7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female?

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1 Math 110 Sample Final Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the perimeter (or circumference) and area of the figure. 1) Give the exact value and an approximation using yd 7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female? 8) If the local sales tax rate is 7.9%, find the total amount charged for a watch priced at $ ) A sales tax of $12.4 is added to an item's price of $ Find the sales tax rate. Round to the nearest whole percent. 10) A $ dress is on sale for 30% off. Find the discount and the sale price. 2) 4 in. Simplify the complex fraction. 11) in. 7 in ) 29 in. 12) 6x 17 2x yd 2 yd Simplify/Solve. 13) (-0.4) ) 0.3x = -0.5 Solve. If necessary, round percents to the nearest tenth, dollar amounts to the nearest cent, and all other numbers to the nearest whole. 4) A company increased the number of its employees from 300 to 360. Find the percent increase. 5) A sales representative is paid a commission rate of 5.3% on all sales. Find her commission if her sales were $109,330. 6) Find the simple interest earned on $3200 saved for 4 1 years at an interest rate of 11%. 2 15) 3(x + 5.7) = 7x ) 2.8x x ) Simplify the expression. 18)

2 19) -4(-5) + 5-1(-2-3) 20) -7 + (-33) ) (6-9)2 (9-5)3 22) (-20) + 90 (-9) 23) (-2)3-18 (-2) 24) 23 - [6 - (5-8)] + (3-5)3 Write the fraction in simplest form. 34) ) - 65x 75 Solve the equation. 36) 1 + 2(3n - 1) = 41 37) 3x - 4-2x - 6 = 28 38) 6(2x + 3) = 2(4x + 9) 25) 2 - (9-7)3 39) -21 = 4y - y 26) -(-8)2 8 (-5) 40) x 2 = -1 - (-8) Solve the proportion for the given variable. 27) 16 x = Graph the linear equation. 41) y = 4x ) n 7 = ) 12 6 = y ) = 1.8 n Write the percent as a decimal. 31) 800% 42) x + y = -7 32) 0.5% Find the perimeter and area of the figure. 33) 1 9 foot 6 13 foot 2

3 43) y = -1 48) The difference of four times a number and seven times the same number is 9. Find the number. 49) The standard dose of medicine for a dog is 5 grams for every 15 pounds of body weight. What is the standard dose for a dog that weighs 95 pounds? 50) x = x 4 44) y = x 51) In a particular city, 1 of the residents 500 subscribe to the local newspaper. Write as a percent. 52) 441 is what percent of 735? 53) In small firms in a certain country, 27.5% of full-time employees receive medical insurance benefits. Write 27.5% as a fraction. 54) Find the perimeter of a square picture frame with a side length of 13.9 inches. 45) 6x + 2y = ) Jackie and her friend Warren ran for an open position on the board of directors of their favorite organization. Jackie received twice the votes that Warren received. There were 120 ballots cast. How many votes did Jackie receive? 56) Given that the triangles above are similar, find the unknown length n. 6 n Solve. 46) A motorcycle can be driven 100 miles in 3 hours, how long will it take to travel 120 miles? 47) A high school graduating class is made up of 550 students. There are 144 more boys than girls. How many girls are in the class? ) A rectangular room measures 10 ft by 19 ft. Find the cost of installing a wallpaper border around the room if the border costs $0.46 per foot. 3

4 58) Find the exact circumference of the circle. Then use the approximation 3.14 for and approximate the circumference. 65) Find the area. 1.2 miles 7 miles 4.3 miles 66) A country reports total exports of $7,725 million last year. Write this number using standard notation. 59) Nick is going to put insecticide on his lawn to control grubworms. The lawn is a rectangle that measures feet by 84 feet. The amount of insecticide required is 0.06 ounces per square foot. a) Find the area of the lawn. b) Find how much insecticide Nick needs to purchase. 60) A nail 3 1 inches long is driven into a board inches thick. How much of the nail 5 protrudes from the other side of the board? 61) What number is 47% of 20? 67) 0.6% of what number is 7.8? 68) x 9 - x 8 = 7 9 Convert. 69) 15 mg to grams 70) 3.1 tons to pounds 71) 0.13 L to milliliters 72) 48 oz to pounds 73) 8.37 kg to grams 62) Approximate to the nearest thousandth of a centimeter, if necessary, the length of the missing side of a right triangle with legs of 9 cm and 3 cm. 63) On an architect's blueprint, 1 inch corresponds to 12 feet. If an exterior wall is 60 feet long, find how long the blueprint measurement should be. 64) On a recent trip, Asha drove 266 miles on gallons of gasoline. How many miles would we expect the car to travel on 1 gallon of gas? 74) 62 in. = ft in. Translate the phrase into a mathematical expression. If needed, use x to represent "a number." 75) Five times a number, subtracted from ) The sum of -39 and a number. Perform the indicated operation. Round the result to the nearest thousandth if necessary. 77) ) ) ( ) (-0.52) 4

5 Write the mixed number as an improper fraction. 80) ) 1a 2 7 4a3 Find the volume of the solid. 81) 5 ft 1 ft 90) y y 91) ft 92) ) Use cm 93) Provide an appropriate response. 94) Find the measure of x. 17 cm 37 Perform the indicated operation and write the answer in simplest form ) ) Multiply: -4(8y + 6) 96) Find the complement of a 53 angle. 84) ) Simplify: -5(3z + 2) - z ) Find the supplement of a 24 angle. 85) ) ) ) Find the average of 2 6, 3 8, and ) Simplify 8x + 3-3x + 7 by combining like terms. Convert. Round to the nearest tenth of a degree, if necessary. 100) 33 F to degrees Celsius 101) C to degrees Fahrenheit Write the percent as a fraction or a mixed number in simplest form. 102) 0.9% 5

6 103) 120% 104) 87.5% A new car dealership has taken an inventory of the vehicles it has in stock. Below is a histogram indicating the number of vehicles in stock in certain price ranges. Use the histogram to answer the question. Solve the problem. 105) City A has an elevation of 14,395 feet above sea level while City B has an elevation of 18,649 feet below sea level. Represent the difference in elevation between these two cities by an integer. 106) Raya has $208 in her checking account. She writes a check for $51, makes a deposit for $81, and then writes another check for $140. Represent the new balance in her account by an integer. Write the decimal as a fraction or mixed number in simplest form. 107) ) Find the average of the list of numbers. 109) -15, 3, -8, 7, -9, 2, -1 Write the fraction as a decimal. If necessary, round to the nearest thousandth. 110) ) 8 15 Translate the sentence into an equation. If needed, use x to represent "a number." 112) The sum of twice 5 and -14 is ) Five added to three times a number equals ) How many vehicles in stock are priced between $14,000 and $20,999? 115) How many vehicles in stock are priced $20,999 or less? Write the fraction or mixed number as a percent. 116) ) Write the improper fraction as a mixed number. 118) 17 6 Find the unknown diameter or radius as indicated. 119) r = 1.6 yd d =? 6

7 Find the coordinates of the points in the graph. 120) 123) 121) Evaluate the expression for the given replacement values. 124) x y; x = 1 6, y = ) -9x; x = Round the decimal to the indicated place value. 126) , nearest thousandth 127) 9.956, nearest tenth 122) Complete and graph the ordered-pair solutions of the given equation. 128) x = 6y; (, 4), (0, ), (-24, ) 7

8 129) y = 3x + 6; (0, ), (1, ), (-1, ) 136) Seven thousand and thirty-seven thousandths, in standard form Write the ratio or rate as a fraction in simplest form. 137) Lake County's smallest forest preserve is 472 acres. Orange County's smallest forest preserve is 482 acres. Find the ratio of the acreage of Lake County's forest preserve to Orange County's forest preserve. 138) 18 inches of rain in 38 days Translate the phrase to an algebraic expression. Use x to represent "a number." 130) a. The product of a number and 10 b. Twice a number subtracted from 11 Find the measures of x, y, and z in the figure. 131) 139) 3.1 to 10 Find the prime factorization of the number. 140) ) 252 Evaluate the expression for x = -2, y = 3, z = ) -5x + 9y + 6z ) 9z 2y Use the circle graph to solve the problem. 144) The circle graph summarizes the results of a survey in which 2500 adults were asked their favorite movie category. 132) 30 Find the unit rate. 133) 1205 miles in 50 hours 134) A high school student created a remote control car that can travel 112 feet in 8 seconds. Write the decimal as indicated. 135) , in words How many of the survey respondents said that they favor action movies? Round to the nearest whole number. Write the decimal as a percent. 145) 9.2 8

9 146) 0.06 Find the square root and simplify. Round to the nearest thousandth if necessary. 147) Find the unit price and decide which is the better buy. 148) Popcorn: 18 ounces for $ ounces for $1.50 Find the mean, median, and mode of the list of numbers. 149) 9, 10, 20, 20, 14, 12, 12, ) 20, 29, 39, 40, 50 9