Basic Math Questions and Answers

Using the following figures, determine closing book inventory (not all information given may be needed): Opening inventory $89,760 Gross purchases $43,620 RTV $860 Cash discounts $320 Markdowns $5,246 Markdown cancellations $318 Employee discounts $784 Gross sales $49,318 Customer returns $2,945 Net markups $760

The dial of a "combination lock" has the numbers 0 through 32. The "combination" to open the lock is actually an ordered sequence of 3 numbers. Each ordered sequence, from your textbook, is called an 'outcome'. How many outcomes are possible for this lock?

Write the sum of 7√28x6 + 4√7x6 in simplest form, if x ≠ 0.

A 10-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 lb/gal is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt in the barrel at time it is Q(t) = 3(1e-0.09t) where t is measured in minutes and Q(t) is measured in pounds. (a) How much salt is in the barrel after 9 min? (Round your answer to two decimal places.) (b) How much salt is in the barrel after 18 min? (Round your answer to two decimal places.)

The manager of a baseball team must determine the batting order of the nine starting players. (a) Is the possible number of outcomes found using permutations or combinations? Explain your reasoning. The possible number of outcomes is found by using a permutation since the order does (b) How many different batting. orders are possible?

For y = -9 cos x/7, its amplitude is its period is

The data in the box plots below represent the average SAT score for students who took one of two types of SAT prep courses. Which of the following is true? We cannot compare the two prep courses because the SAT is not accepted by all colleges. American Prep is a better course because it has higher scores in its 5-number summary. National Prep is a better course because there is less spread in the scores. American Prep had a lower minimum than National Prep so it is not as good as National Prep.

Decide whether the exercise involves permutations or combinations, and then solve the problem. In a club with 11 male and 12 female members, how many 6-member committees can be chosen that have (a) all men? (b) all women? (c) 4 men and 2 women?

Write the function in the form y=f(u) and u = g(x). Then find dy/dx as a function of x. y = tan 7X

Christine is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Christine rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. She loses $4.25 if a 5 or 6 is rolled.

A person invests 8000 dollars in a bank. The bank pays 5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14100 dollars?

Determine if (x - 5) is a factor of x3-14x² + 100.

A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. (a) Write an equation for the temperature y of the liquid t minutes after it is placed in the freezer. (b) How much longer will it take for its temperature to decrease to 48°F? (Round your answer to two decimal places.)

Write an equation of g(x) as a transformed function of f(x)=√x if it is reflected over the x-axis, shifted 5 units to the left and shifted 8 units down.

Find a polynomial f(x) of degree 5 that has the following zeros. -9, 1 (multiplicity 2), 0, -8

Consider the polynomial P(x) = 2x - 7x²-3x² + 21x-9. Given that x = 3 and x = 1/2 are zeros of P(x), find all remaining zeros. Include complex zeros if there are any. (Give your answer in the form of a comma-separated list if needed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if there are no other zeros.)

Suppose a company has fixed costs of $44,800 and variable cost per unit of 4/9 x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1876 - 5/9x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) X = (b) Find the maximum revenue. (Round your answer to the nearest cent.) (c) Form the profit function P(x) from the cost and revenue functions. P(x) = Find maximum profit. (d) What price will maximize the profit? (Round your answer to the nearest cent.)

Roshan SeaSights Touring Company offered a 25% discount on its excursion packages. A group of 15 from Halifax wanted to go on a 2 day excursion that would normally cost $335 each (excluding taxes). How much would each member pay for this excursion (excluding taxes) after the discount?

The graphs of rational functions mand n have the same vertical asymptotes, and both have a single x-intercept at x = 5. Which equation could represent function n?

Downhill Ski n' Board Resort, with 300 suites, has a rack rate of $245, and an actual room rate of $215. If the yield last year was 78.00%, how many suites did the hotel sell?

When two pumps are used, they can fill a tank in 60 minutes. When the first pump is used alone, the tank will be filled in 150 minutes. When x represents the time it takes the second pump to fill the tank when used alone, the situation is represented by this equation: 1/150 + 1/x = 1/60 How long would it take the second pump, working alone, to fill the tank?

F=9C+/532 is the formula to convert from degrees Celsius to degrees Fahrenheit. If the temperature is 35 degrees Celsius what is the equivalent temperature in degrees Fahrenheit?

In Bill the Boring's dryer there are 6 black shirts, 7 gray shirts, 11 black sweaters, and 7 gray sweaters. Bill is going to take one of these pieces of clothing out of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a shirt? Do not round intermediate computations, and round your answer to the nearest hundredth.

Find two angles between θ and 2π such that sin(θ) = 0.51. Start by drawing a sketch. Enter your answers as a comma separated list. Note that all solutions should be in radians. Find two angles between 0 and 2 such that cos(θ) = 0.05. Start by drawing a sketch. Enter your answers as a comma separated list. Note that all solutions should be in radians.

A total of 645 tickets were sold for the school play. They were either adult tickets or student tickets. There were 55 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Try to evaluate 3√27 without using a calculator. Enter DNE if the number is not real.

Let n be the middle number of three consecutive integers. Write an expression for the sum of these integers.

Write the equation for the following transformation: Shift y = 3^x along -x axis by 4 unit and reflect about y axis

A small regional carrier accepted 19 reservations for a particular flight with 16 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 60% chance, independently of each other. (Report answers accurate to 4 decimal places.) Find the probability that overbooking occurs. Find the probability that the flight has empty seats.

Resolve the given vector into its x-component and y-component. The given angle 0 is measured counterclockwise from the positive x-axis (in standard position). Magnitude 2.11 mN, θ = 187.41°

A parabola has its directrix at x = 4 and its focus at (8, k). Which of the following could be the equation of the parabola? Select all that apply. a. y =1/8 (x-8)² +6 b. 4y= (x-8)² + 20 c. x=1/8 (y + 2)² + 6

Determine the resultant of the vectors with the given magnitudes and directions. Positive angles are measured counterclockwise from the positive x-axis, and negative angles are measured clockwise from the positive x-axis. A: 557, 152.0 B: 1244, 232.0 The magnitude of the resultant is (Round to one decimal place as needed.)

At a county fair truck pull, two pickup trucks are attached to the back end of a monster truck. One of the pickups pulls with a force of 4000 pounds and the other pulls with a force of 3000 pounds with an angle of 45° between them. Find the resultant force of the two trucks. The resultant force is pounds. (Round to the nearest hundred pounds as needed.)

At a school-sponsored car wash, the fees charged were: $5 per car, $8 per pickup truck, $10 per full-size van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was $360. A total of $410 was collected at the car wash. Find the number of cars washed. A 40 cars B 25 cars C 20 cars D 65 cars

Roger has a house in Telluride, Colorado, but starts a new job in Denver. Every Monday, he drives his car 332 miles from Telluride to Denver, spends the week in a company apartment, and then drives back to Telluride on Friday. He doesn't use his car for anything else. After 20 weeks of this, his odometer shows that he has travelled 240,218 miles since he bought the car. How many miles were on his car when he started the job? 664 13280 226938 253498 332

The angle between two forces of 34 N (Newtons) and 47 N is 62°. Find the magnitude of the resultant force. The magnitude of the resultant force is

Solve the system of linear equations by graphing. y=2x 3x+y=5

Provide an appropriate response. Find the area under the standard normal curve to the left of z = 1.25. 0.8944 0.7682 0.1056 0.2318

2. Suppose you have a can of paint that you'll use to paint a rectangle whose length is 5 inches more than its width. If the can covers 500 in², what will the dimensions of the rectangle be? [WISE, VIZ]

Leila received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.14 per pound. After buying the coffee, she had $37.44 left on her card. How many pounds of coffee did she buy? pounds X

Boris is putting money into a savings account. He starts with $750 in the savings account, and each week he adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Boris has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 12 weeks. Equation: s= 350 +60] Total amount of money after 12 weeks: $1010 X 0=0 ?

Quadrilateral ABCD has vertices A = (2, 5), B=(2, 2), C= (4, 3) and D= (4, 6). Quadrilateral A'B'C'D' is formed when Quadrilateral ABCD is dilated by a scale factor of 2. Which statement is true? Select all that apply Choose all that apply: None of the answers apply The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.

Given f(x) = 4x³ - 16x² +13x-3, answer the following. Part: 0 / 2 Part 1 of 2 (a) Factor f(x), given that 3 is a zero. f(x) = 0 0°

Find the remaining five trigonometic functions of 8. sin 8= 8 in quadrant II 7 8

armen got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 3 cents per yard. If after that purchase there was $27.27 left on the card, how many yards of ribbon did Carmen buy? yards X S ?

nts: 0 of The exponential model A = 993.4 e 0.0231 describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 1064 million. KOLLERID The population of the country will be 1064 million in Round to the nearest year as needed.)

If the half-life of an element is 67 yr and the initial quantity is 3 kg, write a function of the form Q(t) = Qe^kt to model the quantity the element left after t years. Round k to 4 decimal places. Select one: a. Q(t)=67e^-0.0103t b. Q(t)=67e^-0.0034t c. Q(t) = 3e^-0.0103t d. Q(t) = 3e^-0.0034t

An open-top box is to be made from a square piece of cardboard that measures 6 inches by 6 inches by removing a square from each corner and folding up the sides. What are the dimensions and volume of the largest box that can be made in this way? length width height volume in in in in 3

Use the formula t= In 2 that gives the time for a population, with a growth rate k, to double, to answer the following questions. k The growth model A=9e 0.0061 describes the population, A, of a country in millions, t years after 2003. Part 2 of 2 a. What is the country's growth rate? 0.6% b. How long will it take the country to double its population? years (Round to the nearest whole number.) CELLE Points: 0.5 of 1 Save

Use a calculator with a y key or a key to solve the following. The exponential function f(x)=560(1.032)* models the population of a country, f(x), in millions, x years after 1974. Complete parts (a) — (e). ***** a. Substitute 0 for x and, without using a calculator, find the country's population in 1974. The country's population in 1974 was 560 million. b. Substitute 22 for x and use your calculator to find the country's population, to the nearest million, in the year 1996 as modeled by this function. million. The country's population in 1996 was