Math Questions

There were approximately 6.08 billion people in the world in the year 2000. The population grew about 1.23% each year since. Write an exponential function and use it to estimate the world population today.

Sally worked 7 hours on Monday, 6 hours on Tuesday, 6.75 hours on Wednesday, 5.75 hours on Thursday, and 3.5 hours on Friday. If she is paid $10.18 per hour. Find her gross earnings for the week.

To avoid a storm, a pilot leaves airport A and flies at a bearing of 172°. He travels for one and one-half hours at a speed of 650 mph. At the end of the one and one-half hours, the pilot changes direction and flies at a bearing of 68° for two hours at the same speed. At the end of the two hours, he is at point B, and is now able to continue with a normal flight plan since he has passed the storm. If there had been no storm, the pilot would have flown directly from Airport A to point B. How much further did the plane have to travel because of the storm? b. What is the bearing of the normal flight plan (from A to B)?

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.539, n = 25 Critical values: r = 0.487, no significant linear correlation Critical values: r = 0.396, significant linear correlation Critical values: r = 0.487, significant linear correlation Critical values: r = 0.396, no significant linear correlation

5. A sequence is defined by a₁ = 1, an+1 =1/2(an+3). Which of the following statements is true? (a) {an} is increasing and bounded above by. (b) {an} is decreasing and bounded below by 1. (c) {an] is decreasing and bounded below by 2. (d) {an} is decreasing and bounded above by 2. (e) {an} is increasing and bounded above by 3.

A kite string is being held 3 ft above the ground. The string is 185 ft long and is flying at an angle of elevation of 36°. Round your answer to the nearest tenth. Height of the the kite =

The harmonic motion function d (t) = 5cos(2t), in which dis measured in centimeters and t is measured in seconds, gives the distance a swinging pendulum is from its resting position at time t. How far was the pendulum from its resting position when the motion began? What is the period of the pendulum's motion? How far is the pendulum from its resting position after 7.5 seconds?

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? 77 93 99 105

Carter Motor Company claims that its new sedan, the Libra, will average better than 31 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is not sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is not sufficient evidence to support the claim that the mean is greater than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is greater than 31 miles per gallon.

The mean weight of a box of cereal filled by a machine is 16.0 ounces, with a standard deviation of 0.3 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh less than 15.5 ounces? Type or write all your computations to support the answer Round your answer to 0.01%, for example, 22.22%

In the game of roulette, a player can place a $10 bet on the number 7 and have a 1/38 probability of winning. If the metal ball lands on 7, the player gets to keep the $10 paid to play the game and the player is awarded an additional $350. Otherwise, the player is awarded nothing and the casino takes the player's $10. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $ (Round to the nearest cent as needed.)

Eduardo wants to determine the fuel consumption of his vehicle. He knows that 20 L of gasoline will get him 220 km and that 11 L of gasoline will get him 115 km. a. What is the independent variable? b. What is the dependent variable? c. What would two coordinates be?

A radioisotope is used as a power source for a satellite. The power output is given by the equation P = 50e t/250, where P is the power in watts and t is the time in days. a. Find the power available after 100 days.

Zachary earns $8.00 per hour. He get paid time and a half for any hours over 40 that he works in a week. If Zachary works 9 hours per day from Monday through Friday, what are his gross earnings for the week?

A farmer is comparing the number of eggs laid by two hens. The first hen laid 6 eggs per week for x weeks. The second hen laid 9 eggs per week for y weeks. The total number of eggs laid by the first hen was greater than the total number of eggs laid by the second hen. Write an inequality showing this relationship.

Which statement below describes two polygons which are similar? a) Corresponding angles and sides are congruent. b) Corresponding angles are congruent and corresponding sides are proportional. c) corresponding angles and sides are proportional. d) Neither corresponding angles nor corresponding sides are congruent.

A survey of TV viewing habits of 50 men and 50 women found the following information: Of the 50 men, 20 prefer watching baseball and 30 prefer football. Of the 50 women, 25 prefer watching baseball and 25 prefer football. Construct a data table for this data and answer this question: Out of the entire survey, what is the probability of choosing a man who prefers football? 1/5 3/10 2/5 1/2

The exponential model A = 883.1 e 0.014t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

Find the greatest common factor of 9m4 and 10n³.

Begin by graphing f(x)=2*. Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. h(x)=2x-2-2 Find the equation of the asymptote for h(x)=2x-2-2 using the graph. (Type an equation.) Observe the graph and find the domain of h(x) = 2*-2 -2. (Type your answer in interval notation.) Observe the graph and find the range of h(x)=2x-2-2. (Type your answer in interval notation.)

Find a formula for the inverse. f(x) = 8x

Find the smallest perimeter and the dimensions for a rectangle with an area of 49 in². The smallest perimeter for a rectangle with an area of 49 in² is in. (Simplify your answer.)

Suppose there are five firms in an industry. Their sales (that is, total revenue) are as follows: • Firm 1: $96 million • Firm 2: $48 million • Firm 3: $36 million • Firm 4: $14 million • Firm 5: $6 million The Herfindahl-Hirschman Index (HHI) for this industry is (Enter your response as an integer.)

Grande Prairie to Medicine Hat, Alberta, is 1013 km and takes Suzie 10 hrs and 45 minutes to drive. Suzie's SUV is travelling at a constant rate of speed from Grande Prairie to Medicine Hat. a. What are the independent and dependent variables? b. How could you represent Suzie's starting coordinates and end coordinates?

After a 70% reduction, you purchase a new sofa on sale for $204. What was the original price of the sofa? The original price was $

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. Do twenty-year-old have fewer cavities? The data show the results of a survey of 16 twenty-year-old who were asked how many cavities they have had. Assume that the distribution of the population is normal. 11, 8, 5, 6, 10, 9, 6, 9, 11, 9, 6, 10, 11, 7, 6, 11 What can be concluded at the a = 0.01 level of significance? Write hypothesis, give test stat and p-value. Write conclusions about HO and claim.

A delivery truck is driving along a straight road, and after, hours its distance (in miles) east of its starting point is s = 24t² - 4t³ At time t = 2 hours, where is the truck located? B) 64 miles C) 48 miles A) 96 miles D) 100 miles

WHAT IS THE EQUATION OF THE LINE THAT PASSES THROUGH THE POINT (4.4) AND HAS A SLOPE OF 1/47 Show your work below and put your answer in the blue box. Use point-slope form to start.

The bear population has a growth rate of 1.02. There are 1573 bears this year. Write a function that models the bear population. How many bears will there be in 10 years? a. Find the a and the b for this problem. b. Write the equation that models this situation. How many bears will there be in 10 years?

For the values 1.2, 3, 4, 1.2, 3.2, 4.1, 1.2, 9, 6, 1.2, and 4.5, how much does the standard deviation change if the outlier 9 is removed from the data? attach files

You invest $20,000 into an account that earns 5.2% interest every year. How much would you have after 18 years? a. Find the a and the b for this problem. b. Write the equation that models this situation. C. How much would you have after 18 years?

The point H is plotted on the coordinate grid below. Plot the point H', the reflection of H over the x-axis. on the graph to plot a point.

A bullet is fired straight up into the air. Its velocity after t seconds is given by v(t) = -9.81t + 345 m/sec. Find the total distance travelled by the bullet after 63 seconds. Round your answer to 2 decimal(s) Total distance: m

You spin a spinner that is equally divided into 9 parts. 3 parts are green, 2 parts are speckled, 2 parts are yellow, and 2 parts are black. What is the probability of the spinner stopping at a red section? Write your answer as a fraction.

Determine the probability of choosing a month that starts with a vowel or a month that is represented by an even number. Determine if these are independent events or mutually exclusive events and then show all of your work with the formula you use.

Let A be an n x n matrix. Suppose that there exists an invertible matrix P such that P-¹AP = D, where D is a diagonal matrix. Consider the following statements. (i) A² = P²D² (P-¹)² (ii) A² = P-¹D²P Which of the above statements is always true? (a) (i) only (b) (ii) only (c) (i) and (ii) (d) neither

At 2:00pm a car's speedometer reads 50mph, and at 2 10pm it reads 70mph. Use the Mean Value Theorem to find an acceleration the car must achieve Answer( in mi/h²)

Aisle 2 of a furniture store stocks 4-legged chairs, 4-legged tables, and 3-legged stools. If there are t tables, cchairs, and s stools, which expressions show the total number of furniture legs in aisle 2? 4t+4c+ 3s 4t+4c+4s 4(t+c)+ 3s 4(t+c+s) t+c+s t+c+ 3s

The designers of a standardized test are interested in knowing how long people take, on average, to complete the writing portion of the test. They decide to conduct an observation study at a testing facility. To avoid blas in their study, they create a list of the test takers scheduled to take the test this week. Then, they randomly select 50 test takers from the list to be part of the study. In this situation, what does the list of test takers represent? A. the population B. a sample C. the frame D. a control group

24. Consider the following statements. (i) If u and v are orthogonal in R³ then ||u + v|| = ||u – v|| (ii) ||u||²+ ||v||²||u+v||²+ ||uv||² for all u, v in R³. Which of the above statements is always true? (a) neither (b) (i) only (c) (ii) only (d) (i) and (ii)

Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = -0.01p² + 8p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield. population size of the yield X hundred swordfish X hundred swordfish

For the following expression, identify all the points of discontinuity, list the coordinates of any holes, and list any vertical and horizontal asymptotes. x² - 5x / x+1 Enter DNE if an answer does not exist. Enter as a list of numbers (e.g. 1,-2,3). Points of discontinuity: Enter as a list of coordinates (e.g. (1,2), (-2,3)) Holes: Enter as a list of numbers (e.g. 1,-2,3). Vertical asymptotes: x = Horizontal asymptote: y =

Solve this triangle. Offer the exact solution for the missing angle, but round your answers for each missing side length to the nearest whole meter. A = 39.70°, C = 30.35", b= 39.74m A = 39.70° B = C = 30.35° a= b= 39.74m C

A local hamburger shop sold a combined total of 384 hamburgers and cheeseburgers on Saturday. There were 66 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday? hamburgers

A puzzle contains rectangular wooden pieces with a length of 5 cm and a width of 6 cm. Each puzzle contains 10 of these rectangular pieces. If Tommothy wants to make 4 of these puzzles, find the amount of wood needed to make all of them.

How did Trevor Noah suggest to change the old adage: "Give 1 poin a man a fish, feed him for a day. Teach a man to fish, feed him for a lifetime."?* If you give a man a computer, he could be making a great deal of money and feed his family for the rest of his life. You should also give a man the rod so that he can fish and feed his family. If you teach the man to fish and give him a rod, then you might as well go fishing with him. Why did Trevor decide to stop involving himself in petty crimes? * He was afraid of the consequences if his mother knew of his illegal dealings. He decided to enter college and find a decent job that would help him get out of poverty. 1 point He felt guilty for stealing someone's digital camera where the family's memories were stored.

Mr. Costa randomly surveyed 20 students as they walked through the front door of the elementary school and found that 8 of them were buying hot lunch. If there are 430 students at this elementary school, how many would you expect to buy hot lunch? 172 162 152 142

A company decides to survey its employees about their job satisfaction. The company's managers are responsible for delivering the surveys. The managers Interview the employees they supervise face-to-face, asking the survey questions and writing down the responses. What is a source of blas in this sampling method? A. It is unlikely that employees will claim they are unsatisfied with their jobs while talking to their managers. B. Some people may be sick that day and unable to complete the survey. C. Employees usually complain about their jobs anyway. D. Some people may be on vacation and unable to complete the survey.

The half-life of radium (Ra226) is 1620 years. When will a 20-gram sample of radium (Ra226) be completely gone? Explain.

What is the equation of a line with a y-intercept of -3 and a slope of -4/5? -4x+ 5y = 15 4x + 5y = -15 -4x + 5y = -3 4x + 5y = 3