A manufacturer can produce sunglasses at a cost of $5 a piece. It is estimated that if the sunglasses are sold for x dollars a piece, consumers will buy 2000 − 100x of them.

Q: When building a house, the number of days required to build varies inversely with the number of…

A: Given One house was built in 21 days by 19 workers.How many days would it take to build a similar…

Q: During a nationwide program to immunize the population against a new strain of the flu, public…

A: Since you have posted multiple subparts we solved first three subparts for you To get the solution…

Q: A ribose sugar molecule in RNA contains oxygen,carbon, and hydrogen. The number of oxygen atoms…

A:

Q: ​Alan, Betty, and Carol invested in a corporation in the ratio of 6​:7​:8 respectively. If they…

A: Explanation and solutions is given below....

Q: A metric ton is 1000 kgand a British ton is 2000 Which has the greater weight and by how much

A: Given 1 Metric ton = 1000 kg 1 British ton = 2000 kg We need to find which has greater weight and by…

Q: During a nationwide program to immunize the population against a new strain of the flu, public…

A: Given: The cost of inoculating x% of the susceptible population is given by the function:…

Q: The length of a rectangular box is 8 inches longer than twice the width (x). The height is 9 inches.…

A:

Q: A number w increased by 3 is greater than – 18.

A:

Q: A recipe for cupcakes yields 1 1/2 dozen cupcakes. By how much should the ingredients be multiplied…

A:

Q: The population of Watesville decreases at a rate of 1.6% per year. If the population was 62,500 in…

A: Given: Population in 2014, P = 62,500 Rate of decrease, r = 1.6% Population in 2020, Q = ?   Number…

Q: While examining evidence from a shooting, a ballistics expert informs Detective Bianca that a bullet…

A:

Q: A retired couple have $300,000 to invest and want to earn $30,000 per year in interest. The safer…

A: It is given that principal amount=$300000

Q: Ian can remodel a kitchen in 20 hours and Jack can do the same job in 15hours. If they work…

A: Given that Ian can finish the work in 20 hours.  So in 1 hour Ian does 1/20 work    Jack can finish…

Q: Three of the same cycles sell for $2,640. What is the dollar price of five of these same cycles?

A: Given that,Three of the same cycles sell for $2640 we have to calculate, what is thedollar price of…

Q: A collection of pennies and nickels has the value of $1.59. There is one more than twice as many…

A:

Q: Fahd's age is now twice the age of Faisal. If Fahd's age 6 years ago is equal to four times Faisal's…

A:

Q: 700 is 10 times as much as

A: Let 700 is 10 times as much as x

Q: A box contains only dimes and quarters. The number of dimes is three less than twice the number of…

A:

Q: You discover that the number of hours you sleep each night varies inversely as the square of the…

A: Given  Number of hours you sleep each night varies inversely as the square of the number of cups of…

Q: Suppose the value of a car V is related to the number of years since its purchase by the formula V =…

A: Here the value of car  is given V = 25000-2100n After 5 year then n = 5

Q: A baseball team has home games on Thursday and Sunday. The two games together earn $3509.50  for the…

A: Let $x and $y was generated on Thursday and Sunday game respectively. Given: The two games together…

Q: The product of the ages of A and N is 240. If twice the age of N is more than A’s age by 4 years,…

A: Let the age of A be a and the age of N be n. The given relations can be written as follows.

Q: The pair of numbers whose difference is 18 and whose product is as small as possible is

A:

Q: If darin traveled 30 miles in 2 hours, and ed traveled three times as far in half the time, what was…

A: Darin travelled 30 miles in 2 hours. Ed travels thrice this distance in half the time.

Q: A pool can be filled by one pipe in 6 hours and by a second pipe in 12 hours. How long will it take…

A:

Q: With x people on board, a South African airline makes a profit of (960−3x) rands per person for a…

A: Given problem:- With x people on board, a South African airline makes a profit of (960−3x) rands per…

Q: A man can seed a large field in 8 hours. His daughter can do the job in 6 hours. If she starts an…

A:

Q: Find a positive number for which the sum of its reciprocal and four times its square is the smallest…

A: 1. Let x be the positive number then according to question - S=1x+4x2 and we need to minimize this…

Q: A bicycle and a bicycle helmet cost $240. How much did each cost, if thebicycle cost 5 times as much…

A:

Q: Patrick gets paid three dollars less than four times what Kevin getspaid. If the number of dollars…

A: Number of dollars kevin gets paid = x Patrick gets paid three dollars less than four times what…

Q: Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by…

A: Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by

Q: Suppose Jacqueline takes a 800 mg dose of ibuprofen and every hour that passes the amount of…

A:

Q: Deon's shirt is 4 times larger than Helen's, but costs half as much. Deon's shirt cost $9.35. How…

A:

Q: A recent study found that one's earnings are affected by the mathematics courses one has taken. In…

A: Given that the earning are affected by the mathematics course one has taken. The earning function is…

Q: la) The sum of the ages of Afful and Naomi is 34years. Five years to come, Afful will be 2 times the…

A:

Q: A pond can be filled by one pipe in 8 hours and by a second pipe in 24 hours. How long will it take…

A: Consider the given information. A pipe can be filled in 9 hours and a pipe is fitted in another 12…

Q: Suppose a student got an 82 on an exam that was worth 25% of the final grade, a 75 on another exam…

A: Given data: Category Weight Score Exam 1 25% 82 Exam 2 25% 75 Homework…

Q: Your company can manufacture x hundred grade A tires and y hundred grade B tires a day, where 0…

A: Given Your company can manufacture x hundred grade A tires and y hundred grade B tires a day

Q: The length of a rectangle is 5 inches longer than half of its width. The area of the rectangle is 72…

A: Given:The area of the rectangle is 72 square inches.The length of the rectangle is 5 inches longer…

Q: How far will the driver get if he drives at an average speed of 40 miles per hour for 3 hours and 45…

A:

Q: Currently, a discount appliance store is selling 200 large-screen TVs each month. If the store…

A: Let us assume a function f(x). For the function f(x), the rate of change of function is given by the…

Q: For a particular brand of coffee beans, the cost is proportional to the weight of beans You…

A: Cost of 7 ounces = $3.99  Therefore cost of 1 ounce = ($3.99/7)  Since $15 is spend to purchase the…

Q: Thus, Dani's current age is

A:

Q: A company can manufacture xx hundred items for a total cost of C=500+900x-100x2. Find x if the total…

A: Given: total cost of C=500+900x-100x2. Find x if the total cost is $1,900. To find x .

Q: A leaking pond loses 18 gallons of water in 37 hours. How many gallons of water will it lose in 42…

A:

Q: Today, an antique car that originally cost $3,773 in 1955 is valued today at $69,500 if in excellent…

A: We need to find the value of the car in very nice condition.

Q: In a certain family, 11 times the number of children is greater by 12 than twice the square of the…

A:

Q: Suppose a particular antibiotic that is introduced to a petri dish containing 3000 newly discovered…

A: Introduction: Arithmetic sequence and geometric sequence are two important sequences in mathematics.…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.