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Recent problems solved by 'stanbon'

stanbon answered: 57351 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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Numeric_Fractions/430096: solve f - 3 1/3 = 12 1/4 1 solutions Answer 298666 by stanbon(57424)   on 2011-04-01 20:01:24 (Show Source): You can put this solution on YOUR website! solve f - 3 1/3 = 12 1/4 ------------ f - (10/3) = (49/4) --- Multiply thru by 12: ---- 12f - 40 = 3*49 --- 12f = 187 --- f = 15 29/50 ================= Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/430080: Let Q represent the mass of a quantity of carbon 14, whose half-life is 5437 years. The quantity present after t years is given by Q = 9 (1/2)t/5437 Sketch the graph of the function over the interval t = 0 to t = 10000. a) Find the initial quantity. b) Find the quantity present after 2171 years. 1 solutions Answer 298660 by stanbon(57424)   on 2011-04-01 19:41:59 (Show Source): You can put this solution on YOUR website! Let Q represent the mass of a quantity of carbon 14, whose half-life is 5437 years. The quantity present after t years is given by Q(t) = 9 (1/2)^(t/5437) -------------------------------- Sketch the graph of the function over the interval t = 0 to t = 10000 Note: This site's graphing cannot handle that large a domain. It does not provide a true picture of what is happening to the function values as they decrease over 10,000 years. -----------------------------------. a) Find the initial quantity. Q(0) = 9*(1/2)^0 = 9 units of wt. ===================================== b) Find the quantity present after 2171 years. Q(2171) = 9(1/2)^(2171/5437) = 6.82403.. units of wt. ==== Cheers, Stan H.

Evaluation_Word_Problems/430086: Which of the following expressions is equal to (x+2)+(x-2)(2x+1)? A 2x^2-2x B 2x^2-4x C 2x^2+x D 4x^2+2x 1 solutions Answer 298658 by stanbon(57424)   on 2011-04-01 19:27:52 (Show Source): You can put this solution on YOUR website! (x+2)+(x-2)(2x+1) ----- = (x+2) + 2x^2+x-4x-2 --- = 2x^2-2x ============ Cheers, Stan H.

Polynomials-and-rational-expressions/430082: can you help me factor each polynomial 9y squared + 45y 1 solutions Answer 298657 by stanbon(57424)   on 2011-04-01 19:25:19 (Show Source): You can put this solution on YOUR website! factor each polynomial 9y squared + 45y --- 9y^2+45y --- Greatest Common Factor: 9y --- Factor Form: = 9y(y+5) ============ Cheers, Stan H. ============

Linear_Equations_And_Systems_Word_Problems/430089: x + 3y + z= 6 3x + y - z= -2 2x + 2y - z = 1 1 solutions Answer 298656 by stanbon(57424)   on 2011-04-01 19:22:51 (Show Source): You can put this solution on YOUR website! x + 3y + z= 6 3x + y - z= -2 2x + 2y - z = 1 --- Using the Matrix function on my TI-84 I get: x = -1 y = 2 z = 1 ========== Cheers, Stan H.

Angles/430087: The ratio of two complimentary angles is 7:8. What is the measure of the larger angle? 1 solutions Answer 298654 by stanbon(57424)   on 2011-04-01 19:19:30 (Show Source): You can put this solution on YOUR website! The ratio of two complimentary angles is 7:8. What is the measure of the larger angle? ----- 7:8 is the same as 7x:8x where 8x is the measure of the larger angle. ---- Equation: 7x+8x = 90 degrees 15x = 90 degree x = 6 ----- Larger angle = 8x = 8*6 = 48 degrees =========== Cheers, Stan H. =============

Linear-equations/430073: In 1960, the average American disposed of 2.7 pounds of garbage per day, whereas in 2003 this amount was 4.3 pounds per day. a) Find a linear function "F" that calculates the amount of garbage disposed of by a person in 1960 after "x" days. Find "F (60)" and interpret the result. b) Repeat part (a) for 2003 with a linear function "g". 1 solutions Answer 298650 by stanbon(57424)   on 2011-04-01 19:06:10 (Show Source): You can put this solution on YOUR website! In 1960, the average American disposed of 2.7 pounds of garbage per day, whereas in 2003 this amount was 4.3 pounds per day. --- You have 2 points (0,2.7) and (43,4.3) --- a) Find a linear function "F" that calculates the amount of garbage disposed of by a person "x" years after 1960. ----- slope = (4.3-2.7)/(43) = 0.0372 --- intercept: 2.7 ===================== Equation: F(x) = 0.0372x + 2.7 where "x" is the # of years after 1960 ----- Find "F (60)" and interpret the result. F(60) = 0.0372*60+2.7 = 4.9326 lbs That's the predicted amount in the year 1960+60 = 2020 =============================================================== Cheers, Stan H. ============== b) Repeat part (a) for 2003 with a linear function "g".

Linear-equations/430069: label the lines as parallel or coinciding and explain why x + y = 5 y = 7 - x 1 solutions Answer 298643 by stanbon(57424)   on 2011-04-01 18:24:37 (Show Source): You can put this solution on YOUR website! label the lines as parallel or coinciding and explain why x + y = 5 y = 7 - x --- Put both in slope-intercept form: y = -x+5 y = -x+7 --------- Both have a slope of -1, so the lines are parallel. ===================== Cheers, Stan H.

Polynomials-and-rational-expressions/430072: 20% of A is $300, what is 'A'? 1 solutions Answer 298642 by stanbon(57424)   on 2011-04-01 18:21:46 (Show Source): You can put this solution on YOUR website! 20% of A is $300, what is 'A' -------- Equation: 0.20A = 300 A = 300/0.2 --- A = 300/(2/10) --- A = (300*10)/2 --- A = 1500 ================ Cheers, Stan H. ================

test/430070: Please help me solve this problem: Solve |x + 3| + 10 = 4. Also, i solved this problem Solve 3x + 6 = 3 (x – 5), i got no solution is that correct...my steps: 1.Distribute the 3.. 3x+6=3x-15 2.subtract 5 3x=3x-21 3. subtract 3x.. no solution? 1 solutions Answer 298640 by stanbon(57424)   on 2011-04-01 18:18:12 (Show Source): You can put this solution on YOUR website! Please help me solve this problem: Solve |x + 3| + 10 = 4. --- |x+3| = -6 No solution because absolute value cannot be negative. ====================================================== Also, i solved this problem Solve 3x + 6 = 3 (x – 5), i got no solution is that correct...my steps: 1.Distribute the 3 3x+6 + 3x-15 Subtract 3x from both sides 6 = -15 Contradiction Conclusion: No solution ============================= Cheers, Stan H.

Polynomials-and-rational-expressions/429947: What is the answer to -2.1 divided by -0.08, simplified 1 solutions Answer 298637 by stanbon(57424)   on 2011-04-01 18:06:17 (Show Source): You can put this solution on YOUR website! What is the answer to -2.1 divided by -0.08, simplified --- 2.1/0.08 = 2.1/(8/100) -------- = 2.1(100/8) -------- = 210/8 --- Ans: 26.25 ============== Cheers, Stan H.

Polynomials-and-rational-expressions/430064: im not queit sure how to factor trinomials of the type ax^2+bx+c and get the right answer 1 solutions Answer 298636 by stanbon(57424)   on 2011-04-01 17:59:52 (Show Source): You can put this solution on YOUR website! Im not quite sure how to factor trinomials of the type ax^2+bx+c and get the right answer. ----- Different quadratics are factored in different ways. x^2-16 = (x+4)(x-4) --- x^2+4x+4 = (x+2)^2 --- x^2+4x+5 can be factored with the quadratic formula. ================================ Cheers, Stan H.

Probability-and-statistics/429958: Which hypothesis (H0 or Ha) is the "hoped for" or "suspected" hypothesis. Why? 1 solutions Answer 298634 by stanbon(57424)   on 2011-04-01 17:53:07 (Show Source): You can put this solution on YOUR website! Which hypothesis (H0 or Ha) is the "hoped for" or "suspected" hypothesis. Why? ------ That is not an answerable question. Either statement can be the "claim" for the problem. The only condition you MUST meet is that equality MUST be part of Ho. ----- Maybe you hope for equality or maybe you don't, but equality MUST be part of Ho; it must NOT appear in Ha. --- Possible Ho's are: u = # u <= # u >= # -------- "Hoped for" has nothing to do with determining Ho and Ha. If your text says something else, it is wrong. ============================ Cheers, Stan H.

Polynomials-and-rational-expressions/429906: how can u factor this polynomial completly 2x^2-12x-80? 1 solutions Answer 298567 by stanbon(57424)   on 2011-04-01 10:08:10 (Show Source): You can put this solution on YOUR website! factor this polynomial completley ---------------------- 2x^2-12x-80 --- 2(x^2-6x-40) --- 2(x-10)(x+4) ---------------- Cheers, Stan H.

Trigonometry-basics/429905: Please help me solve this trigonometry problem. I have to "Find the exact values of x and y." Please help me. The problem is a 45-45-90 triangle and the two legs have values of 13 and i need to find the hypotenuse. I tried to work on it and I got: . Im not sure if I am supposed to leave it like that or not. is that the final answer? 1 solutions Answer 298564 by stanbon(57424)   on 2011-04-01 09:46:11 (Show Source): You can put this solution on YOUR website! The problem is a 45-45-90 triangle and the two legs have values of 13 and i need to find the hypotenuse. I tried to work on it and I got: ---------- hypo^2 = 13^2 + 13^2 --- hypo = sqrt(2*13^2) hypo = 13*sqrt(2) ======================= Cheers, Stan H.

Polynomials-and-rational-expressions/429902: When the sum of a number plus 3 is squared, it is 9 more than the sum of the number plus 2 when squared. 1 solutions Answer 298563 by stanbon(57424)   on 2011-04-01 09:42:16 (Show Source): You can put this solution on YOUR website! When the sum of a number plus 3 is squared, it is 9 more than the sum of the number plus 2 when squared. -------------------- Equation: (x+3)^2 = (x+2)^2+9 --- x^2+6x+9 = x^2+4x+13 2x = -4 x = -2 -------- Cheers, Stan H.

Angles/429900: A angle is one-third of its supplementary angle. Measure the angle. 1 solutions Answer 298562 by stanbon(57424)   on 2011-04-01 09:36:46 (Show Source): You can put this solution on YOUR website! An angle is one-third of its supplementary angle. Measure the angle. ---- Let the angle be "x": The supplement is "180-x": ---- Equation: x = (1/3)(180-x) x = 60-(1/3)x (4/3)x = 60 (1/3)x = 15 x = 45 ----------- Cheers, Stan H. ===============

Exponential-and-logarithmic-functions/429883: Evaluate log4 64 1 solutions Answer 298557 by stanbon(57424)   on 2011-04-01 09:13:29 (Show Source): You can put this solution on YOUR website! Evaluate log4 64 ---- Means "the power of 4 that gives you 64". Ans: 4 ============= Algebraic procedure: If x = log4(64) Then 64 = 4^x Then 4^4 = 4^x Then x = 4 =================== Cheers, Stan H.

Numbers_Word_Problems/429892: Jack usually mows his lawns in 6 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn together? 1 solutions Answer 298556 by stanbon(57424)   on 2011-04-01 09:09:25 (Show Source): You can put this solution on YOUR website! Jack usually mows his lawns in 6 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn together? --- Jack's rate: 1/6 job/hr Marilyn rate: 1/5 job/hr Together rate: 1/x job/hr ----- Equation: rate + rate = together rate 1/6 + 1/5 = 1/x ---- Multiply thru by 30x to get: 5x + 6x = 30 11x = 30 x = 30/11 = 2 8/11 hrs (time to do the job together) ================= Cheers, Stan H.

Numbers_Word_Problems/429891: Elaina bicycles 4km/h faster than Robert. In the same time it takes Robert to bicycle 30 km, Elaina can bicycle 42 km. How fast does each bicyclist travel? 1 solutions Answer 298555 by stanbon(57424)   on 2011-04-01 09:03:31 (Show Source): You can put this solution on YOUR website! Elaina bicycles 4km/h faster than Robert. In the same time it takes Robert to bicycle 30 km, Elaina can bicycle 42 km. How fast does each bicyclist travel? ----------------- Robert DATA: rate = x km/h ; dist = 30 km ; time = 30/x hr ----- Elaina DATA: rate = (x+4)km/h ; dist = 42 km ; time = 42/(x+4) hr ----- Equation: time = time 30/x = 42/(x+4) 30(x+4) = 42x 12x = 120 x = 10 km/h (Robert's rate) x+4 = 14 km/h (Elaina's rate) ================================== Cheers, Stan H. ==================

Numbers_Word_Problems/429888: to determine the number of deer in a game preserve, a conservationist catches 330 deer, tags them and lets them loose. Later, 356 deer are caught; 178 of them are tagged. How many deers are in the preserve? 1 solutions Answer 298554 by stanbon(57424)   on 2011-04-01 08:51:26 (Show Source): You can put this solution on YOUR website! to determine the number of deer in a game preserve, a conservationist catches 330 deer, tags them and lets them loose. Later, 356 deer are caught; 178 of them are tagged. How many deers are in the preserve? ------ total #/(caught&tagged) = (caught including tagged)/# tagged ---- total/330 = 356/178 ---- total = 330(356/178) --- total = 660 ================= Cheers, Stan H. ============

test/429885: If (X - A) is multiplied times (X - B), and A and B are both positive numbers, what will be the signs of the last 2 terms of the resulting trinomial? 1 solutions Answer 298553 by stanbon(57424)   on 2011-04-01 08:45:52 (Show Source): You can put this solution on YOUR website! If (X - A) is multiplied times (X - B), and A and B are both positive numbers, what will be the signs of the last 2 terms of the resulting trinomial? --- (X-A)(X-B) = X^2-(A+B)X+AB ---- 2nd term: negative 3rd term: positive ========== Cheers, Stan H.

Exponents/429886: Please help me divide the following: x^4-7x^2+10 divided by x^2-5 1 solutions Answer 298551 by stanbon(57424)   on 2011-04-01 08:41:19 (Show Source): You can put this solution on YOUR website! Please help me divide the following: x^4-7x^2+10 divided by x^2-5 ----- Ans: x^2-2 ============== Cheers, Stan H.

Graphs/429798: I need some assistance with this problem. Graph the following system of inequalities: -2x + y less than or equal to 4 y > x + 2 1 solutions Answer 298501 by stanbon(57424)   on 2011-03-31 21:30:48 (Show Source): You can put this solution on YOUR website! Graph the following system of inequalities: -2x + y less than or equal to 4 --- Solve for "y": y <= 2x+4 Graph the boundary: y = 2x+4 --- --- Graph the inequality: Since y is LESS than 2x+4, shade the half-plane BELOW the boundary. ============================================= y > x + 2 Graph the boundary: y = x+2 as a dashed line. ----------------- Graph the inequality Since yis GREATER than x+2, shade the half-plane ABOVE the boundary: ---- The intersectionof the two graphs is the graph of the system of two inequalities. --- Cheers, Stan H.

Average/429813: Solve the quadratic function by factoring: 4x^2 - 36x = -81 1 solutions Answer 298498 by stanbon(57424)   on 2011-03-31 21:20:38 (Show Source): You can put this solution on YOUR website! 4x^2 - 36x = -81 --- 4x^2 - 36x + 81 = 0 --- Factor: (2x+9)(2x-9) = 0 x = -9/2 or x = 9/2 ======================= cheers, Stan H.

Equations/429808: How do you factor Xsquared + 35x +3 = 77 1 solutions Answer 298495 by stanbon(57424)   on 2011-03-31 21:18:46 (Show Source): You can put this solution on YOUR website! factor Xsquared + 35x +3 = 77 --------------- x^2+35x-74 = 0 --- x^2+37x-2x-74 = 0 --- x(x+37)-2(x+37) = 0 --- (x+37)(x-2) = 0 x = 2 or x = -37 ================== Cheers, Stan H.

Inequalities/429802: if X = 0.87, then what is X squared? 1 solutions Answer 298494 by stanbon(57424)   on 2011-03-31 21:11:00 (Show Source): You can put this solution on YOUR website! (0.87)^2 = 0.87*0.87 = 0.756900 ================================== Cheers, Stan H.

Expressions-with-variables/429804: I feel like I've tried every possible solution and can not find the correct answer. "Which of the following points is a solution to the system?" 5x+3y+3z=-13 8x+6y-8z=-2 3x-y-8z=-12 I know you are suppose to do the addition method but every pairing I've tried does not come out even. I'm stumped! 1 solutions Answer 298490 by stanbon(57424)   on 2011-03-31 21:07:32 (Show Source): You can put this solution on YOUR website! 5x+3y+3z=-13 8x+6y-8z=-2 3x-y-8z=-12 ----------------- I used the Matrix Method on a TI-84 to get: x = -5 y = 5 z = -1 ========== Cheers, Stan H.

Numbers_Word_Problems/429778: When two times the square of a number is decreased by seven times the same number, the result is 15. Find the number. 1 solutions Answer 298483 by stanbon(57424)   on 2011-03-31 20:25:44 (Show Source): You can put this solution on YOUR website! When two times the square of a number is decreased by seven times the same number, the result is 15. Find the number. ---- Equation: 2x^2-7x = 15 ---- 2x^2-7x-15 = 0 --- Factor: 2x^2-10x+3x-15 = 0 2x(x-5)+3(x-5) = 0 (x-5)(2x+3) = 0 x = 5 or x = -3/2 =================== Cheers, Stan H.

decimal-numbers/429769: turning 3.52 into complete mixed fraction 1 solutions Answer 298481 by stanbon(57424)   on 2011-03-31 20:23:03 (Show Source): You can put this solution on YOUR website! turning 3.52 into complete mixed fraction ---- = 3 52/100 --- = 3 13/25 ============ Cheers, Stan H. ============

Functions/429773: How do I find out what the Vertical Asymptote is for this function: 2x^2-6/x^3-8? 1 solutions Answer 298480 by stanbon(57424)   on 2011-03-31 20:20:59 (Show Source): You can put this solution on YOUR website! How do I find out what the Vertical Asymptote is for this function: 2x^2-6/x^3-8? ------------ Factor: [2(x^2-6)]/[(x-2)(x^2+2x+4)] ---- You have a vertical asymptote when the denominator of this problem is zero. --- Solve x^2+2x+4 = 0 x = [-4+-sqrt(4-4*4)]/2 Solution is imaginary since the discriminant is negative. --- Vertical asymptote at x = 2 only. ========================================== =========== Cheers, Stan H.