Math Questions

(b) What is the group of all symmetries of the tetrahedron, including those that reverse orientation (and are therefore no longer rotations in 3-space)? (Hint: it's S₁. Why?)

Find the Maclaurin series of sin(x7)

Estimate the - and y-intercepts from the graph. Write each intercept as an ordered pair. Separate your answers using commas, if necessary. Select "None" if applicable.

Use the simplex method to maximize f= 4x + 4y + z under the constraints x + 2y + 4z ≤ 20 2x + 4y + 4z ≤ 60 3x + 4y + z ≤ 90 x ≥ 0, y ≥ 0, z ≥ 0.

An object is thrown upward at a speed of 115 feet per second by a machine from a height of 4 feet off the ground. The height h of the object after t seconds can be found using the equation h = 16t² + 115t +4 When will the height be 172 feet? Hint: Set h to 172. When will the object reach the ground? 7.22

Some mathematics professors would like to purchase a $140 microwave oven for the department workroom. If 5 of the professors do not contribute, everyone's share will increase by $50. How many professors are in the department? A) 26 B) 21 C) 14 D) 7 E) 9

Given right triangle ABC, right angle at C, side b = 6 inches, side c = 15 inches. Solve the triangle completely. Round all angles to the nearest degree and all sides to the nearest tenth of an inch. a= A= B=

Two woodworkers, Tom and Carlos, earn a profit of $86 for making a table and $65 for making a chair. Tom must work 3 hours and Carlos 2 hours to make a chair. Tom must work 2 hours and Carlos 6 hours to make a table. If neither wants to work more than 42 hours per week, how many tables and chairs should they make to maximize their profit? 3 tables and 12 chairs: $1038 13 tables and 2 chairs: $1227 notables and 15 chairs: $1806 12 tables and 3 chairs: $1227 none of these

You drove 10,000 miles last year. Your expenses were $3,100 in gasoline, $150 in oil and lubrication, $780 in minor repairs, $1,900 in insurance and $60 for license and vehicle sticker. True or False: Your cost for maintaining your vehicle per mile is $0.58. True False

How many solutions does the following system have? 3x - 2y + 3z = 3 9x + 3y + z = -3 -27x11z = -3 Select the correct answer below: No solutions 1 solution Infinitely many solutions

Sketch the logarithmic function h(x)=-4 log(x+2)+4 Find two points on the graph, and determine the domain and the equation of any vertical asymptotes. Fill in the missing coordinates of the points that lie on the graph of y= log 4 x and the corresponding points that lie on the graph of h(x)=-4 log(x+2)+4.

A new restaurant is to contain two-seat tables and four-seat tables. Fire code limits the restaurant's maximum occupancy to 56 customers. If the owners have hired enough servers to handle 17 tables of customers, how many of each kind of table should they purchase? two-seat 7; four-seat 10 two-seat 10; four-seat 7 two-seat 12; four-seat 5 two-seat 5; four-seat 12 two-seat 6; four-seat 11 two-seat 11; four-seat 6

Simplify the fraction. If the fraction is already simplified, so state. 72/88 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 72/88= (Simplify your answer. Type a whole number or a fraction.) B. The expression cannot be simplified.

Suppose tan(a)=5/6 where 0 ≤ α ≤ π/2. Find all solutions in [0, 2π): tan(2x)=5/6 x=

Solve the system of equations: 4x = 3y + 8 2x - 5y = -14 (-41/7, 36/7) (41/7, -36/7) no solutions infinite solutions (41/7, 36/7)

Which of the following reveals the minimum value for the equation 3x2 + 18x+15=0? 3(x+3)² = 6 3(x+9)² = 12 3(x+3)² = 12 3(x+9)² = 228

The following models describe wages for low-skilled labor. p = -0.325x+5.8 demand model p = 0.375x +3 supply model where p represents the price of labor per hour and x is the number of workers available in millions. Determine the equilibrium number of workers, in millions, associated with the equilibrium wage per hour. 5 million workers @ $4.88 an hour 3 million workers @ $4.12 an hour 4.5 million workers @ $4.68 an hour 4 million workers @ $4.50 an hour

Describe the sampling distribution of p. Assume the size of the population is 30,000. n=1300, p=0.288 Describe the shape of the sampling distribution of p. Choose the correct answer below. A. The shape of the sampling distribution of p is approximately normal because n ≤0.05N and np(1-p) ≥ 10. B. The shape of the sampling distribution of p is not normal because n ≤0.05N and np(1-p) ≥ 10. C. The shape of the sampling distribution of p is approximately normal because n ≤0.05N and np(1-p) < 10. D. The shape of the sampling distribution of p is not normal because n ≤0.05N and np(1-p) < 10.

Without using a calculator, find all the solutions of tan(t) = -1 where -π < t ≤ π.

Suppose cos(a)=4/5, where 0 ≤ a ≤ π/2. Find all solutions in [0, 2π): cos(2x) = 4/5.

Suppose sin(a)= 7/10, where 0 ≤ a ≤ π/2 Find all solutions in [0, 2π): sin(2x) = 7/10

Below is a sample of share prices (in dollars) for a particular stock, selected at random over several years: 242 253 261 269 271 235 240 242 230 259 243 242 274 255 232 259 230 273 Use Excel (or other form of electronic assistance) to find the mean, median, mode, and standard deviation for this sample. Round answers to the nearest tenth. Mean = Median = Mode = Standard Deviation = Using the Empircal Rule, what percent of values would be 235.4 or less? % What percent of values would be 281 or more? % If you haven't answered the question correctly in 3 attempts, you can get a hint.

Find all angles between 0 and 360° such that sec =2.705. Round to the nearest degree. a) Find the reference angle. b) Determine the Quadrants in which the solutions are in c) Find the angles in the two quadrants, rounded to the nearest degree. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end.

Consider the function: f(x) = x² + 8x - 20 The direction of the graph is like which of the following: The y-intercept is at y = The x-intercepts are at x = The vertex is at the point

Suppose tan(a)=5/8 where 0 ≤ a ≤ π/2 Find all solutions in [0, 2π):

The table below shows the number of individuals infected with a disease t days after its first detected by the CDC. For each of the following problems, enter regression equation values with at least 3 decimal places. Enter predictions to the nearest whole individual. 1) Use regression to find an exponential equation that best fits the data above. The equation has form y = abt where: a = b= Use the model to predict the number of individuals infected with the disease after 16 days. individuals 2) Use regression to find a linear equation that best fits the data above. The equation has form y = mt + b where:

A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1000 adults in that country, 35% say that they would travel into space on a commercial flight if they could afford it. At a = 0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. % of adults in the country would travel into space on a commercial flight if they could afford it. B. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not C. At least % of adults in the country would travel into space on a commercial flight if they could afford it. D. No more than % of adults in the country would travel into space on a commercial flight if they could afford it. Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State Ho and H₂. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) A. Ho: P Ha:p= D. Ho: P H₂: p B. Ho: P< H₂: p2 E. Ho: p2 H₂: p< C. Ho:p> Haps F. Ho: PS H₂:p> (b) Use technology to find the P-value. Identify the standardized test statistic. Z=

Pick the system of inequalities satisfied by the point (-4,2). y< x +7 and y> 7x-3 y>-x+7 and y> 7x-3 y> -x + 7 and y <7x - 3

Consider the parabola given by the equation: y = 1x² + 14x - 33 Find the following for this parabola: A) The vertex = ( B) The y intercept is the point (0, C) Find the two values of a that correspond to the intercepts of the parabola and write them as a list, separated by commas:

Professor Ivy has the following scores on her final exam: 76, 51, 81, 57, 62, 70, 98 41, 50, 100, 86, 93, 48 Compute the values indicated below. Express your answers rounded to the nearest tenth. Mean: Standard Deviation: Use the 68-95-99.7 Rule to answer the following question. What is the probability of an exam score more than 49.9 ? Express your probability answer as a decimal. If you haven't answered the question correctly in 3 attempts, you can get a hint.

Simplify the rational expression: m-3/3-m -1 m 1

Willie bought a CD for $16.95 and eight blank videotapes. The total cost was $52.55 excluding the tax. Find the cost of each blank videotape. $4.45 $5.35 $3.25

If construction costs are $156,000 per kilometer, find the cost of building the new road in the figure shown to the right.

A ball bounces several times after it is dropped. The graph shows the height of the ball over time. Height is measured in meters and time is measured in seconds. Select all statements that are true about the graph and the situation it represents. The function's minimum occurs at the vertical intercept (also called y-intercept) One of the minimum values occurs at 1.25 seconds The function's maximum value is at the vertical intercept (also called y-intercept) There is only 1 minimum value, and it occurs at 1.25 seconds

The volume of a cone is 113.04 mm2. What is the approximate volume of a sphere that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth. 113.04 mm³ 226.08 mm³ 904.32 mm³ 3,052 mm³

Use the information provided to write the vertex form equation of each parabola. Vertex: (-7,-5), Focus: (-7,-41/8) y = (x +9) ² - 7 y = 2(x - 5)² +7 y- 1/2(x-5)²-7 y = -2(x+7)² - 5 y = 1/2( x − 4 )² + 6

Suppose g (z) = -(z − a)³ (z - b)²(z − 1)². Describe the graph of g (z) a. The graph the x-axis at x = d. b. The graph [zero2] the x-axis at x = b. c. The graph [zero3] the x-axis at x = 1. d. At the ends, the graph (end).

Identify the number of solutions the following equation has: 7-5(z-6) +4=3-2(z-5)-3z +28. No Solution Unique Solution Infinitely Many Solutions

Consider the function f(x) = 5x² - 10x + 1, 0≤x≤ 8. The absolute maximum of f(x) (on the given interval) is at x = and the absolute maximum of f(x) (on the given interval) is The absolute minimum of f(x) (on the given interval) is at x= and the absolute minimum of f(x) (on the given interval) is

From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) x-intercept (x, y) = (0,2 (smaller x-value) x-intercept y-intercept vertical asymptote(s) horizontal asymptote

Sketch the angle and write the sec and tan of the angle if the terminal side of the angle passes through (3, -6). Express each answer as a decimal rounded to the nearest hundredth. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end.

Suppose the random variable is best described by a normal distribution with μ = 20 and a = 8.2. Find the z-score that corresponds to each of the following a values. Express your answers rounded correctly to the hundredths place. (a) x = 15 z= (b) x = 32 z= (c) x= 10 z= (d) x = 25 z= (e) x= 25 z= (f) x=17 z=

The diagram represents a regular pentagonal pyramid. The measurements unit is feet. (Round your answers to two decimal places.) (a) Find the area of the base. ft² (b) Find the lateral area of the pyramid. ft² (c) Find the surface area of the pyramid. ft² (d) Find the volume of the pyramid. ft3

A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h(t)=16t² +96t+ 112 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

A simple random sample of size n = 15 is obtained from a population with µ = 67 and σ = 17. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x. (b) Assuming the normal model can be used, determine P(x < 70.9). (c) Assuming the normal model can be used, determine P(x ≥ 68.3). (a) What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large. B. Since the sample size is large enough, the population distribution does not need to be normal. C. The sampling distribution must be assumed to be normal. D. The population must be normally distributed.

nSeveral years ago, 51% of parents with children in grades K-12 were satisfied with the quality of education the students receive. A recent poll found that 495 of 1,095 parents with children in grades K-12 were satisfied with the quality of education the students receive. Construct a 90% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. Find the 90% confidence interval. The lower bound is 0.485 The upper bound is 0.535 (Round to three decimal places as needed.) What is the correct conclusion? A. Since the interval contains the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. B. Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. C. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. D. Since the interval does not contain the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed.

Which of the following represents vector t = -8i + 6j in trigonometric form? t= 10 (cos 36.87°, sin 36.87°) t= 10 (cos 143.13°, sin 143.13%) t= 10 (sin 36.87°, cos 36.87°) t= 10 (sin 143.13°, cos 143.13%)

Determine whether the following statement is true or false, and explain why. In a Markov chain, the outcome of an experiment depends only on the present state and not on any past states. Is the statement true or false? A. True. B. False. In a Markov chain, the outcome of an experiment depends on past states found using transition matrice C. False. In a Markov chain, the outcome of an experiment depends on past states found using probability vector D. False. In a Markov chain, the outcome of an experiment depends on both past and present states.

The average daily volume of a computer stock in 2011 was μ = 35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 30 trading days in 2018, he finds the sample mean to be 32.1 million shares, with a standard deviation of s = 12.3 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. (a) State the hypotheses for the test. Ho: µ ≠ 35.1 million shares H₁: µ = 35.1 million shares (b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018. million shares and million shares. With 95% confidence, the mean stock volume in 2018 is between (Round to three decimal places as needed.) (c) Will the researcher reject the null hypothesis A. Do not reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval. B. Do not reject the null hypothesis because μ = 35.1 million shares does not fall in the confidence interval. C. Reject the null hypothesis because μ = 35.1 million shares does not fall in the confidence interval. D. Reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval

Graph each of the lines in the following system to find the solution. y = -2x + 6 y=-3x+9