Math Questions

A jewelry store sells 168 diamond bracelets per month at $1100 each. The owners estimate that for each $55 increase in price, they will sell 6 fewer diamond bracelets per month. Find the price per diamond bracelet that will maximize revenue.

Four coins are tossed several times. Which of the following represents the outcome on a coin that may not be fair? 1st coin is tossed 50 times and gives 24 heads and 26 tails. 2nd coin is tossed 250 times so that P(heads) = 0.25. 3rd coin is tossed 16 times and gives P(tails) = 9/16 4th coin is tossed 25,000 times and gives 12,505 heads.

A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at his precious damsel, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?

You work as a cashier for a grocery store and earn $5 per hour. You also mow lawns and earn $10 per hour. You want to earn at least $50 per week, but would like to work no more than 10 hours per week. Which system of inequalities, along with y 20 and x20, would you use to solve the real-world problem?

Find the GCF of the given list. x16y5, xy5, x7y8

State the domain and range for the following relation. Then determine whether the relation represents a function. {(3, 1), (4,-1), (5, 1), (6,-1)} The domain of the relation is. (Use a comma to separate answers as needed.) The range of the relation is. (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same first element and different second elements. B. The relation is a function because there are no ordered pairs with the same second element and different first elements. C. The relation is not a function because there are ordered pairs with 1 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with 3 as the first element and different second elements.

Find the average rate of change of f(x) = 2x² +5 over each of the following intervals. (a) From 4 to 6 (b) From 2 to 0 (c) From 0 to 3 (a) The average rate of change from 4 to 6 is. (b) The average rate of change from - 2 to 0 is (c) The average rate of change from 0 to 3 is

Explain what "80% confidence" means in a 80% confidence interval. What does "80% confidence" mean in a 80% confidence interval? OA. The confidence interval includes 80% of all possible values for the parameter. OB. The value of the parameter lies within 80% of a standard deviation of the estimate. OC. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 80%. The probability that it does not is 20%. OD. If 100 different confidence intervals are constructed, each based on a different sample of size n from the san population, then we expect 80 of the intervals to include the parameter and 20 to not include the parameter.

Decide on the procedure to solve the triangle given the following information, then solve the triangle. a = 50.39, b = 37.46, c=66.07 Which of the following procedures should be used to solve the triangle? A. Use the law of cosines to find the third side and the law of sines to find the smaller of the two remaining angles. Use the angle sum formula to find the remaining angle. B.Use the law of cosines to find the largest angle. Use the law of sines to find either remaining angle. Use the angle sum formula to find the remaining angle. C.Use the angle sum formula to find the remaining angle and the law of sines to find the remaining sides. OD. Use the law of sines to find an angle. Then use the angle sum formula to find the remaining angle. Use the law of sines to find the remaining side. Solve the triangle ABC. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Do not round until the final answer. Then round to the nearest minute as needed.) OA. There is one triangle and A = OB. There are two triangles A₁ = OC. There is no triangle. ...... 1 B= B₁ = and C= 1°₁ C₁ = A₂ = B₂= }', C₂ = '.

The marginal revenue function for Hedgemony, a bush planting service, is given by r(x) = 31 - 0.2x dollars per plant, when x bushes are planted. Find the change in revenue for the first 97 bushes planted. (Round your answer to the nearest cent.)

Your alpha level is 0.05. The probability of observing two sample means that you have gathered if the means of the population are the same is 0.04. Which statement below is true? You will accept that the null hypothesis that the means of the populations are the same. You will reject the null hypothesis that the means of the population are the same. There is no conclusion you can make in this situation. Reject both the null and the alternate hypothesis.

Situation: A 50 gram sample of a substance that's used to treat thyroid disorders has a k- value of 0.1113. N = Noe^-kt No initial mass (at time t = 0) N = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days Find the substance's half-life, in days. Round your answer to the nearest tenth. Enter the correct answer.

A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, S2, and $3, respectively. Fixed costs are $17,000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and $7, respectively. Next year, a total of 8000 units of all three products is to be produced and sold, and a total profit of $12,000 is to be realized. If total cost is to be $54,000, how many units of each of the products should be produced next year?

Enrico deposited $2000 in a savings account. Each month he will deposit an additional $25. Which kind of function best models the relationship between time and the total amount in the savings account? Choose 1 answer: Linear Exponential

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. Complete parts (a) through (g) below. (a) Construct a probability distribution for the random variable X, the winnings of each spin. x P(x) 35 -1 (Type integers or decimals rounded to four decimal places as needed.)

A machine is valued at $10,000. If the depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 4 years.

The mean wage at a company is $25 an hour with a standard deviation of $3 an hour. What is the probability that a worker earns between $22 and $34 an hour? Use the 68-95-99.7 normal distribution curve.

Peter wants to buy a sandwich. He can make his sandwich with sourdough, Italian, or whole wheat bread. He can choose turkey, ham, or salami. Each sandwich comes with either Provolone or American cheese. In how many possible ways can Peter make his sandwich if he chooses one item from each group? 6 8 9 18

Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. f(x)=e8x

The function y = -16x² + 36 represents the height y (in feet) of an apple a seconds after falling from a tree. Find and interpret the x- and y-intercepts. The x-intercept is x = This means the apple hits the ground after seconds. The y-intercept is y=. This means the apple fell from a height of feet.

Suppose there are two routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from Beaver Dam to Star Lake, and three routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Step 2: Choose a route from Step 3: Choose a route from Beaver Dam to Star Lake. There are 2__choices for step 1, 4__to Beaver Dam. (b) How many routes from North Point to Star Lake bypass Beaver Dam? choices for step 3. Thus, the answer is 32

A company estimates that the marginal cost (in dollars per item) of producing x items is C'(x) = 1.7 -0.008x. If the cost of producing one item is $754, find the cost of producing 154 items. (Round your answer to the nearest cent.)

Andrew Merrill, owns a mobile sandwich and pretzel stand. Andrew borrows $5,200 for 135 days at ,9% ordinary simple interest. What total will Andrew need to repay for both interest and principal? (Use a 360-day year.) $175.50 $5,300.50 $5,375.50 $5,373.10

Sketch the region enclosed by x + y² = 2 and x + y = 0. a) Favoring convenience, should you integrate with respect to x or y? b) What are the limits of integration? lower limit and upper limit c) Find the area of the region by integrating.

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.25% compounded quarterly. The annual percentage yield is %. (Do not round until the final answer. Then round to two decimal places as needed.)

A beverage company tested a new flavor of fruit drink on a random, representative sample of consumers. The company found that 47 percent of consumers surveyed liked the new flavor, with a margin of error of 6 percent. Which of the follow- ing is the most appropriate conclusion about how consumers in general will like the new flavor? A) More than half of consumers will dislike the new flavor. B) The researchers who conducted the sampling are between 41% and 53% certain that customers will like the new flavor. C.) It is likely that the percentage of consumers who like the new flavor will be between 44% and 50%. D.) It is likely that the percentage of consumers who like the new flavor will be between 41% and 53%

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? an 18250n - 750 an= 750n + 18250 an = 18250n + 750 an= -750n + 18250

In a piano recital, Toby has to perform one piece from each era of western classical music. There are eight pieces from the Baroque period, five pieces from the Classical period, and six pieces from the Romantic period to choose from. How many possible choices could Toby perform in his recital? 40 48 200 240

Using data starting with 1950 and projected to 2050, the number of women (in millions) in the workforce is given by the function P=0.79x+20.86, where x equals the number of years after 1950. (a) Find the value of P when x=65. Explain what this means. (b) What value of x represents 2030? Use the model to find the number of women in the workforce in 2030. (a) The value of P when x= 65 is million. (Type an integer or decimal rounded to two decimal places as needed.) What is the meaning of this value of P? A. The value of P represents the number of women who will join the work force between the years 1950 and 2015. B. The value of P represents the number of women in the workforce in the year 1965. C. The value of P represents the number of women who will join the work force between the years 1900 and 1965. D. The value of P represents the number of women in the workforce in the year 2015. (b) The value of x that represents 2030 is x = The number of women in the workforce in 2030 will be million. (Type an integer or decimal rounded to two decimal places as needed.)

Inverse variation can be applied in physics. The relationship between wavelength and frequency of light are closely related. The equation λv=c where λ is the wavelength, v is the frequency and c is the speed of light represents the relationship between wavelength and frequency of light. When written as an inverse variation equation, we can write λ=c/v or we can write v=c/λ In this formula, which variable represents the constant of variation k? Is it logical that this variable represents the constant of variation? Explain your answer.

Let f be the function defined as f(x)= 2 for x<4 f(x)= 4x-3 for x≥4 Which of the following statements is true? f is not differentiable at x = 4 because fis not defined at x = 4. f is not differentiable at x = 4 because the graph of f has a cusp at x = 4. f is not differentiable at x = 4 because the graph of f has a vertical tangent at x = 4. f is not differentiable at x = 4 because f is not continuous at x = 4,

You are going to survey a random sample of the 300 passengers on a flight from San Francisco to Tokyo. Name each sampling method described. a. Randomly generate 30 seat numbers and survey the passengers who sit there. b. Randomly select a seat position (right window, center, aisle, etc.) and survey all of the passengers sitting in those seats.

Let S be the event that a randomly chosen voter supports the president. Let W be the event that a randomly chosen voter is a woman. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen voter is a woman, given that the voter supports the president. Select the correct answer below: P(WIS) P(S AND W) P(W) AND P(S) P(SW)

A youth organization collected nickels and dimes for a charity drive. By the end of the 1-day drive, the youth had collected $48.65. If there were three times as many dimes as nickels, how many of each type of coin was collected?

Assume SAT Math scores are normally distributed with a mean of 500 and standard deviation of 100. A) Find the probability that a student scores lower than 575 B) Find the probability that a student scores higher than 393.

For studying the electric current that is induced in wire rotating through a magnetic field, a piece of wire 88 cm long is cut into two pieces. One of these is bent into a circle and the other into a square. Express the total area A of the two figures as a function of the perimeter of the square. Use p for the perimeter of the square. A= (Simplify your answer. Do not factor. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)

Which function translates each point on the graph of y = mx + b so that the slope of the segment from the original point to the translated point is 1/2 ? t(x)=1/2x+b t(x) = m(x-2) +b+1 h(z) = mx + b g(x) = m(x-2) +b-1

On a poultry farm eggs are packed in cartons. Each carton contains 12 boxes and each box contains 15 eggs of mixed size (small, medium and large). On the farm 1 out of 9 eggs is large and the packing machine selects the eggs randomly. Find the expected number of large eggs in a carton.

A 28-year-old man pays $223 for a one-year life insurance policy with coverage of $60,000. If the probability that he will live through the year is 0.9993, what is the expected value for the insurance policy? -$181.00 $59.958.00 $42.00 -$222.84

a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. c. Compute the percent error in the approximation, 100.|approximation - exact|/|exact| where the exact value is given by a calculator. f(x) = 6-x² at a = 1; f(0.9)

An investment grows at 24% compounded monthly. How many years will it take to do the following? (Round your answers to one decimal place.) (a) double (b) increase by 65%

among automobiles of a certain make, 23% require service during a one-year warranty period. A dealer sells 87 of these vehicles. a.) Approximate the probability that 25 or fewer of these vehicles require repairs. b.) Approximate the probability that more than 17 vehicles require repairs.

There's one other alternative-one that takes both skill and courage: Forgoing any cradling action, grasp the cone more firmly between thumb and forefinger and extend the other fingers so that they are out of the way of the dripping from the bottom, then increase the waist-bend angle from twenty-five degrees to thirty-five degrees, and then eat the cone, allowing it to drip out of the bottom onto the ground in front of you! Experienced and thoughtful cone-eaters enjoy facing up to this kind of sudden challenge. What is the author's purpose for including this portion of "How to Eat an Ice- Cream Cone"? A. To entertain the audience with humor B. To appeal to the audience with emotion C. To inform the audience with facts D. To persuade the audience with language

Graph the function f(x) = 7(x + 2)² - 6. Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Use radian measure and enter your answers using at least four significant digits. (b) Determine all solutions for csc(θ)=2 Solutions with base angle in quadrant I: θ= Solutions with base angle in quadrant II: θ= where n is any integer, and both base angles are between 0 and 2π Use radian measure and enter your answers using at least four significant digits.

The product of two numbers is to be minimized. The second number is eight more than twice the first. Call the first number "x." a) Write an equation for the product of the numbers with respect to the first number. (4 points) b) What is their minimum product? (2 points) c) What two numbers make this minimum product? (4 points)

The diagram shows ΔABC with all three medians drawn. If ΔZ = 12 cm, find the length of AF. The diagram shows ΔABC with all three medians drawn. If AZ = 12 cm, find the length of AF. a.12 cm b. 6 cm c. 8 cm d. 18 cm

The Cartesian coordinates of a point are given. (a) (-7,7) (i) Find polar coordinates (r, θ) of the point, where r> 0 and 0 ≤ θ< 2π (r,θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ< 2π (r, θ) = (b) (2,2√3) Find polar coordinates (r, 8) of the point, where r> 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) =

ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA'B'C. What are the coordinates of the vertices of ΔA'B'C? A. A'(-3, 3), B'(-1, 1), C'(-2, 3) B. A'(3, -3), B'(1, -1), C'(2, -3) C. A'(3, -5), B'(1, -7), C'(3, -5) D. A'(-3, 3), B'(-1, 1), C'(-2, -3)

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₁9, the 19-percentile. This is the temperature reading separating the bottom 19% from the top 81%. P19 = °C