Basic Math Questions and Answers

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.

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

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=

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}

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.

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

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.)

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

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)

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.

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

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 9000 Fun Noodles per day during the summer. Raising the price to $4 will cause the sales to fall to 5000 Fun Noodles per day. a. Assume that the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold). The equation is y=-4000x+21000. (Type your answer in slope-intercept form.) b. Predict the daily sales of Fun Noodles if the price is $3.50. sales

Company XYZ has 34 employees in the Finance Department, 45 technicians, and 32 in the Engineering Department. The HR Department received 20 complaints from the whole company. There were 5 complaints from the technicians and 3 from the Finance Department. There were 7 complaints from the Engineering Department. What percent of complaints came from either the technicians or the Finance Department?

A manufacturer of personal computers tests competing brands and finds that the amount of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25 percent and the highest 30 percent are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining computers? Multiple Choice [269.76, 300.24] [278.86, 289.78] [280.22, 289.78] [280.22, 300.24]

Use the change of base formula to evaluate log12(1/5) to two decimal places and type your answer in the space below. If your answer is between -1 and 1, be sure to begin your answer with a0. For example if the calculator reads -0.31415 you would type -0.31. log12(1/5)=___

Assume that a rectangle with sides x and y is expanding with time. Let y=2x and x(t)=3t+1. What is the formula for the rate of change of the area with respect to time? dA/dt=12(3t-1) dA/dt=(3t+1) dA/dt=4(3t - 1) dA/dt=12(3t+1)

An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T for the given interest rate. P = $60,000, r=4.8%, t = 5 yr a) The future value of the investment when interest is compounded annually is $ (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $ (Type an integer or a decimal. Round to the nearest cent as needed.) c) The future value of the investment when interest is compounded daily is $ (Type an integer or a decimal. Round to the nearest cent as needed.) d) The future value of the investment when interest is compounded continuously is $. (Type an integer or a decimal. Round to the nearest cent as needed.) e) Find the doubling time for the given interest rate. T = yr (Type an integer or decimal rounded to two decimal places as needed.)

The total number of public electric charging units available for hybrid vehicles has increased exponentially since 2006. The number of outlets A(t) at these alternative fueling stations t years after 2006 can be approximated by A(t) = 224(2.69), where t= 0 corresponds to 2006. How many outlets were available in 2008, in 2010, in 2011? The number of outlets available in the year 2008 was approximately (Simplify your answer. Round to the nearest integer as needed.)

Assume that 75% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties (≥1) among the 5 people. 0.9990 b. There are exactly 3 lefties in the group. 0.2637 c. There are at least 4 lefties in the group. 0.6328 d. There are no more than 2 lefties in the group. 0.1035 e. How many lefties do you expect? 3.75 f. With what standard deviation?

Ordered: Oxacillin sodium 900 mg in 125 mL D5W IV PB to be infused over 45 min, Drop factor: 20 gtt/mL, Flow rate: gtt / min 5.6 gtt / min 0.56 gtt / min 560 gtt / min 56 gtt / min

Allison buys a spool of thread for sewing. There are 8 yards of thread on the spool. She uses 2 meters. How much thread is left on the spool in meters? Round your answer to the nearest thousandth, if necessary.

Calculate the scaling factor that will adjust the recipe to produce the desired yield. (Round to 2 decimal places). Recipe Yield 12 6-oz crabs Desired Yield 50 2-oz crab cake).Scaling factor is Maximum number of characters (including HTML tags added by text editor): 32,000

The function A(x)= x(x + 10) describes the area A of the opening of a rectangular window in which the length is 10 feet more than the width, x. Find the dimensions of the window if the area of the opening is to be 119 square feet by solving A(x) = 119 The width of the window is feet and the length of the window is feet (Simplify your answers.)

Given the final answer in f(x+h)-f(x)/ h (a) 2x + h²-2 (b) 1 (c) 2x +h+2 (d) h

Solve the equation. 5(x+5)=8x+8-3x+17 Select the correct choice below and, if necessary, fill in the answer box that completes your choice. OA. The solution set is { }. (Type an integer or a simplified fraction.) OB. All real numbers are solutions. OC. The equation has no solution.

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models N(t)=0.194³-7.88+2+12.9t+375 and M(t) = 0.031³-0.25t² +6.7t+173 where t represents the year, with t = 0 corresponding to 2000. Find and interpret (N-M)(t). (N-M)(t) = 0.163+³+7.632-6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³-7.632-6.2t-202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³ +7.632 +6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M) (t) = 0.163³-7.63²-6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³-7.632 +6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel.

Solve the following equation using a graphical method. 12x-16-41-7x x= Type an integer or a simplified fraction.)

A rectangle has a width of x centimeters and a length that is 10 centimeters longer than its width. If the total perimeter is 220 centimeters, what is the measure of the width? 40 centimeters 200 centimeters 50 centimeters 4 centimeters

A town has a population of 14000 and grows at 3.5% every year. What will be the population after 14 years, to the nearest whole number?

The amount of money (in trillions of dollars) that is invested in passively managed mutual funds can be approximated by the function A(x) = 0.35(1.14)*, where x = 1 corresponds to the year 2001. (a) What was the amount of money in passively managed mutual funds in 2012 and 2016? (b) If the trend continues, what is the first full year when the amount of passively managed mutual funds exceeds $7.1 trillion? (a) Which of the following describes how to find amount of money in passively managed mutual funds in 2012 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the amount of money in passively managed mutual funds in 2012, substitute for x and evaluate to find f(x). B. To find the amount of money in passively managed mutual funds in 2012, find the intersection point of the graphs y = 0.35(1.14) and y = of money in passively managed mutual funds in 2012 is represented by the y-coordinate In 2012, the amount of money in passively managed mutual funds was about $ (Type an integer or decimal rounded to the nearest hundredth as needed.) trillion. Which of the following describes how to find the amount of money in passively managed mutual funds in 2016 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the amount of money in passively managed mutual funds in 2016, find the intersection point of the graphs y = 0.35(1.14)* and y= of money in passively managed mutual funds in 2016 is represented by the y-coordinate. B. To find the amount of money in passively managed mutual funds in 2016, substitute for x and evaluate to find f(x).

Suppose an investor deposits $26,000 into a savings account for 6 years at 6.25% interest. Find the total amount of money in the account if the interest is: 1. Compounded annually, then the investment is worth __ after 6 years. 2. Compounded quarterly, then the investment is worth __ after 6 years. 3. Compounded monthly, then the investment is worth __ after 6 years. 4. Compounded weekly, then the investment is worth __ after 6 years. 5. Compounded daily, then the investment is worth __ after 6 years. • Round your answers to the nearest cent. • Use a dollar sign to indicate that your answer is a monetary value.

Match the items. a. 8√2 b. 71 c. -15 d. 2i√12 1. √-49 2.√-48 3. √128 4. √-25 x √-9