Solve the problem.The angle of elevation from the top of a house to a plane flying 6300 meters above the house is x radians. If d represents the horizontal distance, in meters, of the plane from the house, express d in terms of a trigonometric function of x.

 Samuel Morse determined that the percentage of a’s in the English language in the 1800s was 8%. A random sample of 1000 letters from a current newspaper contained 803 t’s. We want to test if the proportion of a’s in this modern newspaper is different from 0.08 using the 0.05 level of significance.  (1) State the null (H0) and alternative (Ha) hypothesis using symbols. (3 pts) (2) Calculate the test statistic. Show your work. (4 pts) (3) Find the p-value using the Normal distribution table shown below for this hypothesis test. Show your work. (3 pts) (4) Determine whether we should reject or not to reject the hypothesis (state the reason to support your answer). Then state the conclusion of the hypothesis test in the context of the question. (5 pts) Assume that all required conditions are met.  

Stanford-Binet IQ scores for children are approximately normally distributed with µ = 100 and σ = 15. Find the score for the 90th percentile using the closest z-score in the below standard normal distribution table. Show your work. 

Find the standard deviation of the below sample data set. Show your work. 3, 2, 1, 2

According to National Safety​ Council, there were​ 13,600,000 soccer players and​ 208,214 injuries were treated in U.S. emergency rooms related to this sport in a particular year. What is the injury rate per​ 1,000 players? Show your work.

The accompanying table shows data for the numbers of pairs of shoes for female (group 1) and male (group 2). We want find the 95% confidence interval of the mean difference in number of pairs of shoes. The StatCrunch output is shown. Assume that the data are from random and independent samples. (1) Interpret the confidence interval in words. (3%) (2) Using the confidence interval, determine whether the true mean numbers of pairs of shoes are significantly different, and if so which group (female or male) has the larger number of pairs of shoes. State the reason to support your answer.  (4%)  

Select a correlation coefficient from the answer choices which matches to each scatter plot A to E.  Answer choices: -0.65 -0.85 1.00 0.01 0.87   Correlation coefficient (r) for scatter plot A is [plotA]. Correlation coefficient (r) for scatter plot B is [plotB]. Correlation coefficient (r) for scatter plot C is [plotC]. Correlation coefficient (r) for scatter plot D is [plotD]. Correlation coefficient (r) for scatter plot E is [plotE].

Which of the following is a reason we can never draw​ cause-and-effect conclusions from observational​ studies? 

Assume that the mean of 1,000 sample newborn infants in the U.S. is 7.2 pounds with a standard deviation of 1.2 pound and the distribution of the weight is symmetric and unimodal. Using the Empirical rule, approximately how many newborn infants in the sample are between 4.8 and 9.6 pounds? Show your work.

EXAM PROBLEM #2 Instructions: Type your answers to the questions in the textbox below. Label your answers A and B. Show all work on your “work” page.  Label which problem it is (#2). Reaction:     4 NH3 (g)  +  5 O2 (g) –>  4 NO (g)  +  6 H2O (g)              ΔH = -906.0 kJ Questions: A.   Is heat released or absorbed by the system in this reaction? Briefly explain how you know. B.   How many grams of ammonia, NH3 must react in order for 53.18 kcal to be released or absorbed in this reaction?