Concept explainers
Focal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece (see Figure 3.42). For a given magnification
|
|
|
|
|
|
|
|
|
|
a. Construct a linear model for the data.
b. In this example, the magnification
c. Solve the equation you obtained in part b for
d. To achieve a large magnification, how should the objective and eyepiece lenses be selected?
FIGURE 3.42
Trending nowThis is a popular solution!
Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra (7th Edition)
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Beginning and Intermediate Algebra
College Algebra: Graphs and Models (6th Edition)
College Algebra (5th Edition)
Elementary & Intermediate Algebra
- We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the fifteen houses. (These products, written in the column labelled "xy", may aid in calculations.) Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) xy 5.0 270.1 1350.5 11.5 205.9 2367.85 5.9 309.4 1825.46 12.2 200.6 2447.32 2.6 307.1 798.46 5.9 266.0 1569.4 8.3 297.3 2467.59 18.3 224.2 4102.86 6.5 242.4 1575.6 12.1 192.6 2330.46 11.6 229.4 2661.04 9.5 230.9 2193.55 10.1 277.0 2797.7 13.5 270.8 3655.8 6.2…arrow_forwardWe want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the sixteen houses. (These products, written in the column labelled "xy", may aid in calculations.) Selling price, y (in thousands of dollars) 289.2 233.9 201.0 306.5 210.9 217.2 234.3 264.6 292.8 267.0 216.8 274.8 234.9 317.1 192.0 259.3 Distance from the beach, x (in miles) 10.7 9.2 13.7 5.8 7.7 17.4 11.4 9.8 6.9 6.9 9.9 5.6 7.5 4.2 14.3 14.2 Send data to calculator ху 3094.44 2151.88 2753.7 1777.7 1623.93 3779.28 2671.02 2593.08 2020.32 1842.3 2146.32 1538.88 1761.75 1331.82…arrow_forwardWe want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given are the products of the distances from the beach and house prices for each of the sixteen houses. (These products, written in the column labelled "xy," may aid in calculations.)arrow_forward
- We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the sixteen houses. (These products, written in the column labelled"xy", may aid in calculations.) Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) xy 11.1 232.2 2577.42 8.8 293.5 2582.8 9.2 279.6 2572.32 12.3 276.2 3397.26 5.5 241.5 1328.25 5.3 303.8 1610.14 4.9 271.1 1328.39 13.9 188.6 2621.54 3.2 321.6 1029.12 10.0 212.1 2121 13.2 199.7 2636.04 15.2 259.5 3944.4 11.2 218.7 2449.44 5.3 275.2 1458.56…arrow_forwardWe want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach ( x , in miles) and the selling price ( y , in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Distance from the beach, x(in miles) Selling price, y(in thousands of dollars) 13.3 224.2 10.0 288.0 13.7 272.4 10.0 229.5 4.6 274.1 12.7 190.6 8.2 289.4 9.1 215.4 11.5 272.8 7.0 244.4 4.9 309.5 12.4 198.9 7.0 305.4 11.8 202.5 5.7 277.1 18.0 228.5 y 150 200 250 300 350 x 5 10 15 20 0 Figure 1 The value of the sample correlation coefficient r for these data is approximately −0.577 . Answer the…arrow_forwardWe want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Distance from the beach, x (in miles) 5.1 6.2 9.5 10.3 10.7 5.3 12.6 13.0 19.4 8.2 5.2 3.8 9.0 11.7 11.5 8.3 Send data to calculator V Selling price, y (in thousands of dollars) 263.5 274.6 238.6 223.7 267.1 306.2 202.5 267.7 217.3 224.7 241.0 312.0 284.6 210.9 185.6 294.2 Send data to Excel thousands of dollars) Selling price 350+ 300+ Figure 1 250 200 150. 0 Distance from the beach (in miles) Español F00 ? D 1 As Marrow_forward
- We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the sixteen houses. (These products, written in the column labelled "xy", may aid in calculations.) Distance from the beach, x (in miles) 7.7 18.5 6.3 11.9 11.0 14.6 11.3 3.0 Selling price, y (in thousands of dollars) 290.8 215.0 304.4 269.9 283.2 203.4 212.4 263.2 197.3 272.2 215.1 241.6 312.3 221.5 279.1 236.1 10.9 4.9 12.5 5.8 3.6 5.7 9.4 8.1 Send data to calculator xy 2239.16 3977.5 1917.72 3211.81 3115.2 2969.64 2400.12 789.6 2150.57 1333.78 2688.75 1401.28 1124.28 1262.55…arrow_forwardThe scatterplot shows how the pulse rate changes with the weight of a person. Pulse Rate 86.41 - 0.09144(Weight) %3D 100 90 80 70 60 50 100 120 140 160 180 200 220 Pulse Ratearrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 74 77 34 96 208 y km/100 14.9 19.1 5.8 11.9 35.7 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (b) Use a 1% level of significance to test the claim ρ > 0. (Round your answers to two decimal places.) t = critical t = Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ >…arrow_forward
- Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 76 79 36 95 207 y km/100 14.2 19.6 5.4 11.2 35.9 (a) Verify that Σx = 493, Σy = 86.3, Σx2 = 65,187, Σy2 = 2029.21, Σxy = 11317.3, and r ≈ 0.93885. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 4.6183, a ≈ 0.5575, and b ≈ 0.1694. Se a b Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2…arrow_forwardThe Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower's stability have done extensive studies on its increasing tilt. The following table shows how the lean has changed in excess of 2.9 meters by year since 1975. Year Lean Year Line Fit Plot 75 642 780 76 644 760 77 656 78 667 740 79 673 720 80 688 700 81 696 680 82 698 660 83 713 84 717 640 85 725 620 70 75 80 85 90 86 742 87 757 • Lean Predicted Lean Year A regression analysis was run on this data, and the results from Excel are shown below. ANOVA Significance F 0.000000000007 df SS MS 1 15804.48 15804.48 904.1198 Regressior Residual 11 192.2857 17.48052 12 15996.77 Total Coefficientstandard Err Intercept -61.12088 25.12982 -2.432205 0.033279 9.318681 0.309914 30.06858 Upper 95%.ower 95.0%Jpper 95.0% -116.4312367 -5.810522 -116.4312 -5.810522 10.0008 8.636565 t Stat P-value Lower 95% Year 6.5E-12 8.636564768 10.0008 a) What would Ho and Ha be to show whether the regression line is useful? b) What…arrow_forwardThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 11.8 8.6 6.8 3.7 2.8 2.6 2.6 0.9 14.1 11.5 9.8 6.9 6.6 6.5 6.2 4.6 thousands of automatic weapons y = murders per 100,000 residents %3D This data can be modeled by the equation y = 0.86x + 3.99. Use this equation to answer the following; A) How many murders per 100,000 residents can be expected in a state with 7.7 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 1.9 thousand automatic weapons? Answer = Round to 3 decimal places.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning