Math Questions

For the regions bounded by y = 6cosx and y= 1/3x²-7 Part A: Find the limits of integration. (10 points) Part B: Write an expression representing the total area. (10 points) Part C: Solve for the total area. (10 points)

Factor the trinomial completely. 4x² +20x+24 Select the correct choice below and fill in any answer boxes within your choice. A. 4x² +20x + 24 = (Factor completely.) B. The polynomial is prime.

Water is leaking from a tank at a rate of R(t) gallons per hour, where t is time in hours. What is the meaning of R(t)dt = 2,430 in terms of the context? (1 point), The tank is leaking at a rate of 2,430 gallons per hour from hours 2 to 4. The tank leaked 2,430 gallons of water over the first 4 hours. The tank leaked 2,430 gallons of water from t = 2 to t = 4. The tank has 2,430 gallons of water left in the tank after the first 4 hours.

Outpatient surgery as a percent of total surgery at hospitals has grown. The logarithmic function f(x) = -1312+ 306 In x, where x is the number of years since 1900, is the best-fitting logarithmic model. Use the function to estimate outpatient surgery as the percent of total surgeries in the year 1998. What does this function estimate for the percent of outpatient surgeries in 1998? % (Round to the nearest percent as needed.)

A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2006, can be approximated by V(t) = 1.7 e0 corresponds to 2006 and V is in billions of dollars. a) Estimate the value of the country's exports in 2006 and 2010. b) What is the doubling time for the value of the country's exports? a) The value of the country's exports in 2006 is $ 1.7 billion. (Simplify your answer. Round to the nearest tenth as needed. Do not include the $ symbol in your answer.) The value of the country's exports in 2010 is $ billion. (Simplify your answer. Round to the nearest tenth as needed. Do not include the $ symbol in your answer.)

The amount of medication, in milligrams, in a patient's bloodstream after t hours, can be represented by the following function: M(t)=75/1+ e^x+0.5 What is the rate of change for the amount of medication in the patient's bloodstream after 2 hours? 5.6894 mg/hr -0.4316 mg/hr -5.2578 mg/hr -5.6894 mg/hr

Determine the magnitude of TU given T(-2, 3) and U(0, 4). 5i 5 √5 -5

In a recent year (365 days), a hospital had 5753 births. a. Find the mean number of births per day. b. Find the probability that in a single day, there are 15 births c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births? a. The mean number of births per day is____ (Round to one decimal place as needed.)

Which lists the possible types of roots for f(x) = 3x^4 + 7x³ + 2x² + x + 9? One rational root and three irrational roots Two irrational roots, one complex root, one real root Three complex roots and one rational root Two rational roots and two irrational roots

Which of the following statements is true? A. The amplitude of f(t)= -2 sin(2t) + 2 is 1. B. The period of g(t) =-1/2 cos(2t) is π C. The period of h(t) = 3 tan(2t) is π/4 D. The amplitude of k(t) = -3 tan t is -3.

Find the derivative of the function. h(x) = log3 x√x - 7/6 h'(x)=

For the planer curve represented by the parametric equations x = 3t and y = t^2 + 5, what is the rectangular equation of the curve? 9x² - y + 5 = 0 3y²-x+15=0 x² + y²-25= 0 x² - 9y + 45 = 0

Kelly bought 4 shirts and 3 skirts for her doll and paid $11.40 total. After she did a doll fashion show for her best friend, Caitlyn wanted to know how much one of the skirts cost. Kelly remembered that each skirt cost $0.30 more than each shirt. How much did one skirt cost? A. $1.50 B. $1.60 C. $1.65 D. $1.75 E. $1.80

The square of a number is equal to 10 less than 7 times that number. What are the two possible solutions? Which of the following equations is used in the process of solving this problem? x² - 7x + 10 = 0 x² - 7x+70 = 0 x² + 7 x-10 = 0

If set A contains seven distinct numbers and set B contains three distinct letters, how many elements are in (A u B)?

Solve for the variable in each of the following equations. Write your answers as whole numbers, proper fractions, Improper fractions, or mixed numbers in simplest form. x + 9 = 14 x= 17z = 7 z= c+ 17 = 20 c= 16d = 6 d= b-9 = 14 b= 19r = 9 r= n - 14 = 16 n= 8y = 10 y=

In a large city, a transportation engineer wants to estimate the proportion of residents who use the bus system regularly. Out of a random sample of 2000 residents, 1220 use the bus regularly. Construct and interpret the 99% confidence interval. (P-hat) = 1220 / 2000 = .61 (Q-hat) 1-.61 = .39 Standard Error = .010906 with a Z score of 2.5758 for the 99% confidence interval. .61 +2.5758 (.010906) = .6380 .612.5758 (.010906) = .5819 (.5819, .6380) So with a confidence interval of 99%, the true proportion of residents who use the bus system regularly is between 58.19% and 63.8%

Find the probability of winning the Jackpot in a lottary if you buy just one ticket. In this lottary, a typical ticket is Formed by selecting 5 different numbers from the range {1,2,...,38}

Triangle ABC is transformed to create AMNand APQR as described. Triangle MNrepresents the translation 2 units left and 2 units down of AABC. Triangle PQR represents the dilation of AABC by a scale factor of 2. Which of these is correct? The transformation of triangle ABC to triangle MNO preserves the angle measures but not the side lengths of the triangle. The transformation of triangle ABC to triangle MNO preserves both the side lengths and angle measures of the triangle. The transformation of triangle ABC to triangle PQR preserves both the side lengths and angle measures of the triangle. The transformation of triangle ABC to triangle PQR preserves the side lengths but not the angle measures of the triangle.

You had the following readings on your water meter: December 1: 7,500 cubic feet January 1: 7,585 cubic feet February 1: 7,671 cubic feet March 1: 7,749 cubic feet What is the number of cubic feet consumed in January?

Cash equivalents by definition a. are a comparison of cash and liabilities. b. are expected to be converted to cash within three months. c. will be converted to cash within one year. d. are long-term investments.

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 6000 batteries, and 2% of them do not meet specifications What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)

The two functions y = (3x + 4)² and 9/√3x + 4 share either an inside function or an outside function. (a) What is this shared function? u = help (formulas) Is u an inside function or an outside function? (b) Writing u for this shared function, express y = (3x + 4)² in terms of u. y = help (formulas) (c) Writing u for this shared function, express 9/√3x + 4 in terms of u. y = help (formulas)

Which expression is equivalent to tan(x) + cot(x)? cos x/sec x cos(x) sin(x) 1/sin(x) cos(x) 2 tan(x)

The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. a. In a letter to an advice column, a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest? b. If the length of pregnancy is in the lowest 3%, then the baby is premature. Find the length that separates premature babies from those who are not considered premature. a. The probability that a pregnancy will last 308 days or longer is (Round to four decimal places as needed.)

Select the correct answer. What is the variable being tested in an experiment? A. control variable B. response variable C. placebo D. explanatory variable

For the piecewise function below, it is known that the function is always continuous, f(x) = 3x - 1, x < -2 f(x) = px² + qx, -2 ≤ x < 4 f(x)=√x, x ≥ 4 A. Find the values of p and q B. Explain if there is a value such that f(x) = 5 in the interval of -2 ≤ x < 4.

If a candy jar has 21 green jelly beans and 12 black jelly beans, and 19 red jelly beans, what is the probability of eating a green and then a red jelly bean? Express the probability to the nearest hundredth.

Give the coordinates of the point obtained from each reflection. (a) Reflect the point (0, 4) across the y-axis: (b) Reflect the point (0, 4) across the X-axis:

Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -1.775°C. P(Z < -1.775) =

Select ALL that apply. Which of the following functions are 6th degree polynomial functions? f(x) = 2x³ − 3x² + 6x +8 f(x) = -3(x-3)(x - 1)²(x - 5)³ ƒ (x) = −6x^5 + 8x^4 − 2x² + 7x + 5 f(x) = 5(x - 9)³ (x + 1)²(x − 2) f(x) = -x² + 2x³ + x² - 4x +9 f(x) = 2x^6 - 3x³ + 4x³ - 7x - 1 f(x) = 2(x − 3)(x + 5)(x - 1) f(x) = -8(x+4)^4 (x - 2)²

The term cash does not include a. money on deposit that is available for unrestricted withdrawal. b. notes receivable. c. money orders. d. checks.

Find the average rate of change of f(x)=2x² +2 over each of the following intervals. (a) From 4 to 6 (b) From 2 to 4 (c) From 2 to 1 (a) The average rate of change from 4 to 6 is

The thermal plot of a gaming system during play time is defined by 10ln(15t³) - 2T+100=T + 10t for 0<t≤ 5, where t represents time in hours and T represents temperature in °C. For which condition does the system reach a possible maximum or minimum temperature? (1 point) 30-10t=0 450t² - 10 = 0 6-90t³ = 0 15t²-10=0

The heat loss of a glass window varies jointly as the window's area and the difference between the outside and inside temperatures. A window 2 feet by 5 feet loses 3000 Btu per hour when the temperature outside is 30° colder than the temperature inside. Find the heat loss through a glass window that is 8 feet by 15 feet when the temperature outside is 15° colder than the temperature inside. The heat loss is ____Btu per hour. (Type an integer or a decimal.)

Strontium-90 is a radioactive material that decays according to the function A(t) = A e ^-0.0244t, where Ao is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium-90 is left after 10 years? (c) When will only 100 grams of strontium-90 be left? (d) What is the half-life of strontium-90? (a) The decay rate of strontium-90 is (Type an integer or a decimal. Include the negative sign for the decay rate.) (b) Approximately ___grams of strontium-90 left after 10 years. (Do not round until the final answer. Then round to the nearest whole number as needed.) (c) Only 100 grams of strontium-90 will be left in about ____years. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x)=7x-4 and g(x)= x+7/4 a. f(g(x)) = (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Find the horizontal asymptote, if any, of the graph of the rational function. g(x) =5x2-9x-8/3x² - 4x + 2 y = 0 y = 5/3 y=9/4 no horizontal asymptote

Solve the equation on the interval [0, 2TT). cos x - 2 cos x sin x = 0 π/6,5π/6 π/6,π/2,5π/6,3π/2 π/6,5π/6,2π 0,π/6,5π/6,3π/2

Using a table of values, what is an approximate solution of the given equation to the nearest quarter of a unit? |x + 3 |= 3x + 1 A.x≈1.25 B.x≈-3.75 C.x ≈ -1.75 D.x≈1.50

Given the toolkit function, f(x) = |x|, write a new equation, g(x), that would represent a transformation to the RIGHT 3 units. g(x) = |x + 3| g(x) = |x - 3| g(x) = |x| +3 g(x) = |x - 3

Which methods can be used to expand (x+3)³? multiply 2 by (2+3), then multiply the product by 3 apply patterns from the third row of Pascal's Triangle find the third power of both 2 and 3, and then add the terms in vertical form, multiply (2+3) three times, then add like terms use horizontal format to find (x+3)², then multiply the product by (x+3)

Based on historical data, your manager believes that 31% of the company's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.27

The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 157.18 lb on earth weighs 26.72 lb on the moon. How much would a 228.24-lb person weigh on the moon?

Let a curve be defined as siny = x + y. Determine which of the following statement(s) is/are true. (1 point) I. The curve has a vertical tangent when cosy - 1 = 0. II. The curve has no horizontal tangents because cosy - 1 * 0. III. The curve has no horizontal tangents because dy/dx≠0. I only III only I and III I and II

A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long, how tall is the mast? Round to the nearest tenth of a foot.

A pharmaceutical corporation has two plants that produce the same over-the-counter medicine. If x₁ and x₂ are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by R = 160x₁ + 160x₂ - 2x₁² - 4x₁x₂ - 2x₂². When x₁ = 11 and x₂ = 7, find the marginal revenue for plant 1, ƏR/0x₁, and the marginal revenue for plant 2, 3R/3x2. (a) Find the marginal revenue for plant 1, 3R/3x₁. (b) Find the marginal revenue for plant 2, ƏR/0x₂.

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 15 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $10.00 on sugar. Multiple Choice .7320 .9474 .0528 .2680

In a random sample of 12 dental assistants, the mean annual earnings was $31,721. The population is normally distributed with a standard deviation of $5260. Construct a 95% confidence interval for the population mean annual earnings for dental assistants. Select the correct answer below: With 95% confidence, you can say that the population mean annual earnings is between $29,942 and $32,991. With 95% confidence, you can say that the population mean annual earnings is between $28,745 and $34,697. With 95% confidence, you can say that the population mean annual earnings is between $29,734 and $35,007. With 95% confidence, you can say that the population mean annual earnings is between $28,877 and $34,598.