1). A group of students plans a tour. The charge per student is $66 if 25 students go on a trip. If more that 25 students participated, the charge per student is reduced by $2 times the number of students over 25. Find the number of students that will furnish the maximum revenue. The number of students that will furnish the maximum revenue is ______? The maximum revenue is $_______?

2) A motorboat is capable of traveling at a speed of 15 miles per hour in still water. On a particular​ day, it took 30 minutes longer to travel a distance of 18 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that​ day?

2. In Pennsylvania, students take the Algebra 1 Keystone exams. If a student scores a 1500 the student earns a Proficient Rating. One teacher claims that his students score above Proficient. In a random sample of 80 students, the mean score was 1505with a standard deviation of 25.578.

a. Is there convincing evidence at the ?=0.05level that his students score above Proficient?(show all four steps)

b. Construct a 90% confidence interval for the meancompletion time of all students who took the exam.(show the math and make the conclusion)

c. How many students would have to be sampled to report a margin of error of 5 points?

In a secondary school, there are 400 male students and 600 female students. 50% of the male students and 55% of the female students are in senior secondary curriculum, the others are in junior secondary curriculum. The school had appointed 8% of senior male students and 10% of senior female students to be the student leaders. No junior secondary student can be student leader.

(a) If a student is selected at random in the school, find the probability that

(i) the student is a senior student.

(ii) the student is a female student leader.

(b) Suppose a student is selected and known to be NOT a student leader, what is the probability that

(i) the student is a male student.

(ii) the student is a senior female student.

Starting at 9 a.m., students arrive to class according to a Poisson process with

parameter λ = 2 (units are minutes). Class begins at 9:15 a.m. There are 30

students.

(a) What is the expectation and variance of the number of students in class by

9:15 a.m.?

(b) Find the probability there will be at least 10 students in class by 9:05 a.m.

(c) Find the probability that the last student who arrives is late.

(d) Suppose exactly six students are late. Find the probability that exactly 15

students arrived by 9:10 a.m.

(e) What is the expected time of arrival of the seventh student who gets

to class?

Is there a difference between community college statistics students and university statistics students in what technology they use on their homework? Of the randomly selected community college students 67 used a computer, 86 used a calculator with built in statistics functions, and 22 used a table from the textbook. Of the randomly selected university students 40 used a computer, 88 used a calculator with built in statistics functions, and 39 used a table from the textbook. Conduct the appropriate hypothesis test using an αα = 0.01 level of significance.

1. What is the correct statistical test to use?
   • Goodness-of-Fit
   • Independence
   • Homogeneity
   • Paired t-test
2. What are the null and alternative hypotheses?
   H0:H0:
   • Type of student and type of technology used for statistics homework are dependent.
   • Type of student and type of technology used for statistics homework are independent.
   • The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
   • The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
   
   
   
   H1:H1:
   • The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
   • Type of student and type of technology used for statistics homework are independent.
   • The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
   • Type of student and type of technology used for statistics homework are dependent.
3. The test-statistic for this data =  (Please show your answer to 2 decimal places.)
   
4. The p-value for this sample = (Please show your answer to 4 decimal places.)
   
5. The p-value is Select an answer less than (or equal to) greater than  αα
   
6. Based on this, we should
   • accept the null
   • fail to reject the null
   • reject the null
7. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
   • There is insufficient evidence to conclude that type of student and type of technology used for statistics homework are independent.
   • There is sufficient evidence to conclude that type of student and type of technology used for statistics homework are dependent.
   • There is insufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
   • There is sufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.

7. Show that the dual space H' of a Hilbert space H is a Hilbert space with inner product (', ')1 defined by
(f .. fV)1 = (z, v)= (v, z), where f.(x) = (x, z), etc.

A Si pn diode has an equilibrium diffusion barrier of 0.7 V and an area capacitance of C2D = 4 nF/cm2 for a reverse bias voltage of -4.3 V. What can you tell about the doping levels?

verify the maxwell relations associated with the helmholtz free energy F and the Gibbs free energy F by using the equaiton of state an ideal gas and the expressions for S(T,V) and S(P,V) when c_v is constant.

Give an algorithm that constructs an undirected connected graph, which allows for labeling of the n vertices u - v <= k for every edge (u,v), where k is some constant. All nodes have a unique label.