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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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 Linear-equations/84998: Write the following phrase using symbols. Use the variable x to represent the number. 7 less than a number1 solutions Answer 61250 by stanbon(57347)   on 2007-06-11 13:07:22 (Show Source): You can put this solution on YOUR website!Use the variable x to represent the number. 7 less than a number -------------- Let the number be "x". Phrase: x-7 ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/85003: Please help me with this question: If you earned an average of \$25,000 over your working life and you retire after 2005 at age 62, 63,or 64, then your annual SS benefit will be \$7,00, \$7500, or \$8,000 respectively. Find the linear equation that gives the annual benefit "b" in terms of age "a"1 solutions Answer 61249 by stanbon(57347)   on 2007-06-11 13:05:35 (Show Source): You can put this solution on YOUR website!If you earned an average of \$25,000 over your working life and you retire after 2005 at age 62, 63,or 64, then your annual SS benefit will be \$7,00, \$7500, or \$8,000 respectively. Find the linear equation that gives the annual benefit "b" ---------------- Pick two of the "points" and find the equation of the line thru them: (63,7500) (64,8000) slope = (8000-7500/(64-63) = 500 ------------------- EQUATION: benefit = 500(age) + k 8000 = 500(64) + k k= 8000 - 32000 k= -24000 EQUATION: Benefit = 500(age) - 24000 ================ Cheers, Stan H.
 Linear-equations/85004: This question is from textbook solve for y. write the answer in the form y=mx+b, where m and b are real numbers. -x/3 + y/2 = 1 1 solutions Answer 61248 by stanbon(57347)   on 2007-06-11 12:57:42 (Show Source): You can put this solution on YOUR website!solve for y. write the answer in the form y=mx+b, where m and b are real numbers. -x/3 + y/2 = 1 ------------- Multiply thru by 6 to get: -2x + 3y = 6 solve for y: y= (1/3)(2x+6) y= (2/3)x + 2 ============== Cheers, Stan H.
 Linear-systems/85008: The sum of two numbers is 84. The second is 9 more than 4 times the first. What are the two numbers?1 solutions Answer 61247 by stanbon(57347)   on 2007-06-11 12:55:13 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 84. The second is 9 more than 4 times the first. What are the two numbers? -------------- Let one of the numbers be "x". The other one must be "84-x" ------------------- EQUATION: 2nd is 4*1st + 9 84-x = 4*x+9 5x= 75 x=15 (1st number) 84-x=69 (2nd number) -------------- Cheers, Stan H.
 Graphs/85016: 1. Evaluate F(x)=3x^5 -5x^3 +2x^2 +6 for: 2x 2. Find the equation for the following line: A line with a slope of zero that passes through (2,-1) 3. Find the equation for the following line: A line with an undefined slope that passes through (-1,2) 1 solutions Answer 61246 by stanbon(57347)   on 2007-06-11 12:51:27 (Show Source): You can put this solution on YOUR website!1. Evaluate F(x)=3x^5 -5x^3 +2x^2 +6 for: 2x If you mean F(2x) you get: F(2x) = 2(2x)^5 - 5(2x)^3 + 2(2x)^2 + 6 I'll let you work that out. -------------------------------- 2. Find the equation for the following line: A line with a slope of zero that passes through (2,-1) If slope is zero the equation has the form y=k But the point goes thru a point where y=-1 So the equation is y=-1 ------------------------ 3. Find the equation for the following line: A line with an undefined slope that passes through (-1,2) If the slope is undefind the equation has the form x=k But the point goes thru a point where x=1- So the equation is x=-1 ================ Cheers, Stan H.
 Exponents-negative-and-fractional/85014: This question is from textbook algebra structure and method How do you solve this problem? x-2/2-x+2/4=1/21 solutions Answer 61245 by stanbon(57347)   on 2007-06-11 12:46:44 (Show Source): You can put this solution on YOUR website!How do you solve this problem? x-2/2-x+2/4=1/2 ---------------- (x-2)/2 - (x+2)/4 = 1/2 Multiply thru by 4 to get rid of the denominators: 2(x-2) - (x+4) = 2 Simplify: 2x-4-x-4 = 2 x-8 = 2 x=10 ============= Cheers, Stan H.
 absolute-value/85021: 15 x y - 15 x 6 =1 solutions Answer 61244 by stanbon(57347)   on 2007-06-11 12:43:46 (Show Source): You can put this solution on YOUR website!15 x y - 15 x 6 = 15y - 30 OR =15(y-2) ================ Cheers, Stan H.
 Graphs/85020: Solve the following system of linear inequalities by graphing. 3x – y < 2 x + y > 2 1 solutions Answer 61243 by stanbon(57347)   on 2007-06-11 12:41:57 (Show Source): You can put this solution on YOUR website!Solve the following system of linear inequalities by graphing. 3x – y < 2 x + y > 2 --------------------------- Solve each for y as follows: y>3x-2 y>-x+2 ------------------ Graph the boundary lines for each of the INEQUALITIES: (Graph these as dashed lines because they are not part of the solution set.) ---------------- Pick a test point like (0,0) Test that point in the INEQUALITY statements, as follows: For y>3x-2 you get 0>0-2; this is false so the halfplane graph of y>3x-2 is on the Other side of the EQUALITY line. The halfplane you should shade is ABOVE the green line. ---------------- For y>-x+2 you get 0>0+2; this is true so the halfplane graph of y>-x+2 is on the same side of the boundary line as the test point. The halfplane you should shade is BELOW the black line ---------------- Darken the INTERSECTION of the two halfplanes. That is the solution set for the system of INEQUALITIES. ================ Cheers, Stan H.
 Quadratic_Equations/85017: Expalin revelance and application of logarithmic function in real life situations?1 solutions Answer 61242 by stanbon(57347)   on 2007-06-11 12:32:09 (Show Source): You can put this solution on YOUR website!The following site will show you examples of applications of logs and exponential functions. cheers, Stan H. http://www.sosmath.com/algebra/logs/log5/log5.html
 Linear-equations/84986: Simplify: –(–3)1 solutions Answer 61231 by stanbon(57347)   on 2007-06-11 09:31:24 (Show Source): You can put this solution on YOUR website!Simplify: –(–3) On a number line -(-3) means "the opposite of 3 to the left" This is equivalent to "three to the right". So, -(=3) = +3 ============ Cheers, Stan H.
 Expressions-with-variables/84984: Investment You plan to invest \$25,000 in two funds paying 3% and 4 1/2% simple interest. YOur goal is to obtain a total annual interest income of \$1,000 from the investments. What is the smallest amount you can invest in the 4 1/2 % fund in order to meet your objective? The answer is \$16,666.67 I want someone else to work this one to see if I worked it right.....thanks!1 solutions Answer 61230 by stanbon(57347)   on 2007-06-11 09:28:42 (Show Source): You can put this solution on YOUR website!You plan to invest \$25,000 in two funds paying 3% and 4 1/2% simple interest. YOur goal is to obtain a total annual interest income of \$1,000 from the investments. What is the smallest amount you can invest in the 4 1/2 % fund in order to meet your objective? ----------- A(t) = P(1+rt) Let x be amount invested at 3%; interest = 0.03x Amount invested at 4 1/2% is (25000-x); interest on this is 0.045(25000-x) = 1125-0.045x ------------ EQUATION: interest + interest = 1000 0.03x + 1125-0.045x = 1000 -0.015x = -125 x = \$83333.33 (amt invested at 3%) 25000-x = \$16,666.67 (amt invested at 4 1/2%) ============= Cheers, Stan H.
 Probability-and-statistics/84799: This question is from textbook Elementary Statistics in social research IQ scores are normally distributed with a mean u=100 and a standard deviation o=15. Based on this distribution, determine A. the percentage IQ scores between 100 and 120. B. the probability of selecting a person at random having an IQ between 100 and 120 C. the percentage of IQ scores between 88 and 100. D. the probability of selecting a person at random having and IQ between 88 and 100. E. the percentage of IQ scores that 110 or above. F. the probability of selecting a person at random having an IQ of 110 or above.1 solutions Answer 61229 by stanbon(57347)   on 2007-06-11 09:20:05 (Show Source): You can put this solution on YOUR website!IQ scores are normally distributed with a mean u=100 and a standard deviation o=15. Based on this distribution, determine A. the percentage IQ scores between 100 and 120. The z-score of 100 is zero; The z-score of 120 is (120-100)/15 = 1.3333 P(0 ------------------ B. the probability of selecting a person at random having an IQ between 100 and 120 Prob = 0.4088 --------------------- C. the percentage of IQ scores between 88 and 100. z-score of 88 = (88-100)/15 = -0.8 z-score of 100 = 0 P(-0.8 ---------------- D. the probability of selecting a person at random having and IQ between 88 and 100. Same answer as C. ----------------------- E. the percentage of IQ scores that 110 or above. z-score of 110 is (110-100)/15 = 0.666667 P(z>0.6666667) = 0.2525 = 25.25% ---------------- F. the probability of selecting a person at random having an IQ of 110 or above. Same as E. ================== Cheers, Stan H.
 Probability-and-statistics/84936: This question is from textbook Algebra 2 Lisa has 9 rings in her jewlery box. Five are gold and 4 are silver. if she randomly selects 3 rings to wear to a party, find each probability: 13.P(2 silver or 2 gold) 14.P(all gold or all silver)1 solutions Answer 61216 by stanbon(57347)   on 2007-06-10 22:39:13 (Show Source): You can put this solution on YOUR website!Lisa has 9 rings in her jewlery box. Five are gold and 4 are silver. if she randomly selects 3 rings to wear to a party, find each probability: 13.P(2 silver or 2 gold) = P(2 silver) + P(2 gold) =(3C2)(4/9)^2(5/9) + 3C2(5/9)^2(4/9) = 3*0.10974 + 3*013717 =0.74074 =============== 14.P(all gold or all silver) P(all gold) + P(all silver) =3C3(5/9)^3 + 3C3(4/9)^3 = 0.17147 + 0.08779 = 0.25926... ======= Cheers, Stan H.
 Trigonometry-basics/84939: Greetings, My question is: The amount A in an account after t years from an initial principle P invested at an annual rate r compounded continuously is given by A = Pert where r is expressed as a decimal. How many years will it take an initial investment of \$1,000 to grow to \$1,700 at the rate of 4.42% compounded continuously? 1 solutions Answer 61214 by stanbon(57347)   on 2007-06-10 22:23:52 (Show Source): You can put this solution on YOUR website!The amount A in an account after t years from an initial principle P invested at an annual rate r compounded continuously is given by A = Pert where r is expressed as a decimal. How many years will it take an initial investment of \$1,000 to grow to \$1,700 at the rate of 4.42% compounded continuously? ------------ A=Pe^(rt) 1700 = 1000e^(0.0442t) 1.7 = e^(0.0442t) Take the natural log of both sides to get: 0.0442t= ln1.7 t = [ln1.7]/0.0442 t = 12.005 years ============ Cheers, Stan H.
 expressions/84946: Tutor can you tell me if I have simplified this expression,writing the result using a positive exponent? thank you Problem (z^5x^5)-3 answer -3 + z^5x^51 solutions Answer 61213 by stanbon(57347)   on 2007-06-10 22:16:37 (Show Source): You can put this solution on YOUR website!Problem (z^5x^5)-3 -------------- The negative sign means "invert". The "3" means cube. ----------------- Cubing 1st you get: z^15x^15 ------------- Inverting you get: 1/(z^15x^15) ================== Cheers, Stan H.
 Linear-equations/84945: IS anyone able to help me? Don't have any idea what do. Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments. Answer: Show work in this space. c) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments. d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than? 1 solutions Answer 61210 by stanbon(57347)   on 2007-06-10 22:12:04 (Show Source): You can put this solution on YOUR website!IS anyone able to help me? Don't have any idea what do. Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: a) What is r, the ratio between 2 consecutive terms? To find "r" divide any term by the term in front of it. Your Problem: 1/9 / 1/3 = 3/9 = 1/3 ----------------- b) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments. Answer: Show work in this space. Formula: S(n) = a(1)[r^(n+1)-1]/[r-1] Your Problem: S(10) = 1 [(1/3)^11 - 1/[(1/3)-1] = [-.999999]/[-2/3] = 1.4999999 ------------------------- c) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments. S(12) = 1[(1/3)^13 - 1]/ [(1/3) - 1] = -0.99999999 / (-2/3) = 1.4999999999 ------------- d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than? Smaller than 1.5 ================ Cheers, Stan H.
 Proportions/84943: This question is from textbook MAthematics exploring your world Will you please hel pme with this problem? I tried really hard on it ans it was counted wrong. Please help me find out what I did wrong and where I messed up! Janine has 4 blouses, and 5 scarves that match. choose one clouse and one scarf I put the answer as 10 combinations total. but I dont know why it was counted wrong!1 solutions Answer 61205 by stanbon(57347)   on 2007-06-10 21:59:17 (Show Source): You can put this solution on YOUR website!Janine has 4 blouses, and 5 scarves that match. choose one clouse and one scarf ----------- The number of outfits is 4*5 = 20 ================== Cheers, Stan H.
 Probability-and-statistics/84937: This question is from textbook Elementary Statistics in Social Statistics Suppose that you purchase a lottery ticket that contains two numbers and a letter, such as 3 7 9 Alright this is what i have so far for #15 A. What is the probability that you match the first? 37P 3P7 73P 7P3 P73 P37 18 chances So it has two chances of being first. P= number of times the out come or events can occur 2 divided by 18=.11 B. What is the probability that you match the second digit? Same thing 18 chances 2 divided by 18=.11 C. What is the probability that you do not match the first digit? 17 divided by 18 =.88 or rounded .89 D. What is the probability that you match both the first and the second digits? .89 is the answer but i don't know how to get it. please show me the formula. E.What is the probability that you match the letter? 1 chance divided by 26 letters in the alphabet = .038 or rounded .04 F. What is the probability of a perfect match (both the digits and the letter)? not sure how to get this one either. please show me the work and the formula 1 solutions Answer 61204 by stanbon(57347)   on 2007-06-10 21:54:46 (Show Source): You can put this solution on YOUR website!Prob of matching 1st digit; 1/10 Prob of matching 2nd digit: 1/10 Prob of matching letter: 1/26 Prob of matching two digits: 1/10 * 1/10 = 1/100 Prob of matching two digits and the letter: 1/100 * 1/26 = 1/2600 =========== Each event is independent so you multiply the probabilities of each of the pieces to get the probility of the whole pattern. --------- Cheers, Stan H.
 Rational-functions/84921: This question is from textbook I have tried to make sense of this one and it bugs me and is even harder with no graphing calculator.:-( Page 795: Problem # 56 solve the inequality and graph the solution set on a real number line. A model rocket is launched from ground level. The function: S(t) = -16t^2 +48t Models the rocket’s height above the ground, s(t) in feet, t seconds after it was launched. During which period will the rocket’s height exceed 32 feet? 1 solutions Answer 61195 by stanbon(57347)   on 2007-06-10 20:35:19 (Show Source): You can put this solution on YOUR website!The function: S(t) = -16t^2 +48t Models the rocket’s height above the ground, s(t) in feet, t seconds after it was launched. During which period will the rocket’s height exceed 32 feet? ------------ s(t) is the height of the rocket above the ground. Let s(t) = 32 feet and solve for time = t. -------- EQUATION: -16t^2+48t=32 t^2-3t+2=0 (t-2)(t-1)=0 t=1 or t=2 the rocket is at or above 32 ft. between t=1 and t=2 seconds 1 < t <2 ----------- Cheers, Stan H.
 Rational-functions/84118: When the discriminant is positive, or b2 - 4ac > 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. When the discriminant equals zero, or b2 - 4ac = 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. When the discriminant is negative, or b2 - 4ac < 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. 1 solutions Answer 60568 by stanbon(57347)   on 2007-06-01 22:34:27 (Show Source): You can put this solution on YOUR website!When the discriminant is positive, or b2 - 4ac > 0, expect 2 unequal root(s). Use cardinal numbers (0,1,2,...) to fill in the blank --------------------. When the discriminant equals zero, or b2 - 4ac = 0, expect 2 equal root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. --------------- When the discriminant is negative, or b2 - 4ac < 0, expect 2 complex root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. ====================== Comment: These are ambiguous questions. The answers could be 2,1,0 also; it depends on what you accept as a root. In general a quadratic always has 2 roots. They may be Real and unequal, Real and equal, or Complex and unequal. ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/84128: I need your help 5x^2+2x-4,x^2-2x-3, and 2x^2-4x-3 The comma is throwing me off. this is not in our exercise for this "adding" and using the vertical method.1 solutions Answer 60566 by stanbon(57347)   on 2007-06-01 22:27:44 (Show Source): You can put this solution on YOUR website!5x^2+2x-4,x^2-2x-3, and 2x^2-4x-3 ------------------- This is like telling you to add 2,4, and 5 -------------- Add the x^2 terms to get: 8x^2 Add the x terms to get: -4x Add the numbers to get: -10 ----------- Answer: 8x^2-4x-10 ============ Cheers, Stan H.
 Graphs/84133: x -2 -1 0 1 2 y .25 .5 1 2 4 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. I understand that it is a line graph. I just can't figure out what the domain and range is for this graph. I someone help me? 1 solutions Answer 60562 by stanbon(57347)   on 2007-06-01 21:52:47 (Show Source): You can put this solution on YOUR website!x -2 -1 0 1 2 y .25 .5 1 2 4 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. I understand that it is a line graph. I just can't figure out what the domain and range is for this graph. I someone help me? ---------- It is not a line graph. The equation is y=2^x ; it is exponential because the variable is in the exponent. ------- Domain: x can take any value; Domain is All Real Numbers. Range: Since 2^x is always positive, Range is all Real #'s > 0. ---------- The Domain that is shown is -2,-1,0,1,2 The Range that is shown is 0.25,0.5,0,2,4 =============== Cheers, Stan H.
 Sequences-and-series/84134: 1. Use the geometric sequence of numbers 1,2,4,8,...to find the following: a. What is r, the ratio between 2 consecutive terms? show work ***r=2/1=2 b. Using the formula for the nth term of a geometric sequence, what is the 24th term? show work ***a n below=a, r 2-1 above answer 615 c. Using the formula for the sum of a geometic series, what is the sum of the first 10 terms? show work ****1,023.00**** Thank you for your help 1 solutions Answer 60558 by stanbon(57347)   on 2007-06-01 21:46:04 (Show Source): You can put this solution on YOUR website!Use the geometric sequence of numbers 1,2,4,8,...to find the following: a. What is r, the ratio between 2 consecutive terms? show work ***r=2/1=2 TRUE ------------------ b. Using the formula for the nth term of a geometric sequence, what is the 24th term? show work a(24) = a(1)*r^(24-1) a(24) = 1*2^23 = 8,388,608 =============== c. Using the formula for the sum of a geometic series, what is the sum of the first 10 terms? S(n) = a(1)[r^(n+1)-1]/[r-1] S(10) = 1 [2^11 -1]/[2-1] S(10) = 2047 =============== Cheers, Stan H.
 Travel_Word_Problems/84101: An object is projected directly upward from te ground. After t secconds. the distance (s) from the ground is given by the equation: s=144t- 16t to the 2nd power. After how many seconds will the object reach 324 feet above the ground?1 solutions Answer 60545 by stanbon(57347)   on 2007-06-01 20:30:30 (Show Source): You can put this solution on YOUR website!An object is projected directly upward from the ground. After t secconds. the distance (s) from the ground is given by the equation: s=144t- 16t^2 . After how many seconds will the object reach 324 feet above the ground? --------- s is the distance above the ground; so let s = 324 and solve for t. -------- -16t^2+144t = 324 16t^2-144t+324 = 0 4(4t^2-36t+81) = 0 (2t-9)^2 = 0 t = 9/2 or 4.5 seconds ============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/84105: this is my problem: let f(x)=5/x^2 and g(x)=6x=1 now it says to find (f 0 g)(x) and to find the domain of these my first instinct is to multiply the two equations together and the domain is the x value of the answer, is this the correct procedure? if it isnt will someone please lay out the steps for solving it for me1 solutions Answer 60544 by stanbon(57347)   on 2007-06-01 20:24:38 (Show Source): You can put this solution on YOUR website!let f(x)=5/x^2 and g(x)=6x+1 now it says to find (f 0 g)(x) and to find the domain of these -------------- (fog)(x) means f[g(x)] = f[6x+1] = 5/(6x+1)^2 ==================== Domain: Since 6x+1 is in the denominator and since the denominator cannot be zero, 6x+1 cannot be 0 So 6x cannot be -1 And finally, x cannot be -1/6 ------ Domain of (fog)(x) is all Real Numbers except x=-1/6 =============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/84106: i need to find the inverse of these relations: (-3,6),(2,1),(0,-7),(-8,-1) the book said for me to take the first two sets of equations and interchange them, what exactly does that mean?1 solutions Answer 60543 by stanbon(57347)   on 2007-06-01 20:15:09 (Show Source): You can put this solution on YOUR website!find the inverse of these relations: (-3,6),(2,1),(0,-7),(-8,-1) -------- All you need to do is interchange the x and the y in each number-pair. ================ You get: (6,-3), (1,2), (-7,0), (-1,-8) ================ Cheers, Stan H.
 Rational-functions/84121: How many different two-digit numbers can be formed using the digits 1, 3, 4, and 5. Repetition of digits is allowed. How many 7-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is allowed? 1 solutions Answer 60542 by stanbon(57347)   on 2007-06-01 20:10:14 (Show Source): You can put this solution on YOUR website!How many different two-digit numbers can be formed using the digits 1, 3, 4, and 5. Repetition of digits is allowed. ------ 4*4 = 16 two-digit numbers ================= How many 7-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is allowed? ------- ways to choose the first digit = 9 ways to choose remaining 6 digits = 10^6 ------- Total number of 7-digit phone numbers = 9*10^6 = 9 million ============= Cheers, Stan H.
 Rational-functions/84119: How many ways can you select pants, a shirt, and shoes if you have 5 pants, 7 shirts, and 3 pairs of shoes to choose from? Use a tree diagram to answer the question: How many ways can you select a lunch combo if you have 6 sandwich choices, 3 side choices, and 4 choices for drinks? A lunch combo consists of 1 sandwich, 1 side item, and 1 drink. 1 solutions Answer 60540 by stanbon(57347)   on 2007-06-01 20:06:42 (Show Source): You can put this solution on YOUR website!How many ways can you select pants, a shirt, and shoes if you have 5 pants, 7 shirts, and 3 pairs of shoes to choose from? # of ways = 5*7*3 = 105 ---------- Use a tree diagram to answer the question: How many ways can you select a lunch combo if you have 6 sandwich choices, 3 side choices, and 4 choices for drinks? A lunch combo consists of 1 sandwich, 1 side item, and 1 drink. 6*3*4 = 72 selections Comment: There will be 72 branches on your tree. ================ Cheers, Stan H.
 Rational-functions/84122: How many ways can you arrange the letters in the word SMILE if the first letter must be an M? Repetition of letters is not allowed, since we only have these 5 letters to arrange. 1 solutions Answer 60538 by stanbon(57347)   on 2007-06-01 20:03:04 (Show Source): You can put this solution on YOUR website!How many ways can you arrange the letters in the word SMILE if the first letter must be an M? Repetition of letters is not allowed, since we only have these 5 letters to arrange. ------------ One way to choose the 1st letter. --------- 4! = 24 ways to arrange the last four letters. ----------- Total arrangements = 1*24 = 24 ================ Cheers, Stan H.
 Functions/84123: State the inverse for the function: g(x) = (7/3)x + 2 I've never done a problem like this before and don't know where to start, I'd like to see the steps and the answer so I can understand what to do. Thank you!1 solutions Answer 60537 by stanbon(57347)   on 2007-06-01 20:00:34 (Show Source): You can put this solution on YOUR website! g(x) = (7/3)x + 2 --------------- 1st: Interchange x and y to get: x = (7/3)y + 2 --------- 2nd: Solve for y: x-2 = (7/3)y y = (3/7)(x-2) --------- That is the inverse. Cheers, Stan H.
 Sequences-and-series/84077: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.1 solutions Answer 60533 by stanbon(57347)   on 2007-06-01 16:39:52 (Show Source): You can put this solution on YOUR website! Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals. ------------ S(10) = a(1)[(r^(11)-1)/(r-1)] Can't tell what this leads to as you gave no series. Cheers, San H.