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All Textbook Solutions for Algebra and Trigonometry (MindTap Course List)
Perform the indicated operations. Write your final answer as an integer or as a fraction in lowest terms. a 13+12 b 223+14 c 4(223) d 1243+16Determine whether the given number is an integer, rational, or irrational. a 10 b 163 c 52 d 5Is the inequality true or false? a 2<0 b 55 c 5>5 d 310 e 2>6Express the inequality in interval notation. a 1<x5 b x<3 c x4Express the interval using inequalities. a (2,) b [3,1] c [0,9)Evaluate the expression without using a calculator. a (3)4 b 34 c 34 d 512510 e (34)2 f 163/4Simplify the expression. Write your final answer without negative exponents. a (4x2y3)(2xy2) b (5a1/2a2)2 c (x2y3)(xy2)21DT2DT3DT4DT1DT2DT3DT4DTD DIAGNOSTIC TEST: The Coordinate Plane Graph the following points in a coordinate plane. (a)(2,4) (b)(1,3) (c)(3,1) (d)(0,0) (e)(5,0) (f)(0,1)2DT3DT4DTPROBLEMS Distance, Time, and Speed An old car has to travel a 2-mile route, uphill and down .Because it is so old, the car can climb the first mile-the ascent-no faster than an average speed of 15mi/h. How fast does the car to travel the second mile-on the descent it can go faster, of course-to achieve an average speed of 30 mi/h for the trip?Comparing Discounts Which price is better for the buyer, a 40 discount or two successive discounts of 20?Cutting up a Wire A piece of wire is bent as shown in the figure. You can see that one cut through the wire produces four pieces and two parallel cuts produce seven pieces. How many pieces will be produced by 142 parallel cuts? Write a formula for the number of pieces produced by n parallel cuts.Amoeba Propagation An amoeba propagates by simple division; each split takes 3minutes to complete. When such an amoeba is put into a glass container with a nutrient fluid, the container is full of amoebas in one hour. How long would it take for the container to be filled if we start with not one amoeba, but two?Batting Averages Player A has a higher batting average than player B for the first half of the baseball season. Player A also has a higher batting average than player B for the second half of the season. Is it necessarily true that player A has a higher batting average than player B for the entire season?Coffee and Cream A spoonful of cream is taken from a pitcher of cream and put into a cup of coffee. The coffee is stirred. Then a spoonful of this mixture is put into the pitcher of cream. Is there now more cream in the coffee cup or more coffee in the pitcher of cream?Wrapping the World A ribbon is tied tightly around the earth at the equator. How much more ribbon would you need if you raised the ribbon 1 ft above the equator everywhere? You dont know the radius of the earth to solve this problem.8PThe model L=4S gives the total number of legs that S sheep have. Using this model, we find that12 sheep have L= legs.2E3E4E5E6E7E3-12 Using Models Use the model given to answer the questions about the object or process being modeled. A mountain climber models the temperature T in F at elevation h in ft by T=700.003h a Find the temperature T at an elevation of 1500 ft. b If the temperature is 64 F, What is the elevation?9E10E3-12 Using Models Use the model given to answer the questions about the object or process being modeled. An ocean diver models the pressure P in lb/in2 at depth d in ft by P=14.7+0.45d a Make a table that gives the pressure for each 10-ft change in depth, from a depth of 0 ft to 60 ft. b If the pressure is 30 lb/in2, what is the depth?12E13E14E15E16E17E18ECost of a Pizza A pizza parlor charges 12 for a cheese pizza and 1 for each topping. a How much does a 3-topping pizza cost? b Find a formula that models the cost C of a pizza with n toppings. c If a pizza cost 16, how many toppings does it have?20E21EVolume of Fruit Crate A fruit crate has square ends and is twice as long as it is wide. a Find the volume of the crate if its width is 20 in. b Find a formula for the volume V of the crate in terms of its width x.Grade Point Average In many universities students are given grade points for each credit unit according to the following scale: A 4 points B 3 points C 2 points D 1 point F 0 point For example, a grade of A in a 3-unit course earns 43=12 grade points and a grade of B in a 5-unit course earns 35=15 grade points. A students grade point average GPA for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)8=3.375. a Find a formula for the GPA of a student who earns a grade of A in a units of course work, B in b units, C in c units, D in d units and F in f units. b Find the GPA of a student who has earned a grade of A in two 3-unit courses, B in one 4-unit courses and C in three 3-unit courses.CONCEPTS Give an example of each of the following: a A natural number b An integer that is not a natural number c A rational number that is not an integer d An irrational number2E3ECONCEPTS The symbol |x| stands for the _____ of the number x. If x is not 0, then the sign of |x| is always _____.CONCEPTS The distance between a and b on the real line is d(a,b)= _____. So the distance between 5 and 2 is _____.6E6-8 Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. a Is ab equal to ba? b Is 2(a5) equal to 2a10?8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80E81E82E83E84E85EAPPLICATIONS Temperature Variation The bar graph shows the daily high temperatures for Omak, Washington, and Geneseo, New York, during a certain week in June. Let To represent the temperature in Omak and TG the temperature in Geneseo. Calculate ToTG and |ToTG| for each day shown. Which of these two values gives more information?87E88E89E90E91E92E93E94ECONCEPTS Using exponential notation, we can write the product 555555 as ________.2E3ECONCEPTS When we multiply two powers with the same base, we _______ the exponents. So 3435= ______.5E6E7ECONCEPTS Scientists express very large or very small numbers using ______ notation. In scientific notation 8,300,000 is _______, and 0.0000327 is _______.9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39-40 Scientific Notation Write the number indicated in each statement in scientific notation. a A light-year the distance that light travels in one year, is about 5,900,000,000,000 mi. b The diameter of an electron is about 0.0000000000004 cm. c A drop of water contains more than 33 billion billion molecules.40E41E42E43E44E45E46E47E48E49E50E51EAPPLICATIONS National Debt As of July 2013, the population of the United States was 3.164108, and the national debt was 1.6741013 dollars. How much was each persons share of the debt? Source: U.S. Census Bureau and U.S. Department of TreasuryAPPLICATIONS Number of Molecules A sealed room in a hospital, measuring 5 m wide, 10 m long, and 3 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains 6.021023 molecules Avogadros number. How many molecule of oxygen are there in the room?54E55E56E57E58E59EUsing exponential notation, we can write 53 as __________.2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80E81E82E83E84E85E86E87E88E89E90E91E92E93ESpeed of a skidding car Police use the formula s=30fd To estimate the speed s in mi/h at which a car is travelling if it skids d feet after the brakes are applied suddenly. The number f is the coefficient of friction of the road, which is a measure of the slipperiness of the road. The table gives some typical estimates for f. Tar Concrete Gravel Dry 1.0 0.8 0.2 Wet 0.5 0.4 0.1 If a car skids 65 ft on wet concrete, how fast was it moving when the brakes were applied? If a car is travelling at 50 mi/h, how far will it skid on wet tar?95EFlow Speed in a Channel The speed of water flowing in a channel, such as a canal or river bed, is governed by the Manning Equation, V=1.486A2/3S1/2p2/3n Here V is the velocity of the flow in ft/s; A is the cross-sectional area of the channel in square feet; S is the down-ward slope of the channel; p is the wetted perimeter in feet the distance from the top of one bank, down the side of the channel, across the bottom, and up to the top of the other bank; and n is the roughness coefficient a measure of the roughness of the channel bottom. This equation is used to predict the capacity of flood channels to handle runoff from heavy rainfalls. For the canal shown in the figure, A=75ft2,S=0.050,p=24.1ft, and n=0.040. a Find the speed at which water flows through the canal. b How many cubic feet of water can the canal discharge per second? Hint: Multiply V by A to get the volume of the flow per second97E