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Q1:10) Using logarithm properties there are multiple ways of expressing the same transformations on a parent function. Given g(x) = 8 log[2(x)], find equivalent functions in the following forms. Round values to 4 decimal places where appropriate. a. g(x) = log(x) + c b. g(x)= logb [k(x)]| c. g(x)= log[k(x)] 11) Not all logarithmic and exponential equations can be solved algebraically. Use technology to solve the equation 3 2x-3 = log2 (2x) to 4 decimal places. Include a sketch or screenshot in your solution. 12) Why must the base of a logarithm be positive? 13) Why can we not calculate the logarithm of a negative number? 14) Rod says that he is thinking of a one variable exponential or logarithmic equation that has the following characteristics: a. has solutions x = 1 and x = 2 b. does not contain the digit "3" c. contains the number -12. What are two different equations that Rod could be thinking of? Are those the only possible answers?See Answer
Q2:6) Write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 units left. Justify your answer. 7) Ethan bought a new car worth $54,000. After 5 years, the car was worth $28,497.52. Calculate the annual depreciation rate of Ethan's car. 8) The hydrogen ion concentration of a lemon is about 0.02. What is its pH? 9) How do the intensities of a magnitude 6.0 earthquake and a magnitude 2.9 earthquake compare?See Answer
Q3:4.) Solve for the unknown using a method of your choice. a. 511x+23= 1257x [3 marks] b. 2" 123 [3 marks] = c. 3x+5+ 3* = 177876 [3 marks] 5) Describe the transformations on the logarithmic function g(x) = -log(x-2) +9See Answer
Q4:1) Convert the following expressions between exponential and logarithmic form. a. 2401 = 74 b. a = logbc | 2) Solve for x. Give your answer to three decimal places where appropriate. a. x = log21 [2 marks] b. c. 2* = 23 [2 marks] d. x 1024 [2 marks] e. 5 = logx 25 [2 marks] f. 3.5 = log36 x [2 marks] x = log22 10 000 [2 marks] 3) Use the properties of logarithms to solve the following equations. a. M = log11 (11²¹) [1 mark] b. 4log.(57) = x [1 mark] x = log100 1000 [1 mark] Office on the web FrameSee Answer
Q5:4. Suppose you want to have $400,000 for retirement in 30 years. Your account earns 5% interest. How much would you need to deposit in the account each month?See Answer
Q6:3. You deposit $300 each month into an account earning 5% interest compounded monthly. a) How much will you have in the account in 30 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?See Answer
Q7:2. How much would you need to deposit in an account each month in order to have $50,000 in the account in 10 years? Assume the account earns 5% interest.See Answer
Q8:1.Suppose you want to have $500,000 for retirement in 35 years. Your account earns 9% interest. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn?See Answer
Q9:5/2/24, 2:55 PM Algebra 2A - Unit 1 Exam Part B Algrims 2X - Usik 1 Exam Par Gogle Docs 5.9x² + 7x = 4 (5 points) 6. 2x²-6x + 3 = 0 (5 points)See Answer
Q10:Clearly indicate your answer and show all work. 1. Utilize the Rational Root Theorem, the Complete Factorization Theorem, and the Quadratic Formula to factor each of the following polynomials into a product of linear functions. (a) (5 points) 2-7³+8+3 Page 2 of 10 NYU Prof. Sanfratello-ATF-Spring 2024 - Written Assignment 7 (b) (5 points) -5x+4x+8x²-13+5See Answer
Q11:3. Complete the chart for each sequence. Is the sequence geometric or arithmetic? Explain your thought process. [K2 each] Recursive formula [K1 each] General formula (simplified if possible) [K1 first] [K2 second] The 10th term [K2 each] The sum of the first 10 terms [K2 each] 4, 12, 36, .... -7, -2, 3, ....See Answer
Q12:2. Use Pascal's Triangle to expand and simplify the following binomial: (4x + 7)5 [K3]See Answer
Q13:1. Find the first 4 terms in each sequence. [K2] a) tn = 3(−2)n-1 b) t₁ = 11, t₂ = 3, tn= 8tn-1 + tn-2 [K2]See Answer
Q14:14 points possible 0/14 answered Question 7 The sales tax rate for South Salt Lake is 7.05%. What is the state sales tax on a $11,500 car in South Salt Lake? $ < > What is the final cost of the car, including tax? S The sales tax rate for Morgan County is 5.95%. What is the state sales tax on that same car purchase in Morgan County? S What is the final cost of the car in Morgan County, including tax? How much money would you save by driving to Morgan County to purchase the vehicle? > Next QuestionSee Answer
Q15:Total # of ways that Describe how you can win this you can win (enter a game number or formula as indicated) You must pick the right first horse and then the right second horse 1,2,3,4 1,2,3,4 1 Probability of Winning 0.1666667% Odds against winning = (1-P)/P 599/nThis is a self grading sheet for columns B, D, F, and G. If your answer is correct it will show green, else you will see red. Game 25 horses ran in the Kentucky Derby. The Exacta bet involves picking the first two finishers in Jorder. Determine the number of outcomes for two horses finishing in the first two spots and the probability of winning the Exacta bet if you pick the horses at random. 25 horses ran in the Kentucky Derby. The Superfecta bet involves picking the first four finishers in order. Determine the number of outcomes for four horses finishing in the first four spots and the probability of winning the Superfecta bet if you pick the horses at random. In a lottery game, 45 numbered ping-pong balls are put in a bin, and 4 are randomly chosen. To win the jackpot, you need to match all 4 numbers in the order in which they were drawn. Determine the number of outcomes for picking 4 different numbers in order from the 45 ping- pong balls and the probability of you picking the correct numbers in order. In a lottery game, 60 numbered ping-pong balls are put in a bin, and 5 are randomly chosen. To win the jackpot, you need to match all 5 numbers. Determine the number of outcomes for picking 5 different numbers from the 60 ping-pong balls and the probability of you picking the correct numbers. In a lottery game, 60 numbered ping-pong balls are put in a bin, and 5 are randomly chosen. You'll get twice your money back if you match exactly three of the five numbers. Still using the same number of outcomes as the game above (choosing 5 different ping-pong balls from the 60), determine the probability of matching three out of five numbers. 25 horses ran in the Kentucky Derby. The Trifecta bet involves picking the first three finishers in order. Determine the number of outcomes for three horses finishing in the first three spots and the probability of winning the Trifecta bet if you pick the horses at random./nIf a cell is shaded Salmon Blue Green Gold Any other color Is this a permutation (the order of picks matters) or a combination (the order does not matter)? Permutation Legend Permutation You should Make a selection Enter a text response Enter a number Enter an Excel formula Make no changes Describe how to calculate the # of outcomes Pick any 2 out of 25 horses, where the order of selection matters. 1st, 2nd, 3rd, 4th Total # of outcomes for the game (use PERMUT() or COMBIN()) 600 303600 3575880See Answer
Q16:For the transition matrix P = 0.7 0.3 0.3 0.7 solve the equation SP = S to find the stationary matrix S and the limiting matrix P. S= (Type an integer or decimal for each matrix element. Round to the nearest thousandth as needed.) P=0 (Type an integer or decimal for each matrix element. Round to the nearest thousandth as needed.)See Answer
Q17:[15 Marks total] Application 8) A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8 m and the cycle are repeated every 4 s. a. Determine a sinusoidal equation to model the vertical position, in metres, of the boat versus the time, in seconds. b. Use your model to determine when, during each cycle, the boat is 0.5 m above its mean position. [5 marks]See Answer
Q18:Question 1 Make a number line that goes from 0 to 300 and counts by 20. You can upload a picture here using the insert image icon (mountain button). BIUX₂ X² Edit Insert Formats ▾ 글로 @ N A ▾ A ▼ <> 0/5 pts 32 Details Σ+ Σ ΑSee Answer
Q19:3 Solve forx: i. ii. iii. iv. 2²x = 8 42x x3 = 5 7x+3x4³ = 9 25x+2x3x+1= 5x+2 4 Solve for x: i) 8 log(√x)-log(9x) = log(x-¹) ii) 2ln(x)-In (2x-2)=In(x-3)See Answer
Q20:3. Analyze and sketch the polynomial function and complete the chart below. f(x)=-4(x + 2)(x-1)³(x-5) a. Leading Term: Leading Coefficient: c. Sketch the graph. Degree: b. List all the zeros of the polynomial with their multiplicities and behavior (touch/cross). Zeros End Behavior: Multiplicity BehaviorSee Answer

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