Math Questions

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. If it is not, give the value of f(k). f(x) = x³+2x²–2x+1, k=2+ i Is 2+ i a zero of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ○ A. The given k is not a zero of the polynomial function. f(2 + i) = ▢ (Simplify your answer. Express complex numbers in terms of i.) ○ B. The given k is a zero of the polynomial function.

Solve the compound inequality. - X+9 > 10 and 1 + 2x ≤ -7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is____ B). The solution set is Ø.

Let B represent the bill for dinner at your favorite restaurant. Write an algebraic expression to represent the total amount paid for dinner if you decide to leave a 15% tip. Simplify your answer.

The demand equation for a certain product is 8p² + 5q² = 1400, where p is the price per unit in dollars and is the number of units demanded. (a) Find and interpret dq/dp. (a) How is dq/dp calculated? A. Use implicit differentiation. Differentiate with respect to q and assume that q is a function of p. B. Use implicit differentiation. Differentiate with respect to q and assume that p is a function of q. C. Use implicit differentiation. Differentiate with respect to p and assume that p is a function of q. D. Use implicit differentiation. Differentiate with respect to p and assume that q is a function of p. Find and interpret dq/dp. Select the correct choice below and fill in the answer box to complete your choice. A. dq/dp is the rate of change of price with respect to demand dq/dp = ▢.

The metal bismuth melts at a temperature of 271 °C and boils at 1560 °C, whereas the metal cobalt melts at a temperature of 1495 °C and boils at 2870 °C. (a) Which metal will be more volatile at room temperature? (b) Predict which of the two molten metals has the larger surface tension at its melting point.

Describe how and when to use multiplication rule 1, P (A and B)=P(A) . P(B), and how and when use multiplication rule 2, P(A and B) = P(A) P(B, given that A has already occured). Use multiplication rule 1 when two events are joined by "and" and the events are. Use multiplication rule 2 when the events are joined by "and" and the events are .

Let T: P₃->P₃, be the linear transformation such that T(2x²) = -2x² + 3x. T(-0.5x - 2) = -4x² - 4x -2, T(5x² + 1) = 2x - 1. Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(ax² + bx + C) =

Assume that you don't know the commission rate, but you do know the actual amount of daily commission you earned and the total dollar value of the shoes you sold. Based on these values, you can derive a formula for the commission rate. Using the slope-intercept form of a line, write an equation to calculate the commission y, based on sales, x. Hint: The y-intercept will be zero since you get no commission if you have no sales.

Let X and Y be two continuous random variables with joint probability density function f(x,y) = 12/5xy(1+y) for 0 ≤x ≤1 and 0 ≤ y ≤ 1 • Find the probability P(1/4 ≤ X ≤1/2, 1/3 ≤ Y ≤ 2/3). • Determine the marginal distribution functions of X and Y • Determine the conditional probability density function of X and Y

Suppose that the local sales tax rate is 6% and you purchase a car for $18,500. a. How much tax is paid? b. What is the car's total cost? The amount of tax paid is $ .

Suppose the binomial expansion of (2x – 3y)n includes the term –15120x4y3 The x4y3 term in the expansion will be The x5y3 term in the expansion will be

Different shapes are drawn on cards and then the cards are placed in a bag. The number of cards for each shape is shown in the table. Shape octagon square circle Number of cards 12 27 91 What is the probability that a randomly selected card has a circle drawn on it? Write your answer as a fraction in simplest form.

Write a system of equations in two variables and solve. 1500 concert tickets were sold for a jazz festival. Tickets cost $25 for covered seats and $15 for lawn seats. Total receipts were $28,500. How many of each type of ticket were sold? System of equations: Number of tickets sold for covered seats: Number of tickets sold for lawn seats:

Hunter invested $580 in an account paying an interest rate of 4.6% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 19 years?

Danielle spins a spinner that contains the following numbers 0, 2, 4, and 6. The probability of getting each number is shown in the table below. Let x = the number of spins that land on a 4. X 0 2 4 6 P(x) 1/4 1/2 1/5 1/20 What is the expected value for the spinner? 2.5 2.1 3.0 1.0

Draw the shape, Find (b) period, (c) amplitude, (d) width, (e) shift (f) (x₀), x₁, x₂, x₃, x₄, x₅, and (g) sketch a graph of the function through one full period, . f(x) = – 3 sec(2πx + π/6) + 1.

In a survey, 17 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $47 and standard deviation of $5. Find the margin of error at a 99% confidence level.

A sample of the length in inches for newborns is given below. Assume that lengths are normally distributed. Find the 99% confidence interval of the mean length. Length 17.7 19.5 23 23 17.3 19 17.9 20.6 16.1 21.5 Do not round in-between steps. Round answers to at least 4 decimal places.

Graph the linear equation. f(x) = 1/2x+7 Use the graphing tool to graph the linear equation.

Calculate the average rate of change of the following functions. 1. f(x) = x² over the interval 2 ≤ x ≤ 3 2. h(x) = 7 - 3x² over the interval 2 ≤ x ≤ 5 Criteria for Success The difference f(x2)-f(x1) is calculated. The difference (x2) - (x1) is calculated. Final answer is expressed with correct units.

A snack bar cooks and sells hamburgers and hotdogs during football games. To stay in business, it must sell at least 10 hamburgers but cannot cook more than 40. It must also sell at least 30 hotdogs but cannot cook more than 70. The snack bar cannot cook more than 90 items total. The profit from each hamburger sold is 33 cents and the profit from each hotdog sold is 21 cents. How many of each item should it sell to make the maximum profit?

A car was valued at $27,000 in the year 1991. The value depreciated to $11,000 by the year 2007. A) What was the annual rate of change between 1991 and 2007? r = Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? r = C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012 ? value = Round to the nearest 50 dollars.

Solve the compound inequality. Graph the solution set and write it in interval notation. x < 4 and x > -1 Choose the correct graph of the solution set. Write the solution set in interval notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The solution set is . (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) (B) The solution set is Ø.

Using the formula for binomial distribution, P(x) = (n x)px qn-x. What would the value of q be in the given scenario? When rolling a die 20 times, what is the probability of rolling exactly a 4 six times. 1/6 4/6 6/20 5/6

At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. What is the probability that the light is red? Using the binomial distribution, what is the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light? P(red) = .15, P(exactly 3 get stopped) = .97 P(red) = .3, P(exactly 3 get stopped) = .8 P(red) = .15, P(exactly 3 get stopped) = .08 P(red) = .3, P (exactly 3 get stopped) = .25

The equation below shows the cost C in dollars, of a small company to produce units in one week. C(x) = 500 + 60x +0.5x^2? How much money will it cost to produce 28 units in one week?

Suppose the average height of US men is 70 inches with a standard deviation of 5 inches, and the average height of women is 65 inches with a standard deviation of a 3.5 inches. What is the z-score for your height relative to your gender? What is the meaning of the associated value from the z-table for your z-score?

An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 935 new employees. If a new route is not granted, it will hire only 175 new employees. If the probability that a new route will be granted is 0.4, what is the expected number of new employees to be hired by the airline?

The median home value in Georgia and Colorado (adjusted for inflation) are shown below. Year Georgia Colorado 1950 31700 43300 2000 111200 166600 If we assume that the house values are changing linearly, a) In which state have home values increased at a higher rate? b) If these trends were to continue, what would be the median home value in Georgia in 2010?

What effect does the "h" value have on the function f(x) = log(x)? The "h" value moves the graph left or right. The "h" value moves the graph up or down. The "h" value reflects the graph across the x-axis. None of the other answers are correct. The "h" stretches the graph vertically by a factor of |h|.

In a study of the effects of diet on blood pressure, one group of 85 people followed a vegetarian diet for 4 months, after which time their mean systolic blood pressure was 15 mm Hg lower than at the start. Another group of 75 people followed a nonvegetarian diet for the same length of time, after which their mean systolic blood pressure was 1 mm Hg lower. If a vegetarian diet had no effect on blood pressure, there would be less than 1 chance in a 100 of getting these results. Which statement is valid based on these results? The result is not statistically significant. The difference in the sample size of the two groups makes a conclusion impossible. The recommended diet for lower blood pressure is nonvegetarian. The result is not practically significance.

You intend to conduct a goodness-of-fit test for a multinomial distribution with 7 categories. You collect data from 58 subjects. What are the degrees of freedom for the x^2 distribution for this test?

A speaker is talking about the principle of charity, and suggests that a person who is truly charitable will offer money to someone in need unreservedly. He illustrates this by saying that one should open their wallet and hand money to another person without looking at how much money they are holding. Suppose this speaker had five bills in his wallet: two $20, one $10, and two $5. If he were to choose one bill at random to give away to the next person who asked him, what is the expected value of his handout?

Graph an exponential that passes through the point (2,6) and has growth factor 3. Plot and label at least 3 other points (include an intercept).

The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t. (3/4, √7/4) Find sin t. A) 3/4 B) 3√7/7 C) √7/3 D) √7/4

Use the following statement to answer parts a) and b). Five hundred raffle tickets are sold for $3 each. One prize of $500 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket. a) Determine his expected value. b) Determine the fair price of a ticket.

All Harold's ties are red except for two. All Harold's ties are blue except for two. All Harold's ties are brown except for two. How many ties does Harold have? Harold has red tie(s), blue tie(s), and brown tie(s).

Two buildings in a sports complex are shaped and positioned like a portion of the branches of the hyperbola 144x^2 -625y^2 =90,000, where x and y are in meters. (a) How far apart are the buildings at their closest point? (b) Find the distance d in the figure. (a) The two buildings are 50 meters apart at their closest point. (Type an integer or a decimal.) (b) The distance d= meters. (Type an integer or decimal rounded to one decimal place as needed.)

The distribution of times that it takes college students to finish a specific exam is strongly skewed to the left. Suppose the professor took many samples of size 55 and calculated the mean time students took to finish the exam. Describe the shape of the sampling distribution of mean times for the exam. Skewed left because of the central limit theorem Approximately normal because of the binomial theorem Approximately normal because of the central limit theorem Skewed left because population is also skewed left

Is the set of negative integers a commutative group under the operation of addition? Is the set of negative integers a commutative group under the operation of addition? If not, why not? Select all that apply. A. Yes, it is a commutative group. B. No, it is not a commutative group. There exist negative integers a, b, and c such that (a + b) + c≠ a + (b + c). C. No, it is not a commutative group. There is no identity element in the set of negative integers under the operation of addition. D. No, it is not a commutative group. There exist negative integers a and b such that a+b≠b+a. E. No, it is not a commutative group. There is at least one negative integer that does not have an inverse in the set of negative integers under the operation of addition F. No, it is not a commutative group. The set of negative integers is not closed under the operation of addition.

Sam's Pizza advertises that their delivery times are the best in town. If their delivery times are normally distributed with mean 30 minutes and standard deviation 5 minutes, what is the probability that your pizza from Sam's will take more than 37 minutes to be delivered? Justify your answer.

Mandy wants to invest $1000 in an account that earns 7.2% interest, compounded quarterly. How many years will it take for he account to have a value of $5000? Round to the nearest whole number

To measure the physical properties of cells, a piezoelectric probe is used. The force applied by the probe is compared against how much the cell deforms. If F is the force applied by the probe, and w is the distance it moves into the cell, then the stiffness of the cell can be calculated from the rate of change, dF/dw. Zhang et al. found that if F is measured in μN and w in μm then for a zebrafish embryo: F = 3 x 10⁻⁴ w³- 4.4 x 10⁻³w² + 3.93w+0.221 Calculate dF/dw for a sample when w= 100μm.

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it take the bar to reach 70° C if it is known that its temperature increases 2º during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.) How long will it take the bar to reach 96° C? (Round your answer to one decimal place.)

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. 1) r=9.7 inches, θ = 315º, s = ? A) 53.3 in. B) 53.6 in. C) 53.4 in. D) 53.5 in.

A certain radioactive element has a half-life of 35 days. If you had a 100 grams of this element, the mass m of the element after t 35- day intervals is represented by m= 100(0.5)t. Find the approximate daily decay rate of this element. a. 98.0% b. 17.5% c. 2.0% d. 1.4%

Recent news articles have discussed the connection between a rare genetic mutation and breast cancer in women. One of the companies offering this BRCA genetic test is Quest, and this company claims a 98% accuracy rate. In the general population about 1 in 405 people would actually carry this BRCA1 genetic mutation. Hint: Construct a table as in your course materials. Use a population size of 40500 women. What is the likelihood that someone has the BRCA mutation, if they test positive? (Round your probability to the nearest tenth of a percent!)

Evaluate each integral using the definition of the definite integral with right endpoints (given in Theorem 4 of the book) and taking the limit. (a) ∫₀³ (x² +2x-5)dx (b) ∫₁⁵ x³ dx Δx=b-a/n= xi=a+iΔx=

A sensor light installed on the edge of a home can detect motion for a distance of 69ft in front and with a range of motion of 262° Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth. 21,770.92 ft2. 10,885.46 ft2. 21,771.02 ft2. 10,885.36 ft2.

You are interested in estimating the the mean lifespan of a cell phone. From past data, you estimate that the standard deviation to be approximately 1.3 years. What sample size would you need to in order to estimate the mean lifespan of a cell phone, with a 90% confidence level, to within 0.5 years? Sample Size: n ≥