sun. ---- Draw the picture. --- cos(89.85) = 240,000/d --- d = 240,000/cos(89.85) --- distance = 91,673,351.94 miles =================================== Cheers, Stan H.
 Miscellaneous_Word_Problems/473663: Consider fractions of the form 5/n, where n is an integer. How many integer values of n make this fraction bigger than 1/3 and smaller than 1/2? 1 solutions Answer 324863 by stanbon(60771)   on 2011-07-24 09:37:31 (Show Source): You can put this solution on YOUR website!Consider fractions of the form 5/n, where n is an integer. How many integer values of n make this fraction bigger than 1/3 and smaller than 1/2? ---- Solve: 1/3 < 5/n <1/2 --- Multiply thru by 6 to get: 2 < 30/n < 3 ---- Invert and reverse the inequality 1/3 < n/30 < 1/2 10 < n < 15 --- Answer: n = 11,12,13,14 How many?: 4 ================================ Cheers, Stan H.
 test/473661: 18 workers do a job in 40 days, if 6 workers were added from the beginning of the job , how many days it will need to finish that job?1 solutions Answer 324862 by stanbon(60771)   on 2011-07-24 09:30:44 (Show Source): You can put this solution on YOUR website!18 workers do a job in 40 days, if 6 workers were added from the beginning of the job , how many days will be needed to finish that job? ---- 18*40 = 720 man-days are needed to do the job. --- With 18+6 = 24 workers the time required would be 720/24 = 30 ------------------ Another way to work it would be: # of men and # of days are inversely related. d = k/m Solve for "k" using "18 men do the job in 40 days" 40 = k/18 k = 720 --- Equation: d = 720/m ---- Then solve "if 6 workers were added from the beginning of the job , how many days will be needed to finish that job"? --- d = 720/24 d = 30 days ================== cheers, Stan H. ============ -- Cheers,
 Quadratic_Equations/473657: The number of non-text books read by college students ranges from 7 to 49. Using B as the variable, write an absolute value inequality that corresponds to this range.1 solutions Answer 324861 by stanbon(60771)   on 2011-07-24 09:23:45 (Show Source): You can put this solution on YOUR website!The number of non-text books read by college students ranges from 7 to 49. Using B as the variable, write an absolute value inequality that corresponds to this range. --- Find the center of the range: (7+49)/2 = 28 Find the distance from the center to the end point: 49-28 = 21 ---- Absolute inequality: |B-28| <= 21 ==================== Cheers, Stan H. ===========
 Quadratic_Equations/473658: If three times the smaller of two integers is added to four times the larger, the result is 39. Find the smaller integer.1 solutions Answer 324860 by stanbon(60771)   on 2011-07-24 09:18:40 (Show Source): You can put this solution on YOUR website!If three times the smaller of two integers is added to four times the larger, the result is 39. Find the smaller integer. ----- Not enough information. Your equation would be: 3x + 4y = 39 --- You need a 2nd equation to solve the system. Or you need to list multiples of 3 and multiples of 4 to see where you get a sum of 39. ========== Cheers, Stan H.
 Travel_Word_Problems/473572: in a stream whose current flows at the speed of 3 km/hr ,a man rowed upstream and returned to his starting point in 6.25 hrs .If the man rows at a speed of 5 km/hr in still water,how long did he row upstream?1 solutions Answer 324818 by stanbon(60771)   on 2011-07-23 22:42:49 (Show Source): You can put this solution on YOUR website!in a stream whose current flows at the speed of 3 km/hr ,a man rowed upstream and returned to his starting point in 6.25 hrs .If the man rows at a speed of 5 km/hr in still water,how long did he row upstream? ------- Upstream DATA: time = t hrs ; rate = 5-3 km/h ; distance = 2t km ---- Downstream DATA: time = 6.25-t hrs ; rate = 5+3 km/h ; distance = 8(6.25-t) km ----- Equation: distance = distance 2t = 8(6.25-t) 10t = 50 t = 5 hr (time to row upstream) ======================================= Cheers, Stan H.
 Mixture_Word_Problems/473567: how many liters of pure alcohol must be mixed with 20 liters of 25% alcohol solution to get 85% mixture?1 solutions Answer 324811 by stanbon(60771)   on 2011-07-23 22:13:34 (Show Source): You can put this solution on YOUR website!how many liters of pure alcohol must be mixed with 20 liters of 25% alcohol solution to get 85% mixture? ------- Eqution: alcohol + alcohol = alcohol x + 0.25*20 = 0.85(x+20) ---- Multiply thru 100 to get: 100x + 25*20 = 85x + 85*20 15x = 60*20 x = 5 liters (amt. of pure alcohol needed) ============================================ Cheers, Stan H. ==================
 Quadratic_Equations/473563: Can anyone help me with this? Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot). P(d) = -8.3m^2 + 53.1m - 26.5 1. Does the graph of this equation open up or down? What algebraic information can you use to determine this? 2. Describe what happens to the profit as the rent per square foot is increased. Discuss the different amounts of profit defined by the graph and the equation. 3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? 4. Will this equation give you a maximum profit or a minimum profit? How do you know? 5. What price should be charged to reach the maximum or minimum profit? 6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units. 7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6? 8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response. 1 solutions Answer 324810 by stanbon(60771)   on 2011-07-23 22:08:48 (Show Source): You can put this solution on YOUR website!Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot). P(d) = -8.3m^2 + 53.1m - 26.5 1. Does the graph of this equation open up or down? What algebraic information can you use to determine this? Ans: Opens down because the coefficient of x^2 is negative. ------------------------------- 2. Describe what happens to the profit as the rent per square foot is increased. Profit rises then falls as square footage increases. --- Discuss the different amounts of profit defined by the graph and the equation. ------------------------ 3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot. Solve -8.3m^2 + 53.1m - 26.5 = 0 m = 0.5456 ; m = 5.852 --------------------------------- What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? --------------------------------- 4. Will this equation give you a maximum profit or a minimum profit? How do you know? Maximum because it has a peak. ----------------------------------------- 5. What price should be charged to reach the maximum or minimum profit? m = -b/(2a) = -53.1/(2*-8.3) = 3.20 ------------------------------------- 6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units. \$58,428 ===================== 7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6? They are the same -------------------- 8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response. Two because the equation is a quadratic. The discriminant is positive so there are 2 Real Number solutions. Cheers, Stan H.
 Exponents-negative-and-fractional/473536: Simplify by factoring. √180x^4=__1 solutions Answer 324794 by stanbon(60771)   on 2011-07-23 21:35:17 (Show Source): You can put this solution on YOUR website!Simplify by factoring. √180x^4=__ --- = sqrt[36x^4*5] ---- = sqrt[36x^4]*sqrt(5) ---- = 6x^2*sqrt(5) ==================== cheers, Stan H.
 Mixture_Word_Problems/473556: how many gallons of pure alcohol must be mixed with 5 gallons of a solution that is 20% alcohol solution that is 50% alcohol?1 solutions Answer 324793 by stanbon(60771)   on 2011-07-23 21:33:14 (Show Source): You can put this solution on YOUR website! how many gallons of pure alcohol must be mixed with 5 gallons of a solution that is 20% alcohol solution that is 50% alcohol? ----- Equation: alcohol + alcohol = alcohol x + 0.20*5 = 0.50(x+5) ---- Multiply thru by 100. 100x + 20*5 = 50x + 50*5 --- 50x = 30*5 x = 3 gallons (amt. of pure alcohol needed) ================= Cheers, stan H.
 Quadratic_Equations/473555: I am having a terrible time trying to figure this out. Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot). 1. Does the graph of this equation open up or down? What algebraic information can you use to determine this? 2. Describe what happens to the profit as the rent per square foot is increased. Discuss the different amounts of profit defined by the graph and the equation. 3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? 4. Will this equation give you a maximum profit or a minimum profit? How do you know? 5. What price should be charged to reach the maximum or minimum profit? 6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units. 7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6? 8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response. 1 solutions Answer 324791 by stanbon(60771)   on 2011-07-23 21:30:49 (Show Source): You can put this solution on YOUR website!You did not post the equation. Cheers, Stan H.
 logarithm/473558: Solve the logarithmic equation. \log _3 x = 21 solutions Answer 324790 by stanbon(60771)   on 2011-07-23 21:29:00 (Show Source): You can put this solution on YOUR website!Solve the logarithmic equation. \log _3 x = 2 ---- base = 3 log = exponent = 2 result = x ---- Equation: x = 3^2 --- x = 9 ============ cheers, stan H.