Math Questions

Yesterday, Martina went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 12 miles per hour. In the two days, she biked for a combined total time of 10 hours. Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.

If f(x) = 2x3/3 - 3x²/2 + 4x, what is f'(x)? f'(x) = 2x³ - 3x² + 4x f'(x) = 2x² - 3x + 4 f'(x) = -2x² + 3x - 4 f'(x) = -2x³ + 3x² - 4x

Find the values of c and d if the trinomial x² + 20x + c can be factored as (x + d)² c = d=

The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even R(x)=200x-x², C(x)=25x+6250, 0≤x≤ 100 The manufacturer must produce units to break even.

The scale on a set of architectural drawings for a house is 1 3/4 inches - 2 feet. If the master bedroom is 14 feet long, what is its length on the drawing? A) 12.25 in grass hula skirts B) 12.75 in life jackets C) 10.5 in Darth Vader masks D) 11.75 in gorilla suits E) 13.5 in clown shoes

Translate "two less than four times a number is ten" into an equation and solve. 4x + 2 = 10; 6 4x - 2 = 10; -3 4x - 2 = 10; 6 None of these

An elevator is constructed using an electric motor at the top which is used to lift the elevator's car via a cable. The cable weighs 6 pounds per foot. The cable is 100 feet long when the elevator car is at the first floor, and it is effectively 0 feet long when the car is at the top floor. The elevator's car weighs 500 pounds How much work W does the motor do just lifting the cable and car when it takes the car from the first floor to the top floor? W =

You are throwing a party in 4 hours. If it takes 40 minutes to bake 12 cupcakes, how many cupcakes will you be able to finish baking before your party begins? 60 min = 1 hour Please report your answer to 1 decimal place. Note: Please only input a numerical answer, no units.

The radius of a cylindrical construction pipe is 2 ft, and its length is 18 ft. Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact volume of the pipe. Write your answer in terms of . Exact volume: (b) Using the ALEKS calculator, approximate the volume of the pipe. To do the approximation, use your answer to part (a) and the button on the calculator. Round your answer to the nearest hundredth. Approximate volume:

The perimeter of a square, p, varies directly as the length of a side, s. The perimeter of a square is 30 when the length of a side is 7.5. Which equation represents the relationship? Select the correct answer below: p = 22.5s p = -22.5s p = 7.5s p = 30s p = 4s p = 0.25s

A homeowner is going to build the raised bed garden shown in the plan, against an existing garden wall. The homeowner will build the new wall by stacking concrete blocks without mortar, and then fill in the walled space with garden soil. The concrete blocks have dimensions 8 inches x 8 inches x 16 inches. The wall will be capped by capstones that have dimensions 8 inches x 2 inches x 16 inches. Concrete blocks cost $1.50 each, capstones cost $1.00 each, and garden soil costs $36 per cubic yard. The homeowner will do all the work and will buy materials. How much will they cost?

A group of 60 students and 4 sponsors took a field trip to a local museum. For their first guided tour, students were given a choice of 1 of 3 art exhibits. Of the 60 students, 1/2 chose Modern, 1/4 chose American Folk, and 1/6 chose Western. Each student that expressed a choice chose exactly 1 exhibit. The remaining students expressed no choice. How many of the students expressed no choice? A. 5 B. 6 C. 10 D. 15 E. 30

Use like bases to solve the exponential equation. 15625.5^(3x+4)=625 x=____

GRADING ON A NORMAL CURVE-MR. SANDERSON MARKS HIS CLASS ON A NORMAL CURVE. THOSE WITH Z-SCORES ABOVE 1.8 WILL RECEIVE AN A, THOSE BETWEEN 1.8 AND 1.1 WILL RECEIVE A B, THOSE BETWEEN 1.1 AND -1.2 WILL RECEIVE A C, THOSE BETWEEN -1.2 AND -1.9 WILL RECEIVE A D, AND THOSE UNDER -1.9 WILL RECEIVE AN F. FIND THE PERCENT OF GRADES THAT WILL BE A, B, C, D, AND F.

Which term is -234,375 for the following sequence, assuming that the pattern continues? 3, -15, 75, -375,... a8 a9 a10 a11

Solve the equation for x. log8(x+3)-log8(x)=log8(25) x=__

The data in the accompanying bar graph are from a random sample of 806 adults. The graph shows four proposals to reduce gun violence in a country and the percentage of surveyed adults who favored each of these proposals. Complete parts (a) and (b) below. a. Find the margin of error for this survey. The margin of error is ±%. (Do not round until the final answer. Then round to the nearest tenth as needed.) b. Write a statement about the percentage of adults in the country's population who favor to restrict ammunition purchases to reduce gun violence. There is 95% confidence that between% and% of all adults in the country favor to restrict. (Use ascending order. Round the nearest tenth as needed.)

The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.5x² + 15x + 14, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? Ticket sales will peak days after the concert was first announced.

Substitute the given values into the formula, and solve for the unknown variable. A=1/2h(B+b); A=42, B = 4, b=3

According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied? A. Yes, because (80)(.173) and (80) (1 - 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions. B. No, because (80)(.10) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions. C. Yes, because the sample is random. It represents the 8th graders in the district. D. No, because 80 students is not enough to be representative of the students in the school district.

If the mean, median, and mode for a given population are all equal and the relative frequency curve has matching tails to the right and left, then we would describe the shape of the distribution of the population as Multiple Choice bimodal skewed to the right symmetrical skewed to the left

y=x² + 3 y = 15x-33 The system of equations shown above is graphed in the xy-plane. If system has two solutions, what is the product of the x-coordinates of the two solutions? A) 36 B) 4 C) -4 D) -36

The half-life of radium-222 is approximately 38 seconds. Step 1 of 3: Determine a so that A(t)=A0a^t describes the amount of radium-222 left after t seconds, where Ao is the amount at time t = 0. Round to six decimal places. Answer How to enter your answer (opens in new window)

Give the equation of the horizontal and vertical lines passing through the point (-1/3,-10). The equation of the horizontal line is: The equation of the vertical line is:

College students take different course loads. Many colleges determine the number of Full-time equivalent' students, F, by using the formula F=15, where n is the total number of credits in which students enroll for a given semester. If students on a campus register for a total of 69150 credits, how many full-time equivalent students does the campus have? The campus has 4610 full-time equivalent students. Solve the formula for n. n=

During the summer time you decide to set up a sprinkler to keep you cool. Assuming with full water pressure the sprinkler can spray everything within a four-foot radius. The sprinkler has been set up to only hit the sector where you are sitting. If it is set to spray a sector area of 9.75 square meters, to what angle is the sprinkler set? Round to the nearest hundredths of a degree. 69.86⁰ 75.23⁰ 109.63⁰ 139.73°

Write an equation and solve it to find the answer to the question below. Remember to define your variable.Susan is buying three different colors of tiles for her kitchen floor. She is buying 25 more red tiles than beige tiles, and three times as many navy-blue tiles as beige tiles. If Susan buys 435 tiles altogether, how many tiles of each color does she buy?

Selected Technologies According to recent surveys, 60% of households have personal computers. If a random sample of 152 households is selected, what is the probability that more than 48 but fewer than 82 have a personal computer? Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places. P (48 < X<82)=

Is the line through points P(0, -9) and Q(2, -8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain. a. Yes; their slopes are equal. c. No; their slopes are not opposite reciprocals. b. Yes; their slopes have product-1 d. No; their slopes are not equal.

An preimage mapped to its prime image maps to (x, y) → (3x, 3y). The prime image is mapped to the double prime image to (x, y) → (x+1, y-4). Describe the composition of transformations. The image was reduced by a scale of 3, then moved one unit up and 4 units over. The image was enlarged by a scale of 3, then moved one unit right and 4 units down. The image was enlarged by a scale of 3, then moved one unit left and 4 units down. The image was reduced by a scale of 3, then moved one unit down and 4 units right.

An elliptical-shaped path surrounds a garden, modeled by (x-22)/225+ (y-26)²/324 =1, where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent? 15 feet; minor axis 18 feet; minor axis 36 feet major axis 225 feet; major axis

CONSTRUCTING A TEST- A TEACHER IS CONSTRUCTING A MATHEMATICS TEST CONSISTING OF 10 QUESTIONS. SHE HAS A POOL OF 28 QUESTIONS, WHICH ARE CLASSIFIED BY LEVEL OF DIFFICULTY AS FOLLOWS: 6 DIFFICULT QUESTIONS, 10 AVERAGE QUESTIONS, AND 12 EASY QUESTIONS. HOW MANY DIFFERENT 10 QUESTION TESTS CAN SHE CONSTRUCT FROM THE POOL OF 28 QUESTIONS IF HER TEST IS TO HAVE 3 DIFFICULT, 4 AVERAGE, AND 3 EASY QUESTIONS?

A jet plane has 180,000 pounds of fuel after the first hour of flight. The four engines consume a total of 15,000 pounds per hour at its cruising altitude. How many pounds of fuel remain after the 8th hour? 60,000 pounds 75,000 pounds 120,000 pounds 285,000 pounds

Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) h(x) = ex² - 4 on [-2, 2] Absolute maximum value: at x = (Enter your answers as a comma-separated list if there are multiple x-values.) Absolute minimum value: at x = (Enter your answers as a comma-separated list if there are multiple x-values.)

What is the solution to the equation? 1/2 In (x+17) = ln (x² - 9) - ln (x+3) x=8 only x-1 and x = 8 x=1 only x= -8 and x = 1

A club swimming pool is 18 ft wide and 34 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 620 ft². How wide can the strip be?

A loan of $14,000 is made at 8.5% interest, compounded annually. After how many years will the amount due reach $41,000 or more? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. years

Suppose that the dollar value v (1) of a certain house that is f years old is given by the following exponential function. v (t)=559,900(0.91)t Find the initial value of the house. $ Does the function represent growth or decay? growth decay By what percent does the value of the house change each year? %

Omar paid $13.29 for a 7.03-kg bag of dog food. A few weeks later, he paid $13.58 for a 7.26-kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 7.03-kg bag: Unit price for the 7.26-kg bag: The better buy: The 7.03-kg bag The 7.26-kg bag Neither (They have the same unit price)

Let f be the function defined as f(x)= 3 for x<5 x+7 for x≥ 5 Which of the following statements is true? f is not differentiable at x = 5 because f is not defined at x = 5. f is not differentiable at x = 5 because fis not continuous at x = 5. f is not differentiable at x = 5 because the graph off has a vertical tangent at x = 5. f is not differentiable at x = 5 because the graph of f has a cusp at x = 5.

1. Find only the area of the shape below. Round your answer according to the guidelines. Include units in your answer.

Which of the following statements is (are) true for all positive integers? 1) n3+2n is divisible by 3. 2) 5^2n- 1 is divisible by 24. Both statements are true. None of the statements are true. Only the first statement is true. Only the second statement is true.

Given the graph of the Logarithmic Function g(x) = log4 x: The graph of the function f(x) = log4 (x-6) can be obtained from the graph of g(x) = log4 x by shifting the graph of g(x) 6 units; Identify the Domain and Range of f(x) using Interval Notation. Domain of the function f(x) is Range of the function f(x) is

AB is a chord of the parabola y² = 4ax. If its equation is y = mx + c and it subtends a right angle at the vertex of the parabola, then (a) c = 4 am (c) c = 4 am (b) a = 4 mc (d) a + 4 mc=0

Suppose a product's revenue function is given by R(q)=8q2 + 900q, where R(q) is in dollars and q is units sold. Find a numeric value for the marginal revenue at 26 units, and record your result in the box below. Answer: MR(26)$ per unit

Solve the triangle, if possible. Determine the number of possible solutions. A = 78.7° a = 11.2 b=9.7 Select the confect choice below and lite answer boxes wil Le choice. (Round to the nearest tenth as needed.) A. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m∠B= m∠C= The length of side c = The measurements for the solution with the shorter side c are as follows. m∠B= mZC= The length of side c = B. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. m∠B= m∠C= The length of side c =

Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion? We can select a higher confidence level and increase the sample size. We can select a lower confidence level and increase the sample size. We can select a lower confidence level and decrease the sample size. We can select a higher confidence level and decrease the sample size.

Which equation describes the circle with center (5,-1) and radius 7? A (x-5)² +(y + 1)² = 7 B (x-5)² +(y+1)² = 49 C (x + 5)²+(y-1)³ = 7 D (x+5)² +(y-1)² = 49

The polynomial function defined by f(x) = π/3x³-5πx² + 500πd/3 can be used to find the depth that a ball 10 cm in diameter sinks in water. The constant d is the density of the ball, where the density of water is 1. The smallest positive zero of f(x) equals the depth that the ball sinks. Approximate this depth for each material and interpret the results. a) A wooden ball with d=0.6. b) A solid aluminum ball with d=2.7. c) A spherical water balloon with d=1. a) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is 5.67 (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined. b) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined. c) Select the correct choice below and fill in any answer boxes in your choice. A. The depth is cm. (Type an integer or decimal rounded to the nearest hundredth as needed.) B. The answer is undefined.

Assume that Jim, Bruce, Valerie, and Simon are four of the 15 members of the class, and that four of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim, Bruce, Valerie, and Simon are selected in that order? The probability that Jim, Bruce, Valerie, and Simon are selected in that order is (Type an integer or decimal rounded to six decimal places as needed.)