Ruth is setting up the locations of the corners of a 10' by 24' rectangular deck she is going to build in her backyard. To make sure she has a perfect rectangle, she checks to make sure the diagonals are the same. a. What should the length of each diagonal be? b. What angle does the diagonal make with the longer side of the deck? Round to the nearest degree. c. What angle does the diagonal make with the shorter side of the deck? Round to the nearest degree.

A man drives his car to work 80% of the time; otherwise he rides his bicycle. When he rides his bicycle to work he is late 25% of the time, whereas when he drives his car to work he is late 15% of the time. On a particular day, the man arrives on time. Find the probability that he rode his bicycle to work on that day.

Mark has a tree in his backyard that he wants to make sure cannot fall on his neighbor's house if there is a bad storm. The tree is 49 feet from his neighbor's house. From a point on the ground 35 feet from the tree, the angle of elevation of the top of the tree is 50 degrees. How tall is the tree? Round to the nearest foot.

Tanya plans to make a square deck. She is not sure what size she is going to make the deck, but she knows it needs to be more than 5 feet long. She represents the deck as a square in which each side is d+5 feet long. Write an expression for the perimeter by multiplying the number of sides by the length of a side. Perimeter = _____

Ed is setting up the locations of the corners of a 16-foot by 30-foot rectangular deck he is going to build in his backyard. To make sure he has a perfect rectangle, he checks to make sure the diagonals are the same. What should the length of each diagonal be?

If you borrow $200,000 at an APR of 4% for 25 years, you will pay more per month than if you borrow the money for 30 years at 4%. a. What is the monthly payment on the 25-year mortgage, to the nearest cent? b. What is the total interest paid on the 25-year mortgage? c. What is the monthly payment on the 30-year mortgage? d. What is the total interest paid on the 30-year mortgage? e. How much more interest is paid on the 30-year loan? Round to the nearest dollar. f. What is the difference between the monthly payments of the two different loans? Round to the nearest dollar.

Jorge is installing a staircase so he can have access to his attic. The rise of the stairs is 8 inches and the run of each stair is 11 inches. What is the slope of the staircase, expressed as a fraction?

The Lamberti family is building a rectangular deck that measures 30 feet by 22 feet. They need to run an electric line across the diagonal, underneath the deck. How long is the diagonal of the deck, to the nearest foot?

Simplify the expression:

$$\sqrt{20}$$

A manufacturer produces drink bottles. He uses 2 machines which produce 60% and 40% of the bottles respectively. 3% of the bottles made by the first machine are defective and 5% of the bottles made by the second machine are defective. What is the probability that a defective bottle came from: a. the first machine b. the second machine?

Examine the loan amortization table for months 92-95 of a $200,000, 8-year mortgage with an APR of 5.025$

$$\begin{matrix} \text{Payment Number} & \text{Beginning Balance} & \text{Monthly Payment} & \text{Toward Interest} & \text{Toward Principal} & \text{Ending Balance}\\ \text{92} & \text{12,514.18} & \text{} & \text{52.40} & \text{2,481.97} & \text{}\\ \text{93} & \text{10,032.21} & \text{} & \text{42.01} & \text{2.492.36 } & \text{7,539.85}\\ \text{94} & \text{} & \text{} & \text{31.57} & \text{2,502.80} & \text{5,037.05}\\ \text{95} & \text{5,037.05} & \text{} & \text{2.513.28 } & \text{2,523.77}\\ \end{matrix}$$

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The Sea Cottage Cooperative is owned by the shareholders. The co-op has a total of 32,000 shares. Linda has an apartment at Sea Cottage and owns 480 shares of the cooperative. What percentage of Sea Cottage does Linda own?

Sarah purchased a condominium at Tulip Meadows. She pays $3,196.80 in property taxes each year. These taxes are taken out of her monthly maintenance fee of$1,480. What percentage of this monthly fee goes to property taxes?

A rectangle is 9.2 m by 3.8 m. What angle does its diagonal make with its longer side?