"In a display window, a grocer wishes to place boxes of detergent in pyramid form so that the bottom row (first row) contains 15 boxes, the next row contains 14 boxes, the next row contains 13 boxes, and so on, with one box on top.' 1. What type of sequence represent the problem? 2. What is the model equation for the problem? (Let y be the number of boxes and x be the order of the row.) 3. How many boxes
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"In a display window, a grocer wishes to place boxes of detergent in pyramid form so that the bottom row (first row) contains 15 boxes, the next row contains 14 boxes, the next row contains 13 boxes, and so on, with one box on top.' 1. What type of sequence represent the problem? 2. What is the model equation for the problem? (Let y be the number of boxes and x be the order of the row.) 3. How many boxes are there in the 10th row? 4. There will be 3 boxes in what row? 5. How many boxes of detergent are necessary for the pyramid?
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- Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…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?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…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?Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 pounds of salt is dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in Figure 3.3.7.(a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1 (t) and x2(t) at time t in tanks A and B, respectively.(b) Find a relationship between the variables x1(t) and x2 (t) that holds at time t. Explain why this relationship makes intuitive sense. Use this relationship to help find the amount of salt in tank B at t = 30 min. FIGURE 3.3.7 Mixing tanks in Problem 9Chapter 3.3, Problem 9E, Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100
- A Ponzi scheme is a fraudulent investment operation in which returns to investors are paid from funds collected from new investors rather than from profit earned by the operator. The scheme takes its name from the notorious operation of Charles Ponzi in 1920. The case of Bernie Madoff is a more recent example.† Suppose the operator of a Ponzi scheme pays an initial return to investors of $23,000. Each month, he must recruit enough new investors to increase the return by 6%. a)Find a formula that gives the return R, in dollars, that the operator must pay after t months. b) How much must the operator pay to investors at the end of 3 years? (Round your answer to two decimal places.) c) Assume that new investors pay $2000 to join the scheme. How many new investors must be recruited at the end of 3 years in order to pay the existing investors? (Enter a whole number of new investors.)A Ponzi scheme is a fraudulent investment operation in which returns to investors are paid from funds collected from new investors rather than from profit earned by the operator. The scheme takes its name from the notorious operation of Charles Ponzi in 1920. The case of Bernie Madoff is a more recent example.† Suppose the operator of a Ponzi scheme pays an initial return to investors of $24,000. Each month, he must recruit enough new investors to increase the return by 3%. (a)Find a formula that gives the return R, in dollars, that the operator must pay after t months. R(t) = (b) How much must the operator pay to investors at the end of 3 years? (Round your answer to two decimal places.) $__________ (c) Assume that new investors pay $2000 to join the scheme. How many new investors must be recruited at the end of 3 years in order to pay the existing investors? (Enter a whole number of new investors.) _____________ new investorsA Ponzi scheme is a fraudulent investment operation in which returns to investors are paid from funds collected from new investors rather than from profit earned by the operator. The scheme takes its name from the notorious operation of Charles Ponzi in 1920. The case of Bernie Madoff is a more recent example.† Suppose the operator of a Ponzi scheme pays an initial return to investors of $21,000. Each month, he must recruit enough new investors to increase the return by 5%. (a) Find a formula that gives the return R, in dollars, that the operator must pay after t months. R(t) = How much must the operator pay to investors at the end of 3 years? (Round your answer to two decimal places.) $ Assume that new investors pay $2000 to join the scheme. How many new investors must be recruited at the end of 3 years in order to pay the existing investors? (Enter a whole number of new investors.) new investors
- Question 6 The revenue per month earned by the Couture clothing chain at time tis R(t) = N(t)S(t), where N(t) is the number of stores and S(t) is the average revenue per store per month. Couture releases a statement to their investors saying that currently they have 50 stores with a total revenue of $7,500,000 and expect to increase the number of stores by about 2 stores per month and increase total revenue by about $250,000 per month. What does this statement imply about the current rate of change of the average revenue per store per month?A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of a specific drug involved only 88 subjects. Assume that we want to treat 88 healthy humans with this new drug and we have 1212 suitable volunteers available. Complete parts (a) through (c) below. a. If the subjects are selected and treated in sequence, so that the trial is discontinued if anyone displays adverse effects, how many different sequential arrangements are possible if 88 people are selected from the 1212 that are available? Choose the correct answer below. A. 19 comma 958 comma 40019,958,400 B. 40 comma 32040,320 C. 479 comma 001 comma 600479,001,600 D. 495495 b. If 88 subjects are selected from the 1212 that are available, and the 88 selected subjects are all treated at the same time, how many different treatment groups are possible? There are…The revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the number of stores andS(t) is the average revenue per store per month. Couturereleases a statement to their investors saying that currently they have 50 stores with a total revenueof$7,500,000 and expect to increase the number of stores by about 2 stores per month and increasetotal revenue by about$250,000 per month. What does this statement imply about the current rateof change of the average revenue per store per month?