Math Questions

Given the following: f(x) = 3x +7x+8x¹; g(x) = -x + 12x - 212³; and h(x) = 8x³ + 12x + 6x² - 14x¹ Complete the following: h(x) - f(x) 8x³+3x+6x - 7x + 12x22x4 82³-3x+62-7x 82³-3x+6x7x 82³ + 3x + 6x + 7x

Wattage Good Defective Total A quality control inspector is checking a sample of light bulbs. The table summarizes her results. If one of the light bulbs is selected at random, find the probability that the light bulb is defective, given that it is a 50 or 100 watt bulb. The probability is

A statue in a harbor is approximately 325 feet tall. If the angle of elevation of a ship to the top of the statue is 23.7°, how far is the ship from the statue's base? The ship is from the statue's base.

A building contractor is to dig a foundation 30 feet long, 24 feet wide, and 9 feet deep. The contractor pays $5 per load for trucks to remove the dirt. Each truck holds 8 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size of a fetus ultrasound and then predict its birthdate. To do this requires formulas for fetus size as a function of age. Verburg et al. (2008) fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in mm) as a function of the fetus age,, (in weeks) and found the following formula: Calculated when t = 20. L = -37.50 +3.71t - 0.000633t³ Does the rate of growth of the fetus increase or decrease as it ages? A. Increases and decreases B. Increases C. Decreases D. Not enough information to tell

How many different license plates can the State of lowa produce if the requirements are as follows: 5 slots The first two slots are for letters. The next three slots are for digits from 0 - 9. 1, 240,000 676,000 82 1,757, 600

What is the value of n in the equation below? B. infinitely many solutions C, no solution 2n + 6 = 2n + 10

The graph shows the velocity, in feet per sec, of an object moving horizontally. A positive velocity represents movement to the right. Negative velocities represent movement to the left. What is the change in position of the object from t=0 to t= 13 seconds? The change in position is feet to the left.

A combination for a keypad is 6 digits long. The digits are from 0-9. The same digits MAY NOT be used more than once. How many different combinations are there? 54 1,000,000 60 151, 200

11. (a) Write the first 5 terms of a power series approximation for f(x) = e-x*² centered at X = 0. (b) Use the above power series approximation to find an approximation to S₁¹₁e-x² dx, rounding to 3 decimal places. Show work needed to produce this approximation. (c) Include a graph, shade the region corresponding to the integration and confirm your answer above using the computer or calculator to evaluate the integral.

The real number 0.9 can be written as an infinite series as shown below: (a) Write the infinite series in sigma notation and use the formula for the sum of a infinite geometric series to find the sum. (b) Write the exact value of the infinite sum (not as a repeating decimal).

Solve the triangle. Round to the nearest tenth. None of the other answers are correct mZK 113°, h 14, p = 13 mZK 113⁰, h = 15, p = 11 mZK 113°, h = 15, p = 10 mZK-113°, h = 15, p = 7

The infectivity of a certain pathogen is quantified by measuring the area between two curves. The greater the area between the curves, the greater the infectivity of the disease and this quantification provides a means to compare infectivity among various different pathogens. As an example, consider the function f(t) = -0.5t(t + 1)(t - 21) which represents number of infected cells carrying a particular pathogen in the blood of a patient as a function of time t, where t is measured in days. Suppose a patient is considered contagious during the period from time t = 3 days to t = 18 days. Compute the infectivity of this particular disease during the contagious period by finding the area between the function f(t) and the line segment connecting the points (3,f(3)) and (18,f(18)). Include a graph of the area computed.

Solve the triangle. Round to the nearest tenth. m/C = 57°, a = 12, b = 22 None of the other answers are correct mZC= 57°, a = 15, b = 19 mZC = 57°, a = 12, b = 19 mZC = 57°, a = 9, b = 19

Jose's teacher announces that the scores on their most recent Algebra test were normally distributed. The mean score was 72 and the standard deviation was 8. When Jose receives his score, he earned a 75. What percentage of students scored lower than Jose? Show your work on the sketch pad and then write your answer in a complete sentence in the text box.

Use the inverse trigonometric keys on a calculator to find the measure of angle A.

A clothing company determines that its marginal cost, in dollars per dress, is given by the function below. Find the total cost of producing the first 210 dresses, disregarding any fixed costs.

Find the angle 0 (in radians) between the vectors. (Round your answer to two decimal places.) u = 6i + 8j v = -2j

Let R be the area bounded by the graph of y = 16-x² and the x-axis over [0,2]. a) Find the volume of the solid of revolution generated by rotating R around the x-axis. b) Find the volume of the solid of revolution generated by rotating R around the y-axis. c) Explain why the solids in parts (a) and (b) do not have the same volume.

Suppose a sample of a certain substance decayed to 69.8% of its original amount after 300 days. (Round your answers to two decimal places.) (a) What is the half-life (in days) of this substance? days (b) How long would it take the sample to decay to one-third of its original amount? days

Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-4x-5. If there is more than one x-intercept, separate them with commas.

How would you interpret a statistical significance level of 0.48? This means that the probability for the null hypothesis to be false is 0.48. This means that the probability for the null hypothesis to be true is 0.48. This means that the probability for the alternate hypothesis to be true is (1 -0.48). This means that the probability for the alternate hypothesis to be false is (1 -0.48).

A tower that is 100 feet tall casts a shadow 154 feet long. Find the angle of elevation of the sun to the nearest degree. The sun's angle of elevation is (Do not round until the final answer. Then round to the nearest whole number.)

You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. a. What is the probability your dart lands in the smallest triangle? b. What is the probability your dart does not land anywhere in the circle?

A lock has a 3-number code made up of 20 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. Slope -6; through (1,6) The equation of the line is f(x) =

A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15°, from a height of 2.2 feet. How far away does the ball land in feet? (5 points) 56.372 feet 67.381 feet 60.646 feet 47.293 feet

You have $ 42,000 to invest. You invest seven times as much into investment A as you do investment B. How much money goes into investment A? A. $ 36,000 B. $ 6,000 C. $5,250 D. $ 36,750

The cost, in millions of dollars, of a 30-second television ad during an annual television event in the years 2000-2010 can be approximated by C(t) = 0.16t+ 1.3 million dollars (0 ≤ t ≤ 10). = 0 represents 2000.) What was the average cost of an ad in the event during the given period?

What is the purpose of constructing a confidence interval? In order to find the exact sample proportion. In order to find a range of values to estimate the population proportion. In order to find a range of values to estimate the sample proportion. To find the exact value of the population proportion.

A ship leaves port on a bearing of 35.0° and travels 12.4 mi. The ship then tums due east and travels 3.9 mi How far is the ship tom port, and what in the bearing from pot? The ship ismi from the part

The length of human pregnancies varies normally with a mean of 266 days and a standard deviation of 16 days. What percentage of pregnancies last between 234 and 298 days? 75% 68% 95% 99.7%

The population in a city is 356,902 people. If this city sees a decline in the population at a rate of 1.4% per year, find the new population after 25 years. A. 250, 883 B. 351,905 C. 277,037 D. 269,001

Set up a simplex matrix (or simplex tableau) for the following standard maximization problem. Find the maximum value of f = 2x + 4y subject to the constraints 3x + 4y ≤ 24 x + 5y ≤ 10 x ≥ 0, y ≥0

A test of significance produces a p-value of .03. Which of the following conclusions is appropriate? Reject H, at a significance level of 5% Accept Ho at a significance level of 5% Reject Ho at a significance level of 5% Accept H, at a significance level of 5%

A plane rises from take-off and flies at an angle of 15° with the horizontal runway. When it has gained 450 feet, find the distance the plane has flown. The plane has flown

Angle C is a right angle. Solve each triangle rounding to the nearest tenth. mA = 53°, c = 13.3 m/B = 37°, a = 10.6, b = 7.7 m/B = 37°, a = 10.6, b = 7.3 m/B = 37°, a = 12.9, b = 10.3 m/B = 37°, a = 10.6, b = 8 None of the other answers are correct

A road is inclined at an angle of 2°. After driving 5050 feet along this road, find the driver's increase in altitude. The driver's increase in altitude is

One transmitting station is located 170 miles north of another transmitting station. Each station simultaneously sends out a radio signal. The signal from the north station is received 800 milliseconds after the signal from the south station. If the radio signal travels 0.18 miles per millisecond, find the equation of the hyperbola on which the ship is presently located.

Solve the following system of equations using a method of your choosing y=-3x+5 5x - 4y=-3 A. The solution is (1,2) OB. The solution is (2,1) C. The solution is (0,0) D. The solution is (0,1)

Warfarin is a drug used as an anticoagulant. After administration of the drug is stopped, the quantity remaining in a patient's body decreases at a rate proportional to the quantity remaining. Suppose that the half-life of warfarin in the body is 37 hours. Write a differential equation satisfied by Q: How many days does it take for the drug level in the body to be reduced to 35 percent of its original level? time =

A test of significance produces a p-value of .06. Which of the following conclusions is appropriate? Fail to reject Ha at a significance level of 5% Fail to reject Ho at a significance level of 5% Reject H₂ at a significance level of 5% Reject Ho at a significance level of 5%

Determine whether the following system of linear equations has no solution, only one solution, or infinitely many solutions. If the system has only one solution, find that solution. Selecting an option will enable input for any required text boxes. If the selected option does not have any associated text boxes, then no further input is required.

Approximate the area under the graph of f(x) = 0.05x - 1.44x² +56 over the interval [2,6] by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval. The area under the graph of f(x) = 0.05x - 1.44x² +56 over the interval [2,6] is approximately.

Dana shoots a basketball at an angle of 45° from the horizontal. It leaves her hands 6 feet from the ground with a velocity of 27 ft/s. Step 3 of 3: Determine the height of the ball when it is 27 feet away horizontally. Round to the nearest tenth.

Find the minimum value of the objective function f(x, y) = x² + y² subject to the constraint y = r +1 (a) Use the constraint to rewrite the objective function with only a single variable. Then use single-variable calculus techniques to find the absolute minimum of the new function.

An amusement park would like to determine if they want to add in a new roller coaster. In order to decide whether or not they should add the new roller coaster, they poll people at the park to see how many rode the current roller coaster. • As people are leaving the park they randomly sample 600 people. • Out of the 600 people, 400 rode the roller coaster at the park. Construct a 90% confidence interval to represent the proportion of riders who rode the roller coaster at the park. All conditions for inference have been met.

Find the projection of u onto v. u = (4,8) v = (6,-3) Write u as the sum of two orthogonal vectors, one of which is projvu

Solve the equation: 3 - 121x = 0 Answer: I = Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and as your answers, then enter 4,-2/3 in the box.

A marine surveyor uses a rangefinder and a compass to locate a ship and an island in the vicinity of the coast on which she stands. The rangefinder indicates that the island is 386 m from her position and the ship is 589 m from her position. Using the compass, she finds that the ship ship's azimuth (the direction measured as an angle from north) is 319° and that of the island is 38°. What is the distance between the ship and the island?