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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
- I need help with part (c) only, I need t statistic and p value. Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m3): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship.No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and…Your company manufactures plastic wrap for food storage. The tear resistance of the wrap, denoted by X, must be controlled so that the wrap can be torn off the roll without too much effort but it does not tear too easily when in use. In a series of tests (see data table below), 15 rolls of wrap are made under carefully controlled conditions and the tear resistance of each roll is measured. The results are used as the basis of a quality assurance specification. If X for a subsequently produced roll falls more than two standard deviations away from the test period average, the process is declared out of specification and production is suspended for routine maintenance. Roll 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X 134 131 129 133 135 131 134 130 131 136 129 130 133 130 133 Write an Excel spreadsheet to calculate the sample mean and sample standard deviations. The {#1} {#2} a)What…Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.
- 1. Use geometric similarity to estimate a relationship between the masses and lengths of a specific fish species 2. Test graphically if the given data below supports the proportionality y ∝ x3 .River Hills Hospital is interested in determining the effectiveness of a new drug for reducing the time required for complete recovery from knee surgery. Complete recovery is measured by a series of strength tests that compare the treated knee with the untreated knee. The drug was given in varying amounts to 18 patients over a 6-month period. For each patient the number of drug units, X, and the days for complete recovery, Y, are given by the following (x, y) data:(5, 53) (21, 65) (14, 48) (11, 66) (9, 46) (4, 56)(7, 53) (21, 57) (17, 49) (14, 66) (9, 54) (7, 56)(9, 53) (21, 52) (13, 49) (14, 56) (9, 59) (4, 56)a. Compute the covariance.b. Compute the correlation coefficient.c. Briefly discuss the relationship between the number of drug units and the recovery time. What dosage might we recommend based on this initial analysis?A statistical program is recommended. Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density,"† was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate Std. Error t value Pr(>|t|) (Intercept) 4.858691 0.059768 81.283 <2e-16 AirVoid −0.074676 0.009923 −7.526 1.21e-06 Residual standard error: 0.03551 on 16 DF Multiple R-squared: 0.7797, Adjusted…
- The following data represent partial pressure of CO2 and the related respiration rates for males and females. Provide a research quality analysis of these data. Show all steps. Please justify your choice of analysisOne effect of the pesticide DDT upon birds is to inhibit the production of the enzyme carbonic anhydrase, which controls calcium metabolism. It is believed that this causes eggshells to be thinner and weaker than normal and makes the eggs more prone to breakage. An experiment was conducted where 16 sparrow hawks were fed a mixture of 3 ppm dieldrin and 15 ppm DDT (a combination often found in contaminated prey). The first egg laid by each bird was measured, and the mean shell thickness was found to be 0.19 mm. A “normal” eggshell has a mean thickness of 0.2 mm. What are the null and alternative hypotheses?where is the graphical estimation method (by hand)