Math Questions

A group of researchers found that the probability of completing a given task was 0.61. They then took a random sample of n = 66 people. (a) What is the value of n*p? Use 2 decimal places in answering this and the next question. (b) What is the value of n*(1 - p)? (c) Determine whether the following statement is true or false. We can conclude that the sampling distribution of the sample proportion is approximately normal. True, because both n*p and n*(1 p) are both greater than or equal to 15 and the CLT applies. True, because only n*P has to be greater than or equal to 15 for the CLT to apply. False, because both n*p and n*(1 - p) are both greater than or equal to 15 and the CLT applies. False, because both n*p and n*(1 - p) are less than 15 and the CLT does not apply.

A single-serving coffee machine is programmed to dispense 8 ounces of coffee per serving. Occasionally, the machine will start to overfill or underfill cups of coffee and require recalibration. According to the company, the coffee machine requires recalibration if it overfills or underfills cups of coffee by 1.5 or more ounces. Determine the probability that a randomly selected cup of coffee was underfilled or overfilled by more than 1.5 ounces. Assume the distribution of the amounts of all coffee dispensed by the machine are normally distributed with a mean of 8 ounces and a standard deviation of 1.13 ounces. The probability that a randomly selected cup of coffee is overfilled or underfilled by 1.5 ounces is

Suppose payroll tax is 6% of wage/salary income up to $100,000 and 2% of income earned in excess of $100,000. How much payroll tax does a person pay whose salary is $167,000? $7,340 $9,340 $8,000 $13,360

Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?

Vaccinations are intended to prevent illness. Suppose a flu vaccine is determined to be effective for 52% of patients administered the shot. A random sample of 75 people will be selected from the population. (a) What is the population proportion of success in the above scenario? (b) Calculate the mean of the sampling distribution of the sample proportion of people for whom the shot was effective. (c) Calculate the standard deviation of the sampling distribution of the sample proportion of people for whom the shot was effective. (Round your answer to three decimal places.)

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of C. [Let "L" designate "locked" and U" designate "unlocked".] {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} (LLL, UUU, LLU, LUL, ULL} LLU, LUL, ULL, LUU, ULU, UUL} O none of these

The number of people afflicted with the common cold in teh winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. Find the following: A- Find the linear function that models the number of people inflicted with the common cold, C, as a function of the year, t. B- Find a reasonable domain and range for the function C. C- If the function C is graphed, find and interpret the x- and y-intercepts. D- When will the output reach 0? E- In what year will the number of people be 9,700?

Find the savings plan balance after 15 months with an APR of 2% and monthly payments of $300.

1. Dora has an after school job at the Children's Zoo. She notices that at one meal, 3 cats will eat 2 cans of food. a How much food does 1 cat eat? b. Write a formula that Dora can use to determine how many cans of food to use for any given number of cats? (You can use the table method to develop the formula) c. If there are 12 cats in the Zoo, how many cans of food should Dora use at each meal time?

At noon, a barista notices that she has $30 in her tip jar. If she makes an average of $0.45 from each customer, how much will she have in her tip jar if she serves n customers during her shift? How much will she make if she serves 134 customers? How many customers did she serve by noon?

Answer the following as true or false. If it is false change the answer to make it true. a) The intersection of the centroid is the center or gravity for the triangle. b) The intersection of the centroid is outside the triangle for an obtuse triangle. c) The intersection of the incenter is sometimes outside the triangle. d) The intersection of the circumcenter is always outside the triangle.

The line of best fit through a set of data is y = - 55.765 - 2.454x According to this equation, what is the predicted value of the dependent variable when the independent variable has value 10? y = Round to 1 decimal place. The attached video is from questions 3 and 4 and applies to this question, too.

Calculate the derivative of y with respect to , if x³y + 3xy³ = x + y. dy/dx=

1. Suppose sin(A) = 3/4 Use the trig identity sin² (A) + cos² (A) = 1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant II. Round to ten-thousandth. -0.8364 0.9648 -1.1339 1.2647

Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible. Through (-4,7), perpendicular to the y-axis What is the equation of the line?

Find composite numbers that have the following characteristics: a. A number greater than 40 whose prime factorization contains 3 prime numbers that do not repeat . b. A number greater than 1000 whose prime factorization contains 1 prime number that does not repeat, 1 prime number that repeats 3 times, and 1 prime number that repeats twice.

f(x) = 2x and g(x) = 2.^x Graph the functions on the same coordinate plane. What are the solutions to the equation f(x) = g(x) Enter your answers in the boxes.

The state of New York reported 1484 live births in which the infants had Down syndrome (trisomy 21) between 2006 and 2010, which averages to about 5.7 cases per week. While the causes of Down syndrome are not fully understood, it is reasonable at this point to assume that live births are independent and the weekly rate is constant. Let X be the count of babies born with Down syndrome in the state of New York in a given week. (a) What values could X take? Notice how there is no clear limit to this range. None of the options are correct. X can take on any positive real number above the mean of X. X can take on any negative integer value. X can take on any non-negative whole number.

If the average price of a television in my store is $900 with stock is morally a standard deviation of $50. Assuming my distributed where is: A. 68% of the computers prices B. 95% of the computers prices C. 99.7% of the computers prices Assuming the data is not normal Chebyshev's states: D. at least 75% of data is between E. at least 88.87% of data is between F. at least 94% of data is between

ΔBCD What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box. is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.

Consider a population of size N = 12, 100 with a mean of u 200 and standard deviation of o = 15. Compute the following 2-values for sampling distributions of with given sample size. Suppose a random sample of 56 observations is selected from the population. Calculate the z-value that corresponds to x̄ = 206. Suppose a random sample of 77 observations is selected from the population. Calculate the z-value that corresponds to x̄ 198. Suppose a random sample of 60 observations is selected from the population. Calculate the z-value that corresponds to x̄ = 205 Suppose a random sample of 69 observations is selected from the population. Calculate the 2-value that corresponds to x̄ = 200.

The offensive line of a football team is larger than in previous years. The program will list a statistic to show this fact. Which statistic (mean, median, or mode) might be most appropriate in this situation? Mean Median Mode

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f (x) = 2x+5 / 5x-2; g(x) = 8x/5x-2

10) A newspaper advertises 5 different movies, 3 plays, and 2 baseball games for the weekend. If a couple selects 3 activities, find the probability that they attend a. 2 plays and 1 movie. b. Three movies c. Two plays and 1 baseball d. 1 of each type.

The distribution of all Indian River County grapefruit weights is known to be normally distributed with a mean of 296 grams and a standard deviation of 35 grams. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 52 grapefruit has a mean weight greater than 292 grams. P(x > 292) = Find the probability that a random sample of 52 grapefruit has a mean weight between 292 and 295 grams. P(292< x < 295) =

Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes?

Sometimes it is easier to figure out the probability that something will not happen than the probability that it will. When finding the probability that something will m happen, you are looking at the complement of an event. The complement is the set of all outcomes in the sample space that are not included in the event. Show two ways to solve the problem below, then decide which way you prefer and explain why. a. The marketing department has interviewed people of all different age groups about the BBQ chicken salad, but now they need information about why the othe salads are less popular. What is the probability that the next person randomly chosen will not prefer the BBQ chicken salad? b. If the probability of an event A is represented symbolically as P(A), how can you symbolically represent the probability of the complement of event

Rabies is an often-fatal disease, which is typically transmitted through the bite of an infected animal. The state of Florida has been recording all known cases of rabies for the past 20 years, with data indicating an average rate of 3.6 cases of rabies per week. Let X be the count of rabies cases reported in a given week. (a) Find the mean of X. (Enter your answer rounded to one decimal place.) mean of X: Find the standard deviation of X. (Enter your answer rounded to three decimal places.) standard deviation of X:

So far this season, the university's football team has executed 147 running plays, 134 passing plays, and 21 "trick" plays. What is the probability that the team will execute a passing play? 0.444 0.477 0.556 0.487

Which of the following expressions are equal to 1,-1, or to neither of those? List the corresponding letter(s), separated by commas if there are more than one. a. a - 4 / - a + 4 b. -4 + a / a- 4 c. a + 4 / a - 4 d. a - 4 / 4 - a e. a + 4 / 4 + a f. -a - 4 / a + 4

A waitress sold 13 ribeye steak dinners and 24 grilled salmon dinners, totaling $565.26 on a particular day. Another day she sold 20 ribeye steak dinners and 12 grilled salmon dinners, totaling $581.84. How much did each type of dinner cost?

Solve the inequality algebraically. 2x³ > -12x²

A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?

Sarah Jones earns $575 per week selling life insurance for Farmer's Insurance plus 4% of sales over $5,750. Sarah's sales this month (four weeks) are $15,500. How much does Sarah earn this month? (Round your answer to the nearest cent.)

A reporter is doing a story on the falling prices of homes in a large neighborhood. The reporter wants to demonstrate how the prices have fallen for all homes, not just the most expensive houses. Which statistic (mean, median, or mode) is most appropriate in this situation? Mean Median Mode

Estimate, then find the sum. Round to the nearest whole number. 2.7+6.87+21.878

An antique table increases in value according to the function v(x)= 750(1.05) dollars, where x is the number of years after 1980. a. How much was the table worth in 1980? b. If the pattern indicated by the function remains valid, what was the value of the table in 1990? c. Use a table or a graph to estimate the year when this table will reach double its 1980 value.

The New York City Marathon is a highly selective race. One way to gain entry into the race is to qualify based on a time from a prior-completed marathon. The NYC Marathon's organizers use this method to limit admission to the top 10% of marathon runners. If the mean completion time of all marathons is 179 minutes with a standard deviation of 17 minutes, what qualifying time should the NYC Marathon organizers set so that only the top 10% of runners will be admitted entry to the NYC Marathon? Round the solution to one decimal place, if necessary. The qualifying time should be set to minutes to ensure that only the top 10% of runners will be

Tara owns a pizza shop. The item purchased most frequently from her shop is a large pizza. For any order, Tara charges $7.00 for each pizza plus $3.00 for delivery services. Tara made a delivery of pizzas to a party for which she charged $45.00. How many pizzas did she deliver? Only an algebraic solution will be accepted.

Oklahoma is a Great Plains state in the south-central part of the United States, a region not historically known for its earthquakes. Seismic records up to 2008 show that Oklahoma has experienced a constant rate about 1.5 perceptible earthquakes (magnitude at least 3) per year, on average. Use the software of your choice to calculate the answers for (a)-(c). (a) Assuming that earthquakes are random and independent, with a constant rate of 1.5 per year, the count of perceptible earthquakes per year in Oklahoma should have a Poisson distribution with mean 1.5. Under this model, what is the probability that Oklahoma had more than 10 perceptible earthquakes in a given year prior to 2008? (Enter your answer rounded to ten decimal places.) P(X> 10) = (b) In 2013, Oklahoma experienced 109 perceptible earthquakes (an average of about 2 events per week). If the rate of 1.5 perceptible earthquakes per year was still true, what would be the probability of recording 109 or more perceptible earthquakes? (Enter your answer rounded to the nearest whole number.)

Analyze the polynomial function f(x) = (x + 7)2 (5-x) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y= for large values of Ix. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The lesser zero of the function is of multiplicity, so the graph of f the x-axis at x = The greater zero of the function is of multiplicity so the graph of f the x-axis at x =

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws The following table presents the results. minor flaw no minor flaw major flaws no major flaws 19 33 66 362 Find the probability that a randomly selected package of mozzarella cheese from this facility has a minor flaw. 0.177 0.137 0.108 0.235

If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)x-1 where p is the probability of success on any one trial. Assume that the probability of a defective computer component is 0.17. Find the probability that the first defect is found in the fifth component tested.

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = 65.37x + 79.52 and the r = -0.074. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.

Destination Weddings Twenty-six percent of couples who plan to marry this year are planning destination weddings. Assume the variable is binomial. In an andom sample of 3 couples who plan to marry, find the probability of the following. Round intermediate calculations and final answers to three decimal places. (a) Fewer than 2 couples will have a destination wedding. (b) At least 2 couples will have a destination wedding.

I tried taking the reciprocal of the fraction on the right so I would not have to do division but I could not get the equation to work. The quadratic on the bottom left is unfactorable. What steps would I take to solve this? x2 – 5x – 24 / 2x² - 11x + 24 / 2x² +7x+3 / x²+x-12

Tables in the dining hall are numbered 1-12 for students who eat there. The principal calls out a number for the table that will go through the buffet line first. The other tables follow in order of the table numbers. One student is sure the principal calls certain tables more often. She keeps track of which numbers are called over a 21-day period. Which statistic (mean, median, or mode) is this student using? Mean Median Mode

An actress has a probability of getting offered a job after a try-out of 0.05. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 8 try-outs.

7. How many different 4-letter "words" can be made from the letters j, o, u, r, n, e, y if a. The first letter must be a vowel and repetitions are allowed? Show the computation used to arrive at your answer. b. The first letter must be an y, the last letter must be an r, and repetitions are not allowed? Show the computation used to arrive at your answer.

Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions. What is Richard's net pay for the week if he earns $1,250? (Use Table 9.1 and Table 9.2). (Round your answer to the nearest cent.) Net pay