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1. What number divided by two is equal to that same number minus 15 ?
2. The number of hours Robert spends in his game room is proportional to the number of hours he spends playing Call of Destiny IV: Modern Battlefield. If he plays Call of Destiny IV for 6 hours, he will spend 8 hours in his game room. How many hours will Robert spend in his game room if he plays Call of Destiny IV for only 3 hours?
3. Twelve Smooth-Glide pens and eight Easy-Write pencils cost exactly $16.00 at Office World. Six Smooth-Glide pens and ten Easy-Write pencils cost $11.00 at the same location. How much will nine Smooth-Glide pens and nine Easy-Write pencils cost at Office World? (Disregard the dollar sign when gridding your answer.)
4. In the equation 3x2 - 16x = -20, what is one possible value of x ?
5. In a certain ancient farming community, anthropologists determine that new dwellings were constructed monthly as modeled by the function f(x) = 2x + 100, where x is the current month of the year and f(x) is the number of dwellings constructed by the end of that month. Additionally, they determine that the population grew exponentially each month, thanks to the discovery of more fertile land for farming. This growth is modeled by the equation g(x) = 3x, where g(x) represents the current population at the end of a given month. What is the smallest integer value of x, with 1 representing the end of January and 12 representing the end
6. In a school-wide competition held at Saul C. Tigh Memorial High School, Olympiad teams are challenged to come up with different circuits involving both real and imaginary currents. Imaginary currents exist in spots where the electrical energy encounters zero resistance, such as through a coil or wire. Real currents exist only where the electrical energy headed through the circuit encounters resistance, such as when a light bulb "resists" the current and takes up some of the energy carried throughout the circuit.
The members of Team Charlie develop a circuit in which the total current, real and imaginary, can be measured at 50 + 12i amps. They then add the current together with the current produced by Team Delta's circuit, 40 - 9i amps. Finally, they decide to multiply the resulting current, in amps, by Team Epsilon's total current, 60 - 2i amps. What is the final current, in amps, after the entire
7. The chart below shows the population distribution for the 2,400 occupants of the city of Centre Hill.
If there are an equal number of adults and children, and adult females outnumber adult males by 200, what is the sum of the women living uptown and the children living in the suburbs of Centre Hill?
8. The chart below shows the population distribution for the 2,400 occupants of the city of Centre Hill.
Centre Hill plans to annex the area around a nearby lake. This new part of Centre Hill will be called, appropriately, The Annex. The Annex will add to the current population of Centre Hill. The percent of adult males living in Uptown will decrease to 6% after incorporating The Annex into Centre Hill. If the information from Part 1 holds true for the original four districts of the city of Centre Hill, then how many adult males live in The Annex?
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