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Recent problems solved by 'stanbon'

stanbon answered: 57156 problems
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, >>Next

Graphs/345790: How do I find the equation of the line passing through (2, -3) and (4,0). And then how do I put it into standard form? 1 solutions Answer 247267 by stanbon(57224)   on 2010-09-20 18:00:26 (Show Source): You can put this solution on YOUR website! How do I find the equation of the line passing through (2, -3) and (4,0). And then how do I put it into standard form? ------------------------------- slope = m = (-3-0)/(2-4) = -3/-2 = 3/2 ------------------------------------------ Form: y = mx+b 0 = (3/2)4+b 0 = 6 + b b = -6 ------------------------------- Equation: y = (3/2)x-6 =================== Cheers, Stan H.

Linear_Algebra/345788: Why does the equation 3x+7=-3x+2+6x have no solution? A. The variable cancels out and leaves a false statement. B. The variable cancels out and leaves a true statement. 1 solutions Answer 247264 by stanbon(57224)   on 2010-09-20 17:53:49 (Show Source): You can put this solution on YOUR website! Why does the equation 3x+7=-3x+2+6x have no solution? --- If you assume the "x" has some particular value you get: 6x+7 = 2+6x 7 = 2 ------------------------ A. The variable cancels out and leaves a false statement. --- B. The variable cancels out and leaves a true statement. ---- Solution: A ================ Cheers, Stan H.

absolute-value/345784: 10+(m-6)=7 how do i solve using absolute value? 1 solutions Answer 247262 by stanbon(57224)   on 2010-09-20 17:50:18 (Show Source): You can put this solution on YOUR website! 10+(m-6)=7 how do i solve using absolute value? ---- Why would you want to? (m-6) = -3 m = 3 --------- Cheers, Stan H.

absolute-value/345775: Solve the inequality and express the solution in interval notation. 2|4x|-9 is >or equal to 3 1 solutions Answer 247260 by stanbon(57224)   on 2010-09-20 17:47:10 (Show Source): You can put this solution on YOUR website! Solve the inequality and express the solution in interval notation. 2|4x|-9 is >or equal to 3 ------------------------- 2|4x|-9 >= 3 --- |4x| >= 6 4x <=-6 or 4x >=6 ---- x <=-3/2 or x >= 3/2 ------------------ (-inf,-3/2]U[3/2,+inf) =========================== Cheers, Stan H.

Permutations/345770: I'm trying to figure out how this answer was derived from this problem. I understand how to do the Permutation problems but not the combinatorics C (17, 4) the answer given was 35. 1 solutions Answer 247256 by stanbon(57224)   on 2010-09-20 17:39:16 (Show Source): You can put this solution on YOUR website! I understand how to do the Permutation problems but not the combinatorics C(17, 4) the answer given was 35. -------------------------------------- Formula: C(n,r) = n!/(n-r)!r! -------- C(17,4) = 17!/[13!*4!] = (17*16*16*14)/(1*2*3*4) = 2380 --------------- The answer is definately not 35. =============== Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/345764: find 3 consecutive integers where four times the smallest is seven more than 3 times the largest 1 solutions Answer 247251 by stanbon(57224)   on 2010-09-20 17:33:17 (Show Source): You can put this solution on YOUR website! find 3 consecutive integers where four times the smallest is seven more than 3 times the largest. ---- 1st: x-1 2nd: x 3rd: x+1 ---------- Equation: 4(x-1) = 3(x+1)+7 4x-4 = 3x+1+7 x = 12 ------------- Cheeers, Stan H. =============

Polynomials-and-rational-expressions/345717: Given that a and b are both positive numbers solve 1)x^2+a^2/x^2+b^2>or equal to 0 2) a/x^2<-b 1 solutions Answer 247240 by stanbon(57224)   on 2010-09-20 16:26:44 (Show Source): You can put this solution on YOUR website! Given that a and b are both positive numbers solve 1)x^2+a^2/x^2+b^2 >= 0 ------------- Solve the equality for "x": (x^2+a^2)/(x^2+b^2) = 0 ----- True when x^2+a^2 = 0 Factor in the Complex Number System: (x+ai)(x-ai) = 0 x = +ai or x = -ai ---------------- Not Real Number solutions. ================================ Cheers, Stan H.

test/345718: X / 3=-3 1 solutions Answer 247237 by stanbon(57224)   on 2010-09-20 16:20:25 (Show Source): You can put this solution on YOUR website! X / 3=-3 X = -9 ============= Cheers, Stan H.

Distributive-associative-commutative-properties/345719: what are the properties of these 5+4=4+5 7(a-2)=7a-14 and 5(12)=5(14-2) 1 solutions Answer 247236 by stanbon(57224)   on 2010-09-20 16:19:05 (Show Source): You can put this solution on YOUR website! 5+4=4+5 commutative ---------------------- 7(a-2)=7a-14 distributive ---------------------- and 5(12)=5(14-2) identity =========================== Cheers, stan H.

Average/345714: if a girl has three tests done and the scores are 89, 76 and 82 how can she get her average to be an 80? create an inequality for this problem. solve this inequality. 1 solutions Answer 247235 by stanbon(57224)   on 2010-09-20 16:17:08 (Show Source): You can put this solution on YOUR website! if a girl has three tests done and the scores are 89, 76 and 82 how can she get her average to be an 80? create an inequality for this problem. (89+76+82+x)/4 >= 80 ----------------------------- (247+x) >= 320 x >= 73 ------------------ Cheers, Stan H.

Angles/345712: Two angles are adjacent and form a 120º. The larger is 20º less than three times the smaller. Please help. Thank you. 1 solutions Answer 247234 by stanbon(57224)   on 2010-09-20 16:12:43 (Show Source): You can put this solution on YOUR website! Two angles are adjacent and form a 120º. The larger is 20º less than three times the smaller. -------------- angle: x angle: 3x-20 ----- Equation: x + 3x-20 = 120 --- 4x = 140 x = 35 degrees --- 3x-20 = 105-20 = 85 degrees =============================== Cheers, Stan H.

Square-cubic-other-roots/345711: What is the LCM of 16x2y5z4 and 21xy3z2? 1 solutions Answer 247233 by stanbon(57224)   on 2010-09-20 16:09:14 (Show Source): You can put this solution on YOUR website! What is the LCM of 16x2y5z4 and 21xy3z2? --------------- 16 = 2^4 21 = 3*7 ----- LCM = (21*16)x^2y^5z^4 ----------------------------- Cheers, Stan H. ============

Probability-and-statistics/345509: 3. Roll a fair die twice. Repeat the experiment a total of 50 times. Record the sum of the two rolls in the table below. Value of x, the sum of the two rolls Frequency 1 solutions Answer 247231 by stanbon(57224)   on 2010-09-20 16:04:14 (Show Source): You can put this solution on YOUR website! This is something you have to do for yourself. Cheers, Stan H.

Finance/345649: solve each formula for the giving variable. V= lwh , solve for w 1 solutions Answer 247213 by stanbon(57224)   on 2010-09-20 14:57:26 (Show Source): You can put this solution on YOUR website! V= lwh , solve for w ---- Divide both sides by lh to get: w = V/(lh) =============== Cheers, Stan H.

Rational-functions/345645: Trying to figure steps to following problem: determine whether m = (-4) is a solution to 5m-1 divided by 6 = 3m-2 divided by 4 I did the following but not sure if correct: 5(-4) - 1 / 6 = 3(-4) - 2 / 4 -21 - 1 / 6 = -14 / 4 -21/6 x 3/3 = -14/4 x 2/2 -7/2 = - 7/2 1 solutions Answer 247211 by stanbon(57224)   on 2010-09-20 14:55:47 (Show Source): You can put this solution on YOUR website! determine whether m = (-4) is a solution to 5m-1 divided by 6 = 3m-2 divided by 4 I did the following but not sure if correct: (5m-1)/6 = (3m-2)/4 ---------- (5(-4) - 1)/6 = (3(-4)-2)/4 ------------------------ (-21/6) = (-14/4) -------------------- -7/2 = -7/2 ================ Cheers, Stan H.

Linear-equations/345623: Find the point of intersection of the pair of straight lines. y = x - 3 8x - 3y - 54 = 0 1 solutions Answer 247198 by stanbon(57224)   on 2010-09-20 14:24:06 (Show Source): You can put this solution on YOUR website! Find the point of intersection of the pair of straight lines. y = x - 3 8x - 3y - 54 = 0 ------ Substitute for "y" and solve for "x": 8x -3(x-3)-54 = 0 8x -3x + 9 -54 = 0 5x - 45 = 0 5(x-9) = 0 --- x = 9 ================== Substitute for "x" and solve for "y": y = 9-3 = 6 ---- Intersection: (9,6) ======================== Cheers, Stan H. Cheers,

Inverses/345621: What is the step-by-step process for finding an inverse? 1 solutions Answer 247195 by stanbon(57224)   on 2010-09-20 14:20:17 (Show Source): You can put this solution on YOUR website! What is the step-by-step process for finding an inverse? --- Assuming you want the inverse of a function: 1st: Interchange x and y 2nd: Solve for "y". ========================= Cheers, Stan H.

expressions/345620: 6.1{4}+2{1.5} can you show me the steps on solving this problem thanks 1 solutions Answer 247192 by stanbon(57224)   on 2010-09-20 14:17:58 (Show Source): You can put this solution on YOUR website! 6.1{4}+2{1.5} --- = 24.4 + 3.0 --- = 27.4 ========== Cheers, Stan H. ==========

Finance/345616: Please help!! :c) A 1987 advertisement in the New Yorker solicited offers on a 1967 Mercury Cougar XR7 (Motor Trend's 1967 car of the year) that had been stored undriven in a climate controlled environment for 20 years. . If the original owner paid $4000 for this car in 1967, what price would he have to receive in 1987 to obtain a 10 percent annual return on his investment? 1 solutions Answer 247190 by stanbon(57224)   on 2010-09-20 14:15:51 (Show Source): You can put this solution on YOUR website! A 1987 advertisement in the New Yorker solicited offers on a 1967 Mercury Cougar XR7 (Motor Trend's 1967 car of the year) that had been stored undriven in a climate controlled environment for 20 years. If the original owner paid $4000 for this car in 1967, what price would he have to receive in 1987 to obtain a 10 percent annual return on his investment? --------- If the 10% is compounded yearly the price is as followed. A(10) = 4000(1+(0.10/1))^(10*1) --- A(10) = 4000(1.1)^10 --- A(10) = $10,374.97 ====================== Cheers, Stan H.

Miscellaneous_Word_Problems/345529: For a certain hot-water heater, the increase in heating expenses is directly proportional to increase in water-temperature setting. If heating expenses increase by $24 when the water-temperature setting is increased by 20 degrees Fahrenheit, by how much will heating expenses increase when the water-temperature setting is increased by 15 degrees Fahrenheit? A. $16 B. $18 C. $19 D. $20 E. $21 1 solutions Answer 247189 by stanbon(57224)   on 2010-09-20 14:08:11 (Show Source): You can put this solution on YOUR website! For a certain hot-water heater, the increase in heating expenses is directly proportional to increase in water-temperature setting. --- E = kt ---- If heating expenses increase by $24 when the water-temperature setting is increased by 20 degrees Fahrenheit, --- Find "k": 24 = k*20 k = 6/5 ---- Equation: E = (6/5)t ------------------------- by how much will heating expenses increase when the water-temperature setting is increased by 15 degrees Fahrenheit? E(15) = (6/5)15 E = 18 ======= Cheers, Stan H. A. $16 B. $18 C. $19 D. $20 E. $21

Probability-and-statistics/345519: If I know P(A^B), how do I get P(A^Bcomplement)...where ^ means intersection ....for example P(A) = P(B)_= 1/3 and P(A^B) = to 1/10 What is (a) P(A U Bcomplement) (b) P(B^Acomplement) (c) P(Acomplement U Bcomplement) 1 solutions Answer 247119 by stanbon(57224)   on 2010-09-20 10:18:51 (Show Source): You can put this solution on YOUR website! If I know P(A^B), how do I get P(A^Bcomplement)...where ^ means intersection .... -------------- P(A) + P(A comp) = 1 So, P(A comp) = 1-P(A) -------------------------- P(A^B comp) = 1 - P(A^B) -------------------------- for example P(A) = P(B)_= 1/3 and P(A^B) = to 1/10 What is (a) P(A U Bcomplement) Find P(AUB) P(AUB) = P(A)+P(B)-P(A^B) = 1/3 + 1/3 - 1/10 = (2/3)-(1/10) = (20-3)/30 = 17/30 --- The P(AUB comp) = 13/30 ============================= (b) P(B^Acomplement) = P(B-(A^B)) = P(B)-P(A^B) = P(B)-[P(A)+P(B)-P(AUB)] = P(AUB)-P(A) = (17/30)-(1/3) = 7/30 =============== (c) P(Acomplement U Bcomplement) = 1-P(A^B) = 1-[P(A)+P(B)-P(AUB)] = 1-[1/3 + 1/3 - (17/30)] = 1-[(20/30)-(17/30)] = 1 - 1/10 = 9/10 ================ Cheers, Stan H. ================

Points-lines-and-rays/345526: find the equation for the perpendicular bisector of THE LINE from (0,0) to (2,2) hint: you need to find the midpoint of THE LINE and give me the equation that is perpendicular to THE LINE. 1 solutions Answer 247115 by stanbon(57224)   on 2010-09-20 10:03:14 (Show Source): You can put this solution on YOUR website! find the equation for the perpendicular bisector of THE LINE from (0,0) to (2,2) hint: you need to find the midpoint of THE LINE and give me the equation that is perpendicular to THE LINE ----------------- The midpoint is (1,1). ------ The slope of the line thru (0,0),(2,2) = 1 ----- Slope of the perpendiuclar line must be -1 ------ Find equation of line with slope = -1 passing thru (1,1) Form : y = mx + b 1 = -1(1) = b b = 2 ------ Equation: y = -x+2 ================= Cheers, Stan H.

Probability-and-statistics/345505: Can you just please tell me if I have done this correctly: This is the data Person Wealth Gates (G) 41 Buffett (B) 31 Albrecht (A) 26 Allen (P) 20 Bin (T) 18 Ellison (E) 17 Prepare a sample and sample mean table for a size 4 sample. Thank you for any help you can give me. A,B,G,P 26,31,41,20 29.5 A,B,G,E 26,31,41,17 28.75 A,B,G,T 26,31,41,18 29 A,B,P,E 26,31,20,17 23.5 A,B,P,T 26,31,20,18 23.75 A,B,E,T 26,31,17,18 23 A,G,P,E 26,41,20,17 26 A,G,P,T 26,41,20,18 26.25 A,G,E,T 26,41,17,18 25.5 A,P,E,T 26,20,17,18 20.25 B,G,P,E 31,41,20,17 27.25 B,G,P,T 31,41,20,18 27.5 B,G,E,T 31,41,17,18 26.75 B,P,E,T 31,20,17,18 21.5 G,P,E,T 41,20,17,18 24 1 solutions Answer 247112 by stanbon(57224)   on 2010-09-20 09:59:29 (Show Source): You can put this solution on YOUR website! Correct Cheers, Stan H.

Angles/345500: Can someone please help me with this question. Two angles are complementary if the sum of their measures is 90 degrees. Find two complementary angles such that one of the angles is 51 degrees less than 2 times the other angle. (Round to two decimal places if necessary) ____________degrees the smaller complementary angle ____________degrees the larger complementary angle Thank you SO much. 1 solutions Answer 247088 by stanbon(57224)   on 2010-09-20 08:45:38 (Show Source): You can put this solution on YOUR website! Find two complementary angles such that one of the angles is 51 degrees less than 2 times the other angle. ------ angle: x complementary angle: 90-x ------------------ Equation: x = 2(90-x)-51 x = 180-2x-51 3x = 129 x = 43 degrees 90-x = 47 ============== Cheers, Stan H.

test/345502: How do you factor polynomial 16x^2+49Y^2 1 solutions Answer 247086 by stanbon(57224)   on 2010-09-20 08:40:31 (Show Source): You can put this solution on YOUR website! factor polynomial 16x^2+49Y^2 In the Real Number System it is not factorable. --- In the Complex Number System it factors as follows: --- = (4x+7yi)(4x-7yi) ====== Cheers, Stan H.

Exponents-negative-and-fractional/345486: Hello! Would love it if someone could be so nice as to help me with this one.. 3x-(x-3)/4=1/2+(2x-5)/6 with thanks, Blob :) 1 solutions Answer 247085 by stanbon(57224)   on 2010-09-20 08:38:23 (Show Source): You can put this solution on YOUR website! 3x-(x-3)/4=1/2+(2x-5)/6 ---- Multiply thru by 12 to get rid of the denominators. ----- 36x-3(x-3) = 6 + 2(2x-5) 33x+9 = 6+4x-10 29x = -13 x = -13/29 ================== Cheers, Stan H.

Numbers_Word_Problems/345495: the sum of two numbers is 29. Find the two numbers if the larger is 11 more than twice the smaller. 1 solutions Answer 247084 by stanbon(57224)   on 2010-09-20 08:26:42 (Show Source): You can put this solution on YOUR website! the sum of two numbers is 29. Find the two numbers if the larger is 11 more than twice the smaller. ---------------- Equations: x + y = 29 x = 2y+11 ------------- Substitute for "x" and solve for "y": 2y+11+y = 29 ------ 3y = 18 y = 6 ---- x = 2y+1 = 13 ================ Cheers, Stan H.

Probability-and-statistics/345069: from past experience, the pass rate of students has been 70%. if 8 students are randomly selected. a) what is the probability at least half will fail? b) what is the standard deviation of the distribution? c)what is the probability that no student will fail? d0 state the name given to the probability distribution being described in the question and state one of its characteristics? 1 solutions Answer 247078 by stanbon(57224)   on 2010-09-20 07:30:27 (Show Source): You can put this solution on YOUR website! from past experience, the pass rate of students has been 70%. if 8 students are randomly selected. ----- Binomial Problem with n = 8 and p = 0.7 -------- a) what is the probability at least half will fail? P(4<= x <=8) = 1-binomcdf(8,0.7,3) = 0.9420 ------------------------------------------------------- b) what is the standard deviation of the distribution? std = sqrt(npq) = sqrt(8*0.7*0.3) = 1.2961 ------------------------------------------------------- c)what is the probability that no student will fail? P(x = 0) = 0.7^8 = 0.0576 ------------------------------------------------------- d) state the name given to the probability distribution being described in the question and state one of its characteristics? binomial; n independent trials. =========================================== Cheers, Stan H.

Probability-and-statistics/345089: 1. For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. This should be in the form of a table similar to Table 5-1 on Page 195 in the textbook. 1 solutions Answer 247075 by stanbon(57224)   on 2010-09-20 07:23:48 (Show Source): You can put this solution on YOUR website! duplicate

Probability-and-statistics/345173: In a deck of cards, five are pulled at random. What is the probabilty that exactly three of them will be spades? 1 solutions Answer 247074 by stanbon(57224)   on 2010-09-20 07:22:46 (Show Source): You can put this solution on YOUR website! In a deck of cards, five are pulled at random. What is the probabilty that exactly three of them will be spades? ----- # of ways to select 3 spades: 13C3 # of ways to select 2 non-spades: 39C2 ----- # of ways to select 5 cards randomly: 52C5 ================ P(3spades and 2 other) = [13C3*39C2)/52C5 = 0.0815 ================================ Cheers, Stan H.

Probability-and-statistics/345412: 1. For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. 1 solutions Answer 247071 by stanbon(57224)   on 2010-09-20 07:17:37 (Show Source): You can put this solution on YOUR website! For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. ---- Draw the sample space. Draw a 6x6 square. Put 1,2,3,4,5,6 along the left edge and along the top. Put the sum of the row and the column numbers for each box in the square. You should see something like the following: 2,3,4,5,6,7 3,4,5,6,7,8 4,5,6,7,8,9 .... .... 7,8,9,10,11,12 ========================= Note that there are 36 sum entries P(2) = 1/36 P(3) = 2/36 P(4) = 3/36 .... P(11) = 2/36 P(12) = 1/36 =================== That is the probability distribution. ========================================== Cheers, Stan H. =============