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Recent problems solved by 'stanbon'

stanbon answered: 57322 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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Geometry_Word_Problems/336792: If an object is propelled upward from ground level with an intial velocity of 64 ft. per sec, its height h in feet t seconds later is: h=-16t^2 = 64t (a) After how many seconds is the height 48 ft? (b) The object reaches its maximum height 2 sec after it is propelled. What is this maximum height? (c) After how many seconds does the object hit the ground? I have read all of the examples that they give me in my math book, but i still have a hard time trying to understand these problems. 1 solutions Answer 241414 by stanbon(57395)   on 2010-08-30 17:26:00 (Show Source): You can put this solution on YOUR website! If an object is propelled upward from ground level with an intial velocity of 64 ft. per sec, its height h in feet t seconds later is: h=-16t^2 + 64t (a) After how many seconds is the height 48 ft? Let h=48 and solve for "t": -16t^2+64t-48 = 0 -16(t^2-4t+3) = 0 (t-3)(t-1) = - t= 1 sec or t = 3 sec --------- Ans: time = 1 sec on the way up and time = 3 sec on the way down. ===================================================================== (b) The object reaches its maximum height 2 sec after it is propelled. What is this maximum height? f(x) = -16t^2+64t f(2) = -16(4)+64(2) = 64 ft. -------------------------------------- (c) After how many seconds does the object hit the ground? Let h = 0 and solve for "t": -16t^2+64t = 0 -16t(t-4) = 0 t = 0 or t = 4 seconds t = 0 seconds refers to the time at which the object is launched. t = 4 seconds refers to the time at which the object is back on the ground. ====================== Cheers, Stan H.

Probability-and-statistics/336667: Each day, two out of the three teams in a class are randomly selected to participate in a MATHCOUNTS trial competition. What is the probability that Team A is selected on at least two of the next three days? Express your answer as a common fraction. 1 solutions Answer 241386 by stanbon(57395)   on 2010-08-30 16:21:59 (Show Source): You can put this solution on YOUR website! Each day, two out of the three teams in a class are randomly selected to participate in a MATHCOUNTS trial competition. What is the probability that Team A is selected on at least two of the next three days? Express your answer as a common fraction. -------------------- P(A is selected on a particular day) = 1-P(A is not selected) = 1-{[2C2]/[3C2]} = 1 - 1/3 = 2/3 ---- Then, p(2<= x <=3) = 1- binomcdf(3,2/3,1) = 0.7407 = 20/27 ============================================================== cheers, Stan H.

Probability-and-statistics/336692: You are given the following information, find the Z-statistic: (95% level of confidence) based on the Z-test Xbar = 980 U = 1000 Sample stdev = 50 N = 36 What is the underlying difference between the T-test and the Z-test? 1 solutions Answer 241384 by stanbon(57395)   on 2010-08-30 16:09:51 (Show Source): You can put this solution on YOUR website! You are given the following information, find the Z-statistic: (95% level of confidence) based on the Z-test Xbar = 980 U = 1000 Sample stdev = 50 N = 36 ------------ z(980) = (980-1000)/50 = -2/5 -------------------------------------- What is the underlying difference between the T-test and the Z-test? In general, the T-test values change depending on sample size. --------------------- Cheers, Stan H.

Probability-and-statistics/336693: 8. The average salary of graduates entering the actuarial field is reported to be $40,000. You sample 20 graduates and find the average salary to be $43,228 with a standard deviation of $4,000. At a 95% level of confidence is the statement regarding the average salary of $40K an accurate statement? (T-test) 1 solutions Answer 241380 by stanbon(57395)   on 2010-08-30 16:05:43 (Show Source): You can put this solution on YOUR website! The average salary of graduates entering the actuarial field is reported to be $40,000. You sample 20 graduates and find the average salary to be $43,228 with a standard deviation of $4,000. At a 95% level of confidence is the statement regarding the average salary of $40K an accurate statement? (T-test) ----------------- Ho: u = 40000 Ha: u is not equal to 40000 ------------------- CV for 2-tail test with df=19 and alpha = 0.95: +/-invT(0.025,19)= +/-2.0930 ---------- TS: t(43,228) = (43228-40000)/[4000/sqrt(20)] = 3.6090 ----- Since the TS is in the reject interval, reject Ho. ============================== Cheers, Stan H.

Probability-and-statistics/336698: Write the H1 and Ha for an individual who states that Policemen are stronger than firemen. 1 solutions Answer 241376 by stanbon(57395)   on 2010-08-30 15:57:57 (Show Source): You can put this solution on YOUR website! Write the H1 and Ha for an individual who states that Policemen are stronger than firemen. --------- Ho: policemen-firemen = 0 Ha: policemen-firement > 0 ============ Cheers, Stan H.

Probability-and-statistics/336702: What is the Z-critical at the 95% level of confidence (AKA the .05 level of significance)? 1 solutions Answer 241375 by stanbon(57395)   on 2010-08-30 15:55:49 (Show Source): You can put this solution on YOUR website! What is the Z-critical at the 95% level of confidence (AKA the .05 level of significance)? --- If the test is two-tail the CV is +/-1.96 ----- If the test is left-tail the CV is invNorm(0.05) = 1.645 ----- If the test is right-tail the CV is invNorm(0.95) = -1.645 =============================== Cheers, Stan H. ========

Surface-area/336584: how many yards there in 1260 inches 1 solutions Answer 241229 by stanbon(57395)   on 2010-08-30 08:47:30 (Show Source): You can put this solution on YOUR website! how many yards there in 1260 inches ------ Unit converter for inches to yds is [1 yd/36 in] ================ Then 1260 in (1yd/36 in) = 1260/36 = 35 yds. =================== Cheers, Stan H.

Graphs/336585: please help. what is the area between the two curves y=-4x+3 and y=x^2 +6. could you be kind enough to show working. thank you. 1 solutions Answer 241228 by stanbon(57395)   on 2010-08-30 08:44:07 (Show Source): You can put this solution on YOUR website! Sorry; I failed to notice that one of your curves was a quadratic. Cheers, Stan H.

Travel_Word_Problems/336586: a motorbike can cover 4km in 30 miutes. what distance can it cover in 5 hours. 1 solutions Answer 241226 by stanbon(57395)   on 2010-08-30 08:42:02 (Show Source): You can put this solution on YOUR website! A motorbike can cover 4km in 30 minutes. What distance can it cover in 5 hours. ----------- Use a Proportion: x km/5 hr = 4km/(1/2)hr ---- x/5 = 8/1 x = 40 km ============== Cheers, Stan H.

Distributive-associative-commutative-properties/336588: how do i change 5*20+5*3 into an indicated product? 1 solutions Answer 241225 by stanbon(57395)   on 2010-08-30 08:38:19 (Show Source): You can put this solution on YOUR website! change 5*20+5*3 into an indicated product? --- Probably you should factor out the "5": 5(20+3) =========== Cheers, Stan H.

Miscellaneous_Word_Problems/336587: Two cities n miles apart are located s inches apart on a certain map that is drawn to scale. What is the distance, in inches, on the map between two cities that are n + 1 miles apart? (A) n/s (B) (n+1)/s (C) s/(n+1) (D) (s(n+1))/n (E) n/ (s(n+1)) 1 solutions Answer 241222 by stanbon(57395)   on 2010-08-30 08:34:15 (Show Source): You can put this solution on YOUR website! Two cities n miles apart are located s inches apart on a certain map that is drawn to scale. What is the distance, in inches, on the map between two cities that are n + 1 miles apart? ----- Develop a unit-comversion factor: n miles = s inches 1 mil = (s/n)inches ---- Then n+1 miles = (s/n)(n+1) inches Ans: D ============== Cheers, Stan H. =============== (A) n/s (B) (n+1)/s (C) s/(n+1) (D) (s(n+1))/n (E) n/ (s(n+1))

Probability-and-statistics/336416: I would like to calculate the test statistics for the following hypothesis: can someone help me?? Do countries that are members of G-20 have a lower unemployment rate than countries that are not members? Null: Mean of member’s unemployment rate is lower Alternative: Mean of member’s unemployment is higher Alpha: 0.05 1 solutions Answer 241197 by stanbon(57395)   on 2010-08-29 22:57:09 (Show Source): You can put this solution on YOUR website! I would like to calculate the test statistics for the following hypothesis: can someone help me?? Do countries that are members of G-20 have a lower unemployment rate than countries that are not members? Null: Mean of member’s unemployment rate is lower Alternative: Mean of member’s unemployment is higher Alpha: 0.05 --------------------- Note: The null hypothesis MUST contain equality. Ho: u(G20 members)-u(not members) = 0 Ha: u(G20 members)-u(not members) > 0 ========================================== Cheers, Stan H.

Functions/336396: A chemical company spends $2.2 million to buy machinery before it starts producing chemicals. Then it spends $0.5 million on raw materials for each million liters of chemical produced. Find a formula that expresses the total cost, C, in millions of dollars, as a function of L, the number of million liters produced. 1 solutions Answer 241153 by stanbon(57395)   on 2010-08-29 19:24:48 (Show Source): You can put this solution on YOUR website! A chemical company spends $2.2 million to buy machinery before it starts producing chemicals. Then it spends $0.5 million on raw materials for each million liters of chemical produced. Find a formula that expresses the total cost, C, in millions of dollars, as a function of L, the number of million liters produced. ---- C(L) = 2.2 mill + 0.5(L mill) =============================== Cheers, Stan H.

Linear-systems/336390: Please help me graph each inequality in two variables. Thank you. y< 2x + 2 2x < 3y + 6 1 solutions Answer 241152 by stanbon(57395)   on 2010-08-29 19:20:51 (Show Source): You can put this solution on YOUR website! Please help me graph each inequality in two variables. Thank you. y< 2x + 2 1st:::You need to graph the boundary. which is y = 2x+2, as a dashed line. 2nd:::Since you want y LESS than ... shade the half-plane BELOW the boundary. ------------------------------ 2x < 3y + 6 1st:::Solve for "y": y > (2/3)x+2 2nd: Graph the boundary y = (2/3)x+2 as a dashed line. 3rd: Since you want y GREATER than ...shade the half-plane ABOVE the boundary. ===================== Cheers, Stan H.

test/336387: What does an upside down v mean in math? 1 solutions Answer 241148 by stanbon(57395)   on 2010-08-29 19:12:05 (Show Source): You can put this solution on YOUR website! Find the perimeter and area of a right triangle if one leg measures 12 yd. and the other leg measures 35 yd. --------- If its (A ^ B) it means intersection --- If its 2^3 it means 2 raised to the 3rd power = 2*2*2 = 8 ========================================= Cheers, Stan H.

Triangles/336381: Can you solve this problem . Find the perimeter and area of a right triangle if one leg measures 12 yd. and the other leg measures 35 yd. Students must show all work step by step to receive full credit for the problem. Include correct units with your solution. 1 solutions Answer 241146 by stanbon(57395)   on 2010-08-29 19:09:01 (Show Source): You can put this solution on YOUR website! Find the perimeter and area of a right triangle if one leg measures 12 yd. and the other leg measures 35 yd. ----- The hypotenuse = sqrt(12^2+35^2) = 37 yd ---- Perimeter = 12+35+37 = 84 yds --- Area = (1/2)12*35 = 210 sq. yds. ==================================== Cheers, Stan H.

Exponential-and-logarithmic-functions/336361: rationalize the denominator: 6/radical 8 1 solutions Answer 241141 by stanbon(57395)   on 2010-08-29 19:02:00 (Show Source): You can put this solution on YOUR website! rationalize the denominator: 6/radical 8 ---- Multiply numerator and denominator by sqrt(2) to get: [6sqrt(2)]/sqrt(16) = [6sqrt(2)]/4 = (3/2)sqrt(2) =================================================== Cheers, Stan H.

Angles/336371: What is the area and the circumference of the circle with a 28yd diameter? 1 solutions Answer 241126 by stanbon(57395)   on 2010-08-29 18:42:52 (Show Source): You can put this solution on YOUR website! What is the area and the circumference of the circle with a 28yd diameter? ---------------------- Perimeter = (pi)d = 28(pi) = 87.96.. yrds --------------- Area = (pi)r^2 = (pi)*14^2 = 196pi = 615.75 sq. yds ==================================================== Cheers, stan H.

test/336370: If you have 5 letters, A,B,C,D,E, how many letter combinations using all 5 letters can you make, letters can be duplicated. 1 solutions Answer 241123 by stanbon(57395)   on 2010-08-29 18:39:26 (Show Source): You can put this solution on YOUR website! If you have 5 letters, A,B,C,D,E, how many letter combinations using all 5 letters can you make, letters can be duplicated. ---- 5 positions; each can be 5 different letters. ---- # of "words" = 5^5 = 3125 ============================== Cheers, Stan H.

absolute-value/336367: solve the equation and graph it on a number line:absolute value sign 2x+4 absolute value sign =8 1 solutions Answer 241121 by stanbon(57395)   on 2010-08-29 18:37:01 (Show Source): You can put this solution on YOUR website! absolute value sign 2x+4 absolute value sign =8 -------------- |2x+4| = 8 --- That thing inside the bars must be 8 or -8 ---- Solve 2x+4=8 or 2x+4 = -8 --- 2x = 4 or 2x = -12 x = 2 or x = -6 ===================== Cheers, stan H.

Probability-and-statistics/336344: In a certain manufacturing process, the diameter of holes drilled in a steel plate is a normally distributed random variable. The process standard deviation is known to be σ=0.005 cm.A sample of 15 plates shows a mean hole diameter of 2.475 cm. Find the 95 percent confidence interval for μ. 1 solutions Answer 241114 by stanbon(57395)   on 2010-08-29 18:26:52 (Show Source): You can put this solution on YOUR website! In a certain manufacturing process, the diameter of holes drilled in a steel plate is a normally distributed random variable. The process standard deviation is known to be σ=0.005 cm. A sample of 15 plates shows a mean hole diameter of 2.475 cm. Find the 95 percent confidence interval for μ. ----- x-bar = 2.475 --- E = invT(0.025 with df = 14) = 0.0028 ----- 95% CI: 2.475- 0.0028 < u < 2.475+ 0.0028 ----- (2.4722,2.4778) =============== Cheers, Stan H.

Geometry_Word_Problems/336201: In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 15 degrees less than that of angle C. Find the measure of the angles. A) 117, 24, 39 B) 78, 24, 39 C) 78, 24, 78 D) 117, 24, 78 I have come up with A= 3x, B=15-x, C=x 1 solutions Answer 241070 by stanbon(57395)   on 2010-08-29 13:54:51 (Show Source): You can put this solution on YOUR website! In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 15 degrees less than that of angle C. Find the measure of the angles. --- A = 3C B = C-15 A + B + C = 180 --- Substitute for A and for B and solve for C: 3C + C-15 + C = 180 5C = 195 C = 39 degrees A = 3C = 3*39 = 117 degrees B = C-15 = 39-15 = 24 degrees ------------------------------------- Cheers, Stan H. ------------------ A) 117, 24, 39 B) 78, 24, 39 C) 78, 24, 78 D) 117, 24, 78

Polynomials-and-rational-expressions/336195: Rational expression: q+7/q = -8 (reads q + 7 over q = -8) What is the solution? Thanks in advance. 1 solutions Answer 241067 by stanbon(57395)   on 2010-08-29 13:49:21 (Show Source): You can put this solution on YOUR website! (q+7)/q = -8 --- Multiply both sides by "q": q+7 = -8q Add 8q to both sides to get: 9q = -7 q = -7/9 =============== cheers, Stan H.

Linear-systems/336180: After robbing a bank in Dodge City, a robber gallops off at 12 mi/h. 10 minutes later, the marshall leaves to pursue the robber at 16 mi/h. How long (in hours) does it take the marshall to catch up to the robber? 1 solutions Answer 241065 by stanbon(57395)   on 2010-08-29 13:45:29 (Show Source): You can put this solution on YOUR website! After robbing a bank in Dodge City, a robber gallops off at 12 mi/h. 10 minutes later, the marshall leaves to pursue the robber at 16 mi/h. How long (in hours) does it take the marshall to catch up to the robber? ------------------- Robber DATA: rate = 12 mph ; time = x hrs ; distance = 12x miles -------------- Marshall DATA: rate = 16 mph ; time = x-(1/6) hr distance = 16(x-(1/6)) miles ---- Equation: distance = distance 12x = 16(x-(1/6)) 12x = 16x-(16/6) -4x = -(16/6) x = 2/3 hr ---- x-(1/6) = (4/6)-(1/6) = 1/2 hr (time needed for Marshall to catch robber) ============== Cheers, Stan H.

Mixture_Word_Problems/336175: How many liters of a 30% alcohol solution must be mixed with 80 liters of a 80% solution to get a 50% solution? I have made a table and tried to work many algebraic solutions but cannot come up with one. 1 solutions Answer 241060 by stanbon(57395)   on 2010-08-29 13:24:57 (Show Source): You can put this solution on YOUR website! How many liters of a 30% alcohol solution must be mixed with 80 liters of a 80% solution to get a 50% solution? ------------------- Equation: alcohol+alcohol = alcohol 0.30x + 0.80*80 = 0.50(x+80) Multiply thru by 100 to get: 30x + 80*80 = 50x + 50*80 -20x = -30*80 x = (3/2)80 x = 120 liters (amt of 30% solution needed in the mixture) ================= Cheers, Stan H.

Probability-and-statistics/336130: The soccer team has jerseys numbered from 10 to 30. Everyone on the team gets a jersey and there are three left over. How many players are on the team? 1 solutions Answer 241057 by stanbon(57395)   on 2010-08-29 13:20:15 (Show Source): You can put this solution on YOUR website! The soccer team has jerseys numbered from 10 to 30. 10 thru 30 is 21 numbers. ================================= Everyone on the team gets a jersey and there are three left over. How many players are on the team? 21-3 = 18 players ==================== Cheers, Stan H. ====================

decimal-numbers/336159: what do you get if you round 19.36 1 solutions Answer 241050 by stanbon(57395)   on 2010-08-29 12:56:45 (Show Source): You can put this solution on YOUR website! duplicate

Permutations/336158: when you round 19.36 what do you get 1 solutions Answer 241049 by stanbon(57395)   on 2010-08-29 12:54:46 (Show Source): You can put this solution on YOUR website! when you round 19.36 what do you get -------------- That depends on what you round down to. -- 19.36 is rounded down to the hundreth place 19.4 would be the number rounded down to the tenth place 19 would be the number rounded down to the units place 20 would be the number rounded to the tens place ================================================== Cheers, Stan H. ==============

Mixture_Word_Problems/336152: When making a telephone call using a calling card, a call lasting 6 minutes costs $2.90. A call lasting 16 minutes cost $6.90. Find a linear function that relates the cost, C, of a making a call length, X, of the call, treating length of the call as the independent variable. 1 solutions Answer 241046 by stanbon(57395)   on 2010-08-29 12:50:33 (Show Source): You can put this solution on YOUR website! When making a telephone call using a calling card, a call lasting 6 minutes costs $2.90. A call lasting 16 minutes cost $6.90. Find a linear function that relates the cost, C, of a making a call length, X, of the call, treating length of the call as the independent variable. --------------------------- You have two points : (6,2.9) and (16,6.9) ----- slope = (6.9-2.9)/(16-6) = 4/10 = 2/5 ----- Linear Form: cost = (slope)(length of call)+b Solve for "b": 2.9 = (2/5)(6)+b b = 2.9-(2/5)(6) b = 0.5 ----------------------- Equation: cost = (2/5)x + (1/2) =========================== Cheers, Stan H.

Linear_Algebra/336139: x/3=36x+7 I don't even know where to start. The book gives no examples that I can work from and I don't know what information is right/ wrong online. Please help! 1 solutions Answer 241045 by stanbon(57395)   on 2010-08-29 12:42:43 (Show Source): You can put this solution on YOUR website! x/3=36x+7 ------ You want to isolate "x" so get them on the same side of the equal sign. --------- x/3 - 36x = 7 --------- Factor out the "x": x((1/3)-36) = 7 --------- Simplify the parenthesis: x(-35 2/3)) = 7 --- Solve for "x": x = 7/(-35 2/3) --- x = 7/(-107/3) --- x = -21/107 ================ Cheers, Stan H.

Complex_Numbers/336144: Express answers in a+bi form for the square root of -75. 1 solutions Answer 241043 by stanbon(57395)   on 2010-08-29 12:29:52 (Show Source): You can put this solution on YOUR website! Express answers in a+bi form for the square root of -75. --------------------- sqrt(-75) = sqrt(-25*3) = 5i*sqrt(3) -- In the form a+bi you get 0+(5sqrt(3))i ======================================== Cheers, Stan H.