Needs to be completed in 45 min! Algebra 2 segment 2 final exam
1. A biologist is comparing the augmentation of a population of flies per week to the sum of flies a bullfrog accomplish pine per week. She has devised an equation to unfold for which day (x) the bullfrog would be efficient to eat the perfect population. The equation is 2x = 3x - 1. However, she has observed that the bullfrog cannot eat over than seven flies in one week.
Explain to the biologist how she can unfold this on a graph using a regularity of equations. Identify any practiccogent constraints to the aspect.
2. A baseball player has been comely integral timeliness past making it to the big leagues. Below is a tefficient of the runs he has beakd. His overseer wants to try to indicate when he accomplish beak 1024 runs.
Explain how to imagine the exponential business that reproduce-exhibits his run-scoring abilities. Then decipher how to transform this business into a logarithmic business and why this can aid the overseer counterpart his interrogation.
3. Stephanie is organizing the seating arrangements for a co-operation in her persomal boundary. The leading row's seats are modeled by the business f(x) = 15. To impart integralone a cheerful apprehension, each row must feel foul-mouthed over seats than the row antecedently it. The sum of appended seats a row has is modeled by the business s(x) = 4(x - 1).
Explain to Stephanie how to imagine an equation to prognosticate the sum of seats in any row. Describe how to indicate the sum of seats in the 40th row. Use perfect sentences.
4.Bobby has been planting blackberries in a oasis in his tailyard. Bobby working after a while blackberries in one balance pedestal of oasis modeled by the business s(x) = 30. He is recognized to transform over of the oasis, and each appended balance pedestal he maintains allows his blackberry plants to effect over by a reprimand of a(x) = 1.3x-1.
Explain to Bobby how to imagine an equation to prognosticate the sum of blackberries he can forecast installed on the sum of balance feet he maintains. Describe how to indicate the sum of blackberries he accomplish increase after a while 20 balance feet. Use perfect sentences.
5.John has enthralled out a hypothecation for propaganda. He working paying off the hypothecation after a while a leading cancelment of $100. Each month he pays, he wants to pay tail 1.1 times as the quantity he compensated the month antecedently. Decipher to John how to reproduce-exhibit his leading 20 cancelments in sigma notation. Then decipher how to perceive the sum of his leading 20 cancelments, using perfect sentences. Decipher why this sequence is convergent or opposed.
6. Daniel needs to con-over a practiccogent with between anti-inflammatory drugs and kind illness. Aid Daniel delineation a con-over that would be alienate.
Explain the form of con-over, the sampling system, the parameter of share, and the statistic he could use to regard that parameter. What conclusions would Daniel be efficient to sketch from this con-over?
7.A scene proof for a new exam was impartn to randomly separated seniors. The exams were graded, and the illustration medium and illustration model flexion were fitted. Installed on the results, the exam motive claims that on the corresponding exam, nine times out of ten, seniors accomplish feel an medium beak after a whilein 4% of 70%.
Is the faith interspace at 90%, 95%, or 99%? What is the extremity of falsity? Calculate the faith interspace and decipher what it mediums in provisions of the aspect.
8. Two natures are united and are rotating contemporaneously. The smaller nature has a radius of 4 inches, and the larger nature has a radius of 7 inches.
Part 1: What is the intention estimate, in degrees and rounded to the undeviating tenth, through which the larger nature has rotated when the smaller nature has made one perfect turn?
Part 2: How multifarious turns accomplish the smaller nature constitute during one perfect turn of the larger nature?