Basic Math Questions and Answers

Mary's car will go 319 miles on 14.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2049 miles from her house to a friend's house? b) How far can the car be driven on 133 gallons of gasoline? a) How many gallons are needed to drive 2049 miles? gallons (Round up to the nearest integer as needed.) b) How far can Mary drive on 133 gallons of gasoline? miles (Round down to the nearest integer as needed.)

Find an angle that is coterminal with an angle measuring -285°, where 0° ≤ 0 < 360°. Do not include the degree symbol in your answer. For example, if your answer is 20°, you would enter 20. Provide your answer below:

Bill Baxter has $24,000 to invest for a year. He can lend it to his sister who has agreed to pay 10% simple interest for the year. Or, he can invest it with a bank at 8% compounded quarterly for the year. How much additional interest would the simple interest loan to his sister generate? Find the effective interest rate for both investments.

Determine whether the object is a permutation or a combination. a 10-digit telephone number (including area code) Choose the correct answer below. A. This is a permutation because repetition is not allowed and the order of the items matters. B. This is a combination because repetition is not allowed and the order of the items does not matter. C. This is neither a permutation nor a combination because repetition is allowed. D. There is not enough information given to make a decision.

A construction worker needs to pour a rectangular slab 23 ft long, 28 ft wide, and 9 in. thick. How many cubic yards of concrete does the worker need? (Assume that the construction worker cannot buy a fraction of a cubic yard of concrete.) The worker needs cubic yards of concrete. (Type a whole number, rounded up to the nearest full cubic yard of concrete.) .....

a) Make a truth table for statement: (p^q) → (pVg). b) Make a truth table for statement: (pv q) → (p^q). c) Which of these statements is a tautology? Explain. d) Could you have answered part c without using a truth table? Explain.

Ellie bought snacks for her team's practice. She bought a bag of popcorn for $3.47 and a 10-pack of juice bottles. The total cost before tax was $23.47. Write and solve an equation which can be used to determine j, how much each bottle of juice costs.

Divide the following. Give your answer in the form quotient+ remainder/divisor 20x3-10x2 -18x -4/4x + 2

It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute. Select one: a. 34.5 minutes b. 29.5 minutes c. 24.5 minutes d. 28.7 minutes

What is the perpendicular bisector of a triangle? the segment from one vertex perpendicular to the opposite side the perpendicular segment that bisects one side of a triangle the side with the middle length measure a segment from one vertex to the midpoint of the opposite side

In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. Solution A is 20% alcohol and Solution B is 6% alcohol. She uses 800 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture a 14% alcohol solution?

1. For the first 7 days of January, the daily low temperatures for Burlington were 20°, 14°, 9º, 8°, -8°, -11°, and -4° Fahrenheit. What was the average daily low temperature, in degrees Fahrenheit, for those 7 days?

Find the domain and range of the function y = f(x) = x² – 6. Domain: Range:

A teacher gives a 15 item science test. For each item, a student receives one point for a correct answer; 0 points for no answer, and loses one point for an incorrect answer. Total test scores could range from +15 points to -15 points. The teacher computes the standard deviation of the test scores for the class to be -2.30. What do we know? A. The standard deviation was calculated incorrectly. B. Most students received negative scores. C. Most students scored below the mean. D. None of the above.

Miguel bikes 23 km per hour and starts at mile 10. Gabby bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation? A. Gabby: d=23t+10 Miguel: d = 28t B. Miguel: d = 10t+23 Gabby: 28d = t C. Miguel: d= 23t+10 Gabby: d = 28t D. Miguel: d= 10t +23 Gabby: d = 28t

Solve the equation using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) 18x - 6 = 9x² (a) Give real answers exactly.

Solve for v. |3v-6|=9 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Grace is an hourly employee, and the line that models her total pay in dollars as it relates to the number of hours she has worked has a slope of 45 and a y intercept of 35. Which statement is true?

Order: Sandostatin (octreotide acetate) 40 mcg subcut. Q.6h. Read the label in the figure. If the recommended dose is 100-600 mcg/d in 2-4 divided doses titrate to response, is the prescribed dose safe? If the prescribed dose is safe, how many milliliters will you administer? Select one: a. Yes; 0.8 mL b. No, the dosage is not safe. c. Yes; 1.2 mL d. Yes; 0.5 ml

(a) Suppose an analog clock strikes 6:00. How many degrees separate the hour hand from the minute hand, measuring clockwise from the hour hand to the minute hand? (Drawing a picture might help.) (b) How many radians separate the hour hand from the minute hand, measuring clockwise from the hour hand to the minute hand? (c) How many degrees will separate the hour hand from the minute hand when the clock strikes 4:30, measuring clockwise from the hour hand to the minute hand? (Remember that the hour hand moves gradually from 4 to 5 as the minutes go by after 4:00.) The number of degrees that separates the hour hand from the minute hand when the clock strikes 4:301s

Suppose two researchers wanted to determine if aspirin reduces the chance of a heart attack.Researcher 1 studied the medical records of 500 randomly selected patients. For each patient, he recorded whether the person took aspirin every day and if the person had ever had a heart attack. Then he reported the percentage of heart attacks for the patients who took aspirin every day and for those who did not take aspirin every day. What type of study did Researcher 1 conduct? A. Observational B. Experimental C. Survey D. None of the above

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? ⠀