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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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 Exponential-and-logarithmic-functions/231152: i need help solve this equation 20(1.05)^x=80+10x 1 solutions Answer 171107 by stanbon(57361)   on 2009-10-25 13:41:39 (Show Source): You can put this solution on YOUR website!solve this equation 20(1.05)^x=80+10x ----------- That is exponential on the left side and linear on the right side. ========== Graph both on the same coordinate system and find the point(s) of intersection. ---------------------- The line intersects the curve at x = 76.8017... and at -6.5468... ======================================================================= ======================================================================= Cheers, Stan H.
 Probability-and-statistics/231070: In a piggy bank, there are twice as many dimes as quarters, five times as many nickels as quarters, and twice as many pennies as all other coins combined. It is equally likely that any one of the coins will fall out when the piggy bank is turned upside down. Calculate the probability that either a nickel or a quarter will fall out. Express your solution as a fraction in lowest terms.1 solutions Answer 171104 by stanbon(57361)   on 2009-10-25 13:30:43 (Show Source): You can put this solution on YOUR website!In a piggy bank, there are twice as many dimes as quarters, d = 2q ----------------- five times as many nickels as quarters, n = 5q ------------------------- and twice as many pennies as all other coins combined. p = 2(n + d + q) (1/2)p - n - d - q = 0 ------------------------- Rearrange: 0p + 0n + d -2q = 0 0p + n +0d -5q = 0 (1/2)p-n- d - q = 0 ----------- Change to an augmented matrix: 0p + 0n + d = 2q 0p + n +0d = 5q p - 2n -2d = 2q ---------------------- Solve p,d,and n for q: d = 2q from the 1st equation: n = 5q --- p = 2(5q)+2(2q)+ 2q p = 16q ---------------- There are a total of 24q coins P(q) = 1/24 ; P(p)=16/24; P(n)=5/24 ; P(d)= 2/24 ----------------------------------------------------- Calculate the probability that either a nickel or a quarter will fall out. Express your solution as a fraction in lowest terms. P(nickel or quarter) = P(nickel) + P(quarter) = (5/24)+(1/24) = 1/4 ======================================================================= Cheers, Stan H.
 Probability-and-statistics/231096: of all computer chips manufactured, 3% are defective. If a company produces 367 chips, approximately how many are defective?1 solutions Answer 171092 by stanbon(57361)   on 2009-10-25 13:04:16 (Show Source): You can put this solution on YOUR website!of all computer chips manufactured, 3% are defective. If a company produces 367 chips, approximately how many are defective? ------------------ # defective = 0.03*367 is approximately 11 ------------------------------- Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/231077: the sum of two numbers is 64 and their difference is 18.what are the numbers?1 solutions Answer 171079 by stanbon(57361)   on 2009-10-25 09:25:19 (Show Source): You can put this solution on YOUR website!the sum of two numbers is 64 and their difference is 18.what are the numbers? Equations: x+y = 64 x-y = 18 ------------- Add and solve for "x": 2x = 82 x = 41 (one of the numbers) ------------ Substitute into x+y = 64 to solve for "y": 41+y = 64 y = 23 (the other number) ---------------------- Cheers, Stan H.
 Rate-of-work-word-problems/231075: It takes 10 hours to fill a pool with water, and 20 hours to drain it. If the pool is empty and the drain is open, how long will it take to fill the pool?1 solutions Answer 171078 by stanbon(57361)   on 2009-10-25 09:22:11 (Show Source): You can put this solution on YOUR website!It takes 10 hours to fill a pool with water, and 20 hours to drain it. If the pool is empty and the drain is open, how long will it take to fill the pool? ---------------------- Fill rate : 1/10 job/hr Drain rate: 1/20 job/hr Together rate: 1/x job/hr -------------------------------- Equation: 1/10 - 1/20 = 1/x Multiply thru by 20x to get: 2x - x = 20 x = 20 (number of hours required to fill the pool) ======================================================= Cheers, Stan H.
 Probability-and-statistics/230976: The sum of three numbers is 9. The first number minus the second plus the third is 3. The first minus the third is 1 more than the second. Find the numbers. What is the first number? _____ What is the second number? ______ What is the third number? ______1 solutions Answer 171050 by stanbon(57361)   on 2009-10-24 22:17:36 (Show Source): You can put this solution on YOUR website!The sum of three numbers is 9. The first number minus the second plus the third is 3. The first minus the third is 1 more than the second. Find the numbers. --------------------- Equations: a + b + c = 9 a - b + c = 3 a + 0 - c = b+1 --------------------- Rearrange: a + b + c = 9 a - b + c = 3 a - b - c = 1 --------------------- Use any method to solve the system to get: a = 5 b = 3 c = 1 ================================= Cheers, stan H.
 Polynomials-and-rational-expressions/230977: Hello my name is Crystal, I need help can you please tell me. How do you determine if a polynomial is the difference of two squares? 1 solutions Answer 171048 by stanbon(57361)   on 2009-10-24 22:08:43 (Show Source): You can put this solution on YOUR website!How do you determine if a polynomial is the difference of two squares? -------------------- It has two terms separated by an negative sign. Each of the two terms is a perfect square. ----- Example: 16x^2 - 49 is a "difference of squares". It factors as (4x-7)(4x+7) ================================= Cheers, Stan H.
 Probability-and-statistics/230978: In the US, the highest incidence of fraternal twins birth occurs among Asian-Americans, then African-Americans, then Caucasians. Of every 14600 births, the total number of fraternal twins births for all three is 701, where there are 176 more for Asian-Americans than African-Americans and 218 more for Asian-Americans than Caucasians. Determine the number for each race. Out of every 14600 births, there are _____ sets of Asian-Americans twins, _____ sets of African-American twins, and _____ sets of Caucasian twins.1 solutions Answer 171047 by stanbon(57361)   on 2009-10-24 22:05:39 (Show Source): You can put this solution on YOUR website!In the US, the highest incidence of fraternal twins birth occurs among Asian-Americans, then African-Americans, then Caucasians. Of every 14600 births, the total number of fraternal twins births for all three is 701, where there are 176 more for Asian-Americans than African-Americans and 218 more for Asian-Americans than Caucasians. Determine the number for each race. -------------------- As + Af + Ca = 701 As = Af +176 As = Ca + 218 ------------------------ Substitute for Af and Ca to solve for As Af = As-176 Ca = As-218 --- As + (As-176) + (As-218) = 701 3As - 394 = 701 3As = 1095 As = 365 (# of Asian-American twin births) ---- Since Af = As-176, Af = 365-176 = 189 (# of African-American twin births) ---------- Since Ca = As-218, Ca = 365-218 = 147 (# of Caucasian-American twin births) ---------------------------------------------------------- Cheers, Stan H.
 Linear-systems/230979: I need help as to how this word problem is to be set up: Suppose a chemist is mixing to acid solutions, one of 20% and the of 30% concentration. Which one o the following concentratons could not be obtained: A 22%, B 24% C 28% D 32% The answer is D. I need some intruction as to how to set this problem up. 1 solutions Answer 171044 by stanbon(57361)   on 2009-10-24 21:53:59 (Show Source): You can put this solution on YOUR website!I need help as to how this word problem is to be set up: Suppose a chemist is mixing to acid solutions, one of 20% and the of 30% concentration. Which one o the following concentratons could not be obtained: A 22%, B 24% C 28% D 32% The answer is D. I need some intruction as to how to set this problem up. ------------------- No setup is needed for this one. It comes down to this: If you add a 20% and a 30% the 20% will dilute the 30% and give you a mixture that is less than 30%. You could not possible end up witha 32% solution. ======================================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/230967: what would you add to 4x^2-6x to make it a complete squre? a.4/9 b.9/16 c.16/25 d.4/25 e.9/251 solutions Answer 171041 by stanbon(57361)   on 2009-10-24 21:50:14 (Show Source): You can put this solution on YOUR website!what would you add to 4x^2-6x to make it a complete square? --------- If you square ax-b you get: a^2x^2 - 2abx + b^2 ----- Your problem: a^2 = 4, so a = 2. -2ab = -6, so -2*2*b = -6 ; So b = -6/-4 = 3/2 --------------------------- You need to add b^2 = 9/4 --- None of the answers you listed is correct. Cheers, Stan H. a.4/9 b.9/16 c.16/25 d.4/25 e.9/25
 Probability-and-statistics/230971: statistics show that 80% of crimes are never solved.suppose a neighborhood district in a large city suffers repeated crimes the police are investigating 6 property crime cases in this district. a) what is the probability that none will ever be solved b0probability at least one will be solved c0expected # of crimes that will be solved and what is the standard deviation1 solutions Answer 171040 by stanbon(57361)   on 2009-10-24 21:38:24 (Show Source): You can put this solution on YOUR website!statistics show that 80% of crimes are never solved.suppose a neighborhood district in a large city suffers repeated crimes the police are investigating 6 property crime cases in this district. a) what is the probability that none will ever be solved 0.8^6 = 0.2621 --------------------------- b) probability at least one will be solved P(at least one solved) = 1 - P(none solved) = 1-0.2621 = 0.737856... -------------------------------------- c) expected # of crimes that will be solved and what is the standard deviation -------------- Expected number = np Expected number = 6*0.8 = 4.8 Std = sqrt(6*0.8*0.2) = 0.9798 ====================================== Cheers, Stan H.
 Money_Word_Problems/230895: Word Problem Six - A group of people come forward to claim a \$1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by \$75,000. How many winners are there and what were their shares? (Show a complete algebraic solution for the problem and check the answer.)1 solutions Answer 171039 by stanbon(57361)   on 2009-10-24 21:06:06 (Show Source): You can put this solution on YOUR website!A group of people come forward to claim a \$1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by \$75,000. How many winners are there and what were their shares? ---------------------- Let the original group size of winners be "x"; The original average prize would be 1,000,000/x dollars ------------------------------- Number of winners after 3 more join is "x+3" New average prize is 1,000,000/(x+3) dollars -------------------------------- Equation: Original - New = 75000 1,000,000/x - 1,000,000/(x+3) = 75000 -------------------------------------- Divide through by 75000 to get: 13.333/x - 13.333/(x+3) = 1 Multiply thru by x(x+3) (40/3)(x+3) - (40/3)x = x^2+3x Multiply thru by 3: 40x + 120 - 40x = 3x^2+9x 3x^2 + 9x -120 = 0 x^2 + 3x - 40 = 0 Positive Solution: x = [-3 + sqrt(9-4*-40)]/2 --- x = [-3 + sqrt(169)]/2 x = [-3 + 13]/2 x = 5 (original number of winners) x+3 = 8 (total number of winners) --------------- 1,000,000/8 = \$125,000 (amount each winner received) =========================================================== Cheers, Stan H.
 Probability-and-statistics/230965: A fair die is rolled. If a number 1 or 2 appears, you will receive \$5. If any other number appears, you will pay \$2. What is the mean value of one trial of this game? 1 solutions Answer 171036 by stanbon(57361)   on 2009-10-24 20:51:29 (Show Source): You can put this solution on YOUR website!A fair die is rolled. If a number 1 or 2 appears, you will receive \$5. If any other number appears, you will pay \$2. What is the mean value of one trial of this game? ------------------------------------- Random Variable X has two values: 5 and -2 The corresponding probabilities are (2/6) and (4/6) -------------------------------------- Mean Value of one trial is (2/6)*5 + (4/6)(-2) = (10/6) - (8/6) = 2/6 dollars = 33 1/3 cents ================================================== Cheers, Stan H.
 Human-and-algebraic-language/230888: If a*b=ab+1 and a~b=a+b+1 what is the value of 4*[(6~8)~(3*5)]?1 solutions Answer 170990 by stanbon(57361)   on 2009-10-24 16:04:12 (Show Source): You can put this solution on YOUR website!If a*b=ab+1 and a~b=a+b+1 what is the value of 4? ------------------------------------------- Evaluate the parentheses: --- = 4*((6+8+1)~(15+1)) --- Simplify: = 4
 Probability-and-statistics/230877: The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.3 inches? (B) What percentage of the oranges in this orchard are larger than 6.75 inches? (C) A random sample of 100 oranges is gathered and the mean diameter obtained was 6.75. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 6.75 inches? (D) Why is the z-score used in answering (A), (B), and (C)? (E) Why is the formula for z used in (C) different from that used in (A) and 1 solutions Answer 170987 by stanbon(57361)   on 2009-10-24 15:42:44 (Show Source): You can put this solution on YOUR website!The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.3 inches? z(6.5)=(6.3-6.85)/0.8 = -0.6875 P(x< 6.3) + P(z < -0.6875) = 24.59% -------------------------------------------- (B) What percentage of the oranges in this orchard are larger than 6.75 inches? Same process. Fid the z-value of 6.75 Find the percentages greater than that z-value. ------------------------------------------------------ (C) A random sample of 100 oranges is gathered and the mean diameter obtained was 6.75. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 6.75 inches? --- The std has changed to 0.8/sqrt(100) = 0.08 --- z(6.75) = (6.75-6.85)/0.08 = -1.25 P(x > 6.75) = (z > -1.25) = 0.8944 (D) Why is the z-score used in answering (A), (B), and (C)? I'll leave that to you. It's probably explained in your text. (E) Why is the formula for z used in (C) different from that used in (A) and The sample means have distribution (u,sigma/sqrt(n)) according to the Central Limit Theorem. ==================================== Cheers, Stan H.
 Probability-and-statistics/230836: i have two questions that are very similiar.. \$8,000 is compounded annually for 3 years at a rate of 6%. How much is in the account at the end of the term? \$4,000 compounded semiannually for 5 years at a rate of 4%. How much is in the account at the end of the term? thank you for your time!1 solutions Answer 170960 by stanbon(57361)   on 2009-10-24 12:32:55 (Show Source): You can put this solution on YOUR website!Amount after t years when n is the # of times compounded each year and rate=r --------------------- A(t)=P(1+(r/n))^(nt) --------------------------- \$8,000 is compounded annually for 3 years at a rate of 6%. How much is in the account at the end of the term? A(3) = 8000(1+ (0.06/1)^(1*3) = 8000(1.06)^3 = 8000*1.1910.. A(3) = \$9528.13 ------------------ 4,000 compounded semiannually for 5 years at a rate of 4%. How much is in the account at the end of the term? A(5) = 4000(1+(0.04/2))^(2*5) A(5) = \$4875.98 ======================== Cheers, Stan H.
 Equations/230834: Find the value of p and the value of q x^-6x+15 = (x-p)^+q1 solutions Answer 170957 by stanbon(57361)   on 2009-10-24 12:07:04 (Show Source): You can put this solution on YOUR website!Find the value of p and the value of q x^2-6x+15 = (x-p)^2+q --------------- x^2 - 6x + 15 = x^2 - 2px + p^2 + q ----------------------------------------- Equating the corresponding coefficients you get: -2p = -6 p^2+q = 15 --------------- solve the 1st for "p": p = 3 ---- Substitute into the 2nd equation and solve for "q": 9 + q = 15 q = 6 ================== Cheers, Stan H.
 Numbers_Word_Problems/230833: a plumber and his apprentice work for 8 hours. The plumber makes \$4.50 more than the apprentice. How much do they each make1 solutions Answer 170955 by stanbon(57361)   on 2009-10-24 12:02:38 (Show Source): You can put this solution on YOUR website!a plumber and his apprentice work for 8 hours. The plumber makes \$4.50 more than the apprentice per hour. How much do they each make ----------------------- Let plumber make x + 4.5 per hour Then aprentice makes x per hr -------------- In 8 hrs the plumber makes 8x + 8*4.5 = (8x+36) dollars In 8 hrs the apprentice makes 8x dollars -------------------------------------------------- Dheers, Stan H.
 Age_Word_Problems/230832: If someone is 2/3's older than someone else how is that written algebraically1 solutions Answer 170952 by stanbon(57361)   on 2009-10-24 11:56:00 (Show Source): You can put this solution on YOUR website! If someone is 2/3's older than someone else how is that written algebraically ---------------------- If you are x yrs old Your father may be x + (2/3)x yrs. old ---------------------------- Equation: F = (1 + (2/3))Y F = (5/3)Y This equation means "your father's age is (5/3)times your age", which means he is 2/3 older than you. ================================================================= Cheers, Stan H.
 logarithm/230830: rewrite the expression as a single logarithm 1/2logX-logY-3logZ+1/4logP having trouble making this into a single logarithm hope you can help thanks nancy1 solutions Answer 170950 by stanbon(57361)   on 2009-10-24 11:50:55 (Show Source): You can put this solution on YOUR website!rewrite the expression as a single logarithm 1/2logX-logY-3logZ+1/4logP --- log[x^(1/2)] - log(y) - log(z^3) + log(p^(1/4)) --- = log{[p^(1/4)*(x)^(1/2)]/[log(y*z^3)]} ================== Cheers, Stan H.
 Numeric_Fractions/230820: How do I solve for r where: (1/(1+r))*(30/r)-100 = 0 I'm getting stuck on the steps in te middle..."the work"...1 solutions Answer 170948 by stanbon(57361)   on 2009-10-24 11:46:19 (Show Source): You can put this solution on YOUR website! How do I solve for r where: (1/(1+r))*(30/r)-100 = 0 ----------------- Multiply thru by r(1+r) to get: (30)-100r(r+1) = 0 --- -100r^2-100r+30 = 0 Divide thru by -10 to get: 10r^2 + 10r - 3 = 0 --- Use the quadratic formula: r = [-10 +- sqrt(100 - 4*10*-3)]/20 --- r = [-10 +- sqrt(220)]/20 --- r = [-10 +- 2sqrt(55)]/20 x = [-1/2 + (1/10)sqrt(55)] or x = [-1/2 + (1/10)sqrt(55)] ======================================== Cheers, Stan H.
 Probability-and-statistics/230708: A study was done to see if allergic hypersensitivity to dental materials was more common in men than women. Seventy-five out of 150 men exhibited allergic hypersensitivity and 60 out of 150 women exhibited allergic hypersensitivity. State the null and alternative hypothesis and perform appropriate statistical test1 solutions Answer 170944 by stanbon(57361)   on 2009-10-24 11:36:27 (Show Source): You can put this solution on YOUR website!A study was done to see if allergic hypersensitivity to dental materials was more common in men than women. Seventy-five out of 150 men exhibited allergic hypersensitivity and 60 out of 150 women exhibited allergic hypersensitivity. State the null and alternative hypothesis and perform appropriate statistical test ------------- Ho: p(men)-p(women) = 0 Ha: p(men)-p(women) > 0 ------------------------------- P-hat(men) = 1/2 p-hat(women) = 60/150 = 2/5 ------------------------------- I ran a 2-prop Ztest and got the following: test statistic: z=1.7408 p-value = 0.0407 ------------------------------------- Conclusion: Reject Ho at the 5% significance level because 4.07% is less than 5% --------------------------------- Fail to reject at the 1% significance level because 4.07% is greater than 1% ============================================= Cheers, Stan H.
 Complex_Numbers/230801: What complex number (a+bi) lets radical i equal to a+bi.1 solutions Answer 170923 by stanbon(57361)   on 2009-10-24 09:22:19 (Show Source): You can put this solution on YOUR website!What complex number (a+bi) lets radical i equal to a+bi. ---- Solve i(a+bi) = a+bi a+bi = (a+bi)/i a+bi = -i(a+bi)/(i*-i) a+bi = -i(a+bi)/1 a+bi = b-ai ------------------- Ans: b-ai ========================= Cheers, Stan H.
 Distributive-associative-commutative-properties/228793: How do i do this problem step by step. 13[7+w+(-9)] &&, -29(p-21-5)1 solutions Answer 170922 by stanbon(57361)   on 2009-10-24 09:18:50 (Show Source): You can put this solution on YOUR website!How do i do this problem step by step. 13[7+w+(-9)] simplify the parentheses = 13[w-2] Use the distributive law to get: = 13w - 26 ====================== &&, -29(p-21-5) simplify the parentheses = -29(p-26) Use the distributive law to get: =-29p + 754 ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/230793: A computer can do one calculation in 1.4 X 10^-7 seconds. How long would it take the computer to do a trillion (10^12) calculations? (Round to one decimal point)Express answer in scientific notation.1 solutions Answer 170921 by stanbon(57361)   on 2009-10-24 09:13:27 (Show Source): You can put this solution on YOUR website!A computer can do one calculation in 1.4 X 10^-7 seconds. How long would it take the computer to do a trillion (10^12) calculations? (Round to one decimal point)Express answer in scientific notation. --- Use a proportion 1/1.4x10^-7 = 10^12/x ---- x = 10^12[1.4*10^-7) = 1.4*10^5 seconds ------------------------------------- ======================================= Cheers, Stan H.
 Miscellaneous_Word_Problems/230794: A semicircular window of radius 16 inchesis to be laminated with a sunblock coating that costs \$0.65 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Use the Area of a Circle and Pi = 3.14)1 solutions Answer 170920 by stanbon(57361)   on 2009-10-24 09:08:25 (Show Source): You can put this solution on YOUR website!A semicircular window of radius 16 inches is to be laminated with a sunblock coating that costs \$0.65 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Use the Area of a Circle and Pi = 3.14) -------------- Area = pi*r^2 Semi-Area = (1/2)pi*r^2 SA = (1/2)(3.14)*8^2 = 100.48 sq.in. ------------------------------------ Cost = 0.65*100.48 = \$65.31 ================================== Cheers, Stan H.
 Graphs/230788: -5x+2y=-10 3x-6y=-18 what would be the steps and the answer to this problem in substitution, elimination and how would it be graphed. PLEASE HELP ME!!!!!!1 solutions Answer 170919 by stanbon(57361)   on 2009-10-24 09:04:06 (Show Source): You can put this solution on YOUR website!1) -5x+2y=-10 2) 3x-6y=-18 what would be the steps and the answer to this problem in substitution, elimination and how would it be graphed. ------------------- Substitution: Solve the 1st for y they substitute that into the 2nd 1)y = (5/2)x -5 2) 3x -6(5/2)x-5) = -18 --- Solve 2nd for "x" 3x-15x+30 = -18 -12x = -48 x = 4 ------- Substitute that into y = (5/2)x-5 to solve for "y": y = (5/2)4-5 = 5 ------------------------- Solution (4,5) ============================================ 1) -5x+2y=-10 2) 3x-6y=-18 --- Elimination: Multiply thru 1st by 3 to get: 1) -15x+6y = -30 2) 3x-6y = -18 ------------------- Add and solve for "x" -12x = -48 x = 4 ----------- Substitute that into 1st or 2nd and solve for "y": 3*4-6y = -18 12-6t = -18 -6y = -30 y = 5 ------------- Same solution as above ============================== 1) -5x+2y=-10 2) 3x-6y=-18 -- Graphing: Solve each equation for "y": 1) y = (5/2)x-5 2: y = (1/2)x+3 ---- Plot two points for each of the equations. Drar a line thru each pair of points and find the intersection. --- ==================== Cheers, Stan H.
 Expressions-with-variables/230789: Here is the question: "A leaky faucet drips at the rate of 1 drip every 3 seconds, and 165 drips will fill one eight-ounce cup. How many gallons of water will drip in one year?" What I don't understand is how to make it into an equation (so that I can solve it). I don't need the solution, just how to put it into an equation. Any help would be greatly appreciated! Thanks!1 solutions Answer 170918 by stanbon(57361)   on 2009-10-24 08:48:48 (Show Source): You can put this solution on YOUR website!Here is the question: "A leaky faucet drips at the rate of 1 drip every 3 seconds, and 165 drips will fill one eight-ounce cup. How many gallons of water will drip in one year?" ------------- You have to take it one step at a time. How many seconds in a year? look it up or figure it out How many intervals of 3-seconds in a year? divide by 3 --------------------- How many sets of 165 drips in the above. divide by 165 ----------------------- How many eight-ounce cups make a gallon. look it up ---------------------------- Cheers, Stan H.
 Exponents-negative-and-fractional/230791: If f(x) = 2x-4, find f^-1(x)1 solutions Answer 170917 by stanbon(57361)   on 2009-10-24 08:42:27 (Show Source): You can put this solution on YOUR website! If f(x) = 2x-4, find f^-1(x) ------------ y = 2x-4 To find the inverse: interchange x and y to get: x = 2y-4 solve for y: y = (x+4)/2 That is the inverse ========================== Cheers, Stan H.
 Radicals/230792: y varies directly as x and inversely as the square root of w; write the sentence as an equationThank you1 solutions Answer 170916 by stanbon(57361)   on 2009-10-24 08:40:33 (Show Source): You can put this solution on YOUR website!y varies directly as x and inversely as the square root of w; write the sentence as an equationThank you ------------ y = k[x/sqrt(w)] ==================== Cheers, Stan H.
 Probability-and-statistics/230751: The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”? 1 solutions Answer 170914 by stanbon(57361)   on 2009-10-24 08:23:43 (Show Source): You can put this solution on YOUR website!The robability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? The probability of no fatal accident in 50,000 trips is (3,999,999/4,000,000)^(50,000) = 0.987578..... So the probability of having a fatal accident is 1-0.987578... = 0.0124... The probability changes from youth to middle age to old age. ----------------------------------------------------------------- (b) Why might a driver be tempted not to use a seat belt “just on this trip”? Because the probability is so small on each individual trip. =============================== Cheers, Stan H.