Check attached image for question. QUESTION 3 a) Apply the Ta... | Filo (2024)

Question asked by Filo student

y. (ii) Find the common difference of the arithmetic progression. (iii) Find the common ratio of the geometric progression. (iv) Find the sum of the first 10 terms of the arithmetic progression. (v) Find the sum of the first 10 terms of the geometric progression.Solution:(i) To find the value of x and y, we can equate the corresponding terms of the arithmetic and geometric progressions. From the given information, we have:4 = x (equation 1)x = y (equation 2)y = 18 (equation 3)From equation 2, we can substitute x with y in equation 1:4 = yTherefore, the value of x is 4 and the value of y is 18.(ii) To find the common difference of the arithmetic progression, we can subtract the first term from the second term. From equation 1, we have:x - 4 = y - xSubstituting the values of x and y, we get:4 - 4 = 18 - 40 = 14Since this equation is not true, there is no common difference for the arithmetic progression.(iii) To find the common ratio of the geometric progression, we can divide the second term by the first term. From equation 2, we have:y / x = 18 / ySubstituting the values of x and y, we get:4 / 4 = 18 / 41 = 4.5Since this equation is not true, there is no common ratio for the geometric progression.(iv) To find the sum of the first 10 terms of the arithmetic progression, we can use the formula:Sn = (n/2)(2a + (n-1)d)Where Sn is the sum of the first n terms, a is the first term, and d is the common difference. Since there is no common difference, we cannot find the sum of the arithmetic progression.(v) To find the sum of the first 10 terms of the geometric progression, we can use the formula:Sn = a(1 - r^n) / (1 - r)Where Sn is the sum of the first n terms, a is the first term, and r is the common ratio. Since there is no common ratio, we cannot find the sum of the geometric progression.

A company that produces cleaning products is considering a proposal to begin production of a new detergent that would cost 1abottletomakeanddistribute,andretailfor2.19 a bottle. Fixed cost for the operation would be $3000 a week. Assume that all output can be sold. (a) What would be the total cost, revenue and profit for a weekly volume of 10,000 bottles? (b) What is the break-even volume?

Please answer ASAP 33. A portion of road climbs steadily 138 feet over a horizontal distance of 5,944 feet. Another portion of road climbs steadily 987 feet over a horizontal distance of 9,240 feet. Find the slope of these portions of each road. Then state which portion is steeper: slope of road 1 or slope of road 2. Which road is steeper?Suppose you expect inflation to continue. Since 2011, inflation has averaged 4%. What would you expect to pay at the end of ten years for goods and services which cost $100 today? Use a continuous model in your calculations. (Hint: Use the formula F = P(1 + r)^t to find the nearest cent.)Math 54 Final Exam Version (130 points) Chapters 2, 3, 4, 5Name:2021 April 28 PageJohn Scalea35. On April 1, 2011, one share of Amazon stock sold for 180.OnApril1,2021,oneshareofAmazonstocksoldfor3,162. Calculate the percent change in the price of one share of Amazon stock over the past ten years.36. Calculate the average annual percent change in the price of one share of Amazon stock over the past ten years. Use the discrete growth model: P(t) = P(0)(1 + r)^t to estimate the price of one share of Amazon stock in t years since 2011.37. Suppose you deposit $3,700 into an account which pays annual interest. Complete the table below to account for the amount your account earns each year. Use the formula P = P(0)(1 + r)^t to calculate the interest earned each year. In the formula, P is the ending balance, P(0) is the beginning balance, r is the annual interest rate, and t is the number of years. Use the decimal notation for the interest rate.Year Beginning Balance Interest Earned Ending Balance1 $3,700.002 3 4