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Recent problems solved by 'stanbon'

stanbon answered: 57135 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next

Linear-systems/444218: I am having trouble simplifying this. {12+[6(9x+2y)]}-[8(4x+19y)] 1 solutions Answer 306268 by stanbon(57203)   on 2011-05-03 08:03:47 (Show Source): You can put this solution on YOUR website! duplicate

Linear-systems/444219: I am having trouble simplifying this {12+[6(9x+2y)]}-[8(4x+19y)] 1 solutions Answer 306267 by stanbon(57203)   on 2011-05-03 08:02:39 (Show Source): You can put this solution on YOUR website! {12+[6(9x+2y)]}-[8(4x+19y)]} ----- = {12+[54x+12y]}-[32x+152y]} = {12+54x+12y-32x-152y} --- = 22x -140y + 12 ==================== Cheers, Stan H. ==========

Probability-and-statistics/444133: Are the following statements a valid pair of null and alternative hypothesis? Ho: U> 5 and Ha: u<17? Is the following a valid null statement? Ho : 13=11? 3.) Assume that a 95% confidence interval for the mean is (13.0, 15.0). What is the result of a hypothesis test of Ho u =1.0 at a (alpha) = 0.05? 1 solutions Answer 306232 by stanbon(57203)   on 2011-05-02 22:56:51 (Show Source): You can put this solution on YOUR website! Are the following statements a valid pair of null and alternative hypothesis? Ho: U> 5 and Ha: u<17? ---- No; Equality must ALWAYS be stated in Ho. ---------------------------------------------------- Is the following a valid null statement? Ho : 13=11? No; it is a contradiction : it does not make a statement about a population parameter. ---------------------------------------------------- 3.) Assume that a 95% confidence interval for the mean is (13.0, 15.0). What is the result of a hypothesis test of Ho u = 1.0 at a (alpha) = 0.05? --- Reject Ho. ============== Cheers, Stan H.

Probability-and-statistics/444075: What are the numbers used in making a box-and-whisker plot? (a) Low value, Q1, mean, Q3, high value (b) Low value, Q1, median, Q3, high value (c) s, mean, s2, interquartile range (d) Q1, Q2, Q3 (e) Low value, interquartile range, high value 1 solutions Answer 306208 by stanbon(57203)   on 2011-05-02 20:59:02 (Show Source): You can put this solution on YOUR website! Ans: b Cheers, Stan H.

Probability-and-statistics/444065: A baseball player has a batting average of 0.16. What is the probability that he has exactly 6 hits in his next 7 at bats? What is the probability ? 1 solutions Answer 306207 by stanbon(57203)   on 2011-05-02 20:56:08 (Show Source): You can put this solution on YOUR website! A baseball player has a batting average of 0.16. What is the probability that he has exactly 6 hits in his next 7 at bats? ----- Binomial Problems with n = 7 and p = 0.16 ----- P(x = 6) = 7C6(0.16)^6*(0.84) = binompdf(7,0.16,6) = 0.00009865.. --------------------- Cheers, Stan H.

Probability-and-statistics/444069: Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American and goes to trial. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant's lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. Compute the probability and discuss the assumptions. 1 solutions Answer 306196 by stanbon(57203)   on 2011-05-02 20:27:17 (Show Source): You can put this solution on YOUR website! Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American and goes to trial. ----------------------------------------------------- Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant's lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. Compute the probability and discuss the assumptions. ------- Binomial Problem with n = 12 and p = 0.30 ----------------- P(x = 2) = 12C2(0.3)^2*(0.7)^10 = binompdf(12,0.3,2) = 0.1678 = 16.78% ------------------------------ So the probabiity of that happenin is close to 17%. I'll leave the discussion to you. ----- Cheers, Stan H.

Numeric_Fractions/444047: Pond depth. On July 1, Garrett’s Pond was 25 ft deep. Since that date, the water level has dropped ft per week. For what dates will the water level not exceed 21 ft? 1 solutions Answer 306185 by stanbon(57203)   on 2011-05-02 19:56:02 (Show Source): You can put this solution on YOUR website! Pond depth. On July 1, Garrett’s Pond was 25 ft deep. Since that date, the water level has dropped ?? ft per week. For what dates will the water level not exceed 21 ft? ----------------------- A number is missing from your post. See ??. Cheers, Stan H.

Polynomials-and-rational-expressions/443904: Biologist want to set up a station to test alligators in the lake for West Nile virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test. a.) write an expression that gives the total cost to test x animals. b.) you can find the average cost per animal by dividing total costs by number of animals. write the expression that gives the average cost per animal. c.) find the average cost per animal for 10 animals, 100 animals, and 1,000 animals. d.) as the number of animals tested increases, what happens to the average cost to test the animals? would the average cost ever fall below $3.00? if so, identify a value that supports your anser. if not, explain how you know. e.) how many animals should be tested for the average cost to be $5.00 per animal? 1 solutions Answer 306118 by stanbon(57203)   on 2011-05-02 16:38:02 (Show Source): You can put this solution on YOUR website! Biologist want to set up a station to test alligators in the lake for West Nile virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test. a.) write an expression that gives the total cost to test x animals. --- C(x) = 2500 + 3x ----------------------------------- b.) you can find the average cost per animal by dividing total costs by number of animals. write the expression that gives the average cost per animal. --- A(x) = (2500+3x)/x ----------------------------------- c.) find the average cost per animal for 10 animals, 100 animals, and 1,000 animals. --- Find A(10), A(100) and A(1000) ----------------------------------- d.) As the number of animals tested increases, what happens to the average cost to test the animals? :::it decreases. ----- would the average cost ever fall below $3.00? :: No ------------------------------------------------------ If so, identify a value that supports your answer. A(5000) = (2000+3*5000)/5000 = 17/5 = $3.40 ------------- if not, explain how you know. e.) how many animals should be tested for the average cost to be $5.00 per animal? --- Solve: 5.00 = (2000+3x)/x 5x = 2000+3x 2x = 2000 x = 1000 ---------------- Cheers, Stan H.

Evaluation_Word_Problems/443903: One gear turns times in a minute. Another gear turns 45 times in a minute. Initially, a mark on each gear is pointing due north. After how many seconds will the two gears next have both their marks pointing due north? 1 solutions Answer 306112 by stanbon(57203)   on 2011-05-02 16:24:25 (Show Source): You can put this solution on YOUR website! One gear turns ?? times in a minute. Another gear turns 45 times in a minute. Initially, a mark on each gear is pointing due north. After how many seconds will the two gears next have both their marks pointing due north? ------------------------ Your post is missing a needed number in the 1st sentence. Cheers, Stan H.

Probability-and-statistics/443770: Please help Records of individuals from France who died recently are selected at random. The individuals lived an average of years with a standard deviation of years. Records of individuals from Germany who died recently are selected at random and independently. The individuals lived an average of years with a standard deviation of years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the level of significance, is there enough evidence to support the claim that the life expectancy, , in France is greater than the life expectancy, , in Germany? Perform a one-tailed test. 1) The null hypothesis 2) The alternative hypothesis 3) The type of test statistic (ex. Z, t, Chi-Square, etc.) 4) The value of the test statistic 5) The p value 6) YES or NO 1 solutions Answer 306026 by stanbon(57203)   on 2011-05-02 12:26:41 (Show Source): You can put this solution on YOUR website! I don't know why this happens so often on this site but your post is missing the "mean" number and the "standard deviation" number. Both are essential to working your problem. Cheers, Stan H.

Triangles/443778: If the lengths of two sides of a triangle are 4 and 13, what is the range of possible lengths for the third side? 1 solutions Answer 306025 by stanbon(57203)   on 2011-05-02 12:22:56 (Show Source): You can put this solution on YOUR website! If the lengths of two sides of a triangle are 4 and 13, what is the range of possible lengths for the third side? ---- Let the 3rd side be "s". --- The 13-4 < s < 13+4 9 < s < 17 ==================== Cheers, Stan H.

Volume/443513: The lenght of the side of a square is increase by 50%. By what % is the area of the square increase. 1 solutions Answer 305901 by stanbon(57203)   on 2011-05-01 21:55:21 (Show Source): You can put this solution on YOUR website! The length of the side of a square is increase by 50%. By what % is the area of the square increase. ------------------------------ If side = "s", area = s^2. --- If s is increased by 50% you get (1.5s) Area will be (1.5s)^2 = 2.25s^2 --- Increase = 2.25s^2-s^2 = 1.25s^2 --- % increase = (1.25s^2)/s^2 = 1.25 = 125% increase =============================== Cheers, Stan H.

Miscellaneous_Word_Problems/443507: "Please help!!! I cannot figure out the answer to this question. I've tried different formulas and still can't get the right answer. If I can find the right formula this will help out tremendously. Here is the question: A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.) 1 solutions Answer 305886 by stanbon(57203)   on 2011-05-01 20:59:48 (Show Source): You can put this solution on YOUR website! A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.) ------ It appears that the sample mean is 15 tons. No unit price sees to be available. No standard deviation value is stated. ----- The margin of error is zs/sqrt(n) -- For a 90% CI z = 1.645 ---- The CI will be 15-1.645s/sqrt(n) < u < 15+1.645s/sqrt(n) -------------------------------------------------------------- Cheers, Stan H.

Mixture_Word_Problems/443407: a recipe for sauce makes 12 1/2 oz., and the recipe calls for 7 oz puree. you want to make thirty 1 1/2 oz servings. how many oz of puree should you use? 1 solutions Answer 305850 by stanbon(57203)   on 2011-05-01 18:26:38 (Show Source): You can put this solution on YOUR website! A recipe for sauce makes 12 1/2 oz., and the recipe calls for 7 oz puree. you want to make thirty 1 1/2 oz servings. how many oz of puree should you use? -------------------- puree/(30*(3/2)) = 7 oz/(25/2)oz --- puree/45 = 7/12.5 ---- puree = (315/12.5) = 25.2 oz. ====================================== Cheers, Stan H.

Polygons/443410: Which polygon has 2 times as many angles as a pentagon? 1 solutions Answer 305842 by stanbon(57203)   on 2011-05-01 18:12:33 (Show Source): You can put this solution on YOUR website! Which polygon has 2 times as many angles as a pentagon? ---------------------- Ans: decagon

Probability-and-statistics/443406: A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probablity that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation. My teacher gave me the answer of 0.995, I was wondering what steps/how to begin this problem. I have tried nCr = n! / r!(n - r)! = nPr / r! to slove this, using p = .65, n = 5, and r = 1. And have not been able to get the correct answer. Thank you!!! 1 solutions Answer 305838 by stanbon(57203)   on 2011-05-01 18:09:51 (Show Source): You can put this solution on YOUR website! A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probablity that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation. My teacher gave me the answer of 0.995, I was wondering what steps/how to begin this problem. ------------------- P(a single student finds a job) = 0.65 P(a student does not find a job) = 0.35 ------------------ Binomial Problem with n = 5 ; p(finds a job) = 0.65 --- Problem: Find P(at least one of 5 finds a job) = 1 - P(none of 5 find a job) --- = 1 - (0.35)^5 --- = 1 - 0.005252 ------------- = 0.9947 ========================== Cheers, Stan H.

Equations/443386: Show the work to solve |2x+5| -1 < 6 Describe the graph of the solution in a complete sentence 1 solutions Answer 305832 by stanbon(57203)   on 2011-05-01 18:00:10 (Show Source): You can put this solution on YOUR website! Show the work to solve |2x+5| -1 < 6 Describe the graph of the solution in a complete sentence ---------------------- |2x+5| -1 < 6 --- |2x+5| < 7 --- 2x+5< -7 or 2x+5> 7 ----- 2x < -12 or 2x > 2 ---- x < -6 or x > 1 ====================== Cheers, Stan H.

Trigonometry-basics/443396: What value of x in the interval 0° ≤ x ≤ 180° satisfies the equation sqrt3 tan x + 1 = 0 1 solutions Answer 305830 by stanbon(57203)   on 2011-05-01 17:52:06 (Show Source): You can put this solution on YOUR website! What value of x in the interval 0° ≤ x ≤ 180° satisfies the equation sqrt3 tan x + 1 = 0 ----- sqrt(3)tan(x) = -1 tan(x) = -1/sqrt(3) --- Take the tan^-1 of both sides to get: x = -30 degrees That angle is in the 4th Quadrant. --- For your problem the equivalent angle in the 2nd Quadrant would be x = 180-30 = 150 degrees ----- Cheers, Stan H. ==========

Polynomials-and-rational-expressions/443391: Solve: 3p(3p-8)-8=9p(p-3)+4 Help? Thanks 1 solutions Answer 305827 by stanbon(57203)   on 2011-05-01 17:37:48 (Show Source): You can put this solution on YOUR website! Solve: 3p(3p-8)-8 = 9p(p-3)+4 ------- 9p^2 - 24p - 8 = 9p^2 - 27p + 4 ------- Subtract 9p^2 from both sides. Add 27p to both sides. ------- 3p = 12 p = 4 ------------ Cheers, Stan H.

Quadratic-relations-and-conic-sections/443389: write in standard form what 5x^2-9x^2=45 1 solutions Answer 305824 by stanbon(57203)   on 2011-05-01 17:26:56 (Show Source): You can put this solution on YOUR website! write in standard form what 5x^2-9x^2=45 -------------- -5x^2 = 45 --- x^2 = -45 --- x = sqrt[-9*5] --- x = +-3i*sqrt(5) =================== Cheers, Stan H. ====================

Graphs/443387: I am having trouble with this equation: m^2 - 1 / (m + 1)^2. Can someone please help me with this equation? 1 solutions Answer 305822 by stanbon(57203)   on 2011-05-01 17:23:25 (Show Source): You can put this solution on YOUR website! I am having trouble with this equation: m^2 - 1 / (m + 1)^2. Can someone please help me with this equation? -------------------------- That is not an equation but it can be simplified. ----- (m^2 - 1 / (m + 1)^2 ---------- Factor: ---- [(m-1)(m+1)] / [(m+1)(m+1)] Cancel the common (m+1) factors to get: --- = (m-1)/(m+1) ============== Cheers, Stan H.

Trigonometry-basics/443351: The expression sin(180-x) is equivalent to 1 solutions Answer 305799 by stanbon(57203)   on 2011-05-01 16:26:21 (Show Source): You can put this solution on YOUR website! sin(x) = sin(180-x) ======================== Cheers, Stan H.

Angles/443348: What would be the non-negative obtuse angle for Q if its sin is square root 3 over 2? 1 solutions Answer 305798 by stanbon(57203)   on 2011-05-01 16:25:10 (Show Source): You can put this solution on YOUR website! What would be the non-negative obtuse angle for Q if its sin is square root 3 over 2? ----- In the 1st Quadrant that angle would be 60 degrees. In the 2nd Quadrant it would be 180-60 = 120 degree. --- Obtuse is greater than 90 so I guess they want 120 degrees. Cheers, Stan H.

Sequences-and-series/443347: find the fourth term in the expansion of (A + 2B)^10 using the binomial theorem 1 solutions Answer 305797 by stanbon(57203)   on 2011-05-01 16:22:13 (Show Source): You can put this solution on YOUR website! find the fourth term in the expansion of (A + 2B)^10 using the binomial theorem ============= Ans: 10C7(A)^7(2B)^2 ========================== Cheers, Stan H.

Rational-functions/443325: This is a long question with multiple parts but is just one single question my professor gave me to work on but that I'm stuck on. Test: 1. y=x to the 4th minus 2x squared 2. y=x to the 3rd minus 6x 3. y=x squared + 2x + 1 for symmetry with respect to: 1. x-axis 2. y-axis 3. the origin (0,0) 4. write them in function notation and say which one is even, odd, or neither? 1 solutions Answer 305794 by stanbon(57203)   on 2011-05-01 15:54:18 (Show Source): You can put this solution on YOUR website! 1. y=x to the 4th minus 2x squared 2. y=x to the 3rd minus 6x 3. y=x squared + 2x + 1 for symmetry with respect to: 1. x-axis 2. y-axis 3. the origin (0,0) 4. write them in function notation and say which one is even, odd, or neither? --------------------------------------------------------------------------------I. y=x to the 4th minus 2x squared f(x) = x^4-2x^2 --- 1. Check f(x) = -f(x) x^4-2x^2 = -(x^4-2x^2) Ans: no x-axis symmetry --------------------- 2. Check f(x) = f(-x) x^4-2x^2 = (-x)^4-2(-x^2) x^4-2x^2 = x^4-2x^2 Ans: yes so y-axis symmetry -------------------------- 3rd: Check f(x) = -f(-x) x^4-2x^2 = -((-x)^4-2(-x)^2) x^4-2x2 = -(x^4-2x^2) Ans: no so no origin symmetry ====================================== Do the same for the other listed problems. Form f(x), -f(x), f(-x) and -f(-x) --- If f(x) = -f(-x) you have x-axis symmetry If f(x) = f(-x) you have y-axis symmetry If f(x) = -f(-x) you have origin symmetry ========================================= Cheers, Stan H.

Triangles/443328: From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 9 miles per hour and Fred rides 13 miles per hour. In how many hours will they be 88 miles apart? 1 solutions Answer 305792 by stanbon(57203)   on 2011-05-01 15:42:53 (Show Source): You can put this solution on YOUR website! From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 9 miles per hour and Fred rides 13 miles per hour. In how many hours will they be 88 miles apart? --- They are separating at the rate of (9+13) = 22 mph. ---- time = distance/rate ---- time = 88 miles/ 22mph = 4hrs. ============================================= Cheers, Stan H.

Rational-functions/443313: Find two functions, f(x) and g(x) such that (fog)(x)=h(x) or (gof)(x)=h(x) where h(x)= sq. rt. of x squared minus 2 over x squared plus 3, and verify. 1 solutions Answer 305791 by stanbon(57203)   on 2011-05-01 15:40:18 (Show Source): You can put this solution on YOUR website! Find two functions, f(x) and g(x) such that (fog)(x)=h(x) or (gof)(x)=h(x) where h(x)= sq. rt. of x squared minus 2 over x squared plus 3, and verify. ------------------ fog(x) = sqrt[(x^2-2)/(x^2+3)] --- Let g(x) = (x^2-2)/(x^2+3) Let f(x) = sqrt(x) --- Then fog(x) = f[g(x)] = f[(x^2-2)/(x^2+3)] = sqrt[(x^2-2)/(x^2+3)] ====================== Cheers, Stan H.

Rational-functions/443318: Suppose f(x)=A ln(x)+B, where A and B are constants. If f(1)=10 and f(e)=1. what are A and B? What are key algebraic concepts needed to solve the problem? 1 solutions Answer 305788 by stanbon(57203)   on 2011-05-01 15:29:12 (Show Source): You can put this solution on YOUR website! Suppose f(x)=A ln(x)+B, where A and B are constants. If f(1)=10 and f(e)=1. what are A and B? What are key algebraic concepts needed to solve the problem? ----------------------- f(x)=A ln(x)+B f(1) = 10 f(1) = A*ln(1)+B = A*0+B = B So, B = 10 ------------------- f(e) = 1 f(e) = A*ln(e)+B f(e) = A*1+B f(e) = A+B --- So, A+B = 1 But B = 10, so A = -9 ================= Cheers, Stan H. =============

Polynomials-and-rational-expressions/443262: FInd the LCM of (3+2s),(9-4s^2), and (3-2s) 1 solutions Answer 305769 by stanbon(57203)   on 2011-05-01 14:07:22 (Show Source): You can put this solution on YOUR website! Find the LCM of (3+2s),(9-4s^2), and (3-2s) ----------------------------------------------- lcm = (9-4s^2) because each of those factors divides into it with no remainder. =========================== Cheers, Stan H.

Quadratic_Equations/443245: beginning with f(x) = squareroot of x, find the function g(x) that shows f(x) shifted to the left 2 units, reflected about the x axis, and then shifted up 7 units? 1 solutions Answer 305761 by stanbon(57203)   on 2011-05-01 13:47:34 (Show Source): You can put this solution on YOUR website! beginning with f(x) = squareroot of x, find the function g(x) that shows f(x) shifted to the left 2 units, reflected about the x axis, and then shifted up 7 units? ---- f(x) = sqrt(x) shifted left 2 units gives a(x) = sqrt(x+2) --- reflected about x axis gives b(x) = -sqrt(x+2) --- shifted up 7 units gives: F(x) = -sqrt(x+2)+7 =============================== Cheers, Stan H. ===============

Square-cubic-other-roots/443238: two investments are made totaling $10,000. In one year these investments yield $650 in simple interest. Part of the $10,000 in invested at 5 1/2%, and the rest at 6 3/4%. How much more money is invested at 6 3/4%? 1 solutions Answer 305746 by stanbon(57203)   on 2011-05-01 13:10:18 (Show Source): You can put this solution on YOUR website! two investments are made totaling $10,000. In one year these investments yield $650 in simple interest. Part of the $10,000 in invested at 5 1/2%, and the rest at 6 3/4%. How much more money is invested at 6 3/4%? ---- 2-variable solution: Quantity Eq. :: x + y = 10,000 Interest Eq. ::0.055x + 0.0675y = 650 ----------------------------------- Multiply 1st by 550 Multiply 2nd by 10000 ------------------------- 550x + 550y = 550*10,000 550x + 675y = 6400000 ---------------------------------------- Subtract and solve for "y": 125y = 9000000 y = $7200 (amt invested at 6 3/4%) =================== Cheers, Stan H.