Math Questions

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

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 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.