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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Travel_Word_Problems/80784: 1 solutions Answer 57936 by stanbon(57246)   on 2007-05-04 20:38:46 (Show Source): You can put this solution on YOUR website!The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water? ----------- Let the speed of the boat in still water be "b" -------- Upriver DATA: distance = 60 mi ; rate = b-3 mph ; time = d/r = 60/(b-3) hrs. ------------ Downriver DATA: distance = 60 mi; rate = b+3 ; time = d/r = 60/(b+3) hrs. ------------------- EQUATION: time up + time down = 9 hrs 60/(b-3) + 60/(b+3) = 9 Divide thru by 60 to get: 1/(b-3) + 1/(b+3) = 3/20 Multiply thru by 20(b-3)(b+3) to get: 20(b+3) + 20(b-3) = 3(b^2-9) 40b=3b^2-27 3b^2-40b-27=0 b=[40+-sqrt(40^2-4*3*-27)]/6 b=[40+-2sqrt(491)]/6 Positive Answer: b=14.0528 mph (this is the speed of the boat in still water) =========== Cheers, Stan H.
 Quadratic_Equations/80766: can i get help with this equation please? x^2-96=01 solutions Answer 57915 by stanbon(57246)   on 2007-05-04 17:48:26 (Show Source): You can put this solution on YOUR website!x^2-96=0 (x-sqrt96)(x+sqrt96)=0 x=sqrt96=4sqrt6 or x=-sqrt96=-4sqrt6 ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/80765: PLEASE HELP ME WITH THIS EQUATION X-squared+5X+6 OVER X-squared+X-61 solutions Answer 57913 by stanbon(57246)   on 2007-05-04 17:44:50 (Show Source): You can put this solution on YOUR website!X-squared+5X+6 OVER X-squared+X-6 =[(x+3)(x+2)]/[(x+3)(x-2)] Cancel the (x+3) factor common to the numerator and denominator. =(x+2)/(x-2) ============= Cheers, Stan H.
 logarithm/80764: Could someone please explain and give an example on how to solve an exponential equation when both sides can be written as a power of the same base. So that I may get a better understanding.Thank you all!1 solutions Answer 57912 by stanbon(57246)   on 2007-05-04 17:37:27 (Show Source): You can put this solution on YOUR website!I suggest you post one or two of the problems you are trying to understand. Cheers, Stan H.
 Equations/80744: 42: The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger number?1 solutions Answer 57909 by stanbon(57246)   on 2007-05-04 17:30:51 (Show Source): You can put this solution on YOUR website!The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger number ? -------- Let the larger even number be 2(n+1) Let the smaller even number be 2n ------------- EQUATION: (2n+2)^2 - (2n)^2 = 52 (2n)^2+8n+4 - (2n)^2 = 52 8n+4 = 52 8n=48 n=6 2n=12 (the smaller even number) 2n+2=14 (the larger even number) ============= Cheers, Stan H.
 Expressions-with-variables/80738: PLEASE I NEED HELP WITH THIS EQUATION X=2Y-1 Y-X=-5 AND I HAVEN'T GOT VERY FAR.1 solutions Answer 57906 by stanbon(57246)   on 2007-05-04 17:11:54 (Show Source): You can put this solution on YOUR website!X=2Y-1 Y-X=-5 -------- Rearrange: x-2y=-1 x-y=5 -------- Subtract the 1st equation from the 2nd to get: y=6 -------- Substitute that into either of the original equations to get: x=2y-1 x=2*6-1 x=11 ========== solution x=11, y=6 ------- Check that solution in the OTHER original equation: x-y=5 11-6=5 5=5 =========== Cheers, Stan H.
 absolute-value/80723: 2: |(x/6) + 5 | + (1/3) = (3/4) 1 solutions Answer 57904 by stanbon(57246)   on 2007-05-04 17:02:11 (Show Source): You can put this solution on YOUR website!|(x/6) + 5 | + (1/3) = (3/4) |(x/6)+5|=9/12 -4/12 |(x/6)+5| = 5/12 (x/6)+5 = 5/12 or (x/6)+5 = -5/12 (x/6)=-55/12 or (x/6)=-65/12 x = -55/2 or x = -65/2 ============= Cheers, Stan H.
 absolute-value/80724: 16: 8(c^3 - c) = c (6c + 1)1 solutions Answer 57903 by stanbon(57246)   on 2007-05-04 16:57:45 (Show Source): You can put this solution on YOUR website!8(c^3 - c) = c (6c + 1) 8c^3-8c = 6c^2+c 8c^3-6c^2-8c-c=0 c(8c^2-6c-9)=0 c(4c+3)(2x-3)0 c=0 or c=-3/4 or c=3/2 ========== Cheers, Stan H.
 absolute-value/80729: 28: Simplify: (2x1/2 + y1/2)(x1/2 - 3y1/2)1 solutions Answer 57902 by stanbon(57246)   on 2007-05-04 16:51:25 (Show Source): You can put this solution on YOUR website![2x^(1/2) + y^(1/2)] * [x^(1/2) - 3y^(1/2)] =[2x-6sqrt(xy)+sqrt(xy)-3y] =[2x-5sqrt(xy)-3y] ========= Cheers, Stan H.
 absolute-value/80725: 26: [1/(x - 3)] + [1/(x + 3)] = [10/(x2 - 9)] 1 solutions Answer 57901 by stanbon(57246)   on 2007-05-04 16:46:00 (Show Source): You can put this solution on YOUR website![1/(x - 3)] + [1/(x + 3)] = [10/(x^2 - 9)] -------- The lcm is x^2-9 or (x+3)(x-3) -------- Multiply thru by the lcm to get: (x+3) + (x-3) = 10 2x=10 x=5 ======== Cheers, Stan H.
 Square-cubic-other-roots/80732: I'm not sure if this is the right section, however it is a sqrt question. Here's the problem. sqrt(2/3.69692*10^2) I'm not understanding how to compute a scientific notation in a sqrt question. Can you help me?1 solutions Answer 57900 by stanbon(57246)   on 2007-05-04 16:42:48 (Show Source): You can put this solution on YOUR website!What does the "2/" mean? Do you mean sqrt(3.69692*10^2)? If so, take the square root of 3.69692 to get 1.922737632 Then take the square root of 10^2 to get 10 Write the sqrt(3.69692*10^2) = 1.922737632*10 ============== Cheers, Stan H.
 Permutations/80736: If the first three digits of someone's phone number (do not include area code) are 777, How many different phone numbers could they have? Please don't just give me and answer. I would like to know how to work this problem. I know that there 7digits in a phone numer, and the first three digits are taken then there are 4digits availiable. is it P=n/(n-r)! where n=7 and r=4 I am not sure.1 solutions Answer 57899 by stanbon(57246)   on 2007-05-04 16:37:39 (Show Source): You can put this solution on YOUR website!If the first three digits of someone's phone number (do not include area code) are 777, How many different phone numbers could they have? ----------- The general counting rule is "if there are n ways to perform the 1st step of a procedure and m ways to perform the 2nd step of the procedure, then there are n*m ways to perform the procedure". Your Problem: Telephone Number 777-???? There are 10 ways to fill the 1st ? 10 ways to fill the 2nd ? 10 ways to fill the 3rd ? 10 ways to fill the 4th ? -------- So, there are 1*1*1*10*10*10*10 ways to build the phone number. There are 1*10^4 = 10,000 phone numbers that start with 777. ========= Cheers, Stan H.
 Trigonometry-basics/80735: If theta is an acute angle such thatsin theta=5/13, what is the value of sin 2theta1 solutions Answer 57894 by stanbon(57246)   on 2007-05-04 15:00:13 (Show Source): You can put this solution on YOUR website!If theta is an acute angle such that sin(theta)=5/13, what is the value of sin (2theta) --------- If sintheta=5/13, y=5 and r=13; Find x: x^2=r^2-y^2; x=sqrt(13^2-5^2)=12 Then cos(theta)=12/13 ----------- sin(2theta)=2sin(theta)cos(theta) =2(5/13)(12/13) =120/169 =0.71 ========== Cheers, Stan H.
 Trigonometry-basics/80734: If (sec x-2)(2sec x-1)=01 solutions Answer 57891 by stanbon(57246)   on 2007-05-04 14:51:38 (Show Source): You can put this solution on YOUR website!(sec x-2)(2sec x-1)=0 ------- 2sec^2x-3secx +2=0 (2secx+1))(secx-2)=0 secx= -1/2 or secx = 2 Since sec has no value between -1 and 1 only secx=2 is a viable answer: Therefore : secx=2 or cosx=1/2: and x = 60 degrees or 300 degrees. ---------- Cheers, Stan H.
 Reduction-of-unit-multipliers/80643: what is the standard form equation of the conic given ? 4x^2-5y^2-16x-30y-9= 01 solutions Answer 57890 by stanbon(57246)   on 2007-05-04 14:45:39 (Show Source): You can put this solution on YOUR website!what is the standard form equation of the conic given ? 4x^2-5y^2-16x-30y-9= 0 -------------- Complete the square for the x-terms and y-terms respectively: 4(x^2-4x+4) -5(y^2+6y+9)=9+16-45 4(x-2)^2 - 5(y+3)^2 = -20 -(x-2)^2/5 + (y+3)^2/4 = 1 ======== Cheers, Stan H.
 Linear-equations/80727: Here is my question' A coffee shop sells coffee for \$7.60 for a 12-ounce bag and \$11.60 for a 20-ounce bag. The store just came out with a 28-ounce bag. What would be a good price for the bag? Solve by making a graph.I need the answer. I really need this A.S.A.P Thankyou1 solutions Answer 57887 by stanbon(57246)   on 2007-05-04 14:23:50 (Show Source): You can put this solution on YOUR website!A coffee shop sells coffee for \$7.60 for a 12-ounce bag and \$11.60 for a 20-ounce bag. The store just came out with a 28-ounce bag. What would be a good price for the bag? -------- You are given two points of a linear function: (12,7.6) and (20,11.6) Find the equation: m=[11.6-7.6]/[20-12]= 4/8 = 1/2 Find the y intercept: 11.6=(1/2)20+b ; 11.6=10+b; b=1.6 EQUATION: y=(1/2)x+1.6 ------- Now, solve for y if x = 28 y=(1/2)28+1.6 = \$15.60 ========= Cheers, Stan H.
 Equations/80722: An employee who produces x unites per hour earns an hourly wage of y=0.85 + 10 (in dollars). Find the hourly wage for an employee who produces 18 unites per hour. A. \$25.30 b. \$25.80 c. \$25.00 d. \$25.701 solutions Answer 57881 by stanbon(57246)   on 2007-05-04 12:54:30 (Show Source): You can put this solution on YOUR website!An employee who produces x units per hour earns an hourly wage of y=0.85x + 10 (in dollars). Find the hourly wage for an employee who produces 18 units per hour. ---------- Let x = 18 y = 0.85*18+10 y= 25.3 dollars =========== Cheers, Stan H.
 Rational-functions/80694: The maximum number of vertical asymptotes a rational function can have is infinite. True False 1 solutions Answer 57865 by stanbon(57246)   on 2007-05-04 09:34:29 (Show Source): You can put this solution on YOUR website!True. If (x-a) is a factor in the denominator and (x-a) is not a factor in the numerator there will be a vertical asymptote for every possible Real value of "a". Since there are infinitely many values a can take there are infinitely many possible vertical asymptotes. Cheers, Stan H.
 Miscellaneous_Word_Problems/80696: David opened his piggy bank and found 3 pennies, 5 nickels, and \$2.95 in dimes and quarters. Find the greatest number of quarters he could have if he had an odd number of dimes.1 solutions Answer 57864 by stanbon(57246)   on 2007-05-04 09:28:00 (Show Source): You can put this solution on YOUR website!David opened his piggy bank and found 3 pennies, 5 nickels, and \$2.95 in dimes and quarters. Find the greatest number of quarters he could have if he had an odd number of dimes. ---------- Let number of dimes be "x"; Value of these is 10x cents Let number of quarters be "y"; Value of these is 25y -------- EQUATION: value + value = 295 cents 10x+25y=295 -------- Make a list of odd multiples of 10: 10,30,50,70...etc Make a list of multiples of 25: 25,50,75,100...etc ------ Find the largest quarter multiple that when added to an odd multiple of 10 gives you 295: 295-10=285 no good 295-30=265 no good 295-50=245 no good 295-70=225 Ah, good because 9*25=295 ------- so, largest number of quarters would be 9 ========= Cheers, Stan H.
 Quadratic_Equations/80698: Can you please help me solve this equation i have been trying for the past 7 hours and it just dosent make any sense: A rectangle is initially 6cm wide and 12cm long. If a strip of uniform width is added to the outside of each of the four sides, the resulting area is 160 square cm. Determine the width of the strip?1 solutions Answer 57863 by stanbon(57246)   on 2007-05-04 09:16:53 (Show Source): You can put this solution on YOUR website!A rectangle is initially 6cm wide and 12cm long. If a strip of uniform width is added to the outside of each of the four sides, the resulting area is 160 square cm. Determine the width of the strip? -------- Draw the picture of the rectangle. Draw the stip bordering the rectangle but outside it. --------- Let the width of the stip be "x" cm. Area of the resulting rectangle including the border is: (6+2x)(12+2x)= 160 sq cm. 4(3+x)(6+x)=160 [18+9x+x^2)= 40 x^2+9x-22=0 (x+11)(x-2)=0 Positive answer: x=2 cm This is the width of the border. --------- Checking: (6+2*2)(12+2*2)= 10*16=160 ========== Cheers, Stan H.
 Linear-systems/80697: I=Prt I do not understand this question, I hope someone can figure this out for me. Thanks!1 solutions Answer 57862 by stanbon(57246)   on 2007-05-04 08:30:34 (Show Source): You can put this solution on YOUR website!I=Prt The formula says "Interest paid on P-amount of money is P times the rate (like 5%) times the time (like 2 years). This is a Simple Interest formula. ============== Cheers, Stan H.
 Probability-and-statistics/80686: looking for some help and need it too. one question has me stoped dead and two others just want someone to check my work thank you. Among 100 people randomly chosen in a survey, 10 stated that they believed that the elected representatives are honest most of the time. The approximate 95% confidence interval for the percentage of the population who believe that such people are honest most of the time is For questions 11 and 12 use the table immediately below. The table shows the number of smokers and nonsmokers by gender among 210 randomly selected people. Smokers Nonsmokers Totals Male 30 60 90 Female 40 80 120 Totals 70 140 210 _____11. If a smoker is chosen at random, the probability that the person is male is 12. If a male is chosen at random, the probability that he is a smoker is would like to get a nother look at 11 and 12 I think 11 is 30/70 and 12 is no answer with this data. thank you for your time.1 solutions Answer 57861 by stanbon(57246)   on 2007-05-04 08:26:30 (Show Source): You can put this solution on YOUR website!Among 100 people randomly chosen in a survey, 10 stated that they believed that the elected representatives are honest most of the time. The approximate 95% confidence interval for the percentage of the population who believe that such people are honest most of the time is ------ E=z*sqrt[(pq)/n] E=1.96sqrt[[(1/10*9/10)/100] E=1.96sqrt[9/10000] E=1.96*3/100 E=0.0588 ---------- p-hat=10/100= 0.1 CI: 0.1-0.0588 or, in interval notation, (0.412,1.0588) ================= For questions 11 and 12 use the table immediately below. The table shows the number of smokers and nonsmokers by gender among 210 randomly selected people. Smokers Nonsmokers Totals Male 30 60 90 Female 40 80 120 Totals 70 140 210 _____11. If a smoker is chosen at random, the probability that the person is male is P(male|smoker) = 30/70 = 3/7 12. If a male is chosen at random, the probability that he is a smoker is P(smoker|male} = 30/90 = 1/3 =============== Cheers, Stan H.
 Probability-and-statistics/80681: I sent this one before but made some misstakes sorry. In the question u is for population mean and o is for Population standards deviation thank you . Let X be a normally distributed random variable with u=100 and o=15 . The probability that is between 80 and 120 is (to the nearest whole percent) a. 8 % b. 82 % c. 91% d. answer not listed 1 solutions Answer 57829 by stanbon(57246)   on 2007-05-03 22:56:24 (Show Source): You can put this solution on YOUR website!In the question u is for population mean and o is for Population standards deviation thank you . Let X be a normally distributed random variable with u=100 and o=15 The probability that is between 80 and 120 is (to the nearest whole percent) a. 8 % b. 82 % c. 91% d. answer not listed -------------- If you have a Ti calulator use normalcdf(80,120,100,15) = 0.8175... ----- If you do not find the z-scores of 80 and of 120: z(80)=(80-100)/15 = -1.333333 z(120)=(120-100)/15 = 1.333333 Probability you want is normalcdf(-1.33333,1,33333)=0.8175... ================== Cheers, Stan H.
 Quadratic_Equations/80675: The boundary line for the linear inequality has been graphed. Determine the correct half-plane and complete the graph. y is greater than 31 solutions Answer 57827 by stanbon(57246)   on 2007-05-03 22:44:04 (Show Source): You can put this solution on YOUR website!The boundary line for the linear inequality has been graphed. Determine the correct half-plane and complete the graph. y is greater than 3 --------- The boundary line is y=3. Pick a test point on either side of the line. Let's say you pick (0.0) --------- Substitute that into the inequality to see if you get a true statement. 0 > 0 That is false. That tells you that the half-place which contains (0,0) is NOT the solution set for the inequality. The half-plane on the other side is the solution set. ============== Cheers, Stan H.
 absolute-value/80662: I hope someone can help me I am stuck. Acme Airlines flies airplanes that seat 12 passengers. From experience, they have learned that, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability that 12 or fewer passengers holding reservations will actually show up for the flight? a. less than 90% b. between 90 and 95%, inclusive c. more than 95% d. cannot be determined from information given Let be a normally distributed random variable with and . The probability that is between 80 and 120 is (to the nearest whole percent) a. 8 % b. 82 % c. 91% d. answer not listed these two qusetion have been killing me all night thanks for your help Mirna 1 solutions Answer 57824 by stanbon(57246)   on 2007-05-03 22:27:59 (Show Source): You can put this solution on YOUR website!Acme Airlines flies airplanes that seat 12 passengers. From experience, they have learned that, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability that 12 or fewer passengers holding reservations will actually show up for the flight? ---- It's a binomial problem: n=13, p=0.8, 0<=x<=12 If you have a TI calculator use 1-binompdf(13,0.8,13)=0.945 If you do not have a TI use 1-(0.8)^13=0.945 ================================ a. less than 90% b. between 90 and 95%, inclusive c. more than 95% d. cannot be determined from information given ANSWER: "b" is the answer. ===================================================== Let be a normally distributed random variable with and . The probability that is between 80 and 120 is (to the nearest whole percent) a. 8 % b. 82 % c. 91% d. answer not listed Comment: A bunch of words are missing from your posting. You will have to post this problem again. =============== cheers, Stan H.
 Graphs/80664: Solve the system by graphing x + y = 3 x + y = -11 solutions Answer 57822 by stanbon(57246)   on 2007-05-03 22:07:13 (Show Source): You can put this solution on YOUR website!x + y = 3 x + y = -1 ---------------- The system is inconsistent; there is no solution. ================ Cheers, Stan H.
 Functions/80658: determine whether this relation is a function please give step by step thanks x=y^41 solutions Answer 57821 by stanbon(57246)   on 2007-05-03 22:03:54 (Show Source): You can put this solution on YOUR website!determine whether this relation is a function please give step by step thanks x=y^4 -------------------- If y=-2, x=16, If y=+2, x=16 Thus two points of the graph have the same domain value but different range values. Thus x=y^4 is not a function. =============== Cheers, Stan H.
 Equations/80649: a running cheetah completed one stride(23feet) in 0.28 seconds. using the formula distance=ratextime find the cheetahs speed per feet per second1 solutions Answer 57820 by stanbon(57246)   on 2007-05-03 21:43:24 (Show Source): You can put this solution on YOUR website!a running cheetah completed one stride(23feet) in 0.28 seconds. using the formula distance=ratextime find the cheetahs speed per feet per second. ------------------- (23 ft/0.28 sec)= (23/0.28) ft/sec = 82.14 ft/sec ============= Cheers, Stan H.