Basic Math Questions and Answers

The solution of differential equation y1y3 = 3y2² is (where a, b, c are arbitrary constants & yn denotes nth derivative of y w rt'x O x = ay² + by + c O y = ax² + bx + c O y = ae^x + be-^x +c O x = ae^y + be^-y+c

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = -1/x, a=1 approximate -1/1.05 a. p₁ (x) =

Consider the set of real numbers: {x| -1 < x ≤0}. Graph the set of numbers on the real number line.

During the 2005 football season, Team Tackle beat Team Sack by 15 points. If their combined scores totaled 39, find the individual team scores. Team Tackle's score was points.

12.Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular. a.Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles. b.Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. c.Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles. d.Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular. A B C D

Each baseball team has nine players and each football team has eleven players. Five schools have both baseball and football teams. Three schools have only a baseball team. How many players are there for all eight schools?

Yesterday, Martina went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 12 miles per hour. In the two days, she biked for a combined total time of 10 hours. Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.

The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even R(x)=200x-x², C(x)=25x+6250, 0≤x≤ 100 The manufacturer must produce units to break even.

The scale on a set of architectural drawings for a house is 1 3/4 inches - 2 feet. If the master bedroom is 14 feet long, what is its length on the drawing? A) 12.25 in grass hula skirts B) 12.75 in life jackets C) 10.5 in Darth Vader masks D) 11.75 in gorilla suits E) 13.5 in clown shoes

Translate "two less than four times a number is ten" into an equation and solve. 4x + 2 = 10; 6 4x - 2 = 10; -3 4x - 2 = 10; 6 None of these

An elevator is constructed using an electric motor at the top which is used to lift the elevator's car via a cable. The cable weighs 6 pounds per foot. The cable is 100 feet long when the elevator car is at the first floor, and it is effectively 0 feet long when the car is at the top floor. The elevator's car weighs 500 pounds How much work W does the motor do just lifting the cable and car when it takes the car from the first floor to the top floor? W =

You are throwing a party in 4 hours. If it takes 40 minutes to bake 12 cupcakes, how many cupcakes will you be able to finish baking before your party begins? 60 min = 1 hour Please report your answer to 1 decimal place. Note: Please only input a numerical answer, no units.

The perimeter of a square, p, varies directly as the length of a side, s. The perimeter of a square is 30 when the length of a side is 7.5. Which equation represents the relationship? Select the correct answer below: p = 22.5s p = -22.5s p = 7.5s p = 30s p = 4s p = 0.25s

A group of 60 students and 4 sponsors took a field trip to a local museum. For their first guided tour, students were given a choice of 1 of 3 art exhibits. Of the 60 students, 1/2 chose Modern, 1/4 chose American Folk, and 1/6 chose Western. Each student that expressed a choice chose exactly 1 exhibit. The remaining students expressed no choice. How many of the students expressed no choice? A. 5 B. 6 C. 10 D. 15 E. 30

The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.5x² + 15x + 14, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? Ticket sales will peak days after the concert was first announced.

Substitute the given values into the formula, and solve for the unknown variable. A=1/2h(B+b); A=42, B = 4, b=3

y=x² + 3 y = 15x-33 The system of equations shown above is graphed in the xy-plane. If system has two solutions, what is the product of the x-coordinates of the two solutions? A) 36 B) 4 C) -4 D) -36

The half-life of radium-222 is approximately 38 seconds. Step 1 of 3: Determine a so that A(t)=A0a^t describes the amount of radium-222 left after t seconds, where Ao is the amount at time t = 0. Round to six decimal places. Answer How to enter your answer (opens in new window)

Give the equation of the horizontal and vertical lines passing through the point (-1/3,-10). The equation of the horizontal line is: The equation of the vertical line is:

College students take different course loads. Many colleges determine the number of Full-time equivalent' students, F, by using the formula F=15, where n is the total number of credits in which students enroll for a given semester. If students on a campus register for a total of 69150 credits, how many full-time equivalent students does the campus have? The campus has 4610 full-time equivalent students. Solve the formula for n. n=

Write an equation and solve it to find the answer to the question below. Remember to define your variable.Susan is buying three different colors of tiles for her kitchen floor. She is buying 25 more red tiles than beige tiles, and three times as many navy-blue tiles as beige tiles. If Susan buys 435 tiles altogether, how many tiles of each color does she buy?

Selected Technologies According to recent surveys, 60% of households have personal computers. If a random sample of 152 households is selected, what is the probability that more than 48 but fewer than 82 have a personal computer? Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places. P (48 < X<82)=

Is the line through points P(0, -9) and Q(2, -8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain. a. Yes; their slopes are equal. c. No; their slopes are not opposite reciprocals. b. Yes; their slopes have product-1 d. No; their slopes are not equal.

An preimage mapped to its prime image maps to (x, y) → (3x, 3y). The prime image is mapped to the double prime image to (x, y) → (x+1, y-4). Describe the composition of transformations. The image was reduced by a scale of 3, then moved one unit up and 4 units over. The image was enlarged by a scale of 3, then moved one unit right and 4 units down. The image was enlarged by a scale of 3, then moved one unit left and 4 units down. The image was reduced by a scale of 3, then moved one unit down and 4 units right.

A jet plane has 180,000 pounds of fuel after the first hour of flight. The four engines consume a total of 15,000 pounds per hour at its cruising altitude. How many pounds of fuel remain after the 8th hour? 60,000 pounds 75,000 pounds 120,000 pounds 285,000 pounds

What is the solution to the equation? 1/2 In (x+17) = ln (x² - 9) - ln (x+3) x=8 only x-1 and x = 8 x=1 only x= -8 and x = 1

A club swimming pool is 18 ft wide and 34 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 620 ft². How wide can the strip be?

A loan of $14,000 is made at 8.5% interest, compounded annually. After how many years will the amount due reach $41,000 or more? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. years

Suppose that the dollar value v (1) of a certain house that is f years old is given by the following exponential function. v (t)=559,900(0.91)t Find the initial value of the house. $ Does the function represent growth or decay? growth decay By what percent does the value of the house change each year? %

Omar paid $13.29 for a 7.03-kg bag of dog food. A few weeks later, he paid $13.58 for a 7.26-kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 7.03-kg bag: Unit price for the 7.26-kg bag: The better buy: The 7.03-kg bag The 7.26-kg bag Neither (They have the same unit price)

1. Find only the area of the shape below. Round your answer according to the guidelines. Include units in your answer.

Which of the following statements is (are) true for all positive integers? 1) n3+2n is divisible by 3. 2) 5^2n- 1 is divisible by 24. Both statements are true. None of the statements are true. Only the first statement is true. Only the second statement is true.

Given the graph of the Logarithmic Function g(x) = log4 x: The graph of the function f(x) = log4 (x-6) can be obtained from the graph of g(x) = log4 x by shifting the graph of g(x) 6 units; Identify the Domain and Range of f(x) using Interval Notation. Domain of the function f(x) is Range of the function f(x) is

AB is a chord of the parabola y² = 4ax. If its equation is y = mx + c and it subtends a right angle at the vertex of the parabola, then (a) c = 4 am (c) c = 4 am (b) a = 4 mc (d) a + 4 mc=0

Suppose a product's revenue function is given by R(q)=8q2 + 900q, where R(q) is in dollars and q is units sold. Find a numeric value for the marginal revenue at 26 units, and record your result in the box below. Answer: MR(26)$ per unit

The polynomial function defined by f(x) = π/3x³-5πx² + 500πd/3 can be used to find the depth that a ball 10 cm in diameter sinks in water. The constant d is the density of the ball, where the density of water is 1. The smallest positive zero of f(x) equals the depth that the ball sinks. Approximate this depth for each material and interpret the results. a) A wooden ball with d=0.6. b) A solid aluminum ball with d=2.7. c) A spherical water balloon with d=1. a) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is 5.67 (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined. b) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined. c) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is cm. (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined.

The posters must be rectangular in shape, and they must have an area of 100 square inches with 2-inch margins on the right and left sides, and a 1-inch margin at the top and bottom. What dimensions should the poster have in order to have the largest printed area?

Fill in each box below with an integer or a reduced fraction. (a) log₂ 32 = 5 can be written in the form 2^A=B where A = and B = (b) log5 125 =3 can be written in the form 5^C=D where C= and D=

For $3.98 you can get a salad, main course, and dessert at the cafeteria. If you have a choice of 5 different salads, 7 different main courses, and 3 different desserts, then how many different meals can you get for $3.98? How many different meals can you get for $3.98?

Angela worked on a straight 9 % commission. Her friend worked on a salary of $900 plus a 6 % commission. In a particular month, they both sold $25,800 worth of merchandise. Step 1 of 2: How much did Angela earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.

If y varies directly with x and y = 35 when x = 7, find y if x = 4. y = 5x Now solve for y if x = 4. y = [?]

Given the recurrence relation x₁ = 3, x₁ = 3X(n-1) What is the solution? Xn= 2^n for all negative integers n Xn= 3^n for all negative integers n Xn= 3^n for all positive integers n Xn= 2^n for all positive integers n

Use the ALEKS graphing calculator to find the x-intercept(s) and vertex for the quadratic function. f(x)=x²+5x+1 Round to the nearest hundredth if necessary. If there is more than one x-intercept, separate them with commas. If applicable, click on "None". x-intercept(s): vertex:

Solve the equation for solutions over the interval [0,2x) by first solving for the trigonometric function. 8 sin x + 20 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an exact answer, using x as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

Use the sinking fund formula to determine the payment needed to reach the accumulated amount. Round to the nearest cent. Quarterly payments with 5.8% interest compounded quarterly for 3 years, and will accumulate to $82,000. A. $2,285.22 B. $6,305.36 C. $1,657.43 D. $1,789.73

Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression. paintings

a. Approximate the given quantity using Taylor polynomials with n=3. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. e^0.09 a. p3 (0.09) (Do not round until the final answer. Then round to seven decimal places as needed.)

Given the angle θ= -7π/6 To which quadrant does θ belong? (Write your answer as a numerical value.) Find the reference angle for θ IN RADIANS. Find the point where θ intersects the unit circle.

Suppose that $2000 is invested at a rate of 4.7%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 8 years. Do not round any intermediate computations, and round your answer to the nearest cent.

David borrowed money from a credit union for 3 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $1890. How much money did he borrow? If necessary, refer to the list of financial formulas.