Math Questions

If f(x) is a function, how is the graph of g(x)=4f(x-1) different from the graph of f(x)? O g(x) has the same shape as f(x) but stretched vertically by a factor of 4 and shifted right I space. O g(x) has the same shape as f(x) but shifted up 4 spaces and shifted left 1 space. Og(x) has the same shape as f(x) but stretched horizontally by a factor of 4 and shifted down 1 space. O g(x) has the same shape as f(x) but the vertex has been transformed to the point (-1, 4).

Jackson is conducting an experiment for his Physics class. He attaches a weight to the bottom of a metal spring. He then pulls the weight down so that it is a distance of 6 Inches from its equilibrium position. Jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. Which function best models the position of the weight? A) s(t) =6Sin(2πt) B) s(t) =6Cos(π/2)t C) s(t) =6Sin(π/2)t D) s(t) =6Cos(2πt)

A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one, there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven? (A) 2,801 (B) 19,531 (C) 19,607 (D) 97,655

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2 She makes these two Statements: (1) As x increases infinitely, the y-values are continually doubled for each single increase in x. (2) As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion? (1) Statement 1 is incorrect because the y-values are increased by 2, not doubled. (2) Statement 2 is incorrect because the y-values are doubled, not halved. (3) The conclusion is incorrect because the range is limited to the set of integers. (4) The conclusion is incorrect because the range is limited to the set of positive real numbers.

A small bakery called Taestry opens today. They expect to make profits continuously, at a rate of s(t) = t2/10 + 100 thousand dollars per year, where t is the time in years since they opened. (a) (3 points) Over their first ten years of operation, what will be the average value of Taestry's profit rate S(t)? Call this average value "A". Please show all of your reasoning. Answer: Over their first ten years of operation, Taestry's average profit rate will be A= thousand dollars per year.

Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are (a, b) and she reflects the figure over the line y = x. What are the coordinates of the image D'? (1)(a, b) (2)(b, a) (3)(-a, b) (4)(-b, -a)

Which expression and justification completes the third step of her proof? (A) log, (b^(xy)); power rule of exponents (B) log,(b^(x-y)); subtraction property of exponents (C) log(b^(x+y)); power rule of exponents (D) log, (b^(x/y)), division property of exponents

Read the excerpt. At the beginning of the mission, since our priority was to identify the origin of the alien's signal. What is the most accurate way to describe the excerpt? (1)It is a complex sentence. (2)It is an independent clause. (3)It is a dependent clause. (4)It is a compound sentence.

It will take Cody 3 months to save up enough money to purchase a stereo. He has a credit card with a 12% interest rate. Cody's friend Mark says it will cost Cody less money if he saves for 3 months instead of using the credit card. Is Mark correct?

Stacy hits the jackpot one day at the gumball machine. She puts in a quarter and gets 4 gumballs rather than 1. The radius of each gumball is 6 mm. What is the total volume of all 4 gumballs? _________mm³

The Roth family has liquid assets of $10,000, use assets of $150,000 and investment assets of $34,000. They also have liabilities totaling $108,000. If their total liabilities increase by $7,000 over the next year, by how much would the Roth family need to increase their assets in order to have a net worth of $100,000? (a) $7,000 (b) $14,000 (c) $21,000 (d) $28,000

6900 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 26 years, to the nearest cent?

From the observation deck of a skyscraper, Meena measures a 45° angle of depression to a ship in the harbor below. If the observation deck is 862 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax² + bx + c, is shown. Step 1: -c = ax² + bx Which best explains or justifies Step 1? subtraction property of equality completing the square factoring out the constant zero property of multiplication

Which sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each subdivision? Choose the correct answer below. Systematic Convenience Cluster Stratified

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?y=6x x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=6x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6. y=x+6; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6

Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. Rounded to the nearest whole degree, what is the measure of angle BOA? Rounded to the nearest tenth of a centimeter, what is the length of arc BAC?

From the table below, determine whether the data shows an exponential function. Explain why or why not. No; the domain values are at regular intervals and the range values have a common factor 0.25. No; the domain values are not at regular intervals although the range values have a common factor. Yes; the domain values are at regular intervals and the range values have a common factor 4. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.

Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount How much did tydla pay for the shirt? $42 $36.60 $34 $33,60

A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 30 cm. To the nearest tenth, what is the area of the wheel? 71.6 cm2 286.6 cm2 23.6 cm2 143.3 cm2

A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment? f(x) = 5000(0.4)^x, with a horizontal asymptote of y = 0 f(x) = 5000(0.6)^x, with a vertical asymptote of x=0 f(x) = 5000(1.4)^x, with a horizontal asymptote of y = 0 f(x) = 5000(1.6)^x, with a vertical asymptote of x=0

Peaches are being sold for $2 per pound. The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y? The values of both x and y can be any real number. The values of both x and y will be real numbers greater than or equal to 0. The value of x and y will always be zero The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

Jenna drives on average 46 miles per day with a standard deviation of 5.3 miles per day. Suppose Jenna's miles driven per day are normally distributed. Let X the number of miles driven in a given day. Then X = N(46,5.3). Suppose Jenna drives 41 miles on Monday. The Z-score when x = 41 is ___ The mean is ___ This Z-score tells you that x = 41 is ___ standard deviations to the left of the mean.

You are testing the null hypothesis p = 0.4 and will reject this hypothesis if z is less than -1.97. (Give your answers correct to four decimal places.) (a) If the null hypothesis is true and you observe z equal to -2.33, which of the following will you do? correctly fail to reject Ho correctly reject Ho commit a type I error commit a type II error (b) What is the significance level for this test? (c) What is the p-value for z = -2.33?

Grayson is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite's string play out. He measures the angle of elevation from his hand to the kite to be 38°. If the string from the kite to his hand is 125 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

In a fictional study, suppose that a psychologist is studying the effect of daily meditation on resting heart rate. The psychologist believes the patients who not meditate have a higher10 points resting heart rate. For a random sample of 45 pairs of identical twins, the psychologist randomly assigns one twin to one of two treatments. One twin in each pair meditates daily for one week, while the other twin does not meditate. At the end of the week, the psychologist measures the resting heart rate of each twin. Assume the mean resting heart rate is 80 heart beats per minute. The psychologist conducts a T-test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate. Which of the following is the correct null and alternative hypothesis for the psychologist's study? A. H₀: µ = 80; Ha: µ > 80 B. H₀: µ= 0; Ha: µ≠0 C. H₀: µ = 0; Ha: µ > 0

The CEof a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees? 000-250 001-250 0-250 1-250

Your friend just purchased a new sports car for $32,000. He received $6,000 for his trade in and he used that money as a down payment for the new sports car. He financed the vehicle at 6.76% APR over 48 months with a monthly payment of $619.15. Determine, from the given information, the finance charge. (A) $3,719.20 (B) $5,476.10 (C) $4,610.64 (D) $6,000

A study was done in 2015 that collected data on teenagers and text messaging. * In 2015, there were about 22 million teenagers (aged 13-17) in the United States. * They each sent an average of 900 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation. No rounding.

Darnell is constructing a rectangle window frame. He measured the length, the width, and the diagonal as 26 inches, 32 inches, and √1700 inches. Use the drop-down menus to answer the following questions of Darnell's window frame. (1)What is the longest side? (2)What is the square of the longest side? (3)What is the sum of the squares of the two shorter sides? (4)Does the window frame form right triangles?

Sarah sells fruit trays at a salad shop. Last week, she sold 450 fruit trays for $8 per tray. In previous weeks, she found that for ever $0.85 Increase in the price, she sold 15 fewer fruit trays. Which equation can be used to find Sarah's weekly sales Income in dollars, y, after x price increases of $0.85? (A) y = –12.75x2 + 262.5x + 3,600 (B) y = –12.75r2 + 482.5x + 3,600 (C) y = –12.75r2 + 272.5x + 3,600 (D) y = –12.75r2 + 502.51 + 3,600

Jerry has taken a random sample of students and determined the number of electives that each student in his sample took last year. There were 19 students in the sample. Here is the data on the number of electives the 19 students took: 6, 6 8,7,7,7,8,9,10,8,7,6 ,9,6,8, 7,9,7, 10. The mean of this sample data is 7.63. What is the sample proportion of students who took fewer than the mean number of electives? (A) 10/19 (B) 6/19 (C) 7/19 (D) There is not enough data to answer this question.

Fiona is pricing two bicycles. One is $175 with 10% off, and the other is $225 with 35% off. Which bicycle can she afford if she has $150 to spend? (1) Fiona can afford the $175 bicycle. It will cost $146.25. (2) Fiona can afford the $175 bicycle. It will cost $96.25. (3) Fiona can afford the $225 bicycle. It will cost $146.25. (4) Fiona can afford the $225 bicycle. It will cost $96.25.

Which of the following actions can be accomplished with electronic banking? A. pay bills without going to the bank B. transfer funds C. view our account status D. foreign exchange transactions

Olive oil is a cooking ingredient. The density of olive oil is 0.92 grams per cubic centimeter. An olive farmer wants to sell bottles that contain 460 grams of oil. What is the volume of the smallest container that holds 460 grams of oil? (A) 423 cubic centimeters (B) 460 cubic centimeters (C) 500 cubic centimeters (D) 552 cubic centimeters

Use the percent formula, A = PB, where A is P percent of B, to solve problem. 31% of what number is 49.6? The answer is (Type an integer or decimal rounded to the nearest tenth as needed.)

Brianna's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. What does the line's y-intercept represent?

Sarah wants to study the time it takes to complete a lab in a regular biology course compared to the time it takes to complete a lab in an honors biology course. Which quantities could Sarah use to make her comparisons? Check all that apply. (1) amount of time needed to complete a cell lab in a regular biology course (2)amount of time needed to complete a cell lab in an honors biology course (3)number of students taking a regular biology course number of students taking an honors biology course (4) amount of time needed to write a cell lab report in a regular biology course (5)amount of time needed to write a cell lab report in an honors biology course

A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. Which statement is true about the box plots? (A)The interquartile range of the trail mix data is greater than the range of the cracker data (B) The value 70 is an outlier in the trail mix data. (C) The upper quartile of the trail mix data is equal to the maximum value of the cracker data. (D)The number of calories in the packs of trail mix has a greater variation than the number of calories in the packs of crackers

Several ordered pairs from a continuous exponential function are shown in the table. What are the domain and range of the function? x y 0 4 1 5 2 6.25 3 7.8125 (1)The domain is the set of integers, and the range is y> 4. (2) The domain is the set of integers, and the range is Y>O. (3) The domain is the set of real numbers, and the range is y> 0. (4)The domain is the set of real numbers, and the range is y> 4.

A student solved the equation below by graphing. log6(x-1)= log₂(2x+2) Which statement about the graph is true? The curves do not intersect. The curves intersect at one point. The curves intersect at two points. The curves appear to coincide.

Caylan is making baked goods for a charity bake sale. He places a tray of scones, a tray of muffins, and a tray of cookies in the oven. The scones bake for 15 minutes, the muffins bake for 12 minutes, and the cookies bake for 10 minutes. When one tray is done, he removes it and replaces it with another tray of the same item. How many minutes after Caylan puts the trays in the oven will he first remove the scones, muffins, and cookies at the same time? __________ minutes

Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.5 cups of flour to make. How much flour is in each loaf of raisin bread? Explain the steps to follow to get the answer

Al Gorithm is going on vacation. He is in his room trying to decide what outfits he wants to bring. He has a total of 50 shirts and 10 shorts. Once he picks a clothing item, he puts it in his luggage. If asked to calculate a probability of picking his next clothing item, would it be considered a dependent or independent event?

The numbers 1 through 8 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order? (A) 0.01429 (B) 0.34296 (C) 0.000595 (D) 0.01428

Researchers compare the body composition of cattle feeding on a grain diet with that of cattle feeding on a grass diet. This method of gathering data is classified as (1)a census. (2)a sample survey (3)an experiment. (4)an observational study.

Which set of transformations is needed to graph f(x) = -0.1cos(x) - 4 from the parent cosine function? (1) reflection across the y-axis, vertical compression by a factor of 0.1, vertical translation 4 units up (2) reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down (3) vertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the y-axis (4) vertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the x-axis

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park?

Adult tickets to the fall play cost $6 and student tickets cost $3. The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected $660 from ticket sales, how many student tickets were sold? The drama class sold_____student tickets.

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book. What are the slope and y-intercept of the line represented by the points shown in the table? x y 0 -20 5 -10 10 0 15 10 20 20 (A) slope: 2, y-intercept: -20 (B) slope: 2, y-intercept: 10 (C) slope: 5, y-intercept: -20 (D) slope: 5, y-intercept: 10