06:00 MOT←Assignment On...Sir Arthur Lewis Community CollegeMathematics for Business - MAT 106Assignment 1Instructions: Answer both questions showing all working where necessary.1. Jane invested a total of $18000 in three different mutual funds. She invested in abond fund that returned 4% in the first year, a growth fund that lost 8% for theyear and an international fund that returned 2%. She invested $2000 more inthe growth fund than in the other two funds combined.Large bagSmall bagIf she had a net loss of -$540 for the year, how much did she invest in each fund?2. A manufacturer produces two sizes of leather handbags. It takes longer to cutand dye the leather for the smaller bag, but it takes more time sewing the largerbag. The production constraints and profit for each type of bag is given in thetable below.||||Qall 77% >Cutting anddying0.6 hr1 hrSewing2 hr1.5 hrProfit$30$25The machinery limits the number of bags produced to at most 1000 per week. Ifthe company has a maximum of 900 hours per week available for cutting anddying and a maximum of 1800 hours available per week for sewing, determinethe number of each type of bag that should be produced weekly to maximiseprofit. (Assume that all bags produced are also sold).

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Answered: 1. Jane invested a total of $18000 in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Altmans z-score Altmans z-score is a financial tool for predicting insolvency in a business. For a certain company, the z-score formula is z=0.84+0.6StockpriceOutstandingsharesTotalliabilty In this exercise, we assume that thre are 45, 000 outstanding shares at a price of 4.80 each. a. Use L, for total liability, in dollard, and give a formula for the z-score for this company. b. Would a larger total liability idicate a better or worese outlook for the company? c. A z-score of 1.81 or lower indicates a high probability of insolvency. What is the smallest value of L that will give a z-score that indicates a high probability on insolvency?
29 A. Between these times, about 2,000 more megawatts of eletricity are used every hour. B. Between these times, about 500 fewer megawatts of electricity are used every hour. C. Between these times, about 500 or more megawatts of electricity are used every hour D. Between these times, about 2,00 fewer megawatts of electricity are used every hour.
A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20 plants in a room all facing the same window, obtaining the same amount of sunlight, and waters them identically each day. For a month, he monitors how much each plant grows. Then, he adds Miracle Grow to every pot and monitors how much each plant grows during a month with Miracle Grow. At the end of two months, he discovers that 14 plants grew more with Miracle Grow. Test the hypothesis that Miracle Grow increases plant growth (using an alpha level of .01). a) Is this a one-tailed or two-tailed test? ( b) State the null hypothesis. c) State the alternative hypothesis. d) Find the critical value(s). e) Calculate the obtained statistic. f) Calculate the P-Value (significance) of the obtained statistic). g) Make a decision. h) What does your decision mean?
A researcher designs an experiment using two drugs, she prepares 15 independent flasks of yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is provided below: Flask T Flask C Flask ND 1 8.2 6 5.2 11 6 2 6.8 7 6.1 12 5.1 3 8 8 6.2 13 5.6 4 7.6 9 5.7 14 5.2 5 7.9 10 6.3 15 6.1 a. Test if mean doubling time is different in Caffeine (C ) when compared to no drug (ND) using an ANOVA method, report an approximate p-value for the level of significance. b. If a drug decreases the doubling time of yeast cells, what could be the purpose of using this drug?
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A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents? Find the z-table here.
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better? A) There is convincing evidence because the interval is entirely above 0. B) There is not convincing evidence because the sample sizes are too small. C) There is convincing evidence because the number of clothing items receiving a…

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