An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star's temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.

B-V index   Distance (ly)
1.1   1380
0.4   556
1.0   771
0.5   304
1.4   532
1.0   751
0.5   267
0.8   229
0.5   552
0.2   896
1.5   1819
0.5   381
0.5   257
1.1   541
0.7   133
0.5   300
0.0   985
0.4   525
1.0   408
1.1   1367
1.07   2848
1.1   128.9
1.12   1766.2
0.64   186.5
0.87   8269.2
0.19   828.9
1.03   153
0.55   223.6
1.39   963.9
0.89   91.7

R=

Two carts sit on a horizontal, frictionless track; the spring between them is compressed. The small cart has mass m, and the mass of the larger cart is M = 5.29m. NOTE: Every velocity needs magnitude and direction (given by the sign).

a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity v = +4.88 m/s. - Find the velocity of the larger cart. V =

Assume now that the mass of the smaller cart is m = 8.91 kg. Assuming there is no loss of energy: find the energy stored in the spring before the explosion. Wk =

If the spring has spring constant k = 935 N/m: find x, the distance the spring was compressed before the "explosion".

b) Suppose the carts are initially moving together, with the spring compressed between them, at constant velocity vo = +9.39 m/s. After the "explosion", the smaller cart is moving at velocity v = +4.88 m/s. Find the velocity of the larger cart.

c) Suppose now that the small cart (mass m) is initially moving at velocity vo = +3.3 m/s. At what velocity would the large cart (mass 5.29m) have to be moving so, when they collide and stick together, they remain at rest?

If you can show the work/ provide explanation I would greatly appreciate it :) Thanks

Ironman steps from the top of a tall building. He falls freely from rest to the ground a distance of h. He falls a distance of h/ 4 in the last interval of time of 1.0 s of his fall.

Hint: First, compute the velocity when Ironman reaches the height equal to the distance fallen. This requires that you do the following: define origin as the bottom of the building. Then use x-x0 = -v0*(t-t0)-(1/2)g(t-t0)^2 where x=0 and x0= (distance fallen) and t-t0 is the time interval given. In this formulation, you are going to get magnitude of v0 since you already inserted the sign. You then insert v0 that you just calculated into the kinematic equation that involves v, g, and displacement (v^2-v0^2 = 2g(height-(distance fallen)), but now v (which is the final velocity is v0 from above) and v0 in this case is the velocity that the Ironman has when he begins to fall, which is 0. This gives a quadratic equation for height h, and you will need to use the binomial equation to solve for h. Choose the larger of the two solutions.

Part A

What is the height h of the building?

Express your answer using two significant figures.

At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate).

The marginal cost of coffee is 5 and the marginal cost of a banana is 20.

The café owner is considering three pricing strategies:

Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.

For simplicity, assume there is just one student with an early class, and one student without an early class.

Pricing strategy   yields the highest profit for the café owner

In a survey of 3276 adults aged 57 through 85​ years, it was found that 88.4​% of them used at least one prescription medication. Complete parts​ (a) through​ (c) below.

a. How many of the 3276 subjects used at least one prescription​ medication? ​(Round to the nearest integer as​ needed.)

b. Construct a​ 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication. ​__% < p < __%(Round to one decimal place as​ needed.)

c. What do the results tell us about the proportion of college students who use at least one prescription​ medication? A. The results tell us​ that, with​ 90% confidence, the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b). B. The results tell us that there is a​ 90% probability that the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b). C. The results tell us nothing about the proportion of college students who use at least one prescription medication. D. The results tell us​ that, with​ 90% confidence, the probability that a college student uses at least one prescription medication is in the interval found in part​ (b).

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 19 nursing students from Group 1 resulted in a mean score of 62.1 with a standard deviation of 4.4. A random sample of 12 nursing students from Group 2 resulted in a mean score of 71.3 with a standard deviation of 7.1. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 4 : State the null and alternative hypotheses for the test. Step 2 of 4 :compute the value if the test statistic Step 3 of 4 : determine the decision rule for the null hypothesis, round to 3 decimal places. Step 4 of 4 Reject or fail hypothesis?

According to a book published in 2011, 45% of the undergraduate students in the United States show almost no gain in learning in their first two years of college (Richard Arum et al., Academically Adrift, University of Chicago Press, Chicago, 2011). A recent sample of 1460 undergraduate students showed that this percentage is 31%. Can you reject the null hypothesis at a 10% significance level in favor of the alternative that the percentage of undergraduate students in the United States who show almost no gain in learning in their first two years of college is currently lower than 45%. Use both the p-value and the critical-value approaches. Round your answers for the observed value of z and the critical value of z to two decimal places, and the p-value to four decimal places. zobserved =Enter you answer; z_observed Entry field with incorrect answer p-value =Enter you answer; p-valueEntry field with incorrect answer Critical value =Enter you answer; Critical valueEntry field with incorrect answer now contains modified data Hence we can conclude that the percentage of undergraduate students in the U.S. who show almost no gain in learning in their first two years of college is currently Choose the answer from the menu in accordance to the question statementEntry field with incorrect answer 45%.

Label the following 2-sample tests as: Proportions, Independent, and Dependent (matched-pairs). Determine the null and alternative hypothesis and whether the test is one-tailed or two-tailed. Then explain in detail the reasons behind your answers. You do not have to work the problems out. 1. The pre-test scores for 6 students were: 5, 5, 6, 7, 7, 8. The post-test scores for the same 6 students were: 7, 6, 7, 7, 9, 9. Is there a statistically significant difference between the two scores if we assume that the post-test scores were higher at the .01 level? 2. One group of 8 students took a pre-test, while another group of 7 students took a post-test. The following are the results: Pre-test: 5,6,4,3,4,6,6,7. Post-test: 6,6,8,7,9,8,8. Is there a difference between pre and post-test scores at the .01 level? 3. Two surveys were conducted asking participants whether they thought the morality of Americans was decaying or not. The percent of those who thought there was a decay in morality was 56% in survey 1, while the percent of those who thought there was a decay in morality was 59.5% in survey 2. Test the claim survey 2's percent was larger at the .05 level.

The legislature of a southern state in the U.S. passed a rule, commonly called "no-pass, no-play", which prohibits a student who fails in any subject from participating in any extracurricular activity for six weeks. Data were collected for students involved in football, volleyball, cross country, and band for the first six-week grading period. Records were kept from last year and this year. The numbers of students is stored in column 1 and the proportions sidelined because of the rule are stored in column 2 of Table C, the first row being for last year and the second for this year.

29. What is the upper 90% confidence limit on the change in proportion of students sidelined because of failure?

30. What was the average (pooled) proportion sidelined?

31. Now use the pooled proportion to calculate the standard error of the difference between the two proportions. ) What is the value of the test statistic for testing the hypothesis that the proportion did not change (remember to divide by the standard error of the difference between the two proportions which was calculated using the pooled proportion)?

32. Was the superintendent of schools justified in saying, "We are very pleased with the improvement. It shows coaches and students are taking the rule seriously"? Answer 1 for yes or 0 for no.

DATA C:

273 0.29827189801646

256 . 0.28966880074687