Basic Math Questions and Answers

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.

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 $ .

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

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

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.

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

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.

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.

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.

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

Assume that Sunday is represented as day 0, Monday is represented by day 1, and so on. If today is Friday (day 5), determine the day of the week it will be at the end of 41 days. Assume no leap years. It will be a _________ , 41 days after Friday.

A commercial claims that 8 out of 10 dentists recommend a certain brand of toothpaste. To test this claim, a random sample of 85 dentists is obtained. Of these 85 dentists, 73 indicated that they recommend that brand of toothpaste. Using a significance level of 5%, test the claim to see if the proportion of dentists who recommend this toothpaste is not 8 of 10. a) State the null and alternative hypotheses b) State the p value c) Make a conclusion about the claim

Solve the system by using Gaussian elimination or Gauss-Jordan elimination. 2x+7y = –15 x+4y = -11 The solution set is {(____,_____)}.

Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.) f(x) = 5 sin πx g(x) = 5 sin πx - 4 Step 1 To sketch the graph of a function, first find its amplitude and period. Recall that the amplitude and period of curves of the form y = a sin bx and y = a cos bx are given by amplitude = |a| and period =2π/b Therefore, the amplitude of the curve f(x) = 5 sin πx is and the period is

Fill in the table using this function rule. y= 2x+4 x y -2 -1 0 1

Find the rate of change for the table of values. x 2 5 6 9 y 5 11 13 19 (A) -2 (B) 2 (C) 1/2

At the fair there is a game: If a player rolls a die and gets a 1, he wins $5. If the person rolls a die and gets a 2, he wins $1. The cost to play the game is $2. Find the expected earnings for the game, including the cost to play. Would you want to play the game? -$3. I would not want to play the game because it is expected that I lose three dollars. $1. I would want to play the game because it is expected that I earn a dollar. -$1. I would not want to play the game because it is expected that I lose a dollar. $3. I would want to play the game because it is expected that I earn three dollars.

Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. a) Something is not in the correct place. b) All tools are in the correct place and are in excellent condition. c) Everything is in the correct place and in excellent condition. d) Nothing is in the correct place and is in excellent condition. e) One of your tools is not in the correct place, but it is in excellent condition.

Suppose a Ferris Wheel reached a maximum height of 80 ft and a minimum height of 3 ft. What would the vertical shift of the sinusoidal function be to model the motion of the Ferris Wheel? 80 40.2 38.5 41.5

Two softball teams submit equipment lists to show their sponsors. BATS SOFTBALLS GLOVES TEAM 1 14 47 16 TEAM 2 13 36 15 If a bat costs $61, a ball costs $7, and a glove costs $55, use matrices to find the total cost of equipment for each team. Team 1: $632, Team 2: $870 Team 1: $1,036, Team 2: $2,780 Team 1: $2,063, Team 2: $1,870 not enough information

Find the indicated terms in the expansion of (2x2 - 4x + 3)(2x – 9) (5x2 + 2x + 4) The degree 1 term is The degree 4 term is

A one-to-one function is given. Write an equation for the inverse function. f(x) = (5 - x)/ 7 f^-1(x) =

Jocelyn is going to invest in an account paying an interest rate of 2.3% compounded continuously. How much would Jocelyn need to invest, to the nearest hundred dollars, for the value of the account to reach $550 in 15 years?

Solve the following system by graphing. 2x - y = 6 4x - 2y = 6 Use the graphing tool to graph the lines. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A) There in exactly one solution. The solution set is _____. (Simplify your answer. Type an ordered pair.) B) The solution set of the system is ((x , y)|2x -y = 6) or {(x , y)|4x - 2y = 6. C) The solution set is ∅.

Graph the linear inequality. y≥ 3x

Graph the linear equation. f(x) = - 3x + 5 Use the graphing tool to graph the linear equation.

A small radio transmitter broadcasts in a 38 mile radius. If you drive along a straight line from a city 49 miles north of the transmitter to a second city 52 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

A plane flies 405 miles with the wind and 315 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air. The speed of the plane in still air is ___ mph

Do each of the following: 1) Describe some of the similarities and differences among Euclidean, Spherical, and Hyperbolic geometries with respect to: a) triangles b) models for the geometries c) parallels

A growing deer population increases by 3 animals per year. If the current population is 47 animals, what will it be in 6 years? In 6 years the population will be _____ animals.

Find the first four terms of the arithmetic sequence. a₁ = -5, d= -9 What is the first term? a₁ = ▢

Graph the feasible region for the following system of inequalities. Tell whether the region is bounded or unbounded. x + y ≤ 4 x - y ≥ 5

A political party is planning a ninety-minute television show. The show will have at least 9 minutes of direct requests for money from viewers. Three of the party's politicians will be on the show-a senator, a congresswoman, and a governor. The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a pre-show survey, it is believed that 39, 44, and 49 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers. The quantity to be maximized, z, is the number of viewers in thousands. Let x₁ be the total number of minutes allotted to the senator, x₂ be the total number of minutes allotted to the congresswoman, and x3 be the total number of minutes allotted to the governor. What is the objective function? The senator should be allotted minutes. (Simplify your answer.) The congresswoman should be allotted minutes. (Simplify your answer.) The governor should be allotted minutes. (Simplify your answer.) The maximum number of viewers is (Simplify your answer.)

There were 636 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number who failed. Number of students who passed Number of students who failed

Tell the maximum number of zeros that the polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial function may have. Do not attempt to find the zeros. f(x) = -x8-9x6-x+6 What is the maximum number of zeros that this polynomial function can have? How many positive real zeros can the function have? (Use a comma to separate answers as needed.) How many negative real zeros can the function have? (Use a comma to separate answers as needed.)

(a) Find the magnitude of an earthquake that has an intensity that is 73.7 (that is the amplitude of the seismograph reading is 73.7 cm). [Round your answer to one decimal (b) An earthquake was measured to have a magnitude of 5,4 on the Richter scale. Find the intensity of the earthquake. (Round your answer to one decimat place)

You need a 25% alcohol solution. On hand, you have a 225 mL of a 20% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution? You will need ml of the 70% solution

You invest $1134 in a special savings account that earns 1.2 % interest, compounded continuously. The money will be invested for t years. Write the equation that represents the situation.

The half-life of radium-223 is approximately 11.43 days. Step 3 of 3: How much of an 8 gram sample of radium-223 would remain after 9 days? Round to three decimal places. Answer

A museum gift shop sells hats with embroidered logos of the museum. The hats are available in small, medium, and large sizes. They are available in the colors red and green. Make a tree diagram to represent all possible varieties of hats sold at the museum

Compute the simple interest. If the time is given in months, let one month be 1/12 of a year. Round the answer to the nearest cent. Principal, Rate, and Time Interest $1,500 at 8% for 2 years Interest: $120.00 Interest: $220.00 Interest: $140.00 Interest: $240.00