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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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 Graphs/83298: Can I get a quik hand on these two, if f(x)=5x-1 then how would i figure out f(a - 2) If an inventor charges \$4 per unit, then her profit for producing and selling x units is given by the function\ P(x)=2.25x-7000 a what is her profit after selling 2,000 units b profit after 5,000 units c. what would the break-even point for sales. thank you ahead of time.1 solutions Answer 59807 by stanbon(57361)   on 2007-05-24 14:42:55 (Show Source): You can put this solution on YOUR website!if f(x)=5x-1 then how would i figure out f(a - 2) f(a-2) = 5(a-2) -1 =5a-11 ---------------- If an inventor charges \$4 per unit, then her profit for producing and selling x units is given by the function\ P(x)=2.25x-7000 a what is her profit after selling 2,000 units P(2000) = 2.25*2000-7000 = -2500 which is a loss of \$2500 b profit after 5,000 units P(5000) = 2.25*5000-7000 = \$4259 c. what would the break-even point for sales. Let P=0 Then 0 = 2.25x-7000 x= 3111.111... Rounding down the break-even occurs when she produces 3111 units. ============= Cheers, Stan H.
 Exponents-negative-and-fractional/83299: I need help with the following equation: ^-3 I am just confused as to what to do with the base. Do I raise the base to the 3rd root, or just multiply it? Thanks.1 solutions Answer 59806 by stanbon(57361)   on 2007-05-24 14:34:16 (Show Source): You can put this solution on YOUR website![(-12a^5b^-2) / (4a^-3b^7)]^-3 ------- =[-3a^8/b^9)]^-3 Comment: The 3 in the exponent means we should cube each factor; the negative means we should invert the result. =[-b^27/27a^24] ============== Cheers, Stan H.
 Equations/83303: Can you help me with this problem? For the equation x – radical sign and the radicand under it of x = 0, perform the following: Solve for all values of x that satisfies the equation. Graph the functions y = x and y = radical sign and the radicand under it of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs. Graph How does the graph relate to part a? 1 solutions Answer 59805 by stanbon(57361)   on 2007-05-24 14:26:09 (Show Source): You can put this solution on YOUR website!For the equation x – radical sign and the radicand under it of x = 0, perform the following: Solve for all values of x that satisfies the equation. EQUATION: x-sqrt(x) = 0 x=sqrt(x) Square both sides to get: x^2=x x^2-x=0 x(x-1)=0 x=0 or x=1 ------------------ Graph the functions y = x and y = radical sign and the radicand under it of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs. Graph Points of intersectin: (0,0), (1,1) ------------------------------ How does the graph relate to part a? It confirms the results of part a. =============== Cheers, Stan H.
 Length-and-distance/83304: what is the length of the major axis of the ellipse 3x(to the second power) + 4y(to the second power)=121 solutions Answer 59803 by stanbon(57361)   on 2007-05-24 14:19:12 (Show Source): You can put this solution on YOUR website!what is the length of the major axis of the ellipse 3x(to the second power) + 4y(to the second power)=12 -------------- Divide thru by 12 to get: (x^2)/4 + (y^2)/3 = 1 a^2 = 4 a = 2 2a = 4 The length of the major axis is 2a = 4 =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/83284: How do I turn this into an algebra equation? In a bag of mixed vegetables, the ratio of peas to carrots is 7 to 2. How many pieces of each vegetable are in a bag if there is a total of 801 pieces in the bag? peas 623 carrots 178 1 solutions Answer 59797 by stanbon(57361)   on 2007-05-24 11:24:21 (Show Source): You can put this solution on YOUR website!In a bag of mixed vegetables, the ratio of peas to carrots is 7 to 2. How many pieces of each vegetable are in a bag if there is a total of 801 pieces in the bag? ------------------ 7:2 is the same as 7x:2x where 7x is peas and 2x is carrots. EQUATION: 7x+2x = 801 pieces 9x = 801 x = 89 # of peas = 7x = 623 # of carrots = 2x = 178 ============ Cheers, Sgan H.
 Miscellaneous_Word_Problems/83276: This question is from textbook introductory algebra an house insurance policy coust \$275. for every \$2000 of coverage. Find the cost for \$25,000 worth of coverage.1 solutions Answer 59796 by stanbon(57361)   on 2007-05-24 11:20:42 (Show Source): You can put this solution on YOUR website!a house insurance policy costs \$275 for every \$2000 of coverage. Find the cost for \$25,000 worth of coverage. ----------- (25000/2000)*250 = \$3125 ========== Cheers, Stan H.
 Numbers_Word_Problems/83277: after taking 3 math quizzes elisa has an average of 89. what must she score on the fourth quiz t raise her average to 91.1 solutions Answer 59795 by stanbon(57361)   on 2007-05-24 11:17:01 (Show Source): You can put this solution on YOUR website!after taking 3 math quizzes elisa has an average of 89. what must she score on the fourth quiz t raise her average to 91. ------------- If she averaged 89 on 3 quizzes she has 3*89 = 267 points. Let x be the score she needs to average 91: (267+x)/4 = 91 267+x = 364 x = 97 (score she needs on the 4th quize) ============ Cheers, Stan H.
 Equations/83282: Can someone please help me with this. It is probably some thing simple that I am overloking but this is beating me down. The numbers arent relavant here that's why i did not include them i am just trying to understand the correct way to write the equation in order to solve first for [Rm], I was provided with a number to reprsent 'Ra, Rf, and B'. and secondly I meed to know how to write the equation to solve for [Rf] with the known information being 'Ra, Rm,and B'. The equation i am starting out with is: So the question is how do i write the equation to solve for Rm and also for Rf using this equation as the base: Ra = Rf + B(Rm - Rf). 1 solutions Answer 59794 by stanbon(57361)   on 2007-05-24 11:13:08 (Show Source): You can put this solution on YOUR website!I meed to know how to write the equation to solve for [Rf] with the known information being 'Ra, Rm,and B'. The equation i am starting out with is: So the question is how do i write the equation to solve for Rm and also for Rf using this equation as the base: Ra = Rf + B(Rm - Rf). ------------------ Solving for Rm: Subtract Rf from both sides to get: Ra-Rf = B(Rm-Rf) Divide both sides by "B" to get: (Ra-Rf)/B = Rm - Rf Add Rf to both sides to get: Rm= [(Ra-Rf)/B] + Rf ---------------------------- Solving for Rf: Ra = Rf + B(Rm - Rf) Ra = Rf + BRm - BRf Get the Rf terms together: Ra-BRm = Rf(1-B) Divide both sides by 1-B to get: Rf = (Ra-BRm)/(1-B) =========== Cheers, Stan H. =================== Is that what you wanted? Cheers, Stan H.
 Numbers_Word_Problems/83278: my grandmother age has a units digit of three, and the aquare of the tens digits is her age reversed. ho old is my grandmother?1 solutions Answer 59793 by stanbon(57361)   on 2007-05-24 11:07:14 (Show Source): You can put this solution on YOUR website!my grandmother age has a units digit of three, and the aquare of the tens digits is her age reversed. how old is my grandmother? -------------- Assuming grandmother's age is a two digit number, it can be written as 10t+3 where t is the ten's digit. The reverse is 3*10 + t ----------- EQUATION: t^2 = 3*10+t t^2-t-30=0 (t-6)(t+5)=0 t=6 ------------ Grandma is 63 ================== Cheers, Stan H.
 Numbers_Word_Problems/83279: in a poll of 46 students 23 liked rap music 24 liked rock music,and 19 liked country music. of all the students 12 liked rap and country. 13 liked rap and rock, and 14 liked country and rock. of those students 9 liked all 3 types. how many students did not like any of these types.1 solutions Answer 59792 by stanbon(57361)   on 2007-05-24 10:49:11 (Show Source): You can put this solution on YOUR website!in a poll of 46 students 23 liked rap music 24 liked rock music,and 19 liked country music. of all the students 12 liked rap and country. 13 liked rap and rock, and 14 liked country and rock. of those students 9 liked all 3 types. how many students did not like any of these types. ----------------- Draw three interlocking circles (Venn Diagram) If you can fill in the various sections you will find the following number of students IN the circles: # in Union = AUBUC-(A and B)-(A and C)-(B and C)+ (A and B and C) = 23+24+19-12-13-14+9 = 36 The number not in the circles is 46-36= 10 ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/83280: This question is from textbook hi i am confused on the subtracting of polynomials (5x^5-5x^4-3x^3-5)-(9x^5-3x^4+7x^3-7) the book does not give enough explanation thanks a lot1 solutions Answer 59791 by stanbon(57361)   on 2007-05-24 10:38:05 (Show Source): You can put this solution on YOUR website!(5x^5-5x^4-3x^3-5)-(9x^5-3x^4+7x^3-7) ----------- Comment: You can only add or subtract "like" terms: =(5x^5-9x^5)+(-5x^4+3x^4)+(-3x^3-7x^3)+(-5+7) = -4x^5 -2x^4 -10x^3 +2 ============== Cheers, Stan H.
 Polynomials-and-rational-expressions/83281: This question is from textbook I cannot figure out the synthetic division can you please help me? (-6x^3-24x^2+28x-10)divided by (x+5) 1 solutions Answer 59790 by stanbon(57361)   on 2007-05-24 10:34:13 (Show Source): You can put this solution on YOUR website!(-6x^3-24x^2+28x-10)divided by (x+5) ------------ -5....-6....-24....28....-10 ........-6....6.....-2..|.. 0 --------------------- Remainder = 0 Quotient =-6x^2+6x-2 ============ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/83231: can you help me out by helping me fine the center and radius of the circle x^2+y^2-6x+4y-4=01 solutions Answer 59747 by stanbon(57361)   on 2007-05-23 21:08:55 (Show Source): You can put this solution on YOUR website!find the center and radius of the circle Complete the square separately onthe x-terms and the y-terms, as follows: x^2+y^2-6x+4y-4=0 (x^2-6x+(6/2)^2) + (y^2+4y+(4/2)^2) = 4+(3^2)+(2^2) (x+3)^2 + (y+2)2 = 17 Center at (-3,-2); radius = sqrt(17) ============== Cheers, Stan H.
 Sequences-and-series/83206: Apply the formulas for motion due to gravitational attraction. A stone is dropped from the top of a building 240 feet high. It is observed to take 0.20 seconds to go past an office floor-to-ceiling window that is 12 feet high. How far is it from the bottom of the window down to the street? 1 solutions Answer 59733 by stanbon(57361)   on 2007-05-23 19:16:56 (Show Source): You can put this solution on YOUR website!A stone is dropped from the top of a building 240 feet high. It is observed to take 0.20 seconds to go past an office floor-to-ceiling window that is 12 feet high. How far is it from the bottom of the window down to the street? ------------ S(t) = -16t^2+240 Velocity = -32t ft/sec ------------------ Velocity of the stone while passing the window: -12ft/0.2 sec = -60 ft/sec -------------- Therefore: -32t =-60 t= 1.875 seconds -------------- So, where is the stone at t=1.875 sec ? ------------- s(1.875) = -32(1.875)^2+240 s(1.875) = 127.5 ft above the ground -------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/83205: Apply the formulas for motion due to gravitational attraction. #1 A diver in Acapulco leaps horizontally from a point 112 feet above the sea. (a) How long does it take for the diver to reach the water? (b) At what speed does the diver enter the water? 1 solutions Answer 59732 by stanbon(57361)   on 2007-05-23 19:08:05 (Show Source): You can put this solution on YOUR website!Apply the formulas for motion due to gravitational attraction. #1 A diver in Acapulco leaps horizontally from a point 112 feet above the sea. (a) How long does it take for the diver to reach the water? (b) At what speed does the diver enter the water? -------------- Formula: s(t) = -16t^2+112 s is height above the ground; when he hits the water s = zero. ------------- a) -16t^2=-112 t^2 = 7 t = (sqrt7) sec for him to hit the water. ----------- b) velocity = -32t ] -21sqrt7 ft/sec or approximately 84.66 ft. sec. ================ Cheers, Stan H.
 Miscellaneous_Word_Problems/83193: This question is from textbook introductory algebra Rowing with the current of a river, a rowing team can row 25 miles in the same amount of time it takes to row 15 miles against the current. The rate of the rowing team in calm water is 20 mph. Find the rate of the current.1 solutions Answer 59714 by stanbon(57361)   on 2007-05-23 16:54:14 (Show Source): You can put this solution on YOUR website!Rowing with the current of a river, a rowing team can row 25 miles in the same amount of time it takes to row 15 miles against the current. The rate of the rowing team in calm water is 20 mph. Find the rate of the current ----------------- With current DATA: Distance = 25 mi ; Rate = c+20 mph ; Time = 25/(c+20) ---------------------- Against current DATA: Distance = 15 mi ; Rate = 20-c mph ; Time = 15(20-c) ================== EQUATION: time with = time against 25/(c+20) = 15/(20-c) 5/(c+20) = 3/(20-c) 100-5c = 3c+60 8c = 40 c= 5 mph ( rate of current) ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/83171: #24 Marginal Cost of Coffee The manager of a restaurant found that the cost to produce 100 cups of coffee is \$11.02, while the cost to produce 400 cups is \$40.12. Assume the cost is a linear function of x, the number of cups produced. a. Find a formula for C(x). b. What is the fixed cost? c. Find the total cost of producing 1000 cups. d. Find the total cost of producing 1001 cups. e. Find the marginal cost of the 1001st cup. f. What is the marginal cost of any cup and what does this mean to the manager? 1 solutions Answer 59683 by stanbon(57361)   on 2007-05-23 13:30:21 (Show Source): You can put this solution on YOUR website!The manager of a restaurant found that the cost to produce 100 cups of coffee is \$11.02, while the cost to produce 400 cups is \$40.12. Assume the cost is a linear function of x, the number of cups produced. --------- You have two points: (100,11.02) and (400,40.12) --------------- a. Find a formula for C(x). slope - [40.12-11.02]/[400-300] = 29.10/300 = 0.097.. Form is y=mx+b where y=31.02 when x=100 and m=0.097... 31.02 = 0.097(100)+b 31.02 = 9.7 + b b= 21.32 EQUATION: Cost(x) = 0.097x + 21.32 ------------------ b. What is the fixed cost? \$21.32 ----------------------- c. Find the total cost of producing 1000 cups. C(1000) = 0.097(1000)+21.32 = \$118.32 ----------------------- d. Find the total cost of producing 1001 cups. Add 9.7 cents the the cost of part c. ------------------------ e. Find the marginal cost of the 1001st cup. The slope is the marginal cost: 9.7 cents ---------------------- f. What is the marginal cost of any cup and what does this mean to the manager? The marginal cost for any cup is 9.7 cents. If he produces no cups his overhead is \$21.32 For each cup he sells he gains 9.7 cents. ================== Cheers, Stan H. -------------
 Radicals/83160: I’m going crazy trying to figure this one out. 3 is the index with a radical sign and the radicand under it is x squared = 4 Can someone help me? 1 solutions Answer 59680 by stanbon(57361)   on 2007-05-23 13:08:57 (Show Source): You can put this solution on YOUR website!3 is the index with a radical sign and the radicand under it is x squared = 4 ------------------ (x^2)^(1/3) = 4 x^(2/3) = 4 Raise both sides to the (3/2) power to get: x = 4^(3/2) x= 8 ============ Cheers, Stan H.
 Rate-of-work-word-problems/82989: This question is from textbook introductory algebra the bird capable of the fastest flying speed is the swift. a swift flying with the wind to a fovorite feeding spot traveled 26 mi in 0.2 h. on returning now aganst the wind. the swift was able to travel only 16 mi in the same amount of time. what is the rate of the swift in clam air and what was the rate of wind?1 solutions Answer 59633 by stanbon(57361)   on 2007-05-22 22:47:38 (Show Source): You can put this solution on YOUR website!a swift flying with the wind to a fovorite feeding spot traveled 26 mi in 0.2 h. on returning now aganst the wind. the swift was able to travel only 16 mi in the same amount of time. what is the rate of the swift in clam air and what was the rate of wind? -------------- With the wind DATA: Distance = 26 mi ; Time = 0.2 hrs ; Rate = d/t = 26/0.2 = 130 mph ---------- Against the wind DATA; Distance = 16 mi ; Time = 0.2 hrs ; Rate = d/t = 16/0.2 = 80 mph ----------------- Let rate in calm air be c and rate of wind be w: EQUATIOS: c+w = 130 mph c-w = 80 mph ----------------- 2c = 210 c = 105 mph (rate of swift in calm air) w = 130=105 = 25 mph ( rate of wind) ============= Cheers, Stan H.
 Functions/82994: Can you explain how a graph shows whether relations are functions or not functions? I get confused when using the vertical-line test.1 solutions Answer 59631 by stanbon(57361)   on 2007-05-22 22:38:34 (Show Source): You can put this solution on YOUR website!If any vertical line intersects the graph more that once the relation is not a function. Why? Because that would imply that for some value of "x" there is more than one corresponding "y" value. That contrdicts the definition of a function. ============= Cheers, Stan H.
 Rate-of-work-word-problems/83079: This question is from textbook introductory algebra A twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin-engine plane is 50 mph faster than that of the single-engine plane. Fine the rate of the twin-engine plane.1 solutions Answer 59630 by stanbon(57361)   on 2007-05-22 22:19:01 (Show Source): You can put this solution on YOUR website! twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin-engine plane is 50 mph faster than that of the single-engine plane. Fine the rate of the twin-engine plane. -------------------- Twin plane DATA: Distance = 800 mi ; Rate = x+50 mph ; time = d/r = 800/(x+50) hrs. ------------------- Single Plane DATA: Distance = 600 mi ; Rate = x mph ; time = d/r = 600/x =============== EQUATION: time = time 800/(x+50) = 600/x 8/(x+50) = 6/x 8x = 6x + 300 x= 150 mph x+50 = 200 mph (twin-engine plane rate) =========================== Cheers, Stan H.
 Rate-of-work-word-problems/83076: This question is from textbook introductory algebra The president of a company traveled 1800 mi by jet and 300 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took a total of 5 h. Find the rate of the jet plane.1 solutions Answer 59628 by stanbon(57361)   on 2007-05-22 22:11:20 (Show Source): You can put this solution on YOUR website!The president of a company traveled 1800 mi by jet and 300 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took a total of 5 h. Find the rate of the jet plane. ------------------ Jet travel DATA: Distance=1800 mi ; Rate = 4x mph ; Time = d/r = 1800/4x = 450/x hrs. --------------- Prop travel DATA: Distance=300 mi ; Rate = x mph ; Time = d/r = 300/x hrs. ---------------------- EQUATION: time + time = 5 hrs. 450/x + 300/x = 5 90/x + 60/x = 1 x=150 mph 4x= 600 mph (jet plane rate) ==================== Cheers, Stan H. 450/x +
 Miscellaneous_Word_Problems/83051: The number G of gears a machine can make varies directly as the time T it operates. If it can make 4810 gears in 12 hours, how many gears can it make in 20 hours?1 solutions Answer 59626 by stanbon(57361)   on 2007-05-22 22:02:57 (Show Source): You can put this solution on YOUR website!The number G of gears a machine can make varies directly as the time T it operates. If it can make 4810 gears in 12 hours, how many gears can it make in 20 hours? ---------- G=kT 4810=k*12 k=400.83333 EQUATION: G = 400.833333 T G = 400.83333*20 = 8016.6666667 ============== Cheers, Stan H.
 Equations/83068: First of all you guy's are fantastic! Here is my last one: (x^4+3x^2-1)(x^2-x+2) instructions are to multiply1 solutions Answer 59625 by stanbon(57361)   on 2007-05-22 21:57:09 (Show Source): You can put this solution on YOUR website!(x^4+3x^2-1)(x^2-x+2) x^6-x^5+2x^4+3x^4-3x^3+6x^2-x^2+x-2 x^6-x^5+5x^4+2x^2+x-2 ================== Cheers, Stan H.
 Quadratic_Equations/83062: Solve by completing the square. 3x^2-9x-31=01 solutions Answer 59624 by stanbon(57361)   on 2007-05-22 21:51:19 (Show Source): You can put this solution on YOUR website!Solve by completing the square. 3x^2-9x-31=0 3(x^2-3x+(3/2)^2=31+3(3/2)^2 3(x+(3/2))^2 = 151/4 (x+(3/2))^2=151/12 x= (-3/2) + (sqrt(151/12)) or x=(-3/2)-(sqrt(151/12)) x=-2.0473 or x=-5.047 ========================= Cheers, Stan H.
 Quadratic_Equations/83064: Mrs. Niss put \$500 in a savings account upon opon which the bank pays an annual yeild of 4%. Because 4% of \$500 is \$20, and 10 times 20 is \$200, Mrs. Niss thinks that the amount in the account after 10 years will be \$700(\$500 + \$200). explain why this reasoning is incorrect. If the annual yield continues to be 4%, what will be the amount in the account after 10 years?1 solutions Answer 59619 by stanbon(57361)   on 2007-05-22 21:25:51 (Show Source): You can put this solution on YOUR website!Mrs. Niss put \$500 in a savings account upon opon which the bank pays an annual yeild of 4%. Because 4% of \$500 is \$20, and 10 times 20 is \$200, Mrs. Niss thinks that the amount in the account after 10 years will be \$700(\$500 + \$200). explain why this reasoning is incorrect. If the annual yield continues to be 4%, what will be the amount in the account after 10 years? -------------------- The interest earned each year must be included in the amount that increases by 4%. A(t)=500(1+0.04)^10 = \$740.12 Cheers, Stan H.
 Linear-equations/83063: WORD PROBLEM.....FOOD BUDGET YOU ARE PLANNING THE MENU FOR YOUR RESTAURANT.EACH EVENING YOU OFFER TWO DIFFERENT MEALS AND HAVE AT LEAST 240 CUSTOMERS.FOR SATURDAY NIGHT YOU PLAN TO OFFER ROAST BEEF AND TERIYAKI.YOU EXPECT THAT FEWER CUSTOMERS WILL ORDER THE CHICKEN .THE ROST BEEF COSTS \$5 PER SERVING AND THE CHICKEN COSTS YOU \$3 PER SERVING . YOU HAVE A BUDGET OF AT MOST \$1200 FOR MEAT FOR SATURDAY NIGHT THE QUESTION: WRITE A SYSTEM OF LINER INEQALITIES THAT SHOWS THE VARIOUS NUMBERS OF ROAST BEEF AND TERIYAKI CHICKEN MEANS YOU COULD MAKE FOR SATURDAY NIGHT? 1 solutions Answer 59617 by stanbon(57361)   on 2007-05-22 21:19:09 (Show Source): You can put this solution on YOUR website!YOU ARE PLANNING THE MENU FOR YOUR RESTAURANT.EACH EVENING YOU OFFER TWO DIFFERENT MEALS AND HAVE AT LEAST 240 CUSTOMERS.FOR SATURDAY NIGHT YOU PLAN TO OFFER ROAST BEEF AND TERIYAKI.YOU EXPECT THAT FEWER CUSTOMERS WILL ORDER THE CHICKEN .THE ROST BEEF COSTS \$5 PER SERVING AND THE CHICKEN COSTS YOU \$3 PER SERVING . YOU HAVE A BUDGET OF AT MOST \$1200 FOR MEAT FOR SATURDAY NIGHT THE QUESTION: WRITE A SYSTEM OF LINER INEQALITIES THAT SHOWS THE VARIOUS NUMBERS OF ROAST BEEF AND TERIYAKI CHICKEN MEANS YOU COULD MAKE FOR SATURDAY NIGHT? -------------- Let B be the number of Roast Beef Meals; Let T be the number of Teriyaki Meals. B + T <=240 5B + T <= 1200 T-B <0 =============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/83066: Hi, help! I clicked on the link for the formula plotting system but it takes me to a wiki page with a huge list of pharmaceuticals...! Here's the problem, please note that the exponent says .75 but it should read 3/4, I just couldn't figure out how to do it so it would come out right. For the function f, defined above, what are all the values of x for which f(x) is a real number?1 solutions Answer 59613 by stanbon(57361)   on 2007-05-22 21:13:02 (Show Source): You can put this solution on YOUR website!f(x) = (x+1)^(3.4) For the function f, defined above, what are all the values of x for which f(x) is a real number? -------------- The 4 in the exponent means you are taking the 4th root. For the result to be Real x+1 must be >= zero: x+1>=0 x>=-1 =================== Cheers, Stan H.
 Miscellaneous_Word_Problems/83067: Please help me factor out this polynomial: 6x^2-7x-5.1 solutions Answer 59611 by stanbon(57361)   on 2007-05-22 21:08:24 (Show Source): You can put this solution on YOUR website!factor out this polynomial: 6x^2-7x-5. -------------- Rewriteas: Replace the middle term with -10x+3x to get: 6x^2-10x+3x-5 Factor the 1st two and then the last two terms to get: 2x(3x-5)+(3x-5) Factor out the common factor: (3x-5)(2x+1) =================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/83069: Hello! Here's my problem. for all positive values of x, the function f is defined by . Of the following, which is the best approximation of f(x) for values of x greater than 1,000? a. b. c. 1 solutions Answer 59610 by stanbon(57361)   on 2007-05-22 21:04:20 (Show Source): You can put this solution on YOUR website!x^3 because x^-2 gets smaller as x gets larger. ---------- Cheers, Stan H.
 Quadratic_Equations/83070: Please help me solve these three problems. Thanks Solve -9(x-3)^2=-7 Solve 9x^2=14 Solve 5(x-2)^2=31 solutions Answer 59609 by stanbon(57361)   on 2007-05-22 21:02:05 (Show Source): You can put this solution on YOUR website!Solve -9(x-3)^2--7 Divide thru -9 to get: (x-3)^2=7/9 Take the square root to get: x =3+(sqrt7)/3 or x=+3-(sqrt7)/3 ----------------------- Solve 9x^2=14 x^2=14/9 x=(sqrt14)/3 or x=(-sqrt14)/3 ------------------ Solve 5(x-2)^2=3 Divide thru by 5 then take the square root of both sides. ========== Cheers, Stan H.