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A bank wishes to invest a $180,000 trust fund in three sources: bonds paying 12%; certificates of deposit paying 10%; and first mortgages paying 16%. The bank wishes to realize an $21,500 annual income from the investment. A condition of the trust is that the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages. How much should the bank invest in each possible category? Let x, y, and z, respectively, be the amounts invested in bonds, certificates of deposit, and first mortgages. Solve the system of equations by the Gauss-Jordan elimination method.
If the compant plans to increase monthly advertising expenditures at the rate of 1.5 thousand dollars per month, how fast will sales rise?
Probabilities of deck of cards. A card is drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining a diamond or a card smaller than 5?
if f and g are differentiable function on [a,b], what identifies the extrema of f+g or fg. Do these extrema relate to the extrema of the functions?
A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 14 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances to the nearest tenth of a kilometer.
Find the line integral of f(x,y,z)=x+y+z over the straight-line segment from (2,1,4) to (1,-2,2). The answer is 4(sqrt(14)). Can you show the work.
A tennis court has a perimeter of 228 feet. The length of the tennis court is 42 feet longer than the width. Write a linear equation of the problem. What is the length and width of the court?
phyisical sicence the weight ofan object on the moon is 16 its weight on earth.ifa bowling ball weighs 1212 pounds on earth, how much would it weigh on the moon ?
Use a Venn diagram and the given information to estimate the number of elements in the indicated region.
In a group of 97 students, the number taking English is twice the number of those taking Math. 53 students are taking one of these subjects and 15 are taking neither. How many students are taking math? How many are taking English?
the selling price s(c) after 45% markup of an item as a function of the stores' cost c.
Using data, I need to find out how to calculate the gravitational acceleration on each of the three planets selected. Note: With the masses measured in kilograms and the radii in meters, the units of gravitational acceleration would turn out to be..
A function f is continuous on interval [1,3]. A horizontal line is drawn somewhere between the lines y=f(1) and y=f(3). According to the intermediate value theorem, how many times is such a line guaranteed to intersect the graph of f(x)?
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