Tutors Answer Your Questions about Linear-systems (FREE)
Question 1165132: Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of 317 five-syllable sequences from the newly discovered manuscript showed that 61 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato's Republic? Use α = 0.01.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic.
Click here to see answer by CPhill(2138)   |
Question 1165134: Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α = 0.01.
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value.
Click here to see answer by CPhill(2138) |
Question 1165201: Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α = 0.01.
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
0.640
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.
Click here to see answer by CPhill(2138) |
Question 1165202: Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.
3.7 2.9 3.8 4.2 4.8 3.1
The sample mean is x bar = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use α = 0.10
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)
Click here to see answer by CPhill(2138) |
Question 1166583: Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft.
Write and solve a compound inequality to model the possible length of the dog run
This situation is modeled by the compound inequality 100 less than or equal to _____ less than or equal to 200.
(Use integers or decimals for any numbers in the expression. Do not include the $ symbol in your answer.)
Solving this compound inequality yields
_____ .
(Type a compound inequality. Use integers or decimals for any numbers in the expression.)
The dog run can be between
______ ft and
______ ft long.
(Type integers or decimals. Use ascending order.)
Click here to see answer by josgarithmetic(39669) |
Question 1209934: a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice
Click here to see answer by ikleyn(53295)  |
Question 1209934: a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice
Click here to see answer by CPhill(2138) |
Question 1169746: 4) The equations defining a model of two trading nations are given by
𝑌 𝑌 𝐶1 = 0.7𝑌1 + 50 𝐶2 = 0.8𝑌2 + 100 𝐼 𝐼 𝑀1 = 0.3𝑌1 𝑀2 = 0.1𝑌2
a. Express this system in matrix form and hence find the values of 𝑌1 and 𝑌2.
b.Calculate the balance of payments between these countries
Click here to see answer by CPhill(2138) |
Question 1173100: Mr.Agoncillo has a savings account in two banks. The combined amount of these savings is at least Php 150,000. One bank gives an interest of 4% while the other bank give 6%. In a year, Mr. Agoncillo receive at most Php. 12,000.
Write and graph a system of linear inequalities that shows all the posible solutions.
Click here to see answer by CPhill(2138) |
Question 1174275: A certain mobile company offers a monthly plan of Php 799 and an additional charge of Php 7.50 per minute when calling to other networks.How much is the monthly bill if the costumer made a 5 minute call to other networks?
A.What is the independent and dependent variable?
B.What is the slope,y-intercept and the linear inequalities?''.
C.What is the value of y?
Click here to see answer by CPhill(2138) |
Question 1176798: Determine which of A-D form a solution to the given system for any choice of the free parameter s1. List all letters that apply. If there is more than one answer, type them as a comma separated list.
-8x1 + 3x2 + 15x3 = -52
-3x1 + x2 + 6x3 = -20
HINT: All of the parameters of a solution must cancel completely when substituted into each equation.
a)(5+3s1,7-6s1,s1)
b)(8+3s1,4+3s1,s1)
c)(4+s1,s1,-(4-s1/3))
d)(-(6-3s1/16),s1,-(2-2s1/45))
Click here to see answer by CPhill(2138) |
Question 1209773: If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + a_1 = 17,
a_{18} + a_{19} + a_1 + a_2 = 18,
a_{19} + a_1 + a_2 + a_3 = 19,
what is the value of a_19?
Click here to see answer by ikleyn(53295) |
Question 1209773: If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + a_1 = 17,
a_{18} + a_{19} + a_1 + a_2 = 18,
a_{19} + a_1 + a_2 + a_3 = 19,
what is the value of a_19?
Click here to see answer by CPhill(2138) |
Question 1178476: According to the American Society of Heating, Refrigerating
and Air-Conditioning Engineers, Inc. (ASHRAE), a nonsmoking classroom
should have a ventilation rate of 15 ft3 per min for each person in the room.
(a) Write an equation that models the total ventilation V (in cubic feet per hour)
necessary for a classroom with x students.
(b) A common unit of ventilation is air change per hour (ach). One ach is equivalent
to exchanging all the air in a room every hour. If x students are in a classroom
having volume 15,000 ft3, determine how many air exchanges per hour (A) are
necessary to keep the room properly ventilated.
(c) Find the necessary number of ach (A) if the classroom has 40 students in it.
(d) In areas like bars and lounges that allow smoking, the ventilation rate should
be increased to 50 ft3 per min per person. Compared to classrooms, ventilation
should be increased by what factor in heavy smoking areas?
Click here to see answer by CPhill(2138) |
Question 1184642: A landscaping supply company produces decorative stones. A ton of coarse stones requires 2 hours ofcrushing, 5 hours of sifting, and 8 hours of drying. A ton of fine stones requires 6 hours of crushing, 3hours of sifting, and 2 hours of drying. The coarse stones sell for$400 per ton. The fine stones sell for$500per ton. In a work week, the plant is capable of 36 hours of crushing, 30 hours of sifting, and 40 hours ofdrying. Based on the demand forecast, the quantity of coarse stones produced should be at least twice thequantity of fine stones produced.
First
1. Formulate an optimization model to decide how much of each kind of stones to produce to maximizetotal revenue.
2. Solve your model using the Excel solver.
3. Using a two-dimensional plot, solve your model graphically.
Then, by modifying your two-dimensional plot, answer the following questions:
4. How much would it be worth to get another hour of crushing time?
5. How much would it be worth to get another hour of sifting time?
6. Could you find the range of the prices for the fine stones such that in the optimal solution, thequantity of coarse stones produced is exactly twice the quantity of fine stones produced.
Click here to see answer by CPhill(2138) |
Question 1186380: Ridership on a small regional airline has been declining, approximately at a linear rate. In 1981 the number of passengers was 245,000; in 1986 the number was 215,000. If n equals the number of passengers using the airline per year and t equals time measured in year (t=0 for 1981)
Determine the linear estimating function n=f(t)
Interpret the meaning of the slope
What is the number of riders expected to equal in the year 2000?
It is estimated that the airline will go out of business if ridership falls below 180,000. According to your function in part a, when will this happen?
Click here to see answer by CPhill(2138) |
Question 1199840: ABC Dairy Company wishes to make a new cheese from two of its current cheeses: Cheese X and Cheese Y. The mixture is to weight at least than 4 pounds and is to contain 6 ounces of the sharpness Ingredients S. Each pound of X costs $4 and contains 3 ounces of S, whereas each pound of Y costs $1 and contains one ounce of S. find the minimum cost of the mixture if the amount of Cheese Y cannot exceed the amount of Cheese X by more than one pound.
Click here to see answer by ElectricPavlov(122) |
Question 1201735: Let X be the design matrix of a linear regression problem with m rows (samples) and d columns (variables/features). Let y∈R^m be the response vector corresponding the samples in X. Recall that for some vector space V⊆R^d the orthogonal complement of V is: V^⊥:={x∈R^d∣⟨x,v⟩=0∀v∈V}
1. Prove that: Ker(X)=Ker(X^⊤X)
2. Prove that for a square matrix A:Im(A^⊤)=Ker(A)^⊥
3. Let y=Xw be a non-homogeneous system of linear equations. Assume that X is square and not invertible. Show that the system has ∞ solutions ⇔y⊥Ker(X^⊤).
4. Consider the (normal) linear system X^⊤Xw=X^⊤y. Using what you have proved above prove that the normal equations can only have a unique solution (if X^⊤X is invertible) or infinitely many solutions (otherwise).
Please help me to solve question 3 and 4.
Click here to see answer by asinus(45) |
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