4.2)Two books are accelerating to the right on a frictional surface and the coefficient of kinetic friction between the floor
ction between the floor and book is µk. Using the information given in the figure:
(a) draw free body diagrams for both the books, and also for the combined system (of mass m1+m2),
(b) find acceleration of the books along horizontal direction, and
(c) find the magnitude and direction of the force exerted by the left book on the right book.
3.A car of mass 1500-kg enters a circular path at point P and leaves at point Q (see the figure) at constant speed of 5.0m/s, and the frictional force acting on its tires is 2500-N.
a) how long it takes to reach point Q from point P, and
b) what should be the minimum value of the coefficient of static friction between the tires and the road?
4)In an elevator which is accelerating downward at 2.5ms−2 , a 25-kg block hangs from a spring attached to the ceiling of the elevator. If spring gets stretched by 0.15m, find its spring constant.
5.Can domestic dogs understand human body cues such as leaning? The experimenter leaned toward one of two objects and recorded
two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 42 out of 70 times when the experimenter leaned towards the correct object.
(a) (2 points) Let the parameter of interest, π, represent the probability that the long-run probability that Augie chooses correctly. Researches are interested to see if Augie understands human body cues (better than gussing).
Fill in the blanks for the null and alternative hypotheses.
H0 : Ha :
(b) (6 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 10%? (If you use an applet, please specify which applet you use, and the inputs.)
(c) (5 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 5%? (If you use an applet, please specify which applet you use, and the inputs.)
(d) (2 points) Are your conclusions from part (b) and (c) the same? If they are different, please provide an explanation.
(e) (5 points) Shown below is a dotplot from a simulation of 100 sample proportions under the assump- tion that the long-run probability that Augie chooses correct is 0.50. Based on this dotplot, would a 90% confidence interval for π contain the value 0.5? Explain your answer.
(f) (4 points) Compute the standard error of the sample proportion of times that Augie chose the object correctly.
(g) (5 points)
(h) (3 points) question?
(i) (4 points)
(j) (4 points) A.
Construct an approximate 95% confidence interval for π using the 2SD method. What is the margin of error of the confidence interval that you found in the previous
How would you interpret the confidence interval that you found in part (g)?
Which of the following is a correct interpretation of the 95% confidence level?
If Augie repeats this process many times, then about 95% of the intervals produced will capture the true proportion of times of choosing the correct objective.
About 95% times Augie chooses the correct objective.
If Augie repeats this process and constructs 20 intervals from separate independent sam- ples, we can expect about 19 of those intervals to contain the true proportion Augie chooses the correct objective.
(k) (4 points)
object 21 out of 35 times.
Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval.
The center of the confidence interval would . The width of the confidence interval would .
(l) (4 points) Suppose that we repeated the same study with Augie, and this time he chose the correct object 17 out of 35 times, and we also change the confidence level from 95% to 99%. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval.
Suppose that we repeated the same study with Augie, and this time he chose the correct
The center of the confidence interval would The width of the confidence interval would
7.Directions: You are part of a fireworks crew assembling a local fireworks display.
There are two parts to the fireworks platforms:
rts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and 0 h is the initial height is
0 ht t h ( ) 16 =− + .
• The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity
in feet per second is 2
0 0 ht t vt h ( ) 16 =− + + .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
First, conduct some research to help you with later portions of this portfolio
• Find a local building and estimate its height. How tall do you think the
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, 2
0 ht t h ( ) 16 =− + . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.
8.1.Under the microscope, she can see that DNA in one cell has been replicated, and it appears to be starting
tarting the process of meiosis. Draw the chromosomes, depicting them inside the cell, as you would expect them to appear during Metaphase I. (Note: there is more than one correct answer for this prompt. You only need to draw one of the answers.)
2.How many copies of gene A are present in this parent cell during Metaphase I?
3.How many total chromosomes would you have after DNA replication (synthesis)?
4.While examining a specific tissue in this organism, Bridget noticed some cells with more than one nucleus (this is commonly found in many species, including humans!). What could have happened during the process of cell division to yield these multinucleate cells?
5.In one of her harebrained experiments, Dr. Milam remembers treating some cells from one of her organisms with a drug that resulted in the cell being unable to replace RNA primers with DNA. Which protein in the cells was most likely affected by this drug treatment?
6.In another one of her experiments, Dr. Milam treated cells with a different drug that caused an adenosine in gene A to be paired with a cytosine instead of a thymine during DNA replication. However, Dr. Milam remembers that the amino acid sequence of the protein product of gene A wasn’t actually changed. How could you explain this observation?