Basic Math Questions and Answers

Consider the following fractions. 31/60 , 29/36 Step 2 of 2: How much larger is the larger fraction? Express your answer in simplest form.

The count in a bateria culture was 700 after 20 minutes and 1600 after 35 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 115 minutes. When will the population reach 14000.

Solve the given system of equations. 5x + 4y - 5z = -21 2x - 5y + 2z = 26 4x - 2y + 4z = 20 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

Use a calculator with a yX key or a A key to solve the following. The exponential function f(x)=544(1.026)X models the population of a country, f(x), in millions, x years after 1975. Complete parts (a) – (e). a. Substitute 0 for x and, without using a calculator, find the country's population in 1975. The country's population in 1975 was 544 million. b. Substitute 27 for x and use your calculator to find the country's population, to the nearest million, in the year 2002 as modeled by this function. The country's population in 2002 was 1088 million. c. Find the country's population, to the nearest million, in the year 2029 as predicted by this function. The country's population in 2029 will be 2175 million. d. Find the country's population, to the nearest million, in the year 2056 as predicted by this function. The country's population in 2056 will be million.

Find the value of the expression below and write your answer in mixed number form. Reduce if possible. 2/5 of 3 3/4

A car was valued at $43,000 in the year 1991. The value depreciated to $15,000 by the year 2002. A) What was the annual rate of change between 1991 and 2002? 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 2007 ? value = $ Round to the nearest 50 dollars.

The points (3, 10) and (1, 9) fall on a particular line. What is its equation in point-slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

The area of a square depends on the length of its sides. This can be written in function notation as a(s). What is the best interpretation of a(2) = 4? A. The area of a square is always two times the side length. B. A square with sides 2 units long has an area of 4 square units. C. A square with sides 4 units long has an area of 2 square units. D. The area of a square is always one-half of the side length.

The formula A=21.2e0.0411t models the population of a US state, A, in millions, t years after 2000. a. What was the population of the state in 2000? b. When will the population of the state reach 29.8 million? a. In 2000, the population of the state was million. b. The population of the state will reach 29.8 million in the year (Round down to the nearest year.)

A car was valued at $35,000 in the year 1991. The value depreciated to $13,000 by the year 2006. A) What was the annual rate of change between 1991 and 2006? 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 2011? value = $ Round to the nearest 50 dollars.

Company XYZ closed at $47.87 per share with a P/E ratio of 14.14. Answer the following questions. a. How much were earnings per share? b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14? a. How much were earnings per share?

The diameter of a bicycle wheel is 29 in. How many revolutions does the wheel make when the bicycle travels 200 ft? Round your answer to the nearest whole number. Use 3.14 for л. revolutions

The mass of a gas is determined as in the experiment described in Experiment 8. The mass is de- termined to be 2.01 g. The volume of the water, which is equal to the volume of the gas, is meas- ured to be 243 mL, the boiling water temperature was 99.8°C and the barometric pressure was 755 mm Hg. Calculate the molar mass of the gas.

At age 19, someone sets up an IRA (individual retirement account) with an APR of 6%. At the end of each month he deposits $100 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period. After retirement the IRA will contain $

The sum of three numbers is 16. The sum of twice the first number, 3 times the second number, and 4 times the third number is 55. The difference between 5 times the first number and the second number is -2. Find the three numbers. first number: second number: third number:

A line with a slope of 4 passes through the point (-5, -3). What is its equation in point-slope form? Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x)=x³-4x² + 5x-20, where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even? A. year 1 B. year 2 C. year 3 D. year 4

You want to purchase a new car in 4 years and expect the car to cost $84,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How much should you deposit each month to end up with $84,000 in 4 years?

The 1985 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere. The function f(x)=1000(0.5) describes the amount, f(x), in kilograms, of a radioactive element remaining in the area x years after 1985. If even 100 kilograms of the radioactive element remains in the atmosphere, the area is considered unsafe for human habitation. Find f(40) a determine if the area will be safe for human habitation by 2025.

The diameter of a bicycle wheel is 27 in. How many revolutions does the wheel make when the bicycle travels 100 ft? Round your answer to the nearest whole number. Use 3.14 for π.

The formula S=C(1+r)' models inflation, where C=the value today, r= the annual inflation rate (in decimal form), and S = the inflated value t years from now. If the inflation rate is 6%, how much will a house now worth $142,000 be worth in 8 years? Round your answer to the nearest dollar. The house will be worth $. (Round to the nearest dollar as needed.)

Aldo has two coupons for pants. Coupon A: $55 rebate on $87 pants Coupon B: 60% off of $87 pants Choose the coupon that gives the lower price. Then fill in the blank with the correct value. Coupon A gives the lower price. The price with coupon A is S $ less than the price with coupon B. Coupon B gives the lower price. The price with coupon B is less than the price with coupon A.

Consider a right triangle that contains a 90° angle. If the hypotenuse of this triangle is 34 meters and the shorter leg is 16 meters, find the longer leg of this right triangle. longer leg = meters

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 7%. How much should you deposit monthly to accumulate $82,000 in 17 years?

The exponential function f(x)=544(1.026)* models the population of a country, f(x), in millions, x years after 1975. Complete parts (a)-(e). a. Substitute 0 for x and, without using a calculator, find the country's population in 1975. The country's population in 1975 was million. b. Substitute 27 for x and use your calculator to find the country's population, to the nearest million, in the year 2002 as modeled by this function. The country's population in 2002 was million. c. Find the country's population, to the nearest million, in the year 2029 as predicted by this function. The country's population in 2029 will be million.

Calculate the annual interest that you will receive on the described bond. A $500 Treasury bond with a current yield of 2.9% that is quoted at 105 points

A police officer counted 22 revolutions of a wheel to measure the length of a skid mark. The diameter of the wheel was 15 in. About how long was the skid mark in feet? Round your answer to the nearest whole number. Use 3.14 for π.

Select the correct answer from each drop-down menu. A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK is a different code from BAIK.) The size of the sample space is The probability that the first three letters of the four-letter code are vowels is

Find the inverse f(x)=-3x by thinking about the operations of the function and then reversing, or undoing, them. Choose the correct answer below. A. f-¹(x) = x 3 B. f-¹(x) = - 1 3 C. f-¹(x) = - x 3 D. f-¹(x) = - y 3

An amount of $20,000 is borrowed for 12 years at 4.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.

A building casts a shadow 30 m long. At the same time, the shadow cast by a 41-cm tall pole is 72 cm long. Find the height of the building. A. 17.1 m B. 52.7 m C. 15.6 m D. 51.2 m

A survey of 12,052 men in a particular country found that 46.9% received an influenza vaccine for a recent flu season. Identify the population and the sample. Identify the population for the given problem. Choose the correct answer below. A. The 12,052 men selected B. The collection of immunization statuses of all men in the country C. All men in the country D. The collection of immunization statuses of the 12,052 men selected

Which geometric figure has 72 rotational symmetry? A. equilateral triangle B. regular pentagon C. rhombus D. regular hexagon

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE = 11x - 3 and CE = 12-4x. Find the length of AC. A. 8 B. 1 C. 16 D. 18

Solve the system by the addition method. 2x - 4y = 14 3x + 5y = -1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

The area of a rectangular wall in a classroom is 171 square feet. Its length is 8 feet shorter than three times its width. Find the length and width of the wall of the classroom.

Two pulleys of diameter 6 meters and 3 meters are connected by a belt. The larger pulley rotates 47 times per minute. Find the angular speed of the smaller pulley. 282π radians per min 941π radians per min 188π radians per min 141π radians per min

If a rectangle is not a square, what is the greatest number of lines of symmetry that can be drawn? A.0 B. 1 C. 2 D. 3 or more

Solve the given system of equations. 3x + 4y - 3z = -5 2x - 5y + 2z = -8 4x - 4y + 4z = -28 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is (()). (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

Solve the system. If there is no solution or if there are infinitely many solutions and the system's equations are dependent, so state. 5x - 10y + 3z = 21 x + 5y - z = 0 10x - y - z = 12 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is {(..)}. (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

A house was valued at $120,000 in the year 1985. The value appreciated to $165,000 by the year 2000. Use the compund interest formula S = P(1 + r)t to answer the following questions. A) What was the annual growth rate between 1985 and 2000? r = Round the growth rate to 4 decimal places. B) What is the correct answer to part A written in percentage form? r = %. C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2003? value = $ Round to the nearest thousand dollars.

Lucy earns $75,000 and is filing her taxes as a single woman. What amount of taxes does she owe? Type in the number and do not include: commas, decimals, dollar sign.

Lucas earns $55,000 and is filing his taxes as a single man. What amount of taxes does he owe? Type in the number and do not include: commas, decimals, dollar sign.

A person starts walking from home and walks: 2 miles East 5 miles Southeast 6 miles South 3 miles Southwest 4 miles East This person has walked a total of miles Find the total displacement vector for this walk: If this person walked straight home, they'd have to walk miles

Which of the following statements is false? A. Given quadrilateral ABCD, AB and CD are adjacent B. The height of a trapezoid is the distance between its bases. C. A rhombus is a parallelogram. D. A rectangle is a parallelogram.

Select the correct answer from each drop-down menu. Use the remainder theorem to verify this statement. (x+5) is a factor of the function f(x) = x3 + 3x2 - 25x - 75 1. Find the of f(x) and x + 5. 2. The of this operation is 0. 3. Therefore, (x+5) is of function f. 4. So f() = 0.

Graph the solution set of the system of inequalities. x-y≤3 x≥3

One number is 4 less than a second number. Twice the second number is 32 more than 5 times the first. Find the two numbers. A. -7 and - 3 B. -9 and −5 C. 4 and 8 D. -8 and -4

At the beginning of an experiment, a scientist has 316 grams of radioactive goo. After 270 minutes, her sample has decayed to 4.9375 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 38 minutes? You may enter the exact value or round to 2 decimal places.

Solve the system by the addition method. x + 4y = - 17 4x + 3y = - 16 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.