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Problem 1: You stand at the bottom left corner of your property, which is shaped like a triangle. You look straight to your right and see the marker at the right corner of the bottom of your property. You then turn through an angle of 40o and look at the mailbox at the top corner of your property. You now walk 60 feet to the right corner at the bottom of your property. You look back at the left corner of the bottom of your property and then turn through an angle of 35o and look at the mailbox. How far is it from each each corner of your property to the mailbox?
Problem 2: You are designing a park that will be shaped like a triangle. It is bounded by three straight roads - Boros Boulevard, Luke Lane, and Gallagher Avenue. Boros Boulevard is 1.4 miles long, Luke Lane is 2.2 miles long, and the angle between them is 72o. How long is Gallagher Avenue?
Problem 3: If sina A = 5/13, and cos B = -(4/9), and both angles are in the second quadrant, find:
a) sin(A + B)
b) cos (A + B)
c) tan (A - B)
Problem 4: If cotθ = -(7/11), and tanφ = 9/7, with π/2 < θ < π and π < φ < 3π/2, find:
a) sin(θ - φ)
b) cos (θ + φ)
c) tan (θ + φ)
Let S be a subset of a set X. Let R be the ring of real-valued functions on X, and let I be the set of real-valued functions on X whose restriction to S is zero.
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?
What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Write your answer as a fraction in simplest form.
Find an equation of the line that passes through the point (0,4) and is (a) parallel to and (b) perpendicular to the line 5x+2y=3.
what is the probability of drawing an orange marble? Give solutions exactly in reduced fraction form.
What is the estimated OR (odds ratio) between favoring cutting living standards and paying higher taxes? What is the 95% confidence interval for the true odds ratio?
An open rectangular box is to be constructed from material that costs $12/ft2 for the bottom and $10/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $81.
23% of the seniors at a high school failed pre-calculus.if 1138 students failed pre-calculus, how many seniors are at t his high school?
A business school claims that the average income of graduates of this school three years after graduation is $700.
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to the longest side.
this test results prompts a state school administrator to declare that the mean score for the state's eighth graders on the examination is more that 260. at a=0.04 is there enough evidence to support the administators claim?
The lengths of Chinese giant salamanders can be modeled by a normal distribution with a mean of 113 cm and a standard deviation of 22 cm. 1. What percent of the Chinese giant salamanders do you expect to measure between 100 and 135 cm?
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