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1. What number is 40% greater than the sum of 40 and 80?
The table above shows a set of ordered pairs that correspond to the function . What is the value of k?
3. hx + 4y = -3
The equation above is the equation of a line in the xy-plane, and h is a constant. If the slope of this line is -13, what is the value of h?
4. The sum of two numbers is four times their difference. The smaller of these numbers is 15. What is the greater number?
5. If 0 < x < 2π and, what is the value of
Note: Figure not drawn to scale.
In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?
7. An Internet service provider offers three different plans for residential users. Plan A charges users $500 for the first year of service, and $80 per month thereafter. Plan B charges users $68 per month. Plan C is a "high speed" plan that offers 200% higher speeds for $92 per month.
Isabelle has been using Plan A for over a year. She recently reviewed her plan and realized that if she had been using Plan B for same amount of time, she would have saved $104 for Internet service over the entire period. At the time of her review, how many months had Isabelle been on Plan A?
8. An Internet service provider offers three different plans for residential users. Plan A charges users $500 for the first year of service, and $80 per month thereafter. Plan B charges users $68 per month. Plan C is a "high speed" plan that offers 200% higher speeds for $92 per month.
Isabelle is now considering switching to either Plan B or Plan C for her home business, but she calculates that having the "high speed" plan will save her only approximately 45 minutes of work each month. At what minimum hourly rate, in dollars per hour, would she have to value her work (that is, how much more would she have to value one hour of free time over one hour of work time) for Plan C to be worth the extra cost over Plan B?
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