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Question 1. System of Linear Equations.
Solve the following system of linear equations by using Determinant Method:
Question 2. Matrix Algebra
Compute each of the following matrices:
a) A+B
b) C-D
c) CD
d) (CD)T
e) Verify that (CD)T = DTCT
f) Verify that (A+B)T = AT+BT
Question 3. Graphing Strategy
f(x) = -x3 + 27x
a) Find the domain of the function.
b) Find x and y intercepts.
c) Find the stationary points for and determine the intervals where is increasing and decreasing.
d) Determine the minimum and maximum value of the function.
e) Sketch the graph.
Solving probability problems based on Binomial distribution
Prove that there exists only one 4-regular maximal planar graph.
Chuck recives loans totaling $12000 from two banks. one bank charges 7.5% annual interest, and the second bank charges 6% annual interest. he paid $840 in total interest in one year. how much was loaned at each bank?
Let S and T be subsets of the universal set U. Draw an appropriate Venn diagram and use the given data to determine the number of elements in each basic region.
find the number of weak compositions of 25 into five odd partsfind the number of weak compositions of 25 into five odd parts.
A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?
Calculate the yield of a wafer with a 15 cm diameter, a cost of 12, contains 84 dies and has a 0.020 defects/cm^2
A manufacture has been selling 1050 television sets a week at 390 dollars each. A market survey indicates that for each 13 -dollar rebate offered to a buyer, the number of sets sold will increase by 130 per week.
Find the sample size needed to assure with 95.44 percent confidence that the sample mean will not differ from the population mean by more than 2 units.
R2 is misleading when used for time-series analysis. what additional measures are available?
How many days and hours since the Christian era commenced, 1811 years (Zerah usually assumed a 365-day year and a 30-day month)? How many days and hours since the Christian era commenced, 1811 years (Zerah usually assumed a 365-day year and a 30-d..
From the top of a 300 ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse? Round your answer to the nearest foot.
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