#1. [Water Slide & Swing] You are designing a slide for a water park. In a sitting position, park guests slide a vertical distance h down the water slide, which has negligible friction. When they reach the bottom of the slide, they grab a handle at the bottom end of a 6.00-m-long uniform pole. The pole hangs vertically, initially at rest. The upper end of the pole is pivoted about a stationary, frictionless axle. The pole with a person hanging on the end swings up through an angle theta max , and then the person lets go of the pole and drops into a pool of water. Treat the person as a point mass. The pole’s moment of inertia is given by I = (1/3)ML , where L = 6.00 m is the length of the pole and M = 24.0 kg is its mass. In your design, a person of mass m = 70.0 kg is to have a maximum angle of swing of theta max = 72.0˚ after their collision with the pole.

(a) In the "collision" between the slider and the pole, why is angular momentum about the pole's pivot conserved, but linear momentum and kinetic energy are not conserved? Assume that the slider is moving horizontally when they grab the handle on the vertically hanging pole.

(b) What is the angular speed of rotation of the pole & swinger just after the swinger grabs on, in terms of the final height the swinger reaches?

(c) What is the speed of the swinger at the bottom of the slide just before reaching the pole, in terms of their speed just after grabbing the pole?

(d) For a person of mass m = 70.0 kg, what must be the starting height h in order for the pole with person to have a maximum angle of swing of theta max =  72.0˚ after the collision?

Suppose a group of volunteers is planning on building a park near a local lake. The lake is known to contain low levels of arsenic (As). Therefore, prior to starting construction, the group decides to measure the current level of arsenic in the lake.

a) If a 15.7 cm3 sample of lake water is found to have 164.5 ng As, what is the concentration of arsenic in the sample in parts per billion (ppb), assuming that the density of the lake water is 1.00 g/cm3?

One of the volunteers suggests hiring an on-site water treatment company to remove the arsenic from the lake. The company claims their process takes 2.74 days to remove 41.90 kg of As from a water source.

b) Calculate the total mass (in kg) of arsenic in the lake that the company will have to remove if the total volume of water in the lake is 0.710 km3?

c) Based on the company\'s claim and the concentration of arsenic in the lake, how many years will it take to remove all of the arsenic from the lake, assuming that there are always 365 days in a year?

For questions 5 – 6, assume that to ride the Whirling Dervish at an amusement park, riders must be no taller than 75 in. Assume that men have normally distributed heights with a mean of 70 in. and a standard deviation of 2.8 in. 5. Find the percentage of men who will not meet the height requirement. Round to two percentage decimal places (for example, 38.29%). 6. If the height requirement is changed so that only the tallest 5% of men will be excluded from riding the Whirling Dervish due to height restrictions, what is the new height limit? Round to the nearest inch.

For questions 5 – 6, assume that to ride the Whirling Dervish at an amusement park, riders must be no taller than 75 in. Assume that men have normally distributed heights with a mean of 70 in. and a standard deviation of 2.8 in. 5. Find the percentage of men who will not meet the height requirement. Round to two percentage decimal places (for example, 38.29%). 6. If the height requirement is changed so that only the tallest 5% of men will be excluded from riding the Whirling Dervish due to height restrictions, what is the new height limit? Round to the nearest inch.

21. A public park is a public good because:

a. it is both excludable and rival good.

b. it is excludable but non rival

c. it is non-excludable but rival

d. it is non-excludable and non-rival.

22. If there are 5 firms in the market each with 10% of the market share, and another 10 firms that have the remaining market split between them equally, we can say that C4 or Concentration Ratio is 55%.

True or False

23. Regulated monopolies THAT operate on cost plus pricing, may make some positive economic profit.

True or False

24.

A monopoly faces a demand curve like:

if it finds that it's MR = MC occurs at Q = 3, what is the profit that the firm will make?

a. 60

b. 20

c. There is insufficient information

d. 6.66

The following data show the length of the coasters at the Mega Park (x) and height of the same coasters (y). The regression equation for the data is given by y = 21.94 + 0.018x

a.      State and interpret the slope in the context of this problem, given the regression equation above.

b.      How tall does the linear regression model predict a coaster of 3450 feet long will be?

c.       Find and interpret the residual for the coaster which is 3450 feet long and has a height of 100 feet?

1. A politician wants to open a new park in the middle of town. She needs to make sure that the local community supports the plan. A nearby town recently found that 60% of the community supported a similar plan and she believes that the same proportion will support it in her district. She takes a random survey of 40 people and find that the 10 people are supportive of her plan. She wants to be certain that this is not just due to statistical error. She is going to use an alpha of .01 for her study.
   1. What is the null and alternative hypotheses? (2)
   2. What are the critical values for this study? Please list all relevant information. (2)
   3. What is the statistic for the sample? (1)
   4. What is the P value for this sample (2)
   5. Do we reject the null hypotheses? Please interpret the hypotheses. (3)

Suppose a group of volunteers is planning on building a park near a local lake. The lake is known to contain low levels of arsenic (As). Therefore, prior to starting construction, the group decides to measure the current level of arsenic in the lake.

a) If a 15.7 cm3 sample of lake water is found to have 164.5 ng As, what is the concentration of arsenic in the sample in parts per billion (ppb), assuming that the density of the lake water is 1.00 g/cm3?

One of the volunteers suggests hiring an on-site water treatment company to remove the arsenic from the lake. The company claims their process takes 2.74 days to remove 41.90 kg of As from a water source.

b) Calculate the total mass (in kg) of arsenic in the lake that the company will have to remove if the total volume of water in the lake is 0.710 km3?

c) Based on the company\'s claim and the concentration of arsenic in the lake, how many years will it take to remove all of the arsenic from the lake, assuming that there are always 365 days in a year?

The manager of an amusement park would like to be able to predict daily attendance in order to develop more accurate plans about how much food to order and how many ride operators to hire. After some consideration, he decided that the following three factors are critical:
Yesterday’s attendance
Weekday or weekend (1 if weekend, 0 if weekday)
Predicted weather
Rain forecast ( 1 if forecast for rain, 0 if not)
Sun ( 1 if mostly sunny, 0 if not)
He then took a random sample of 40 days. For each day, he recorded the attendance, the previous day’s attendance, day of the week, and weather forecast. An example of the first few lines of Data and the regression output are below:
Attendance   Yest Att   I1   I2   I3
7882   8876   0   1   0
6115   7203   0   0   0
5351   4370   0   0   0
8546   7192   1   1   0

SUMMARY OUTPUT                  
                      
Regression Statistics                  
Multiple R   0.836766353                  
R Square   0.700177929                  
Adjusted R Square   0.665912549                  
Standard Error   810.7745532                  
Observations   40                  
                      
ANOVA                      
    df   SS   MS   F   Significance F  
Regression   4   53729535   13432384   20.43398   9.28E-09  
Residual   35   23007438   657355.4          
Total   39   76736973                 
                      
    Coefficients   Standard Error   t Stat   P-value   Lower 95%   Upper 95%
Intercept   3490.466604   469.1554   7.439894   1.04E-08   2538.031   4442.903
Yest Att   0.368547078   0.077895   4.731349   3.6E-05   0.210412   0.526682
I1   1623.095785   492.5497   3.295294   0.002258   623.1668   2623.025
I2   733.4646317   394.3718   1.85983   0.071331   -67.1527   1534.082
I3   765.5429068   484.6621   -1.57954   0.123209   -1749.46   218.3734
Test to see if the model is valid. Use alpha = .05
Can we conclude that weather is a factor in determining attendance?
If the manager is looking for a way to help predict attendance, Is this a good model to use? How would you suggest making this model better?

please give proper details for the answer. Thank you

The manager of an amusement park would like to be able to predict daily attendance in order to develop more accurate plans about how much food to order and how many ride operators to hire. After some consideration, he decided that the following three factors are critical: Yesterday’s attendance Weekday or weekend Predicted weather He then took a random sample of 36 days. For each day, he recorded the attendance, the previous day’s attendance, day of the week, and weather forecast(mostly sunny, rain, cloudy). The first independent variable is interval, but the other two are nominal. a. Create the three indicator variables you need. b. Conduct a regression analysis. c. Is this model valid? Explain. d. Can we conclude that weather is a factor in determining attendance? e. Do these results provide sufficient evidence that weekend attendance is, on average, larger than weekday attendance? f. Do these results provide sufficient evidence that mostly sunny attendance is, on average, larger than cloudy attendance?