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a small corporation borrowed 1,500,000 to expand its line of shoes. some of the money was borrowed at 7%, some at 8%, and some at 10%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $130,500 and the mount borrowed at 10% was four times the amount borrowed at 7%. solve the system using matrices.
0 2 4 1 3 5 (imagine the vertical sets of numbers are surrounded by a large parenthesis, as it is in a binomial expression)
A tree has 11 vertices of degree 3, 12 vertices of degree 2, 10 vertices of degree 4 and the remaining vertices are of degree 1. How many vertices does it have?
Probability problems based on Poisson & Normal distribution
The perimeter of a square is 68 meters. The side length can be represented as (8x - 3) meters. What is the value of x?
an existing rectangular corral such that the total area of the new corral is 1.5 times that of the original corral. the current corral's dimensions are 250 feet by 160 feet. The rancher wants to increase each dimension by the same amount.
Each of the numbers 1 through 10 inclusive has been written on a separate piece of paper. The 10 pieces of paper have been placed in a hat
Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x.
Determine the probability when standard deviation and mean is given by using normal distribution - Show the entire calculation
a 34% solution is mixed with a 66% solution to produce 216 liters of a 42% solution. How many liters of each solution were mixed?
The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 40 mi/h can stop in 136 ft. What is the maximum speed it can be traveling if it needs to stop in 160 ft? (..
Calculate the reduced row echelon form of the following matrices. Approximate answers should be entered to at least 4 decimal places.
Maximizing the Sustainable Yield, A lake has a carrying capacity of 10,000 fish. At the current level of fishing, 2000 fish per year are taken and the fish population seems to hold fairly steady at about 4000.
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