Basic Math Questions and Answers

In a class of 45 students, 26 are Democrats, 9 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major. P(Democrat or business major) = (Simplify your answer. Type an integer or a simplified fraction.) .....

Suppose that your bank pays 6% interest, compounded quarterly. Use Table 12-2 to find how much should be deposited now to yield an annuity payment of $1,700 at the end of ea three months, for 3 years. (Round your answer to the nearest cent.) $

Rent-A-Reck Incorporated finds that it can rent 60 cars if it charges $80 for a weekend. It estimates that for each $5 price increase it will rent two fewer cars. What price should it charge to maximize its revenue? $ How many cars will it rent at this price?

A passenger train traveled 120 miles in the same amount of time it took a freight train to travel 70 miles. The rate of the freight train was 30 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train. Rate of the passenger train: miles/hour 00

Determine what the key terms refer to in the following study. A study was conducted in a local community to analyze which voters would be likely to vote and how on an upcoming bond. Variable ✓ Parameter Statistic ✓Population ✓ Data Sample a. the number of eligible voters who actually plan to vote b. all eligible voters in the comunity c. the attendance of a single voter d. a group of voters in the community who voted, randomly selected e. the number of eligible voters in the study who actually plan to vote f. voted, didn't vote, voted

A line segment has endpoints A(2, -1) and B(3,5). What is the output of the transformation T(AB)((-4,0)? A. a line segment with endpoints A'(-2,-5) and B'(-1, 1) B. a line segment with endpoints A'(-2, -1) and B'(-1, 5) C. a line segment with endpoints A'(6, -1) and B'(7,5) D. a line segment with endpoints A'(6, 3) and B'(7,9)

Michelle is picking up sandwich ingredients at the grocery store. She goes to the deli counter and finds roast beef for $10.00 per pound and cheddar cheese for $11.25 per pound. She buys some of each and walks away with 1.5 pounds of meat and cheese costing a total of $16.25. How many pounds of each ingredient did Michelle buy? Michelle bought | pounds of roast beef and pounds of cheddar cheese.

Follow the steps for graphing a rational function to graph the function R(x)= If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of R(x). Select the correct choice below and, if necessary, fill in the answer box A. R(x)= B. R(x) cannot be factored further. What is the domain of R(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. {x1x² OB. {xx< (Type your answer in factored form. Do not simplify.) x+3 x(x + 7) } (Type an integer or a simplified fraction.) } (Type an integer or a simplified fraction.) C. {x|x -7,0} (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers. Write R(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. R(x) = (Simplify your answer.) OB. R(x) is already in lowest terms. ****E

Determine whether the relation is a function. c={(8,4), (-4,-3), (2, 1), (5,-8)} - Is the relation a function? O No O Yes

Choi Home Repair needs to accumulate $24,000 in 6 years to purchase new equipment. What sinking fund payment (in $) would they need to make at the end of each three months, at 4% interest compounded quarterly? Use Table 12-1. (Round your answer to the nearest cent.) $

Julio invests $6100 in two different accounts. The first account paid 2 %, the second account paid 3 % in interest. At the end of the first year he had earned $150 in interest. How much was in each account? $ at 2% S at 3%

Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is $0.90 more than the value of the nickels. How many nickels and dimes does Jamil have? O 6 nickels and 12 dimes O 7 nickels and 14 dimes O 5 nickels and 10 dimes O 12 nickels and 6 dimes

A pool is being filled and the water level of the pool is given by the function: L(h) = 1.5 +0.5h Where h = number of hours the pool has been filling L(h)= water level in the pool (feet) Find the missing value in the ordered pair described by the function notation and then choose the option that best describes the meaning of that ordered pair. L(2) means... and O The water level of the pool is 2 feet which happens after 2.5 hours of filling. O The water level of the pool is 2 feet which happens after 1 hour of filling. O After 2 hours of filling the water level the pool is 1 foot. O After 2 hours of filling the water level of the pool is 2.5 feet. O It will take a total of 2 hours to fill the pool.

A right triangle has an area of 44 square inches. The square of the hypotenuse is 185. Find the lengths of the legs of the triangle. Round your answer to the nearest inch. 4 inches and 22 inches O 16 inches and 5.5 inches 64 inches and 121 inches 8 inches and 11 inches

A bank loaned out $31,000, part of it at the rate of 9% annual interest, and the rest at 8% annual interest. The total interest earned for both loans was $2,620.00. How much was loaned at each rate? was loaned at 9% and was loaned at 8%. Question Help: Video Submit Question >

5. Stewart has to make a tessellation poster for his art class. His parallelogram ABCD is A(2, 3), B(3, 5), C(8,5), D(7, 3) is reflected across the y-axis. What will the new coordinates be on his project? A. A'(-2, 3), B'(-3, 5), C'(-8, 5), D'(-7, 3) B. A'(2, -3), B'(3, -5), C'(8,-5), D'(7, -3) C. A'(2, 3), B'(3, 5), C'(8, 5), D'(7,3) D. A'(-2,-3), B'(-3, -5), C'(-8, -5), D'(-7, -3)

A certain forest covers an area of 4300 km². Suppose that each year this area decreases by 6%. What will the area be after 10 years? Use the calculator provided and round your answer to the nearest square kilometer. 3 ?

1 Use the fact that the derivative of the function g(x)=√x is g'(x) = to find the equation of the tangent line to the graph of g(x) at the point x = 121 2√x S The equation of the tangent line is y= (Simplify your answer.) *****

The formula for finding the area of a trapezoid is A = a= top width, b is the bottom width and h is the height. Rearrange the formula to solve for the top width (a). Question Help: Video Message instructor (a + b) ₁ 2 Submit Question h, where A is the area, a is the

A farmer bought a number of pigs for $270. However, 7 of them died before he could sell the rest at a profit of 6 per pig. His total profit was $50. How many pigs did he originally buy? He originally bought Question Help: Video Submit Question pigs. Message instructor

the point where all three centroid medians meet the point where all three othocenter altitudes meet the point where all three circumcenter perpendicular bisectors meet a segment connecting the [Choose ] midpoint of the side of a triangle to the opposite angle a line/segment perpendicular to Choose]centroid/circumcenter/othocenter/ a side at the midpoint of that altitude/perpendicular bisector/median side a segment from a vertex perpendicular to the opposite [Choose ] side

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by C(p) = 6400p 100 - P (a) Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.) p= (b) What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.) (c) What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.) (d) What happens to the cost as the percent of pollution removed approaches 100%? The cost decreases without bound as p increases. The cost decreases (bounded by 0) as p increases. The cost increases (bounded by 6400) as p increases. The cost remains constant as p increases. The cost increases without bound as p increases. Need Help? Read It

Path A and Path B are walking paths used for horses. Path A is 118 feet long. Path B is 180 feet long. Carlos walks his horse down each path 3 times. Which path did Carlos use to walk his horse about 500 feet? Explain.

Graph the quadratic function f(x) = -3x² - 36x-96. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and (f) the largest open interval over which the function is decreasing. (a) The vertex is. .....

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = ² (7x − 2), x≤ 3 - absolute maximum value absolute minimum value DNE local maximum value(s) local minimum value(s)

Which type of asymptote will never intersect the graph of a rational function? Choose the correct answer below. O horizontal O oblique vertical all of these

The five number summary of a dataset was found to be: 1, 2, 9, 17, 19 An observation is considered an outlier if it is below: An observation is considered an outlier if it is above: Question Help: Video Post to forum Calculator Submit Question

The force applied (F) to a wrench is directly related to the torque (T) of the wrench. If the torque of a wrench is 9 N m when the force on the wrench is 27 N, find the torque of the wrench when the force on the wrench is 18N.

If 135 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $3 and total receipts for the concert was $448.25, how many of each went to the concert? adults children

Which phrases are used to describe a two-tail test? (Select all that apply.) O is greater than is less than is not the same as is smaller than O is bigger than is shorter than O is longer than is different from is decreased from is increased from has changed from is above is below is not equal to

Analyze the polynomial function f(x)= x²(x-8) using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function. The graph of f behaves like y= for large values of |x|.

Type "oo" (two lower case o's as in octopus) for oo if there are infinite solutions (all real numbers). Type "DNE" (Does Not Exist) if there is no solution. -5(5-2) + 3 = -25z + 14 7(62-3) +9= 42z - 12

A buoy floating in the ocean is bobbing in simple harmonic motion with amplitude 4 ft and period 7 seconds. Its displacement d from sea level at time 1 = 0 seconds is 0 ft, and initially it moves upward. (Note that upward is the positive direction.) Give the equation modeling the displacement d as a function of time t.

Maria invests a total of $27,500 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 3% loss in the same time period. At the end of one year, the total amount of money gained was $1,045.00. How much was invested into each account?

The volume of a gas varies inversely as the pressure upon it. The volume of a gas is 100 cm³ under a pressure of 64 kg/2. What will be its volume under a pressure of 40 kg/cm²? cm³ Question Help: Video Message instructor Submit Question

Transversal CD cuts parallel lines PO and RS at points X and Y respectively. The point nearest to Cis X, and the point nearest to Dis Y. Points P and R lie on one side of CD, while Q and Slie on the other side. According to the Alternate Exterior Angles Theorem, which angle is congruent to 2 CXP? OA LRYD OB. LSYD OC ZCXQ OD. ZXYS

The time required to do a job varies inversely as the number of people working. It takes 5hr for 7 bricklayers to build a park well. How long will it take 14 bricklayers to complete the job? (round answer to 1 decimal place)

Quadrilateral DEFG has vertices at D(6, 1), E(2, 4), F(5, 4) and G(-1, 1). Round answers to the hundredths place (2 decimal places). A) Calculate the area of DEFG Area = square units B) Calculate the perimeter of DEFG Perimeter = units C) Identify the type of quadrilateral. Choose one: square, rhombus, kite, rectangle, trapezoid

1 CREATE Shade the models at the right to show how the value of 0.04 is related to the value of 0.4. Then write a division equation to represent the relationship. Equation 54 2 ANALYZE Kiran showed 0.08 with the model below. + 0 al a2 0,3 0.4 0.5 0.4 0.7 0.8 0.9 1 What is wrong with Kiran's model? Describe how the length she shaded relates to the length that she should have shaded. How can Kiran change her model to show 0.08? Kirah 3 COMPARE How does the value of the digit 8 in 1.8 compare to the value of the digit 8 in 486? Explain.

Degree 3 polynomial with integer coefficients with zeros -7i and Select one: a. f(x) = 25x³-75x²+296x - 112 b. f(x) = 25x³-5x²-264x + 112 c. f(x) = 5x³-4x² - 245x + 196 d. f(x) = 5x³ - 4x² + 245x - 196

If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

Tell whether Mrs. Hense sells a roll of coastal Bermuda horse hay for $58. She says she will make $174 if she sells 3 rolls. A A AB

If the length of an arc intercepted by a central angle of 1.25 radians is 32 inches, which proportion could be used to find the radius of the circle? 1.25/360=32/2πr 1.25/2π=2πr/32 1.25/2π=32/2πr 1.25/2π=32/πr2

Name the location and type of discontinuities in the given function. f(x) =(x-1)(x+3)/(x-2)(x+3) Hole at x=-3. Vertical asymptote at x=2. There are no holes. Vertical asymptotes at x=-3, 2. Hole at x=-3. Vertical asymptotes at x=-3, 2. Hole at x=3. Vertical asymptote at x=-2.

It is estimated that t years from now the population of a city will be P(t) = 20(45 + 5)² - 1700t. Step 2 of 2: Find the rate of change in population in 7 years. Answer How to enter your answer (opens in new window)

2. The population of a certain town is increasing at the rate of 300 people per year. The population is 2500 today. a) What is the independent variable? What is the dependent variable? b) Write an equation expressing the population (p) as a function of time (t). c) Create a table of values showing the population for the next 6 years starting at t = 0.

$5000 is invested in a savings account which pays 2% annually. How much interest is earned by the account in 3 years? What is the value of the account after 3 years?

Utilize the Difference of Squares method to find an equivalent expression for the following: 16x² - 9y² O (4x+3y)(4x-3y) O (8x+3y)(8x-3y) o (4x² - 3y²) (4x² + 3y²) ○ (8x² + 3y²) (8x² − 3y²)

Suppose that a wheel whose diameter is 25 inches rolls along a flat surface at a speed of 46.3 inches per second. Which of the following equals the rate at which the wheel is rotating? 1.852 radians per second 578.75 radians per second 1157.5 radians per second 3.704 radians per second None of these

Which of the given statements is correct? The margin of error includes uncertainty because some variables are not measured properly. Undercoverage bias can introduce uncertainty that is larger than the margin of error. The confidence interval accounts for nonresponse because the final sample size is smaller than planned. As the sample mean increases, the margin of error increases.