Math Questions

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t) = 750e-0.144t, where t is the time in years? Round to the nearest hundredth year.

The exponential model A = 84.3 e0.032t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 165 million. The population of the country will be 165 million in (Round to the nearest year as needed.)

A restaurant owner wants to determine the effectiveness of his servers. The owner places a survey regarding the servers' effectiveness with randomly selected customer bills. What is the sample? A. The sample is the servers. B. The sample is all customers of the restaurant. C The sample is the owner of the restaurant. D. The sample is the randomly selected customers.

A veterinarian is interested in the average number of pets her clients own. Over the course of a month, she questions each client she meets with and records their responses. The veterinarian calculates the average and draws a conclusion from her data. What kind of statistical study did the veterinarian conduct? A. experiment B. survey C. theoretical study D. observational study

Find the coordinates of any local extreme points and inflection points. Use these to graph the function y=x- sin(-x) on the interval 0≤x≤2R. Choose the correct answer regarding local extreme points. A. The function as no local extreme points. B. Local minimum: (0,0) Local maximum: (2x,2x) C. Local maximum: (0,0) Local minimum: (21,2x) D. The function has a local maximum at (x,x).

Stacy Arrington is paid $.73 for sewing a jacket collar, $.86 for a sleeve with cuffs, and $.94 for a lapel. One week she sewed 318 jacket collars, 112 sleeves with cuffs, and 37 lapels. Find her gross earnings.

Suppose a rectangle has width W and length L both in feet. Choose the correct translation of the following into symbolic algebra: "Five feet more than four times the width is half of the length." 4W + 5 = L/2 (4W) = (1/2)L 4W = L/2+5 4W (L+5)/2 none of these are correct 4W+5+ (1/2)L

Suppose a certain baseball diamond is a square 95 feet on a side. The pitching rubber is located 61.5 feet from home plate on a line joining home plate and second base. How far is it from the pitching rubber to first base?

Find the following product and write the result in standard form, a + bi. (-4+ i)(3+ i) (-4+ i)(3+i)=

Two marbles are to be pulled from a bag that contains 2 yellow marbles, 4 green marbles, and 6 orange marbles. After the first marble is drawn, it is not replaced. What is the probability that two orange marbles are chosen from the bag? 1/2 5/24 11/12 5/22

Let E represent the set of all of the prime numbers that are less than 20. Let T represent the set of the factors of six. If x represents the amount of elements that are in ur, find the value of -3x+11. -22 -31 -19 -13 -28

A bag has 3 red balls, 3 blue balls, and 2 yellow balls. Two balls are taken out of the bag, 1 at a time. Is each statement True or False? The probability of drawing 2 red balls is 3/28. True False The probability of drawing a blue ball and then a yellow ball is 3/28. True False If the first ball drawn is blue, the probability that the second ball is also blue is 3/8.

Select the correct answer. As the number of samples increases, which value can be used to approximate a population mean? A the mean of the sample means B. the standard error of the mean C the confidence interval D. the standard deviation

The dimensions of a triangular lot are 143 feet by 65 feet by 137 feet. If the price of such land is $3 per square foot, how much does the lot cost? The lot costs $ (Do not round until the final answer. Then round to the nearest cent as needed.)

3. Mr. Jones observes that the angle of elevation to the top of a nearby building is 41.5°. After moving back a distance of 265 feet from the building, he finds that the angle of elevation to the top of the building is now 21.6°. Find the height of the building.

Which is the equation of a circle that passes through (2,2) and is centered at (5,6)? (+ 5)² + (y + 6)² = 25 (x - 5)² + (y-6)² = 25 (x-6)² + (y-5)² = 25 (x - 5)² + (y-6)² = 5

Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 100 workers 6 weeks to build 4 miles of highway. How many workers would be needed to build 16 miles of highway in 15 weeks?

(A) Use interval notation to indicate where f(x) is increasing. Note: Use 'INF' for oo, '-INF' for -oo, and use 'U' for the union symbol. Increasing: (B) Use interval notation to indicate where f(x) is decreasing. Decreasing: (C) List the values of all local maxima of f. If there are no local maxima, enter 'NONE' values of local maximums = (D) List the values of all local minima of f. If there are no local minima, enter "NONE" values of local minimums = f(x) = 4x² - 4x

Emily has 50 gallons of water to share between 6 different fish tanks. She puts an equal amount of water in each fish tank. What is the total amount of water, in gallons, in each tank? A. 3/25 gallon B. 8 1/25 gallon C. 9 2/25 gallon D. 10 1/25 gallon

Write the expression in the standard form a + bi (2+2i)-(9-5i) (2+2i)-(9-5i) =

The volume of a fixed amount of a gas varies directly as the temperature I' and inversely as the pressure P. Suppose that V= 120 cm³ when T=260 kelv and P=13-2 Find the pressure when T-380 kelvin and V=152 cm³.

Explain the difference between finding P(A or B) and P(A and B). Suppose A and B are dependent events. Provide an example for each probability.

Construct a normal bell curve with the mean, the deviations from the mean, and the percentages of the three areas under the curve. Upload the image for your teacher to grade.

Solve the following exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. 37x+4 = 5x-2 The solution set expressed in terms of logarithms is. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is {} (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Hans will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $52 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $57 and costs an additional $0.13 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?

Show that the function f(x)=x² +8x+2 has exactly one zero in the interval [-1.0]. Which theorem can be used to determine whether a function f(x) has any zeros in a given interval? A. Rolle's Theorem B. Extreme value theorem C. Intermediate value theorem D. Mean value theorem

Find the domain and range for the following exponential function. f(x) = 7.e-9 +5 a) Record the horizontal asymptote below. Be sure to record you answer as y = # b) Record the domain below using interval notation. c) Record the range below using interval notation.

Suppose a certain company gave raises of 3% each year for three years followed by raises of 5% for the next two years. a. If an employee has an annual salary of $52,500 after those 5 raises, what was their starting salary? Show a formula or some calculations and explain in words what you are doing. The anual Salary after 5 years = x dollars.1.051.030. b. What was their 'average annual growth' over those 5 years? In other words, if they had the same percentage raise each year, but had the same increase over the 5-year span, what would that constant 1 percentage raise be?

A car traveled at an average speed of 80 miles per hour for 3 hours and consumed fuel at a rate of 34 miles per gallon. Approximately how many gallons of fuel did the car use for the entire 3-hour trip? A) 2 B) 3 C) 6 D) 7

A biologist observed a population of bacteria that grew at a rate expressed by the exponential equation f(t) = 256e(0.0611r) where I is in minutes. How long will it take the population to reach 5 times its initial value? Round to two decimal places and do not include "t=" in your answer.

A researcher found a Person correlation, r=-0.42 between frequency of binge drinking and GPA in a sample of n = 29 undergraduate students. With the 2-tails test, he should conclude that there is a significant negative relationship between these variables with p <.05 but not with p <.01. there is a significant negative relationship between these variables with p <.01 but not with p <.05. there is a significant negative relationship between these variables with either, p <.05 or p <.01 there is no significant relationship between these variables with neither, p <.05 nor p <.01

A football player attempts a total of 8 passes in overtime. Each pass can result in one of 3 possible outcomes (a completion, an incompletion, or a turnover). How many ways could they complete the 8 passes?

At Imelda's fruit stand, you bought 5 apples and 4 oranges for $10, and your friend bought 5 apples and 5 oranges for $11. Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not? Choose 1 answer: Yes; they should charge $1.00 for an apple and $1.25 for an orange. Yes; they should charge $1.20 for an apple and $1.00 for an orange. No; the system has many solutions. No: the system has no solution.

The average driver spends $54 at the gas station each week with a standard deviation of $8. Assuming that the amount a driver spends on gas follows a normal distribution, solve for the percentage of drivers who spend: 1. More than $40? 2. Less than $30? 3. Between $30 and $40 Include your work with your answer to receive full credit.

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. This is common difference common ratio 20, 15, 10, ...

Two cyclists leave towns 180 miles apart at the same time and travel toward each other. One cyclist travels 8 slower than the other. If they meet in 5 hours, what is the rate of each cyclist? h Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the slower cyclist: Rate of the faster cyclist: ?

Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects Probability 0.260 0.291 0.240 0.155 0.044 (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is

Exactly 62% of the teachers in your school are under 47 years old. In addition, 4% of the teachers are over 49 years old. What is the probability that a teacher chosen at random is under 47 or over 49 years old? 62% 72% 66% 58%

The Jones family and the Griffin family each used their sprinklers last summer. The water output rate for the Jones family's sprinkler was 20 L per hour. The water output rate for the Griffin family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1075 L. How long was each sprinkler used?

One month Rachel rented 7 movies and 9 video games for a total of $71. The next month she rented 5 movies and 3 video games for a total of $31. Find the rental cost for each movie and each video game.

A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

f(x)=32-15 ln(3x) on the interval [3,9]. Enter DNE for any absolute extrema that does not exist. Absolute maximum = Absolute minimum =

An airplane is flying at an altitude of 12,600 feet above the ground. The angle of depression from the plane to the base of a tree is 15° 45'. How far horizontally must the plane fly in order to be directly over the tree?

Jack is a teacher and takes home 86 papers to grade over the weekend. He can grade at a rate of 11 papers per hour. Write a recursive sequence to represent how many papers Jack has remaining to grade after working for n hours.

The formula d = rt is used to calculate the distance an object travels over a period of time, t, at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t? A) r = d/t B) r = dt C) r = t/d D) r = d - t

Cindy measured a community college and made a scale drawing. The scale she used was 1 centimeter: 3 meters. A building at the college is 53 centimeters long in the drawing. How long is the actual building?

A dairy farmer uses a storage silo, shown below, that is in the shape of a right circular cylinder below. If the volume of the silo is 72pi cubic yards, what is the diameter of the base of the cylinder, in yards? 3 6 7 9

Find the amount of money (Future Value) in an account where $3,700 is deposited (Present Value) at an interest rate of 2.5% per year compounded continuously and the money is left in the account for 6 years.

A population of frogs in a pond increases at an annual rate of 22%. If there are 100 frogs in the pond, which equation gives you a model for how many frogs there will be in time t years? a. Pt = 100e^0.22t b. Pt = 100e^0.22/t c. Pt = 100e^-0.22/t d. Pt = 100e^-0.22t

Point R is located at (1, 2) on a coordinate grid. Point S is located at (4,-5) on the same coordinate grid. What is the distance from point R to point S, rounded to the nearest tenth? A 3.2 units B. 4.6 units C. 7.6 units D. 10.0 units