Basic Math Questions and Answers

Use synthetic division to find the function values. Then check your work using a graphing calculator. f(x) = 2x5 - 4x4 + 2x³ - 3x + 9; find f(20) and f(-3). f(20) = f(-3) = (Simplify your answer.) (Simplify your answer.)

How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 40% antifreeze? Use the six-step method. You need gallons. (Round to the nearest whole number.)

For a given function f(x), the operation f(3x) will A) stretch the graph vertically by a factor of 3. B) shrink the graph horizontally by a factor of ¹/3. C) shrink the graph vertically by a factor of ¹/3. D) stretch the graph horizontally by a factor of 3.

A tennis ball is thrown into the air from the top of a hotel that is 216 feet above the ground. The height of the ball from the ground is modeled by D(t) = 16t² + 10t + 216 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground?

Two cars are 261 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 3 mph faster than the other. What is the average speed of each car? Select one: a. 42 mph; 45 mph b. 41 mph; 44 mph c. 39 mph; 42 mph d. 40 mph; 43 mph

Which of the following describes the end behavior of the function f(x) = -5x³ + 3x²+ X-9? A) As x → -∞, y → B) As x → -∞, y →+∞ and as x → +∞, y→ +∞ +∞ and as x → +∞, y → – C) As x-∞, y → --∞ and as x-+∞, y → --0 D) As x → -∞, y → -∞ and as x → +∞, y → +∞

Sydney earned 91, 93, 93, 94, and 96 points on the 5 essays each out of a total of 100 points— given so far this semester. How many points must she earn on her sixth essay, which is also out of 100 points, to average 90 points for the six essays assigned this semester? A. 73 B. 80 C. 86 D. 90 E. 93

Bernie the Gambler reviews the number of bets he has won in his lifetime of gambling. Since he has made so many bets, he selects a random sample of 100 games and records the number of wins he has made. He sees that he has made 59 wins out of the 100 in his sample. (a) Calculate the point estimate for Bernie's sample. (b) Compute the margin of error for Bernie's winning bets given a confidence level of 99%. (Use a table or SALT. Round your answer to three decimal places.)

Sasha and Amir are running around a circular track. Their coach is standing in the center of the circle, recording their times. (a) If Sasha runs 3 times around the track, so that the coach turns 3 full rotations while watching him run, through how many degrees has the coach turned? The coach turns through (b) Through how many radians has he turned? The coach turns through 9 (d) Through how many radians has he turned? The coach turns through radians. (c) Through how many degrees does the coach turn if Amir runs 1.75 times around the track? The coach turns through radians.

A researcher is studying the relationship between a vitamin supplement and cholesterol level. What type of study needs to be done in order to establish that the amount of vitamin supplement causes a change in cholesterol level? A. Correlational study B. Randomized experiment C. Time Series study D. Survey

. You take your cup of coffee outside to stand in the sun and review calculus formulas. The coffee cup warns you that the coffee is "Hot Hot Hot" and tells you that the temperature of the cup of coffee at time 1, in minutes, is T(t) = 70+ Cekt. When they sold you the cup of coffee, the temperature was 200°F. By the time you walked down the block, three minutes later, the temperature was 180°F. According to the coffee company, when the temperature is above 150°F it is difficult to taste the coffee. When will the temperature of the coffee be 150°F so you can start to drink and enjoy the coffee experience?

At a poster shop, Han paid $16.80 for 2 large posters and 3 small posters of his favorite band. Kiran paid $14.15 for 1 large poster and 4 small posters of his favorite TV shows. Posters of the same size have the same price. Find the price of a large poster, e, and the price of a small poster, s.

The volume of a right circular cylinder varies jointly as the height and the square of radius of the base. Suppose a right circular cylinder has the measurements V = 44465.54 cubic yards, r = 17 yards and h = 49 yards. Step 1 of 2: Find the constant of proportionality k, rounded to two decimal places if necessary, and use it to write an equation that models the relationship.

Diego has a 6 foot ladder. He places it against a wall so that the angle it forms with the ground is equal to 30 degrees. On a separate piece of paper, we recommend sketching the situation, labeling as many parts of your drawing as possible from the information given. (a) How high off of the ground is the top of Diego's ladder? (b) How far away from the wall is the foot of the ladder? ⠀

A random sample was taken to determine the left foot length of female bears based on measuring their tracks. The following statistics were calculated for this sample: Mean = 12.8 inches, median = 12.7 inches, standard deviation = 1.4 inches, interquartile range = 2 inches. The distribution is mound-shaped and symmetric. Based only on this information, choose the best estimates for the minimum and maximum values of the distribution. A. min=11.4 and max = 14.2 B. min=10.7 and max = 14.7 C. min = 8.6 and max = 17.0

Tax in Benton and Franklin counties is 8.6%. A TV costs $549.99. Use your answer from the last question to find the total cost of the television after tax. Round your answer to the nearest cent. Enter your solution in the answer box without units.

A population culture begins with 15 strands of bacteria and then doubles every 4 hours. This can be modeled as 15(2)1/4, where t is time in hours. How many strands of bacteria are present at 12 hours? 252 strands of bacteria 200 strands of bacteria 120 strands of bacteria 400 strands of bacteria

The action figure toys of a multinational toy company are based on the usual ideal human figure of 6 feet for standardization purpose. If a common scale factor of 1 inch = 2 feet is applied, determine the height of an action figure toy.

Graph the following function over a two-period interval. Give the period and the amplitude. y = -2cos 6x

The distance from Jupiter to Mercury is 7.201 × 108 kilometers. How long would it take a rocket, traveling at 2.88 × 104 kilometers per hour to travel from Jupiter to Mercury? Round your answer to the nearest whole number of hours.

True or false? A larger sample size produces a longer confidence interval for μ. False. As the sample size increases, the margin of error decreases, resulting in a shorter confidence interval. True. As the sample size increases, the margin of error increases, resulting in a longer confidence interval. False. As the sample size increases, the margin of error increases, resulting in a shorter confidence interval. True. As the sample size increases, the margin of error decreases, resulting in a longer confidence interval.

You are choosing between two different cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round up to the nearest whole minute.

Miguel Rodriguez borrowed $400 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.4% a) How much will the interest amount to? b) What amount must Miguel pay Julio at the end of 6 months?

Bilquis is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 7 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?

United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $24.75 for shipping a 6-pound package and $53.75 for a 26-pound package. Find the base price and the surcharge for each additional pound. The base price is $. The surcharge for each additional pound is $

Bashir is a waiter at a restaurant. Each day he works, Bashir will make a guaranteed wage of $30, however the additional amount that Bashir earns from tips depends on the number of tables he waits on that day. From past experience, Bashir noticed that he will get about $7 in tips for each table he waits on. How much would Bashir expect to earn in a day on which he waits on 14 tables? How much would Bashir expect to make in a day when waiting on t tables?

Diana has 480 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) =

The approximate average distances from the sun to Earth and Mercury are listed below: Earth: 1.5 × 108 kilometers Mercury: 5.79 × 107 kilometers How much farther from the sun is Earth? Express your answer using scientific notation.

One month Elsa rented 5 movies and 3 video games for a total of $25. The next month she rented 2 movies and 6 video games for a total of $40. Find the rental cost for each movie and each video game.

Southwest Dry Cleaners believes that it will need new equipment in 6 years. The equipment will cost $26,000. What lump sum should be invested today at 2% compounded semiannually, to yield $26,000? Round to the nearest cent.

Compare the definition of scale factor of a dilation to the definition of scale factor of two similar polygons. How are they alike? How are they different? Choose the correct answer below. A. Each type is a constant ratio of corresponding lengths. For a dilation, the scale factor is always the ratio of an image length to a corresponding preimage length, while for similar figures, the scale factor ratio can relate the two figures in either order. B. Each type of scale factor can only be written in a specific order. For a dilation, the scale factor is not constant, while for similar figures, the scale factor is constant. C. While each type is a constant ratio of corresponding lengths, neither is constant. For a dilation, the scale factor is always the ratio of an image length to a corresponding preimage length, while for similar figures, the scale factor ratio can relate the two figures in either order. D. Each type is a ratio of corresponding lengths. For a dilation, the scale factor is not constant, while for similar figures, the scale factor is constant.

A hummingbird needs 10 grams of sugar and 8 grams of protein each day. One honeysuckle flower provides 20 mg of sugar and 10 mg of protein. One nasturtium flower provides 10 mg of sugar and 10 mg of protein. It takes 10 seconds to feed from a nasturtium and 15 seconds per honeysuckle. How many minutes does it take to get exactly the food it needs? (Remember that 1 gram equals 1000 mg.)

The sample proportion p is important in calculating a confidence interval. Find for a sample with 36 "yes" responses out of a total of 60 responses if we are trying to find the proportion of people who said "yes." p

A company that produces widgets has a fixed cost of $400 and a unit cost of $80 per widget. Each widget sells for $96. (Use the interactive figure to find your answer.) Click here to launch the interactive figure. (a) How many widgets must the company produce and sell in order to break even? What is the cost and revenue at the break-even point? The company must produce and sell widgets. The cost and revenue both equal. (b) What is the company's profit or loss when 50 widgets are produced and sold? A. The company makes a profit of $ B. The company incurs a loss of $ (c) If the company incurs a loss of $240, how many widgets did they produce and sell? The company produced and sold widgets.

On a daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have a.Between 40 and 43 passengers. b. Fewer than 42 passengers c. More than 48 passengers

Over a period of 120 days, Shawna Johnson earned $400 interest in a retirement account paying interest at a rate of 5%. Find (a) the principal at the beginning of the 120 days and (b) the amount in the account at the end of 120 days. (a) The principal was $ (b) The amount in the account at the end of 120 days is $.

Ayat's van traveled 88 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 220 miles? Ayat will need gallons. (Type an integer or a decimal.) ……..

Solve the equation by factoring. 49 - 64x² = 0

The 30 introductory statistics students took another quiz worth 30 points. On this quiz, the standard deviation of the scores of that quiz was 1 point. Which of the following gives the most suitable interpretation? A. all of the individual scores are one point apart B. the difference between the highest and lowest score is 1 C. the difference between the upper and lower quartile is 1 D. a typical score is within 1 point of the mean

The approximate areas of Oregon and Hawaii are listed below: Oregon: 2.55 x 105 square kilometers Hawaii: 2.83 × 104 square kilometers What's the difference between the areas of the two states? Express your answer using scientific notation.

Keisha puts 4 oranges into each of 5 baskets. She puts 6 lemons into each of 2 baskets. What is the total number of oranges and lemons in the baskets?

Find the midpoint of PQ with endpoints P(-4, 3) and Q(4, -1). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 45 minutes of calls is $23.25, and the remaining credit after 72 minutes of calls is $19.20. What is the remaining credit after 79 minutes of calls?

A sample of 300 g of lead-210 decays to polonium-210 according to the function given by A(t) = 300e^-0.032t, where t is time in years. What is the amount of the sample after 60 years (to the nearest g)? 2046 g 44 g 230 g 32 g

The population of Ukraine in 2015 was 44.4 million and the expected continuous annual rate of change k of the population is -0.006. (a) Find the exponential growth model P = Ce^kt (b) Use the model to predict the population of the country in 2031. ( (c) Discuss the relationship between the sign of k and the change in population for the country.

The approximate areas of South Carolina and Puerto Rico are listed below: South Carolina: 8.29 × 104 square kilometers Puerto Rico: 5.33 x 10³ square kilometers What's the difference between the areas of the two states? Express your answer using scientific notation.

Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home. A) c+ 25 = 10p + 5h B) c= 25 +10+5 C) c= 25-10p - 5h

Think about the meaning of relative to. Then rephrase this sentence in your own words: The altitude of the bird is 4 feet relative to the rooftop.

In a busy flu season, the rate of infection on a college campus is proportional to the product of the number of people who have the flu and the number who do not have the flu. Let P be the total population and let F be the number of people who have the flu. Which differential equation models this event? a. dF/dt = kF (P-F) b. dF/dt = e^k(P-F) c. dF/dt = k(P-F) d. dF/dt = kP(P-F) e. None of these

Determine f^-1 if f (x) = x+1/2-2 where ≠ 2 f^-1 (x) = x-2/x+1 f^-1 (x) = x-1/x+2 f^-1 (x) = 2x+1/x-1 f^-1 (x) = x-1/2x+1