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A mason lays 120 blocks in 1 hr 40 min. How long will it take her to lay 300 blocks? Write the equation and then find the solution. (a) To what decimal value is (5 + 1)/2 approximately equal? (b) To what decimal value is (5 - 1) /2 approximately equal? (c) By how much do the results in parts (a) and (b) differ? Determine the quantity needed to replace the question mark to make the scale balance. The weight times the distance on both sides of the fulcrum (the triangle) must be the same to make the scale... A manufacturer sells Blu-ray Disc players for $150 per unit. Manufacturing costs consist of a fixed cost of $3850 and a production cost of $115 per unit. (a) Write the cost and revenue equations. (b)... Place these variables in the following classification tables. For each table, summarize your observations and evaluate if the results are generally true. For example, salary is reported as a... Determine the median and the first and third quartiles in the following data. 46 47 49 51 53 54 54 55 49 55 59 LO Suppose you know and you want an 85% confidence level. What value would you use as z in formula (91)? The estimate of the population proportion should be within plus or minus .10, with a 99% level of confidence. The best estimate of the population proportion is .45. How large a sample is required? HighTech Inc. randomly tests its employees about company policies. Last year, in the 400 random tests conducted, 14 employees failed the test. Develop a 99% confidence interval for the proportion of... In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x) = 2 x + 1 Use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. (-/-)* f(x) = 3. The cost of Berber carpeting is $9.99 per square foot. This price includes the cost of installation. Determine the cost for Nancy to have this carpeting installed in all three bedrooms. Nancy has... One serving of whole milk contains 8 g of fat. Reduced-fat milk contains 41.25% less fat per serving than whole milk. How many grams of fat does one serving of reduced-fat milk contain? Where... For b > 0, what are the domain and range of f(x) = b x ? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse. f(x) = 1/x 2 Find the inverse function (on the given interval, if specified) and graph both f and f -1 on the same set of axes. Check your work by looking for the required symmetry in the graphs. f(x) = x 4 + 4,... Use a right triangle to simplify the given expressions. Assume x > 0. cot (tan -1 2x) Let f(x) = |x|, g(x) = x 2 - 4, F(x) = x, and G(x) = 1/(x - 2). Determine the following composite functions and give their domains. F g g Use shifts and scalings to graph the given functions. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed. h(x) = -4x... a. Find the linear function C = f(F) that gives the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that C = 0 when F = 32 (freezing point)... How much interest did Patty pay for the use of the money? Patty borrowed $1640 from a bank for 18 months to buy a new office computer. The simple interest rate charged is 3.15%. Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent. $4000 for 2 years at 6% compounded semiannually. Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent. $2000 for 4 years at 3% compounded quarterly. The Nejems found a house selling for $550,000. The taxes on the house are $5634 per year and the insurance is $2325 per year. The Nejems are requesting a conventional loan from a local bank. The bank... Graph the function. Graph should contain at least two periods. Use the graph to determine the domain and the range of function. y = csc x + 4 4. Remote control has keys for channels 0 through 9. If you select one key at random, (a) What is the probability that you press a key for channel 6? (b) What is the probability that you press a key for... Assume that the spinner cannot land on a line. Determine the probability that the spinner lands on (a) Red. (b) Green. (c) Yellow. (d) Not yellow. If one ball is selected at random, determine the odds against it containing a number greater than or equal to 9. Use the rack of 15 billiard balls shown. 1 15) (14 (13) (12 (11 10 Bobbi, an investment counselor, is advising her client on a particular investment. She estimates that if the tax law does not change, the client will make $15,000 but if the tax law changes, the... One thousand raffle tickets are sold for $2 each. One prize of $600 is to be awarded. Rena purchases one ticket. (a) Determine her expected value. (b) Determine the fair price of a ticket. Assume that a person spins the pointer and is awarded the amount indicated if the pointer points to a positive number but must pay the amount indicated if the pointer points to a negative number.... Determine 28% of their adjusted monthly income. The Leungs decided to build a new house. The contractor quoted them a price of $144,500, including the lot. The taxes on the house would be $3200 per... Harrys credit card company deter-mines his minimum monthly payment by adding all new interest to 2.5% of the outstanding principal. The credit card company charges an interest rate of 0.03164% per... The Nicols are buying a house selling for $245,000. They pay a down payment of $45,000 from the sale of their current house. To obtain a 15-year mortgage at a 4.5% interest rate, the Nicols must pay... On April 15, the billing date, Gabrielle had a balance due of $57.88 on her credit card. She is redecorating her apartment and has the following transactions. (a) Determine the finance charge on May... Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question. What is 15% of $45.00? In a mathematics class, eighteen students received an A on the third test, which is 150% of the students who received an A on the second test. How many students received an A on the second test?... Mr. Browns present salary is $36,500. He is getting an increase of 7% in his salary next year. What will his new salary be? Where appropriate, round your answer to the nearest tenth of percent. Mayas present salary is $42,500. As part of a promotion her salary will increase by 4% next year. What will Mayas new salary be? Where appropriate, round your answer to the nearest tenth of percent. Fill in the blank with an appropriate word, phrase, or symbol(s). Probability problems that contain the words and or or are considered __________ probability problems. Use the table to answer the questions. The elements that compose seawater, along with the corresponding percents, are shown in the table below. Where appropriate, round your answers to two decimal... The manager at Arango Automotive has found that the probability that a car brought into the shop requires an oil change is 0.6, the probability that a car brought into the shop requires brake repair... A single die is rolled one time. Determine the probability of rolling. A 5 or 6. One card is selected from a deck of playing cards. Determine the probability of selecting. A 10 or a 4. One card is selected from a deck of playing cards. Determine the probability of selecting. A card less than 6 or a club. (The ace is considered a low card.) A board game uses the deck of 20 cards shown. Two cards are selected at random from this deck. Determine the probability of the following (a) With replacement. (b) Without replacement. The first... Use the deck of cards. If one card is selected, determine the probability that the card shows. A lion or an even number. 3 5 3 2 5 5 2. 2. Assume that the pointer in Fig. 11.15 is spun and then the pointer in Fig. 11.16 is spun. Determine the probability of the pointers landing on Red on both spins. Figure 11.15 Figure 11.16 Assume that the pointer in Fig. 11.15 is spun and then the pointer in Fig. 11.16 is spun. Determine the probability of the pointers landing on Yellow on the first spin and red on the second spin.... Assume that the pointer in Fig. 11.15 is spun and then the pointer in Fig. 11.16 is spun. Determine the probability of the pointers landing on A color other than red on both spins. Figure 11.15... Sears has 10 different microwaves and six different dishwashers in stock. The manager wants to place three of the 10 microwaves and two of the six dishwashers on sale. In how many ways can the... The expected value when you purchase a lottery ticket is -$1.50,and the cost of the lottery ticket is $5.00. Determine the fair price of the lottery ticket. A bag contains five red chips, three white chips, and two blue chips. Three chips are to be selected at random, without replacement. Determine the probability that. The first is red, the second is... A couple plans to have two children. (a) Determine the number of sample points in the sample space of the possible arrangements of boys and girls. (b) Construct a tree diagram and list the sample... You decide to take a science course, an English course, and a mathematics course during the next term. The available courses that you can take are listed below. If the courses are selected at random,... Mr. and Mrs. Frank just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list below. (a) Determine the... Consider the following wheel. If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on. An even number, given that the... Consider the circles shown. Assume that one circle is selected at random and each circle is equally likely to be selected. Determine the probability of selecting. A 3, given that the circle is... Consider the circles shown. Assume that one circle is selected at random and each circle is equally likely to be selected. Determine the probability of selecting. A red number, given that the circle... Two fair dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total. 3 if the first die is a 1. Two fair dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total. 3 if the first die is a 3. Two fair dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total. A number greater than 7 if the second die is a 5. Assume that a hat contains four bills: a $1 bill, a $5 bill, a $10 bill, and a $20 bill. Each bill is equally likely to be selected. Two bills are to be selected at random with replacement. Construct... What percent of head circumferences were greater than 35.75 cm? Assume that anthropologists have determined that the akidolestes, a small primitive mammal believed to have lived with the dinosaurs,... What percent of head circumferences were less than 50 cm? Assume that anthropologists have determined that the akidolestes, a small primitive mammal believed to have lived with the dinosaurs, had a... Use the following data on weekly salaries at Donovans Construction Company. What salary represents one standard deviation above the mean? First quartile Third quartile $825 79th percentile $832 $770... Determine the equation of the line of best fit from the data indicated in the exercise. Round both m and b to the nearest hundredth. Exercise 19. Data from exercise 19: x . . . . . . . . y 4 . . . .... Determine the equation of the line of best fit from the data indicated in the exercise. Round both m and b to the nearest hundredth. Exercise 20. Data from exercise 20: x . . . . . . . . y 8 . . . .... A mean average of 80 or greater for five exams is needed for a final grade of B in a course. Jorges first four exam grades are 73, 69, 85, and 80. What grade does Jorge need on the fifth exam to get... The following table gives the distribution of annual salaries for employees at Kulzers Home Improvement. Annual Salary . . . . . . . . . . . . . . . . Number Receiving Salary $100,000 . . . . . . . .... Consider the following two normal curves. (a) Do these distributions have the same mean? If so, what is the mean? (b) One of these curves corresponds to a normal distribution with a standard... The drawing below shows the floor plan of the first floor of the Oleander model home offered by Nisely Builders of Albuquerque, New Mexico. Place vertex O near the bottom of the graph. Use a graph to... Use Table 12.8 to determine the percent of data specified. Table 12.8: Less than z = 0.79 Table of Areas to the Left of z When z Is Negative 00 .02 .04 .05 .01 .03 .06 .07 .08 .09 -3.4 .0003 .0003... Evaluate the following limits. 4 sint x3 100 lim ( 5 + x x- The following table gives the position s(t) of an object moving along a line at time t. Determine the average velocities over the time intervals [1, 1.01], [1, 1.001], and [1, 1.0001]. Then make a... Given the function f(x) = 1 - cos x and the points A(/2, f(/2)), B(/2 + 0.05, f(/2 + 0.05)), C(/2 + 0.5, f(/2 + 0.5)), and D(p, f(p)) (see figure), find the slopes of the secant lines through A and... Analyze the following limits and find the vertical asymptotes of a. b. c. F(x) x 25 lim f(x) x5* Determine the following limits. -6 lim x Determine the following limits. -11 lim x Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x-00 Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x-00 The amount of an antibiotic (in mg) in the blood t hours after an intravenous line is opened is given by m(t) = 100(e -0.1t - e -0.3t ). a. Use the Intermediate Value Theorem to show the amount of... Find the derivative of the following functions. y = tan t / 1 + sec t The graph of f (t) = e -kt sin t with k > 0 is called a damped sine wave; it is used in a variety of applications, such as modeling the vibrations of a shock absorber. a. Use a graphing utility to... The economic advisor of a large tire store proposes the demand function D(p) = 1800 / p - 40, where D(p) is the number of tires of one brand and size that can be sold in one day at a price p. a.... Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x-00 Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x-00 For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. 2 %3 2 The table lists average annual cost (in dollars) of tuition and fees at private four-year colleges for selected years. (a) Determine a linear function (x) = ax + b that models the data, where x = 0... (a) Draw a bar graph that appears to show a small increase in the median age at first marriage for females. (b) Draw a bar graph that appears to show a large increase in the median age at first... Evaluate the expression. -4 - 4 Fill in the blanks with an appropriate word, phrase, or symbol(s). With the zero exponent rule, the expression 7 0 can be simplified to ________. Twelve red chips and 8 blue chips are in a bag. If four chips from the bag are to be selected at random, determine the probability of selecting four red chips. Set up the problem as if it were to be... Each of the digits 09 is written on a slip of paper, and the slips are placed in a hat. If three slips of paper are selected at random, determine the probability that the three numbers selected are... The number of hours of daylight at any point on Earth fluctuates throughout the year. In the northern hemisphere, the shortest day is on the winter solstice and the longest day is on the summer... The energy (in joules) released by an earthquake of magnitude M is given by the equation E = 25,000 10 1.5M . (This equation can be solved for M to define the magnitude of a given earthquake; it is... Carry out the following steps. a. Use implicit differentiation to find dy/dx. b. Find the slope of the curve at the given point. y 2 + 3x = 8; (1, 5) Use logarithmic differentiation to evaluate f'(x). (x + 1)10 (2x 4) f(x) A ship leaves port traveling southwest at a rate of 12 mi/hr. At noon, the ship reaches its closest approach to a radar station, which is on the shore 1.5 mi from the port. If the ship maintains its... From the graph of g, state the intervals on which g is continuous. y. + -3 -2 1 2.
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