The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1 AU (astronomical unit) is the mean distance from Earth to the sun, about 93 million miles.

Astronomers tell us that it is reasonable to model these data with a power function.

(a)

Use power regression to express velocity as a power function of distance from the sun. (Round regression parameters to two decimal places.)

v = 29.73 × d^0.50

v = 21.41 × d^−0.50

v = 29.73 × d^−0.73

v = 29.73 × d^−0.50

v = 21.41 × d^−0.29

(b)

Plot the data along with the regression equation.

(c)

An asteroid orbits at a mean distance of 3 AU from the sun. According to the power model you found in part (a), what is the mean orbital velocity of the asteroid? (Round your answer to two decimal places.)

_______ km/sec

A student working in the physics laboratory connects a parallel-plate capacitor to a battery, so that the potential difference between the plates is 225 V. Assume a plate separation of d = 1.27 cm and a plate area of A = 25.0 cm². When the battery is removed, the capacitor is plunged into a container of distilled water. Assume distilled water is an insulator with a dielectric constant of 80.0.

(a) Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes.)

before Q_i = ___ pC

after Q_f = ___ pC

(b)

Determine the capacitance (in F) and potential difference (in V) after immersion.

C_f = ___ F

ΔV_f = ___ V

(c) Determine the change in energy (in nJ) of the capacitor.

ΔU = ___ nJ

(d)

What If? Repeat parts (a) through (c) of the problem in the case that the capacitor is immersed in distilled water while still connected to the 225 V potential difference.

Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes.)

before Q_i = ___ pC

after Q_f = ___ pC

Determine the capacitance (in F) and potential difference (in V) after immersion.

C_f = ___ F

ΔV_f = ___ V

Determine the change in energy (in nJ) of the capacitor.

ΔU = ___ nJ

About 43% of students are dog owners. 20 students are selected at random. Indicate what key was used on your calculator. Round your answers to three significant digits.

a. What type of a distribution is the above?

b. What I s the probability that exactly 6 students are dog owners?

c. What is the probability that less than 4 students are dog owners?

d. What is the probability that more than 4 students are dog owners?

e. What is the probability that at most 15 students are dog owners ?

f. What is the probability that between 9 and 15 students (inclusive) are dog owners? (2 points)

he score distribution shown in the table is for all students who took a yearly AP statistics exam. An AP statistics teacher had 41 students preparing to take the AP exam. Though they were obviously not a random​ sample, he considered his students to be​ "typical" of all the national students.​ What's the probability that his students will achieve an average score of at least​ 3? Score Percent of students 5 12.1 4 22.6 3 24.3 2 18.1 1 22.9 The probabability that his students will achieve an average score of at least 3 is nothing . ​(Round to four decimal places as​ needed.).

Do online students perform differently than students in a traditional classroom? Last semester there were 100 students registered for the online version of a statistics course, and 100 students registered for the traditional classroom. All students took the same final exam. Suppose the group of online students had a mean exam score of 75 with a standard deviation of 3. The classroom students had a mean score of 76 with a standard deviation of 4. Does the sample data provide evidence that there is a difference in the average exam scores between the two groups? Test the relevant hypotheses at a significant level of x = 0.05.

Show your work.

Specific competition strategies for V energy

what is michael v. university about?

Show that for a student not belonging to Category (New Asia students(N) who did not attend the 2015 Wei Lun Lecture.(W))

, if the student did not attend the 2015 Wei Lun Lecture(W), then the student does not belong to New Asia.(N)

***for more details ***

For simplicity, assume that CUHK has only four colleges: Chung Chi, New Asia, United, and Shaw. Let C,N,U, and S be the sets of all Chung Chi students, New Asia students, United students, and Shaw students, respectively. Let M be the set of all Music Major students. Let Y be the sets of all students living in Ying Lin Tang (a Chung Chi hostel). Let W be the set of all students who attended the Wei Lun Lecture.

The American Journal of Public Health (July 1995) published a study of the relationship between passive smoking and nasal allergies in Japanese female students. The study revealed that 40% of the students from heavy-smoking families showed signs of nasal allergies on physical examination. Let x denote the number of students with nasal allergies in a random sample of 6 Japanese female students exposed daily to heavy smoking.

a. What is the probability that at least four of the students will have nasal allergies?

b. What is the probability that at least two of the students will have no nasal allergies?

c. Suppose instead of 6, a random sample of 20 Japanese female students were exposed daily to heavy smoking, what is the probability that between 4 and 14 (both points inclusive) of the students will have nasal allergies?

1. The general formula of alkanes is: (i) CnH2n+2 (ii) CnH2n-2 (iii) CnH2n (iv) CnH2n+4 (v) Cn+2H2n

2. The name of the following compound is: a. Tetrabenzene b. Chrysene c. Coronene d. Anthracene e. Pyrene

3. To achieve noble gas configuration, hydrogen requires………………..whereas chlorine requires…………………in outermost shell. a. Octet, duet b. Singlet, duet c. Duet, octet d. Octet, singlet e. None of the above

4. The ……………. the number of relatively stable resonance contributors, the …………… the resonance energy. a. Higher, lower b. Lower, higher c. Higher, higher d. Lower, lower e. None of the above

5. The other name of Methylbenzene is: (i) Phenyl (ii) Xylene (iii) Pyrene (iv) Toluene (v) Naphthalene

6. In pericondensed polyaromatic hydrocarbon, one or more carbon atoms must be a common member of (i) one (ii) two (iii) three (iv) four (v) five benzene rings.

7. The name of the compound (I) is: H2NCH2CH2CH2CO2H (I) (i) N-methylpropylamine (ii) N,N-dimethylethylamine (iii) 2-aminoethanol v) 4-aminobutanoic acid (v) Succinic acid

8. Benzoyl chloride is an example of (i) Aliphatic acid chloride (ii) Alicyclic acid chloride (iii) Heterocyclic acid chloride (iv) Aromatic acid chloride (v) None of the above

9. Acetyl chloride is an example of (i) Aliphatic acid chloride (ii) Alicyclic acid chloride (iii) Heterocyclic acid chloride (iv) Aromatic acid chloride (v) None of the above

10. Acetic anhydride is an example of (i) Aliphatic acid anhydride (ii) Alicyclic acid anhydride (iii) Heterocyclic acid anhydride (iv) Aromatic acid anhydride (v) None of the above

11. Phthalic anhydride is an example of (i) Aliphatic acid anhydride (ii) Alicyclic acid anhydride (iii) Heterocyclic acid anhydride (iv) Aromatic acid anhydride (v) None of the above

12. Formamide is an example of (i) Aliphatic amide (ii) Alicyclic amide (iii) Heterocyclic amide (iv) Aromatic amide (v) None of the above

13. Benzamide is an example of (i) Aliphatic amide (ii) Alicyclic amide (iii) Heterocyclic amide (iv) Aromatic amide (v) None of the above