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1. In a market where approximately 44% of all book purchases are made online, customer reviews are extremely important from a sales and marketing perspective. Early reviews are most important, as they help or hinder a book's momentum in the marketplace. The frequency table shown above gives the first 20 customer ratings for a certain book sold online. What is the mean rating for this book?
2. Hardwood trees take much longer to grow than softwood trees. Once harvested, however, hardwood is much stronger and more durable. Because of its higher density, a piece of hardwood that is the same size as a piece of softwood weighs considerably more. A lumberyard ships both kinds of wood to home improvement stores. The cost C, in dollars, to ship a pallet of wood weighing p pounds can be found using the equation C = 6.5p + 16. What is the cost difference to ship a pallet of hardwood weighing 170 pounds versus a pallet of softwood weighing 80 pounds?
3. The First Transcontinental Railroad, which was 1,907 miles long, was completed in 1869 to connect the West Coast of the United States to the existing rail system that ran from the Missouri River to the East Coast. During the early years after building the railroad, dangerous conditions and mechanical problems could delay the train significantly. For a person traveling from one end of the First Transcontinental Railroad to the other, which inequality represents all possible values of t, where t is the time it took to complete the journey, if the train traveled at an average speed of m miles per hour?
Which value of x satisfies the equation given above?
5. The table above shows the price per square foot, the average customer rating (out of 10), and the life expectancy (before needing replacement) of the bargain version and the high-end version of carpet at a flooring warehouse. If the ratio of the life expectancies is roughly the same as the ratios of the prices and the ratings, about how many years can the high-end carpet be expected to last?
The bar graph shows median household incomes in a certain geographic region according to the age of the highest earner in the household. When presenting the data, the researcher decides to exclude the first age bracket (15-24), because it includes minors, which will likely skew the results because most minors do not have full-time jobs. The researcher also decides to exclude the last age bracket (65+) because it includes retirees, which is again likely to skew the results for the same reason. Which of the following statements most likely describes how this will affect the data overall?
7. If the graph of y = mx + b passes through quadrants I, III, and IV on a coordinate plane, which of the following must be true about m and b?
Manufacturing companies typically have a number of fixed costs (such as rent, machinery, insurance, etc.), which do not depend on output, and variable costs (such as wages, utilities, materials, etc.), which vary with output, usually at a constant rate. The graph shows a company's costs for manufacturing a particular product over the course of two years. Which of the following could explain the difference between the 2013 and 2014 costs?
Which of the following is the y-coordinate of the solution to the system of equations given above?
10. Premature babies are typically born underweight and are cared for in a neonatal intensive care unit (NICU). At a certain NICU, the mean weight of all the male babies is 4 pounds, and the mean weight of all the female babies is 3.6 pounds. Which of the following must be true about the mean weight w of the combined group of male and female babies at this NICU?
Based on the figure above, what is the approximate length of side AB?
12. When most people buy a house, they take out a mortgage to cover at least part of the cost of the home and then pay the loan back over time. The most common kind of mortgage is a 30-year loan. A couple buys a home and takes out a 30-year loan in the amount of $220,000 (called the principal). They decide they want to pay it off early to save money on interest. They set a goal of reducing the principal amount of the loan to $170,000 in four years. Suppose during the first two years of their four-year timeline, the couple pays down the loan by 10%. By what percent do they need to pay down the rest of the loan to reach their overall goal?
13. The table above shows several points through which the graph of a quadratic function f(x) passes. One of the x-intercepts for the graph is given in the table. What is the other x-intercept for the graph?
14. A college cafeteria received a petition from students to offer healthier meat, vegetarian, and vegan dishes. In response to the petition, the cafeteria conducted an analysis of its existing menu to determine the current state of those options. The results are summarized in the table below. The analyst used a sliding scale based on the nutrient levels compared against calorie, sugar, and sodium counts to determine the health score, a score of 1 being the least healthy and 5 being the healthiest.
What fraction of the vegetarian and vegan dishes has a health score of 3 or higher?
15. A college cafeteria received a petition from students to offer healthier meat, vegetarian, and vegan dishes. In response to the petition, the cafeteria conducted an analysis of its existing menu to determine the current state of those options. The results are summarized in the table below. The analyst used a sliding scale based on the nutrient levels compared against calorie, sugar, and sodium counts to determine the health score, a score of 1 being the least healthy and 5 being the healthiest.
If a student chooses a dish at random for lunch one day, what is the probability that it will be a meat dish with a health score of at least 4?
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