Basic Math Questions and Answers

A bacteria culture contains 1200 bacteria initially and doubles every hour. (a) Find a function / that models the number of bacteria after t hours. N(t) = (b) Find the number of bacteria after 24 hours.

A Norman Window is a window that has the shape of a semicircle on top of a rectangle. Let's say that we have a Norman window with height of the rectangle y feet tall and a semicircle with radius x feet. The contractor building the window knows that there is going to be exactly 14 feet of trim around the outside of the window (three sides of the rectangle plus the semicircle). Now would be a great time to draw a picture for this problem. Go ahead, I'll wait. (A) Recalling that the circumference of a circle is C = 2πr, write a formula for the amount of trim and solve your formula for y in terms of x. y(x) = (B) Now recalling that the area of a circle is A = 72, write a formula for the area of the Norman window in terms of x. You will need to replace any instance of y with your answer from part (A). A(x) =

List the potential rational zeros of the polynomial function. Do not attempt to find the zeros. f(x) = 11x4-5x³+x²-x+1 Choose the answer below that lists the potential rational zeros.

Analyze the polynomial function f(x) = -4(x + 4)(x-3)³ using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function. The graph off behaves like y= for large values of x.

For the first 80 miles of her road trip. Lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip. If s represents Lina's speed during the first part of her trip, which expressions represent the total time of her trip in hours? 130s - 800/s(s-10) 130s +800/s(s+10)

Use logarithmic differentiation to find the derivative of y with respect to the given independent variable. y = (sin x) 4x

Brett, a sales person at Arya Sunshine Tours, sold a vacation package to Chelsea and her partner for $11,000 to travel to the Bahamas for 10 days. If the commission on this sale is 8%, calculate the amount of commission received.

Katie is building a rectangular wall. The wall will be 332 bricks wide and 39 bricks tall. She has 15,000 bricks. Does she have enough bricks to build the wall? Explain. Show your work in the box.

The area of a rectangle is 14 ft², and the length of the rectangle is 3 ft less than twice the width. Find the dimensions of the rectangle.

The time it takes to clean up after an anniversary party varies inversely as the number of people cleaning. If 3 people work together to clean, it will take them 90 minutes. How long will it take if the number of people cleaning is increased to 5? A 54 minutes B. 72 minutes C.150 minutes D. 162 minutes

Find the quotient and remainder using long division. -42³-14x² - 8x + 2/2x + 2 The quotient is The remainder is

Your cousin has a budget plan but unexpected expenses keep coming up. She is trying to understand where she went wrong last month so she took a rainy Saturday morning to compare her budget plan to her actual expenses. Her plan was to spend 1/4 of her budget on housing; 1/5 on car related expenses like gas, insurance, maintenance and lease; 3/10 on food; 1/10 on cell phone & other tech; 1/20 on savings; and 1/10 on entertainment. She is trying not to use her credit card because of fees so she has no credit card payments right now. First, make sure that her math was right and that the fractions add up to one whole. You may want to turn them into decimals first. Write the calculations below.

A child flies a kite at a height of 100 ft, the wind carrying the kite horizontally away from the child at a rate of 52 ft/sec. How fast must the child let out the string when the kite is 260 ft away from the child? Let x represent the horizontal distance through which the kite is blown and let y represent the distance between the child and the kite. Write the equation that relate these rates.

Factor the given polynomial completely into a product of linear factors of the form ax + b where a is a real number and b is a real or complex number. P(x) = 27x³ - 125 (Express numbers in exact form. Use symbolic notation and fractions where needed.) 27x³ - 125 =

The intensity of sound is measured on the decibel scale, dB. The equation dB = 10 log I represents the decibel level, where I is the ratio of the sound to the human hearing threshold. A noise is 150,000 times greater than the human hearing threshold. Which shows a valid step in the process of finding the decibel level of the noise? Select the correct answer below:

Subtract 1/x+9 - 9/x+9 z2 +52 – 36 State the difference in simplest form.

A faucet can fill a bathtub in 6 minutes. The drain can empty the tub in 10 minutes. If both the faucet and the drain are open at the same time. this situation is represented by this expression, where t is the number of minutes it will take to completely fill the bathtub. t/6 - t/10 Which expression can also represent this situation?

A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $81,900 per month. A television ad costs $2000, a radio ad costs $100, and a newspaper ad costs $600. The department wants to run 68 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month? television ads radio ads newspaper ads

A person invests 1000 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 1600 dollars?

Density: A Rectangular Prism has a height of 4cm, a width of 5cm, a length of 1.2 cm, and a mass of 85,000 g. What is it's density? .00000035416 g/cm^3 .00035416 g/cm^3 354.16 g/cm^3 3541.6 g/cm^3

Leila has two coupons for a bicycle. Coupon A: 35% off of a $93 bicycle Coupon B: $36 rebate on a $93 bicycle 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 $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.

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.