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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Miscellaneous_Word_Problems/180795: This question is from textbook During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person. 1 solutions Answer 135525 by stanbon(57307)   on 2009-02-07 18:43:41 (Show Source): You can put this solution on YOUR website!During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person. ------------------------- Ans: 13/20 -------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/180796: This question is from textbook If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 6? A) 2 out of 3 B) 1 out of 3 C) 1 out of 6 D) 1 out of 2 E) 5 out of 6 1 solutions Answer 135524 by stanbon(57307)   on 2009-02-07 18:40:03 (Show Source): You can put this solution on YOUR website!If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 6? --- P(<6) = 1 - P(6) P(<6) = 1 - (1/6) P(<6) = 5/6 Ans: 5 out of 6 ================================== Cheers, Stan H. A) 2 out of 3 B) 1 out of 3 C) 1 out of 6 D) 1 out of 2 E) 5 out of 6
 Miscellaneous_Word_Problems/180797: This question is from textbook A jar contains 5 yellow marbles, 16 green marbles, and 8 black marbles. If one marble is selected at random, what is the probability that it is not green? 1 solutions Answer 135522 by stanbon(57307)   on 2009-02-07 18:28:23 (Show Source): You can put this solution on YOUR website!A jar contains 5 yellow marbles, 16 green marbles, and 8 black marbles. If one marble is selected at random, what is the probability that it is not green? ------------------------------------------------------- P(not green) = 1 - P(green) P(not green) = 1 - (16/29) P(not green) = 13/29 ========================== Cheers, Stan H.
 Volume/160357: A cylinder is inscribed in a sphere of radius 1. Express the volume of the sphere as a function of the base radius. PLEASE HELP ME!!!1 solutions Answer 135513 by stanbon(57307)   on 2009-02-07 17:55:17 (Show Source): You can put this solution on YOUR website!A cylinder is inscribed in a sphere of radius 1. Express the volume of the sphere as a function of the base radius. ------------ The volume of every sphere is V = (4/3)pi*r^3 ================================================== Cheers, Stan H.
 Volume/180783: I WANT TO FIND THE LATERAL AREA OF A REGULAR PYRAMID 3,2AND 21 solutions Answer 135510 by stanbon(57307)   on 2009-02-07 17:44:28 (Show Source): You can put this solution on YOUR website!That is not enough information. You have to indicate which numbers are the dimensions of the base and the dimension of the height. =============== Cheers, Stan H.
 Quadratic_Equations/180787: Connect English with Mathematics and Graphing Lines 4. Translate each sentence into an algebraic equation. a) One sixth of a number, increased by 15, is 42. b) Three times a number, decreased by four, is five more than six times the number. c) When tickets to a soccer game cost \$4 each, the revenue at the gate is \$320. d) the total length of the base and height of a triangle 15cm. PLeaseeeeeeeeeeeeeeeeeee thankssssssssssssssss alottttttttttttttttttt1 solutions Answer 135509 by stanbon(57307)   on 2009-02-07 17:40:21 (Show Source): You can put this solution on YOUR website!Connect English with Mathematics and Graphing Lines 4. Translate each sentence into an algebraic equation. a) One sixth of a number, increased by 15, is 42. (1/6)x +15 = 42 ---------------------------- b) Three times a number, decreased by four, is five more than six times the number. 3x - 4 = 6x + 5 ---------------------------- c) When tickets to a soccer game cost \$4 each, the revenue at the gate is \$320. 5x = 320 ------------------------------- d) the total length of the base and height of a triangle 15cm. b + h = 15 =========================================== Cheers, Stan H.
 Graphs/180788: This question is from textbook Elementary and Intermediate Graph a line. The line through (-2,5) with slope -1.1 solutions Answer 135507 by stanbon(57307)   on 2009-02-07 17:36:07 (Show Source): You can put this solution on YOUR website!Graph a line. The line through (-2,5) with slope -1. --------------------- y = mx + b You know y = 5 when x = -2 and m = -1; so solve for "b": 5 = -1*-2 + b b = 3 -------------------------- Equation: y = -x + 3 Graphing: when x = 0, y = 3 giving you point (0,3) Plot (0,3) and (-2,5) and draw a line thru them: =========================================== Cheers, Stan H.
 Rational-functions/180779: This question is from textbook Sullivan Algebra and Trigonometry f(x)= 2x^2/ x^4+1 In regards to 27c, d, e, and f. c>> if f(x)=-1, what is x? what points are on the graph of f? My understanding... -1=2x^2/x^4+1 My confusion is really how to solve for x (due to the fraction with exponents) d>> what is the domain of f? The answer is all real numbers. Why? e>> List the X Intercept. f>> List the Y Intercept. My understanding... both intercepts are zero. My graph comes out to be a short line symmertrical to the y axis where both x and y are intercepting at the orgin (0,0)1 solutions Answer 135500 by stanbon(57307)   on 2009-02-07 15:55:35 (Show Source): You can put this solution on YOUR website!f(x)= 2x^2/(x^4+1) In regards to 27c, d, e, and f. c>> if f(x)=-1, what is x? My understanding... -1=2x^2/x^4+1 Cross-multiply to get: -x^4-1 = 2x^2 Rearrange: x^4 + 2x^2 + 1 = 0 Factor: (x^2+1)(x^2+1) = 0 x = +i or x = -i ----------------------------- what points are on the graph of f? ----------------------------------------- f(x) = 2x^2/(x^4+1) d>> what is the domain of f? The answer is all real numbers. Why? The domain of a function is always "all Real Numbers" unless the equation of the function excludes certain values. The x^4+1 in the denominator is always positive so no x-values are excluded from the Domain. ------------------------------------------- e>> List the X Intercept. f(x) = 2x^2/(x^4+1) y can only be zero if 2x^2 = 0; so the x-intercept is (0,0) -------------------------------------------------------------- f>> List the Y Intercept. If x = 0, y = 0; so the x-intercept is the same as the y-intercept. ================================ Cheers, Stan H.
 Complex_Numbers/180780: 2 + i/ i + 51 solutions Answer 135499 by stanbon(57307)   on 2009-02-07 15:40:39 (Show Source): You can put this solution on YOUR website!(2 + i) / (5+i) = [(2+i)(5-i)] / [(5+i)(5-i)] = [10 + 3i +1] / 25 + 1] = (11+3i) / 26 ================== Cheers, Stan H.
 Trigonometry-basics/180775: Find the exact value of cot(75º). PLEASE HELP ME!!!!! I really dont know what to do!!!1 solutions Answer 135498 by stanbon(57307)   on 2009-02-07 15:36:43 (Show Source): You can put this solution on YOUR website!Find the exact value of cot(75º). ------- cot(x+y) = [cot(x)cot(y)-1] / [cot(x) + cot(y)] Your Problem: cot(30 + 45) = [cot(30)cot(45)-1] / [cot(30) + cot(45)] = [sqrt(3)*sqrt(2)/2 - 1] / [sqrt(3) + sqrt(2)/2] = [(sqrt(3)*sqrt(2) - 2)/2] / [(2sqrt(3) = sqrt(2))/2] = etc. ========================= Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/180776: What is the answer for this problem? Find two consecutive even integers such that the sum of their squares is 52.1 solutions Answer 135495 by stanbon(57307)   on 2009-02-07 15:23:15 (Show Source): You can put this solution on YOUR website!Find two consecutive even integers such that the sum of their squares is 52. ------------- 1st: 2x 2nd: 2(x+1) ---------------- Equation: (2x)^2 + (2(x+1))^2 = 52 4x^2 + 4(x+1)^2 = 52 x^2 + (x+1)^2 = 13 2x^2 + 2x + 1 = 13 2x^2 + 2x - 12 = 0 x^2 + x - 6 = 0 (x+3)(x-2) = 9 Positive solution: x = 2 --------- 1st: 2x = 4 2nd: 2x+2 = 6 --- Checking: 4^2 + 6^2 = 52 16 + 36 = 52 52 = 52 ================== Cheers, Stan H.
 Trigonometry-basics/180777: Simplify to a single trig function: (cos3x-cosx)/ (sin3x-sinx) PLEASE HELP ME I DON'T KNOW WHAT TO DO!!!1 solutions Answer 135493 by stanbon(57307)   on 2009-02-07 15:16:53 (Show Source): You can put this solution on YOUR website!Working with just the cos(3x) you get the following: cos3x = cos(x)cos(2x) - sin(x)sin(2x) =cos(x)[1-2sin^2(x)] - sin(x)[2sin(x)cos(x)] =cos(x)-2cos(x)sin^2(x) - 2sin^2(x)cos(x) =cos(x) - 4sin^2(x)cos(x) ----------------------------- So subtracting cos(x) from this result you would get: = - 4sin^2(x)cos(x) ========================== Cheers, Stan H.
 Probability-and-statistics/180108: Suppose that 48% of the women who gave birth at a certain hospital last year were over 30 years old, and that 46% were unmarried. If 65% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30 ? 1 solutions Answer 135492 by stanbon(57307)   on 2009-02-07 15:09:33 (Show Source): You can put this solution on YOUR website!Suppose that 48% of the women who gave birth at a certain hospital last year were over 30 years old, and that 46% were unmarried. If 65% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30 ? ---------------------------- Formula: P(A and B) = P(A) + P(B) - P(A or B) ----------------------------- Your problem: P(un and >30) = P(un) + P(>30) - P(un or >30) P(un and >30) = 0.46 + 0.48 - 0.65 = 0.29 ========================== Cheers, Stan H.
 Pythagorean-theorem/180768: an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides? thnxx1 solutions Answer 135490 by stanbon(57307)   on 2009-02-07 15:02:42 (Show Source): You can put this solution on YOUR website!an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides? --------- Let each of the equal sides have length "x" 15^2 = x^2 + x^2 2x^2 = 15^2 x = (15/2)sqrt(2) ====================== Cheers, Stan H.
 Pythagorean-theorem/180767: an apartment building casts a shadow. From the tip of the shadow to the top of the building is 100 m. The tip of the shadow is 72 m from the base of the building? How tall is the building? thnakyou1 solutions Answer 135486 by stanbon(57307)   on 2009-02-07 14:52:01 (Show Source): You can put this solution on YOUR website!an apartment building casts a shadow. From the tip of the shadow to the top of the building is 100 m. The tip of the shadow is 72 m from the base of the building? How tall is the building? -------------------- Draw the picture and label the height of the building "x". ----------------------- Use Pythagoras or use trigonometry if you know it. 100^2 = 72^2 + x^2 x^2 = 10000 - 5184 x^2 = 4816 x = 69.40 meters ======================= Cheers, Stan H.
 Miscellaneous_Word_Problems/180745: This question is from textbook ) One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a spade. 1 solutions Answer 135485 by stanbon(57307)   on 2009-02-07 14:46:58 (Show Source): You can put this solution on YOUR website!One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a spade. -------------- There are 13 spades and 39 other cards --- P(spade) = 39/52 = 3/4 =========================== Cheers, Stan H.
 Miscellaneous_Word_Problems/180759: This question is from textbook A couple plan to have exactly three children. (a) Construct a tree diagram and list the sample space. (b) Find the probability that the family has at least two girls 1 solutions Answer 135484 by stanbon(57307)   on 2009-02-07 14:43:18 (Show Source): You can put this solution on YOUR website!A couple plan to have exactly three children. (a) Construct a tree diagram and list the sample space. 1st column(root) has boy/girl 2nd column(branch) has boy/girl; boy/girl 3rd column(2nd branch) has boy/girl; boy/girl; boy/girl; boy/girl ---------------------------------------------------------------------- (b) Find the probability that the family has at least two girls bgg, bgb, gbb, ggg Probability = 4/8 = 1/2 =========================== Cheers, Stan H.
 Functions/180761: I need help find the domain and how you obtain the answer. 1. f(t)=4.5e^t 2. g(x)=log(x+3) 3. g(x)=2^t 4. g(t)=1n(t-1) 1 solutions Answer 135483 by stanbon(57307)   on 2009-02-07 14:38:13 (Show Source): You can put this solution on YOUR website!I need help find the domain and how you obtain the answer. --- Comment: The domain of a function is "all Real Numbers" unless you can see some reason in the equation that would exclude one or more. --------------------- 1. f(t)=4.5e^t Domain: All Real Numbers ------------------------------- 2. g(x)=log(x+3) The x+3 must be positive: x+3 > 0 implies x >-3 So Domain is "all Real Numbers greater than -3". ----------------------------------- 3. g(x)=2^t Domain: All Real Numbers ------------------------------------- 4. g(t)=1n(t-1) The t-1 must be positive t-1 >0 implies t > 1 So Domain is "all Real Numbers greater than 1" ================================================= Cheers, Stan H.
 Functions/180751: The simples form of (f-g)(x) , given that f(x)= 1-x/2+x, g(x)= 2x-3/x-2 is ?1 solutions Answer 135474 by stanbon(57307)   on 2009-02-07 10:57:53 (Show Source): You can put this solution on YOUR website! (f-g)(x) , given that f(x)= 1-x/2+x, g(x)= 2x-3/x-2 is ? ------------------------------------------ (f-g)(x) = f(x) - g(x) = (1-x)/(2+x) - (2x-3)/(x-2) --- Rearrange: = -(x-1)/(x+2) - (2x-3)/(x-2) = [-(x-1)(x-2) - (2x-3)(x+2)] / [x^2-4] = [-(x^2-3x+2) -(2x^2+x-6)] / [x^2-4] = [-3x^2 + 2x + 4] / [x^2-4] ================================== Cheers, Stan H.
 Miscellaneous_Word_Problems/180747: This question is from textbook The last 40 violent crimes committed in Sconeville were 2 homicides, 25 robberies, and 13 assaults. What is the empirical probability that the next violent crime committed in Sconeville will be a robbery? 1 solutions Answer 135473 by stanbon(57307)   on 2009-02-07 10:48:54 (Show Source): You can put this solution on YOUR website!The last 40 violent crimes committed in Sconeville were 2 homicides, 25 robberies, and 13 assaults. What is the empirical probability that the next violent crime committed in Sconeville will be a robbery? ------------------------ Ans: 25/40 = 5/8 ========================= Cheers, Stan H.
 Miscellaneous_Word_Problems/180750: This question is from textbook How many different four-digit numbers can be formed from the digits 0 through 9 if the first digit must be even and cannot be zero? 1 solutions Answer 135472 by stanbon(57307)   on 2009-02-07 10:44:00 (Show Source): You can put this solution on YOUR website!How many different four-digit numbers can be formed from the digits 0 through 9 if the first digit must be even and cannot be zero? -------------------------- # of ways to select the 1st digit: 4 # of ways to select the 2nd, 3rd, 4th digits: 10 --------------------------- Ans: 4*10^3 = 4000 digits ============================== Cheers, Stan H.
 Travel_Word_Problems/180758: On a trip of 800 km, Charlie drove at two different speeds. In one province he drove at 100 km/h and in another at 110 km/h. If the entire trip took seven and one-half hours, the distance travelled at the 110 km/h speed is?1 solutions Answer 135471 by stanbon(57307)   on 2009-02-07 10:39:57 (Show Source): You can put this solution on YOUR website!On a trip of 800 km, Charlie drove at two different speeds. In one province he drove at 100 km/h and in another at 110 km/h. If the entire trip took seven and one-half hours, the distance travelled at the 110 km/h speed is? ---- 1st: Province DATA: distance = x km ; rate = 100 km/h ; time = d/r = x/100 hrs ---------------------- 2nd: Provice DATA: distance = (800-x) km ; rate = 110 km/h ; time = d/r = (800-x)/110 hrs --------------------- Equation: time + time + time x/100 + (800-x)/110 = 7.5 hrs 110x + 100(800-x) = 100*110*7.5 110x + 100*800 - 100x = 100*825 10x = 100*25 x = 250 km ---- Find distance traveled at 110 km: 800-x = 800-250 = 550 km ====================================== Cheers, Stan H.
 Rational-functions/180752: This question is from textbook Saxon Algebra 2 Find an equation for the inverse of y=3/4x+7 This is what I got so far: x=3/4y+7 x-7=3/4y ...and then what? 1 solutions Answer 135468 by stanbon(57307)   on 2009-02-07 10:28:02 (Show Source): You can put this solution on YOUR website!Find an equation for the inverse of y=3/4x+7 -------------- 1st: Interchange x and y to get: x = (3/4)y + 7 2nd: Solve for "y": (3/4)y = x - 7 y = (4/3)(x-7) y = (4/3)x - (4/3)7 y = (4/3)x - (28/3) ======================= Cheers, Stan H.
 Travel_Word_Problems/180710: Mr. Johnson rode his bike from his house to a store in Woodland Park at a rate of 10.3 miles per hour. He immediatly turned around and came home at an average rate of 22.5 miles per hour. If the total trip took him approximatley 5.15 hours, how far is it from his house to the store?1 solutions Answer 135456 by stanbon(57307)   on 2009-02-07 08:14:28 (Show Source): You can put this solution on YOUR website!Mr. Johnson rode his bike from his house to a store in Woodland Park at a rate of 10.3 miles per hour. He immediatly turned around and came home at an average rate of 22.5 miles per hour. If the total trip took him approximatley 5.15 hours, how far is it from his house to the store? --------------------------------- House to Store DATA: rate = 10.3 mph ; distance = x miles ; time = d/r = x/10.3 ---------------------- Store to House DATA: rate = 22.5 mph ; distance = x miles ; time = d/r = x/22.5 --------------------- Equation: time + time = 5.15 hrs x/10.3 + x/22.5 = 5.15 (22.5x + 10.3x) = 10.3*22.5*5.15 32.8x = 1193.5125 x = 36.39 miles (distance between house and store) ========================= Cheers, Stan H.
 Money_Word_Problems/180711: Greg 'acquired' \$25,000 and invested the money into two seprate accounts. In one of the accounts he earned 5.5% and in the second he earned 9%. In a year he took a total of \$26,842.25 out of the accounts, closing them out. How much money did he invest at each rate?1 solutions Answer 135454 by stanbon(57307)   on 2009-02-07 08:07:41 (Show Source): You can put this solution on YOUR website!Greg 'acquired' \$25,000 and invested the money into two seprate accounts. In one of the accounts he earned 5.5% and in the second he earned 9%. In a year he took a total of \$26,842.25 out of the accounts, closing them out. How much money did he invest at each rate? --------------------------------------- Equation: interest + interest = interest 0.055x + 0.09(25000-x) = 26842.25-25000 Multiply thru by 1000 to get: 55x + 90*25000 - 90x = 1842250 -35x = -407750 x = \$11,650 (amt invested at 5.5% 25000-11,650 = \$13,350 (amt. inveted at 9%) ============================================= cheers, Stan H.
 Mixture_Word_Problems/180727: A famous shop blends yogurt that is 3% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low fat yogurt?1 solutions Answer 135453 by stanbon(57307)   on 2009-02-07 07:59:29 (Show Source): You can put this solution on YOUR website!A famous shop blends yogurt that is 3% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low fat yogurt? ------------------------ Fat Equation: fat + Fat = Fat 0.03x + 0*(60-x) = 0.01*60 Multiply thru by 100 to get: 3x + 0 = 60 x = 20 lbs (amt. of 3% yogurt in the mixture 60-x = 40 lbs (amt of 0% yogurt in the mixture) =========================== Cheers, Stan H.
 test/180701: find all solutions of the equation algebraically. 36t^4 + 29t^2 - 7 = 0 1 solutions Answer 135433 by stanbon(57307)   on 2009-02-06 22:16:44 (Show Source): You can put this solution on YOUR website!find all solutions of the equation algebraically. 36t^4 + 29t^2 - 7 = 0 36t^4 + 36t^2 - 7t^2 - 7 = 0 36t^2(t^2 + 1) -7(t^2+1) = 0 (t^2+1)(36t^2-7) = 0 t^2 = -1 or 36t^2 = 7 t = i or t = -i or sqrt(7)/6 or -sqrt(7)/6 ============================================== cheers, Stan H.
 test/180702: find all solutions of the equation algebraically. 1/t^2 + 8/t + 15 = 0 1 solutions Answer 135430 by stanbon(57307)   on 2009-02-06 21:58:18 (Show Source): You can put this solution on YOUR website!find all solutions of the equation algebraically. 1/t^2 + 8/t + 15 = 0 Multiply thru by t^2 to get: 1 + 8t +15t^2 = 0 Rearrange: 15t^2 + 8t + 1 = 0 (3t+1)(5t+1) = 0 t = -1/3 or t = -1/5 ------------------------- Cheers, Stan H.
 expressions/180697: The width of a rectangle is fixed at 17 cm. What lengths will make the perimeter greater than 82 cm.1 solutions Answer 135428 by stanbon(57307)   on 2009-02-06 21:47:50 (Show Source): You can put this solution on YOUR website!The width of a rectangle is fixed at 17 cm. What lengths will make the perimeter greater than 82 cm. -------------------------------------- Perimeter = 2(L + W) Equation: 2(L + 17) > 82 L + 17 > 41 L > 64 ============ Cheers, Stan H.
 Inequalities/180695: how do you sketch the graph of the inequality. y+x<-6?1 solutions Answer 135427 by stanbon(57307)   on 2009-02-06 21:40:00 (Show Source): You can put this solution on YOUR website!how do you sketch the graph of the inequality. y+x<-6? -------------- You do not directly graph an inequality; you graph the boundary of the inequality which is the equality, y+x=-6 Boundary: y = -x - 6 ----------------------- You graph THIS boundary as a dashed line. Then you shade the half-plane BELOW the boundary because your problem calls for y < -x-6 ----------------- Your graph is the shaded half-plane. ======================================= Cheers, Stan H.
 expressions/180693: 6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? A. 8 B. 10 C. 14 D. 19 E. 21 1 solutions Answer 135426 by stanbon(57307)   on 2009-02-06 21:24:48 (Show Source): You can put this solution on YOUR website!If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? ------------------ NOW DATA: Let Sue be x yrs. old Then Leah is x+6 yrs old And John is x+11 yrs old ------------------------------- Equation: x + x+6 + x+11 = 41 3x + 17 = 41 3x = 24 x = 8 yrs old (Sue's age) =========================== Cheers, Stan H. ============ A. 8 B. 10 C. 14 D. 19 E. 21