Math Questions

The population of Dublin, Ohio, in 2013 was 43,607 people. The area of the City of Dublin in 2013 was 24.79 square miles. Find the population density of Dublin in 2013 rounded to the nearest person.

Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). In order to test this, the lengths of the last 15 meetings were recorded in minutes: 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6. Using this data, test the null hypothesis at the alpha=0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. What is the p-value and conclusion of this test? p-value = 0.046; Fail to reject the null hypothesis p-value=0.046; Reject the null hypothesis p-value = 0.990; Fail to reject the null hypothesis p-value = 0.990; Reject the null hypothesis

In how many possible ways can you arrange frults in a row out of a basket of two oranges, one apple, and four lemons? 105 630 5,040 823,543

The number of astronomy papers published increases by 5% every year. If 27,000 astronomy papers were published in a particular year, how many will be published 2 years later?

On a spelling test. Michelle spelled 17 words correctly. There were 20 words on the test. What percent of the words did she spell correctly.

Two similar solids have volumes of 576 in³ and 1125 in³. If the smaller solid has a side length of 12 inches, how long is the corresponding side in the larger solid (in inches)?

This function: f(x)=- 40x4e-x has critical numbers: On the graph of y = f(x) the smallest critical number corresponds to: a local maximum a local minimum neither a local maximum or a local minimum On the graph of y = f(x) the largest critical number corresponds to: a local maximum a local minimum neither a local maximum or a local minimum

A bear is an animal and a zoo contains many animals, including bears. Three classes Animal, Bear, and zoo are declared to represent animal, bear, and zoo objects. Which of the following is the most appropriate set of declarations?

Circle P is dilated to form circle P'. Which of the following statements is always TRUE? A. The length of any chord in circle P is greater than the length of any chord in circle P'. B. The radius of circle P is equal to the radius of circle P'. C. The diameter of circle P is greater than the diameter of circle P'. D. The ratio of the diameter to the circumference is the same for both circles.

The probability of an employee at a large company being out sick on any given day is 0.08, and the probability of an employee at a large company being out sick and there being a fire drill on any given day is 0.0004. a. Find the probability of there being a fire drill given that an employee is out sick. b. If the probability of there being a fire drill is .005, what can you conclude?

At the gym, Diana always spends more minutes running than lifting weights. Part A Which equations describe the relationship between the number of minutes Diana runs, r, and the number of minutes she lifts weights, w. Select all that apply. 12+w=T r=w-12 w= 12 + r r-12= w r+w=12 Part B If Diana spends 25 minutes running at the gym, how many minutes does she spend lifting weights?

Elizabeth rolls a number cube four times such that each roll represents a digit of a four-digit number. Which of the following expressions represents the number of four-digit numbers that are even that Elizabeth could obtain? 6x3 6 x 4 6x6x6x3 6x6x6x6

A basketball player has a free throw percentage of 0.75. In the first half of a game, he made 12 attempts. How can a spinner be created to simulate data collection for this experiment? Create a spinner with two halves where one side represents made shots and one side represents missed shots. Create a spinner with four quarters where two sections represent made shots and two sections represent missed shots. Create a spinner with four quarters where three sections represent made shots and one section represents missed shots. Create a spinner with twelve sections where each section represents a shot.

A four-digit number is divisible by 10 and is smaller than 5,000. Which of the following expressions represents how many possible numbers there are? 4 x 10 x 10 x 1 4 x 10 x 10 x 10 10 × 10 × 10 × 1 10 x 10 x 10 × 10

Which of the following can be classified as a binomial probability experiment? A coin is tossed 10 times. The random variable X is the number of heads that appear. A bag contains 20 marbles. Eight marbles are red, nine marbles are blue, and three marbles are yellow. Three marbles are drawn out of the bag without replacement. The random variable X is the number of blue marbles. Five customers walk into a store. The random variable a represents the number of customers who buy at least one product. A random sample of 30 cars selected from a used car lot and their mileages are recorded.

Caleb was given a gift card for a coffee shop. Each morning, Caleb uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and after buying 8 cups of coffee, the card had a $25 remaining balance. Write an equation for A, in terms of x, representing the amount money remaining on the card after buying x cups of coffee.

Consider the parabola given by the equation: f(x)=x²-12x + 13 Find the following for this parabola: A) The value of f(-5): B) The vertex = C) The y intercept is the point (0, D) Find the two values of a that make f(x) = 0. Round your answers to two decimal places. Write the values as a list, separated by commas:

Determine whether the planes are parallel, perpendicular, or neither. 3x + 12y - 9z = 1, -15x + 30y + 35z = 0 parallel perpendicular neither If neither, find the angle between them. (If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)

What can the unit fraction 1 meter/3 feet be used for? To convert 25 inches to meters. To convert 15 meters to inches. To convert 5 meters to centimeters. This cannot be used to convert anything.

Owen's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y = 67 + 6x, where y represents the expected quiz score and a represents hours spent on homework that week. What is the meaning of the x-value when y = 99? A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 99 hours on their homework. The change in expected quiz score for every additional one hour students spend on their homework. The number of hours a student should spend on their homework to expect a score of 99 on the quiz.

16. If one student can complete the decoration for the prom in five days working alone, another student can do it in three days, and a third can do it in four days, how long will it take them working together?

The path of a marble rolling off of a desk can be modeled by the parametric equations: x(t)=2.5t y(t)=-16t^2+3 In these equations, the horizontal and vertical positions of the marble x(t) and y(t) are in feet and t is measured in seconds. Use Desmos and scratch paper to complete the following prompts. A. The marble will hit the ground after how many seconds? =0.433 seconds. B. Using your answer to (A), how far (horizontally) from the edge of the table will the marble first hit the ground? C. The parametric equations above can be expressed as the following single rectangular equation:

In how many possible ways can you arrange the digits in the order confirmation number 3018281268? 151,200 301,400 3,628,800 1,000,000

Write the negation of the conditional statement. If she can't take out the trash, then I will. If she can take out the trash, then I can't. She can't take out the trash, and I won't. If she can't take out the trash, then I won't. She can take out the trash and I will.

In Texas, the distance from Austin to Brownwood is 141 miles. It is 171 miles from Brownwood to Corsicana and 157 miles from Corsicana to Austin. Determine the angle between the routes from Brownwood. Show your work.

You bought an appliance and the salesperson offered you a warranty that costs $99 a year. You did some research and found that the average cost of a repair for your appllance Is $500. Which statement is true? Using your knowledge of probability and expected value, you decide you are more likely to come out ahead if you buy the warranty. Using your knowledge of probability and expected value, you decide your best option is to refuse the warranty. A person who uses the item more frequently than you is less likely to benefit from the warranty. It is never a good decision to buy a warranty.

The probability that a randomly chosen American household owns a gun is 0.43 (source). The probability that a randomly chosen American household owns a microwave is 0.968. Assuming that these events are independent, what is the probability that a randomly chosen American household owns neither a gun nor a microwave? 0.0182 0.0223 0.0514 0.3980

A company sells tires and rents out a portion of its warehouse to another company for a fixed rent of $8,000. The accounting department claims the company's monthly profit is determined by the profit function: P(x) = x³ - 8x² + 16x + 8 in thousands of dollars (already taking the rent into account). What is the company's maximum profit during the first three months?

The population of Columbus, Ohio, in 2013 was 822,553 people. The area of the City of Columbus in 2013 was 223.1 square miles. Find the population density of Columbus in 2013 rounded to the nearest person.

For the example below, prorate the given expenses to find the monthly cost. Sara pays $5300 for tuition and fees for each of the two semesters, plus an additional $320 for textbooks each semester. The prorated monthly cost for tuition and fees and textbooks is $ (Round to the nearest dollar as needed.)

Suppose it takes a force of 42 N to hold a spring that has been stretched from its natural length of 15 cm to a length of 18 cm. How much work (in J) is done in stretching the spring from 20 cm to 25 cm?

In 1970 the population of the United States was 203 million. Ten years later, in 1980, the population of the United States was 226 million. Write a function for the exponential growth of population in the U.S. using: ● t(0) = 203 ● t(10) = 226 Write your answer in the space provided.

Emma is driving on a long road trip. She wrote an equation to represent how many gallons of gas she has left in her tank, g = 14.5-0.45h, where g represents the number of gallons and h represents time in hours. What could the number 0.45 represent in the equation? How quickly the car uses gas, in gallons per hour. The number of gallons in the tank after one hour. How long it takes Emma to run out of gas. The number of gallons of gas initially in the tank.

The value of a painting can be predicted by the expression 120(1.08)t, where t is the . number of years since 2014. What does the value 120 represent? A. the predicted value of the painting in 2014 B. the predicted change in the value of the painting each year C. the predicted percent change in the wue of the painting each year D. the number of years for which the value of the painting is predicted to continue changing

At a large university in Conway, South Carolina, the Dean wants to know what proportion of students enjoyed their introductory statistics course. In order to answer this question, 200 randomly selected students who have taken an introductory statistics course were contacted and asked whether they enjoyed this course. 145 out of the 200 answered that they enjoyed the course. Using this data, construct a 99% confidence interval for the true proportion of students who enjoyed their introductory statistics course. (0.6631,0.7869) (0.7206, 0.7294) (0.6437,0.8063) (0.6731, 0.7769)

A park ranger measures the change in height of all trees of a similar species and age over a month. Half the trees are within a quarter of a mile from a large lake and half are further away. Observation Experiment

Kylie is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y = 3.5+2.3x, where y represents the total cost in dollars and cents, and a represents the number of miles she travels. What could the number 3.5 represent in the equation? How much the taxi costs per mile. The flat charge to order the taxi. The total charge for 1 mile. How far Kylie can ride for $1.

A company manufactures electronic pedometers. One out of 60 pedometers Is faulty, but the company cannot pinpoint the faulty ones until a consumer complains. Say that the company makes a profit of $10 on the sale of every pedometer but takes a loss of $100 for every faulty one, as they have to replace the unit. What is the expected average profit on the sale of a single pedometer in the long run? $7.80 -$1.20 -$7.80 $2.56

Evaluate the expression - 3+1i/5i and write the result in the form a + bi. The real number a equals The real number b equals

A local club plans to host a tennis tournament. The club will Invest $12,000 and hopes to sell tickets worth $18,000. The weather forecast Is a 20% chance of rain. If It does rain, the tournament will be cancelled, and the club will lose all of its Investment. Do you think this is a good Idea? Find the expected value of hosting the tournament. $6,000 $2400 $12,000 $8,400

You are earning a salary of $80,000 a year, and your position is steady. However, you have an opportunity to start your own business. You have done the research and It has shown that starting your own company gives you a 20% chance of earning $400,000 a year, a 30% chance of earning $100,000 a year, and a 50% chance of complete fallure. What is the expected value of giving up your $80,000 salary and starting your own business? $45,000 $12,000 -$4,600 $30,000

Suppose the probability an Insurance salesman makes a sale (the probability of success) is 0.6. Would you use a binomial distribution or geometric distribution to determine the probability that the salesman makes the first sale on the third presentation? What Is that probability? binomial; 0.096 geometric; 0.096 binomial; 0.144 geometric: 0.144

Find equations of the lines that pass through the given point and are parallel to and perpendicular to the given line. 4x - 2y = 7, (2, 1) (a) parallel to the given line (b) perpendicular to the given line

When the function f(x) is divided by 32 - 5, the quotient is 2x² + 7x + 3 and the remainder is -3. Find the function f(x) and write the result in standard form.

You survey four people about their opinion on a yes or no Issue. X Is the number of "yes" responses. What is E(X)? 1/16 1/4 3/8 8/4

You entered an essay contest that awards $5,000 In scholarship money to the top essays. The contest scholarship award has an expected value of $12. Which statement is true? If you enter an essay in one contest, you will earn $12 for submitting your essay. If you enter many similar contests competing against equally talented writers, you are likely to earn $12 per contest. If you enter many similar contests competing against equally talented writers, you will certainly earn $12 per contest. If you enter an essay in one contest, you might earn $12 for submitting your essay.

A new type of grass seed was developed by an agricultural research company. It was determined that the probability of a seed germinating Is 0.92 (given the correct soll conditions, water, and sunlight). If 5 seeds are planted, what is the probability that at least 3 seeds will germinate? 0.045 0.995 0.92 0.08

Suppose the probability that a basketball player makes a foul shot (the probability of success) is 0.35. On what attempt can the player expect to make a shot? 1 2 3 4

Captive primates, such as monkeys, often experience fractured bones. The probability distribution from a study of the X- rays of 500 captive spider monkeys shows that fifteen percent of them had one healed fracture; twenty percent had two healed fractures; twenty-five percent had three healed fractures; and forty percent had four healed fractures. About how many healed fractures would you expect a randomly selected captive spider monkey to have based on this probability distribution?

A surveyor is measuring the height of a building from a sidewalk two meters away from the building. The angle of elevation from the surveyor's eye to the top of the building is 74.393° and the angle of depression from the surveyor's eye to the base of the building is 40.030°. How tall is the building? 2 tan(114.423°) meters (74.393) (40.030) sin(2) meters 2 (sin(74.393°) + sin(40.030°)) meters 2 (tan (74.393°) + tan(40.030°)) meters 2 + tan(74.393°) meters