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MATHEMATICS DEPARTMENT 12 Advanced Functions - Exponential and Logarithmic Functions Name: Date: Answer all questions in the space provided. Neat and complete solutions are required for full marks. Good luck! KNOWLEDGE AND UNDERSTANDING 1. Express as a single logarithm. Simplify, but do not evaluate. a) $$\frac{\log 14}{\log 7}$$ [1 mark] b) $$2\log_3 5+\log_3 9-\log_3 3$$ [2 marks]

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Does the 14th Amendment's incorporation of the Bill of Rights onto the states, in addition to the federal government, alter the importance of the Bill of Rights?

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The cost of capital has many uses in financial analysis. It can be a good estimate of an organization's discount rate, which is used for net present value calculations when examining risk control and risk financing options. Identify the four sources of capital for an organization and identify which one is the least expensive and why.

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Two hi-tech firms consider a joint venture. Each firm simultaneously chooses an investment level.

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When a war breaks out in the Middle East, the price of gasoline rises, while the price of a used SUV falls.

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Question 1: In a cross between a black and a white guinea pig, all members of the F1 generation are black. The F2 generation is made up of approximately 3/4 black and 1/4 white guinea pigs. Let’s call the gene associated with guinea pig color (A). What are the parent genotypes? A. (AA) and (AA) B. (AA) and (aa) C. (Aa) and (aa) D. (Aa) and (Aa) E. There is more than one correct answer What are the F1 genotypes? A. All (AA) B. All (Aa) C. (1)/(2) (Aa) and (1)/(2) (aa) D. ¼ (AA), (1)/(2) (Aa), ¼ (aa) E. (1)/(2) (AA) and (1)/(2) (Aa) Question 2: Examine the pedigree below. The phenotype of interest is represented in blue when observed in an individual. Is the phenotype Dominant or recessive? A: Dominant B: Recessive

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Support your overall argument about the importance of learning from the past with evidence from the articles in the M15 learning module about why we study history. In total, you must reference at least three of the M15 articles in your paper,

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The following error were discovered in May 2021 by the controller for Caribbean Networks. ERROR In May routine maintenance costing $600 to service the office computer equipment was recorded as a debit to Computer Equipment and a credit to Cash. USE THE REVERSING ENTRY APPROACH TO CORRECT THE ERROR What is the reversing entry to correct the error? Choose... What would have been the correct entry? Choose...

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4. a. Write the equation of an ellipse, centered at the origin, with intercepts ($\pm\sqrt{8}$,0) and (0,$\pm\sqrt{2}$) b. What kind of shape is $3x^2 - y^2 = 11$? c. Set up and solve the corresponding system to find the intersection points of these two shapes

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2. The All-Powerful Theorem of Calculus [10 marks] Using all your knowledge acquired in this unit during the last three lectures, calculate the derivative in terms of $t$, $\frac{dy}{dt}$, for the following expression: $y = \int_0^{t^4} \sqrt{u} du$

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