Math Questions

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

You ask four people to the prom. If X is the number of "yes" responses, what is E(X)? Assume equal probability for "yes" and "no" response.

ATM passwords at a local bank consists of four digits. Paula remembers the first two digits of her password, but forgot the last two. What is the probably that Paula correctly guesses her password on the first try? 1/10000 1/100 1/10 1/1000

Suppose that the dollar value V (t) of a certain car that is f years old is given by the following exponential function. v (t) = 20,000 (1.16)^t Find the initial value of the car. Does the function represent growth or decay? growth decay By what percent does the value of the car change each year?

Julia just lit a new candle and then let it burn all the way down to nothing. The candle burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an equation for L, in terms of t, representing the length of the candle remaining unburned, in inches, t hours after the candle was lit.

Which statements about a probability distribution are always true? The probability of an outcome is never 0. The expected value of a probability distribution is the mean of the distribution. The sum of the probabilities in a probability distribution is equal to 1. Values for for a discrete random variable X in a probability distribution are always positive. A probability distribution must have more than one outcome.

Suppose the probability that a pitcher throws a strike (the probability of success) is 0.5. What is the probability of the pitcher throwing a strike on the first attempt? 0 0.25 0.5 1

Determine the number and type of solutions for the equation 2x2 + 5x + 5 = 0 Two different irrational-number solutions One repeated irrational-number solution One repeated rational-number solution Two different rational-number solutions Two imaginary-number solutions

Which line is parallel to the line y = −4x+6 and passes through the point (-2, 5)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = −3x/4+1, you would type your answer as y=(-3/4)x+1

The number of users on a social networking site was 45 thousand in February when they officially went public and grew to 60 thousand by October. If the site is growing exponentially, and growth continues at the same rate, approximately how many users should they expect two years after they went public? 142 thousand 150 thousand 1420 thousand 107 thousand 90 thousand

Find all real solutions of the equation 3s² = 75. Write your answers as a list, using a comma to separate answers.

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1500 pounds. At a 99% level, how many elephants need to be weighed so the average weight will be accurate to within 350 pounds? 147 176 166 123

Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), a seconds after diving, is modeled by h(x) = -5(x + 1)(x − 3) How many seconds after diving will Ana hit the water?

By completing the square, the expression x² + 12x + 87 equals (x + A)² + B where A = and B =

Squirrels are running wild on the campus, so Building and Grounds decides to tag 100 of them. In the spring, 50 squirrels are caught and 5 of them are tagged. What is the estimate for the number of squirrels living on campus?

A dance company charges $300 for a package of 20 dance lessons. Research shows that 20 percent of people attend all the lessons. The rest miss an average of 12 lessons. What is the expected value of a single dance for the company? $33.00 $28.00 $24.90 $31.00

In filing his income tax, Raul reported annual contributions of $300 to a public radio station, $180 to a public TV station, $200 to a local food bank, and $300 to other charitable organizations.

Enter values in the t-table for the piecwise function that is shown on the graph. Make sure that you are using the correct equation based for the x-value.

Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of 3.5e^0.05t billion metric tons/year, t years from 1980 (which corre sponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1980 might have been only 3.5e^0.01t billion metric tons/year, t years from 1980. Determine how much additional coal was produced between 1980 and 2000 as an alternative energy source.

Amanda needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.

Which line is perpendicular to the line y = 1/5 x - 1 and passes through the point (-2,-4)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y=-3/4x+1. you would type your answer as y=(-3/4)x+1 -

Find all real solutions of the equation 9t²-7=29. Write your answers as a list, using a comma to separate answers.

Suppose 33.3% of high school students eat pizza and 42% drink soda. If 17.3% of high school students eat pizza and drink soda, what is the probability that a randomly chosen high school student will either eat pizza, drink soda, or both? 8.7% 58.0% 75.3% 92.6%

Suppose you invest $1,000 in an account paying 7% compounded annually. Assuming no other deposits or withdrawals, how many years would it take for the amount in the account to double to $2,000? Round to the nearest 10th

If the distance between the points (-5, − 3) and (x, 45) is 50 then the possible values for x are: List all possible values, separated by commas.