Math Questions

Find the volume of the rectangular pyramid whose base is 3 m x 6 m and whose height is 5 m. 60 m³ 90 m³ 30 m³

Find the exact value of the expression. tan cos[-1(√3/2)] Select the correct choice and fill in any answer boxes in your choice below. A.=tan cos[-1(√3/2)]=36.7 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the B. There is no solution.

6. BMI for Miss America A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) FOR RECENT Miss America winners. Use a 0.01 significance level to test the claim that recent winners are from a population with a mean BMI less than 20.16, which was the BMI for winners from the 1920's and 1930's. Given that BMI is a measure of the relative amounts of body fat and height, do recent winners appear to be significantly smaller than those from the 1920's and 1930's. 19.5 20.3 19.6 20.2 17.8 17.9 18.8 17.6 16.8 19.1

Consider the function f(x,y) = x² - 2x²y+3y² +5 and the point P(-1,3). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. a. What is the unit vector in the direction of steepest ascent at P? <_,_> (Type exact answers, using radicals as needed.) What is the unit vector in the direction of steepest descent at P? <_,_>(Type exact answers, using radicals as needed.) b. Which of the following vectors is in a direction of no change of the function at P? A. (8,-16) B. (-16,8) C. (-8,16) D. (-16,-8)

Evaluate the series. 4Σ (i+1) i=1 i=14Σ (i+1) = (Simplify your answer. Type an integer or a simplified fraction.)

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

Each bag of different colored jelly beans is supposed to have 30% blue jelly beans. Ramon believes there are actually a greater proportion of blue jelly beans. He randomly selects 25 bags of jelly beans and finds the proportion of blue jelly beans to be 36%. He uses a significance level of a = 0.1 and calculates a p-value of 0.256. What null and alternative hypothesis did Ramon use for the test, and what conclusion can he make? (1 point) H0: p=0.36 He p > 0.36 Ramon fails to reject the null hypothesis because the p-value is greater than the significance level. H0: p=0.3 He p > 0.3 Ramon fails to reject the null hypothesis because the p-value is greater than the significance level. H0: p=0.3 He P=0.3 Ramon rejects the null hypothesis because the p-value is greater than the significance level. H0 p = 0.3 He: p=0.3 Ramon rejects the null hypothesis because the p-value is greater than the significance level.

Which is an example of an experiment? A company asks its website users to rate its new features to navigate the site. Researchers working for a company test their new sneaker design to see if it helps athletes run faster. A scientist watches a group of local birds to see what type of tree they prefer to make their nests in. An ice cream company asks people to identify their top three ice cream flavors.

There are three types of solutions to any system of two equations. What are the types? What do those solutions look like graphically?

Sylvia makes pizzas at an Italian restaurant. A large pizza is listed on the menu as being 16 inches. Sylvia wants to know how accurate she is at throwing dough to that size. A coworker measures all the pizzas Sylvia throws, and they randomly select 35 data points. They use this data to calculate the following 95% confidence interval: (15.85, 16.10). Use this to recommend a strategic decision. Sylvia should use more dough since the least value of the confidence interval is less than 16 inches. Sylvia should use less dough since the greatest value of the confidence interval is greater than 16 inches. Sylvia should continue using the same amount of dough since 16 inches is contained within the confidence interval. Sylvia should use more dough so that the entire confidence interval is greater than 16 inches.

For the rotation 1409°, find the coterminal angle from 0° 0 < 360°, the quadrant and the reference angle. The coterminal angle is __° which lies in Quadrant __ with a reference angle of __ °

Give a geometric description of the following set of points. x² + y² +2²-12x+8y-10z+61 = 0 Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answers.) A. A sphere centered at (__,__,__) with radius __ B. The exterior of a ball centered at (__,__,__) with radius __ C. A ball centered at ;(__,__,__) with radius __

For the rotation 435°, find the coterminal angle from 0° 0 < 360°, the quadrant and the reference angle. The coterminal angle is __° of which lies in Quadrant with a reference angle of ____°

The Central Limit Theorem says that the mean of the sampling distribution of the sample means is A) exactly equal to the population mean. B) equal to the population mean divided by the square root of the sample size. C)close to the population mean if the sample size is small D)close to the population mean if the sample size is large.

Find the area of an obtuse triangle with a base of 8 inches and a height of 5 inches. A. 40 square inches B. 20 square inches C. 45 square inches

Find an equation of the line where the planes Q and R intersect. Q: -2x+3y-z = 1; R: x+y+z= -1 Choose the correct answer below. A. An equation of the line is given by x = -5t, y = -1/5+4t,z=-4/5+t, where -∞<t<∞. B. An equation of the line is given by x =-4/5+4t,y=-1/5+t,z=-5t,where -∞<t<∞. C. An equation of the line is given by x =-5/4+4t,y=-5+3t,z=-2t,where -∞<t<∞o. D. An equation of the line is given by x= -5+3t, y = -2t, z =-5/4-t,where - ∞<t<∞.

A study of 468 randomly selected kindergarten students showed that they have seen on average 5723 hours of television. If the sample standard deviation of the population is 951, find the upper bound limit of the 95% confidence interval of the mean for all students.

Consider a population with u-58.5 and o-5.7 is taken. Find the standard deviation of the sampling distribution of the sample means with a sample size of 76.

Call a metric space sequentially compact if every sequence has a convergent subsequence. Prove that a metric space is sequentially compact if and only if every infinite subset has a cluster point.

Which statements are true about the fully simplified product of (b-2c)(-3b+c)? Select two options. The simplified product has 2 terms. The simplified product has 4 terms. The simplified product has a degree of 2. The simplified product has a degree of 4. The simplified product, in standard form, has exactly 2 negative terms.

Use Descartes' Rule of Signs to determine the number of possible combinations of positive and negative real zeros of f(x) = 4x³ + 7x* + 102x³+174x²+ 50x-25 Also, use the Rational Root Theorem, the Remainder Theorem, and synthetic division to determine all roots and factors(linear and quadratic) of the polynomial. Answer the following questions in your analysis: (a-d one point each) a. Degree = b. # of zeros: c. Max. # of turns:

Jeffrey wanted to purchase a high quality music player that was in the middle of the price range. The price ranges are $79.99, $210.99, $109.99, $69.99, $325, $100.99, and $75.00. Identify the cost of the music player he selected. Median: $109.99 Median: $79.99 Median: $100.99

A bank auditor claims credit card balances are normally distributed, with a mean of $3,500 and a standard deviation of $1,250. A random sample of 25 individuals is taken. What is the probability that the mean of the credit cards is greater than $4,100?

A bus company is doing research to determine if it can save money by switching from gasoline-powered buses to electric-powered buses. The company randomly selects records of gasoline usage from 30 days and calculates that the buses use a mean 22 gallons of gas each day with a standard deviation of 1.8 gallons. The gas station the buses use charges $2.95 for a gallon of gas. The company also knows it would cost $62 to charge the buses enough to be able to run for one day. Use a 95% confidence interval to recommend a strategic decision for the bus company. The bus company should switch to the electric buses because 22 gallons of gas costs more than $62. The bus company should switch to the electric buses because the least amount of mean gas per day in the confidence interval costs more than $62. The bus company should not switch to the electric buses because the least amount of mean gas per day in the confidence interval costs less than $62. The bus company should not switch to the electric buses because the greatest amount of mean gas per day in the confidence interval costs less than $62.

Solve the following equation in the complex number system. Express solutions in both polar and rectangular form. x³-(3-√2+3√/2i)=0 Write the solutions as complex numbers in polar form. Choose the correct answer below. A 3√6 (cos 15°+ i sin 15°). 3√6(cos 135°+ i sin 135°). 3√6 (cos 45°+ i sin 45°) B 3√6 (cos 15° + i sin 15°), 3√6(cos 135°+ i sin 135°). 3√6(cos 255°+ i sin 255°) C. 6(cos 15°+ i sin 15°), 3√6(cos 45°+ i sin 45°), 6(cos 255° + i sin 255°) D.3√6(cos 15°+ sin 15°), 3√6(cos 135° sin 135°), 3√6(cos 45°+ i sin 45°)

A poll of 1146 U.S. adults found that 972 U.S. adults, or 84.817% regularly used Facebook as a news source. Find the margin of error and confidence interval for the percentage of U.S. adults who regularly use Facebook as a news source, at the 90% level of confidence. Express all answers as percentages rounded to 2 decimal places. Do not write the percent sign. Margin of Error (as a percentage): Confidence Interval: % to % Now find the margin of error and confidence interval for the percentage of U.S. adults who regularly use Facebook as a news source, at the 95% level of confidence. Margin of Error (as a percentage): Confidence Interval: % to %

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter and the diameter of the spherical part is 8.5 cm. Find the volume of the flask. Use π= 3.14 355.76 cm³ 350.25 cm³ 346.51 cm³

Write the standard equation for a circle. center (10, -6), r = 6 Select one: a. (x-10)² + (y + 6)² = 36 b. (x + 6)² + (y - 10)² = 36 c.(x + 10)² + (y - 6)² = 6 d. (x-10)² + (y + 6)² = 6

Consider the following pattern. 2◊6=12 22◊6=132 222◊6=1332 2222◊6=13332 Predict the result of 222222◊6.

A boy owns 2 pairs of pants, 6 shirts, 2 ties, and 8 jackets. How many different outfits can he wear to school if he must wear one of each item? He can wear __________ different outfits.

A general contractor is constructing a building that requires a concrete foundation that is to be 15 feet by 18 feet and 18 inches thick. If the local home supply store sells concrete for $75 per cubic yard, what will be the cost of the concrete for the foundation? Express your answer rounded up to the next whole dollar.

A couple needs $50,000 as a down payment for a home. If they invest the $35,000 they have at 12% compounded quarterly, how long will it take for the money to grow to $50,000? (Round your answer to the nearest whole number.)

Drew is planting grass. The lawn is a rectangle that measures 120 feet by 75 feet. Drew uses 1 pound of grass seed for every 200 square feet. How much grass seed does Drew use. A. 195 pounds B. 90 pounds C. 45 pounds D. 390 pounds

A farmer needs to enclose three sides of a plot with a fence (the fourth side is a river). The farmer has 35 feet of fence and wants the plot to have an area of 150 sq-feet. What should the dimensions of the plot be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.) length= feet width= feet

Identify the surface defined by the following equation. 16z² + y² = 9 The surface defined by the equation is _____

The population of a southern city follows the exponential law. Use this information to answer parts a and b. (a) If N is the population of the city and t is the time in years, express N as a function of t. N(t) = Noekt (Type an expression using t as the variable and in terms of e.) (b) If the population doubled in size over 24 months and the current population is 60,000, what will the population be 3 years from now? The population will be approximately __ people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

According to an insurance company, the probability that a woman will survive one year is 0.992, and the probability that she will die in one year is 0.008. If she buys a $10,000 one-year term policy for $100, what is the company's expected gain or loss? What can the company expect? A. Gain of $20.00 B. Loss of $20.00 C. No gain or loss

A ball is thrown up from the ground with an initial velocity of 80 feet per second. The height s in feet can be expressed as a function of time t in seconds by s(t) = 80t - 16t². When does the ball reach its maximum height and what is the maximum height attained? Solve the inequality x³ - x² - 12x < 0 Solve the inequality 4/x-2≥-4/x+2

The equation x²-6x + y² +6y+9=0 is an equation of a circle in expanded form. Complete the square to find the center and radius, and then write the equation of the circle in standard form. To earn full credit, you must show your work. a. center b. radius c. Equation..

Find the future value of an ordinary annuity of $4,000 paid quarterly for 5 years, if the interest rate is 7%, compounded quarterly. (Round your answer to the nearest cent.)

Find a counterexample to the statement. The sum of a negative number and a positive number will always be negative.

The surface area of a cubical box is 121.5 square feet. Find the length of the base. 4.5 ft 3.75 ft 3.5 ft

Suppose you want deposit $200 each month into an account earning 3.5 % APR compounded monthly. a) Write an equation to find how many years N it will take to save $12,000? b) How many years will it take to save $12,000? Round to two decimals.

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required? n =

Identify the leading question. How much would you be willing to pay for a new living room furniture set? During what time of day are you most likely to watch TV? How interested would you be in purchasing a blue car? How much did you enjoy your great experience at our waterpark?

There are 232 people going on the fourth grade field trip. They are taking 4 busses. If each bus has an equal amount of passengers, how many passengers will be on each bus? A. 58 people B. 135 people C. 223 people D. 928 people

The following is a list of 12 measurements. 35, -24, -7, -1, -93, 49, 15, 40, 29, 46, 92, 3 Suppose that these 12 measurements are respectively labeled x₁, x₂, ..., x₁2. (Thus, 35 is labeled x₁, −24 is labeled x2, and so on.) Compute the following 38 +12Σi=1 Xi

Which is an important aspect of a randomized survey's design? The survey should always contain at least 5 questions. Each survey question should have at most 3 choices. The survey participants should be randomly selected. The survey should have questions for multiple populations.

Why type of symmetry does the sine function have? Sine is an odd function, meaning it has symmetry with respect to the y axis. Sine is an even function, meaning it has rotational symmetry about the origin. Sine is an even function, meaning it has symmetry with respect to the y axis. Sine is an odd function, meaning it has rotational symmetry about the origin.

cos α =-24/25, α a lies in quadrant II, and sin B = √21, ß lies in quadrant II Find cos (α + β). -48-7√21/125 14-24√21/125 -14+24/21/125 48+7√21/125