to x years is Ix = -0.000354x 3 + 0.00452x²³² + 0.848x²-34.9% + 20,000 age 0≤x≤ 95.2 Find the rate of change of Ix with respect to x, and evaluate your answer for x=65
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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.A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rates in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations are normally distributed. The physician uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is computed as t≈5.627, which has 10 degrees of freedom. What range contains the p-value?A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rate in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations are normally distributed. The test statistic is t≈5.627, α=0.05, the corresponding rejection regions are t<−2.228 and t>2.228, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd≠0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is significantly not equal to…
- The variability of the scores in a sample tends to be _____ the variability of the scores in the population from which the sample was obtained. a. unrelated to b. larger than c. exactly the same as d. smaller thanA survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. What is the critical value of z if we need to conclude that the population proportion with a history of intrapartum or postpartum infection is less than 0.25.The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
- Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. 7.14 Of the 15 new MI cases in the preceding study,5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010Suppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 2 units?A company has found that its profits Y are related to its sales X by the formula Y = 0.2X + 100. If next year’s sales have a Normal distribution with a mean of 7,500 and a variance of 160,000. What is the distribution of next year's profit?
- What is your conclusion using a one sided z test if you assume α=0.01 and test the hypothesis that the proportion of colic is less among infants of mothers who don’t smoke than among the infants of mothers who smoke?The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuingto decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
