Basic Math Questions and Answers

Mary's car will go 330 miles on 16.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2183 miles from her house to a friend's house? b) How far can the car be driven on 149 gallons of gasoline?

On the planet Maximillian live Sprogs and Graks. Initially there were 2400 sprogs and 300 Graks. The population of Sprogs doubles every 6 years and that of Graks doubles every 3 years. a. How many Graks were there after 1/2 years? b. When are there as many Sprogs as Graks?

The dean of a college would like to determine the feelings of students concerning a new registration fee that would b used to upgrade the recreational facilities on campus. All registered students would pay the fee each term. Which of the following data collection plans would provide the best representation of students' opinions at the school? A. Survey every 10th student who enters the current recreational facilities between the hours of 1:00 and 5:00 pm until 100 students have been asked. B. Randomly sample fifty student ID numbers and send a survey to all students in the sample. C. Place an ad in the campus newspaper inviting students to complete an online survey. Collect the responses of the first 200 students who respond. D. All of the above would be equally effective.

An art teacher made a copy of a small painting. To make the painting easier to see, the teacher enlarged the area of the painting by 48%. Let c represent the area of the original painting. The expression below is one way to represent the area of the new painting. Find two equivalent expressions that would give the area of the new painting. c+0.48c Which expressions will give the area of the new painting? Select all that apply. A. c(1+0.48) B. 148c C. 0.48c D. c +48c E. 1.48c

Use the fact that the derivative of the function f(x) = 3/x is f'(x) = -3/x2 to find the equation of the tangent line to the graph of f(x) at the point x = -7. The equation of the tangent line to the graph of f(x) at the point x = -7 is

Use the discriminant to determine the type and number of solutions. -2x2 + 5x + 5 = 0 Select one: a. One rational solution b. Two imaginary solutions c. Two rational solutions d. Two irrational solutions

Carl is making a garden that is half as long as it is wide. He wants to cover 271 square feet with the garden. Which equation best represents the situation if x represents the length of the garden? x-2x = 271 x. 1/2x=271 x+1/2x = 271 x+ 2x = 271

In a class of 60 students, on average, 8 will be left-handed. If a class includes 20 "lefties", estimate how many students are in the class. The class has approximately students.

Diana has 1600 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 light display has three colored lights, each of which flashes on for an instant at regular intervals. The yellow one flashes 15 times per minute, the blue one flashes 6 times per minute, and the red one flashes 12 times per minute. You see all three lights flash on simultaneously. How much longer must you wait before the three lights flash on simultaneously again? The correct answer is 20 seconds. Solve this problem and explain each step of your process so that a 5th grader will understand.

Select the correct answer from each drop-down menu. A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. The relationship between the number of months after the first year and the amount remaining on the card is T he Independent variable is the The dependent variable is the

An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying. Lisa studies 9 hr for a particular test and gets a score of 75. At this rate, how many hours would she have had to study to get a score of 94? She would have had to study hr to get a score of 94. (Round to the nearest hundredth as needed.)

Dante runs each lap in 7 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today? Use t for the number of minutes he will run today. Write your answer as an inequality solved for t.

Leo's Lawn Mowing Service has $300 in start-up expenses, and charges $30 for each yard. Yan's Yards does not have any start-up expenses and charges $20 for each yard. After how many yards will the profits of the two businesses be the same?

The graph of y = 5x6 - 3x4 + 2x-9 has at most how many turning points? Choose the correct answer below. 5 -9

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