Math Questions

Thunderstorm Speeds A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 17 miles per hour. The standard deviation of the sample was 1.6 miles per hour. Use a graphing calculator and round the answers to at least one decimal place. Find the 97% confidence interval of the mean. Assume the variable is normally distributed.

On a scientific or graphing calculator, approximate the following value. In 0.9090

Graph the system below and write its solution. 6x-2y=-4 y=3x+3 Note that you can also answer "No solution" or "Infinitely many" solutions.

Consider the following absolute value inequality. |9x+6| < 24 Rewrite the given inequality as two linear inequalities.

Thunderstorm Speeds A meteorologist who sampled 11 thunderstorms found that the average speed at which they traveled across a certain state was 13 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Use a graphing calculator and round the answers to at least one decimal place. Find the 82% confidence interval of the mean. Assume the variable is normally distributed.

Which of the following equations display= Select all that apply: r = 2sin θ+5θ T = -sinθ T = 5sin²θ+3cos²θ + 5sinθ+θ r = -sin²θ + 4θ+5 T = = -4cos²θ-sinθ + 2θ symmetry based on the test for θ = symmetry? Select all that apply.

Graph the linear equation by finding and plotting intercepts. y = 3x

Type the correct answer in the box. Round your answer to the nearest hundredth. Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26°. Scarlett's height is 1.65 meters, so the height of the dam is meters.

Two ant colonies are growing at the exact same rate. The first colony, however, has a larger population than the second colony. The equation f(t) = 300 (1.03)t models the population of the first colony over time. What equation models the second colony g(t) if g is 85% the size of f?

All 3 medians of a triangle will have the same length. True False

7. Given the following information, write the standard form equation of each hyperbola and determine the equations for the asymptote lines of the hyperbola. a. Vertices: (-5, 5), (-5, 3): Foci: (-5, 6), (-5, 4) b. Vertices: (-10, 1), (-10, 17); Perimeter of Central Rectangle = 76

Consider the following absolute value inequality. |9x + 7| < 10 Determine which graph represents the original inequality.

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.000165 moles per liter. Write this number in scientific notation. (b) A black rhinoceros can weigh up to 6.4 × 10³ pounds. Write this number in standard notation.

Which of the following are reasonable ways to estimate 15% of $29.95. There may be more than one reasonable method. 0.15 times 29.95 is $4.4925 30% is 3 out of 10, so that would be 9 out of 30. 15% is half of that, so $4.5 15 times 30 is $450. Adjusting the decimal place gives $45 10% of 30 is 3. 5% is half of that, so 1.5. Together, 15% is $4.5 15 times 30 is $450

Drag the blue point to a location on the coordinate plane so that the vector 7 (shown below in blue and centered at the origin) has magnitude 15 and direction 36.87° (relative to the positive x-axis). Provide your answer below:

A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time? A 57⁰ B. 50⁰ C. 40⁰ D. 33°

Suppose that the total profit (in dollars) from the sale of x skateboards is given by P(x) = 30x - 0.6x² - 240 Determine the marginal average profit to approximate the profit from the sale of the 20th skateboard.

Perform the following additions and/or subtractions: (10w² + 11w + 4) + (7w² + 8w + 3) =

Write an equation in point-slope form of the line that passes through the point (-8, -2) and has a slope of m = 5.

Expand and simplify the following expression. log₂ (4x3/y2z4) 2+3 log₂ (x)-2 log2(y)-4 log2(z) 2+log3(x)-log2(v)-log4(z) 2+3 log3(x)-2 log(y) - 4 log(z) 2+3 log2(x)-2 log2(v) +4 log2(z)

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. 12x-8y = 12 Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

Find the equation of a 3D figure matching each of the descriptions below: a. A set of points equidistant from the origin. b. A plane parallel to the xy-plane. c. A plane parallel to the yz-plane. d. A plane parallel to the xz-plane. e. A point on the x-axis in 3D space. f. A point on the y-axis in 3D space. g. A point on the z-axis in 3D space. h. A plane centered at the origin with normal vector < 2, 3, -4 >

Consider the following equation of a circle. (x - 3)² + (y - 3)² = 16 Graph the circle.

A jet leaves an airport at 3:00 pm with a course of 150° and a speed of 510 mph. At 5:00 pm, the jet pilot changes the course to 210° and keeps traveling in that direction at 510 mph. Determine how far the jet is from the airport at 8:00 pm. 310.91 miles 883.35 miles 916.56 miles 2223.04 miles

Given the points (-5, -4) and P(-3,7), determine the position vector of PQ. Select the correct answer below: (-2,11) (11,2) (-11, -2) (2,11) (-11,2) (-2,-11)

A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule using function notation to represent the situation.

Consider the equations below and complete the following: Before completing any calculations, consider the equation and write down an educated guess as to which type of conic section is represented. Explain briefly how you made your prediction. Complete the square to rearrange each equation into standard form and identify the conic section. Compare the equation in standard form to the original version. Look closely at the coefficients of each term (specifically which terms are positive or negative). Is there anything you notice that is similar between the two equations? How can this help you to identify conic sections that are not in standard form? a. x² + y² + 6x - 4y - 15 = 0 b. 49x² + 196x + 4y² - 40y + 100 = 0 c. x² - y² - 2x - 8=0

High Cholesterol: A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after treatment for each individual, with the following results: (a) Construct a 99.8% confidence interval for the mean reduction in cholesterol level. Let d represent the cholesterol level before treatment minus the cholesterol level after. Use tables to find the critical value and round the answers to at least one decimal place.

Suppose that the price - demand equation and the cost function for the production of table saws are given, respectively, by P = 300 81,000+ 90x where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws. Find the revenue function in terms of x. - 50 and C(x) Y

Strength of concrete: The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows. Can you conclude that the mean strength after three days differs from the mean strength after six days? Let H represent the mean strength after three days and HH₁-H₂. Use the a 0.01 level and the critical value method with the table.

Suppose that the total cost (in dollars) of producing x food processors is given by C(x) = 1,800 + 36x -0.6 x². What is the average cos t (in dollars) of producing the 21st food processor? Round your answer to the nearest whole number.

Use a symmetry test to determine which of the following equations demonstrate θ = symmetry. Select all that apply. Select all that apply:

The activity on Denise Hellings' Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $155.27, and the annual simple interest rate is 21%. (Round your answers to the nearest cent.)

Solve for x. (x + 1)² = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The equation has no real solutions.

Ernesto is considering buying a dishwasher for $600. According to a consumer magazine, he can expect to pay $40 per year for the electricity to run the dishwasher. He created the table below to represent the average cost per year, C(t), of owning the dishwasher, including the original price and the cost of electricity, if he keeps it for tyears. What is the average rate of change for the annual cost of owning the dishwasher between 4 years of ownership and 10 years of ownership?

The unknown triangle ABC has angle A = 44° and sides a = 15 and c = 20. How many solutions are there for triangle ABC? Select the correct answer below: 0 triangles 1 triangle 2 triangles Infinitely many triangles

Consider the following points. (-3,7), (6,0) and (6, 7) Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene

Mia and Vincent are asked to choreograph a dance for the school musical.. Mia can choreograph the dance for the show in 20 hours and Vincent can choreograph the dance by himself in 16 hours. How long would it take to choregraph the dance for the musical if they worked together? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

Given that 3 - 2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = x4 - 9x³ - 9x² + 201x - 520

An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 2 IQ points of the true mean. Assume that o = 14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (Round up to the nearest integer.) The required sample size is Would it be reasonable to sample this number of students? No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly large number.

Use the formula for nPr, to evaluate the following expression. 9P6

Your itinerary contains a grid map of New York, with each unit on the grid representing 0.5 miles. If the Rockefeller Center is located at (2,-3) and Central Park is located at (6,-3), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.

Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 2.68 × 10-6 meters. Write this number in standard notation. (b) The diameter of Jupiter at its equator is approximately 143,000 kilometers. Write this number in scientific notation.

Given the points C(-3,-1) and D(-1,-6), express the vector CD in terms of i and j. Select the correct answer below: - 2i - 5j 2i - 5j -5i +2j 2i + 5j -2i+ 5j 5i-2j

This exercise uses the radioactive decay model. Radium-221 has a half-life of 30 sec. How long will it take for 96% of a sample to decay? (Round our answer to the nearest whole number.)

Use dimensional analysis: Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S.= 0.678 euros, find the cost of the souvenirs in United States dollars. Round to the nearest cent.

Connie and Rashim have to survey 2500 homeowners. Connie can do the job alone in 12 hours. If Rashim helps, they can get the job done in 4 hours. How long would it take Rashim to do the job by himself? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

Consider the following. e5 - 3x = 15 (a) Find the exact solution of the exponential equation in terms of logarithms. (b) Use a calculator to find an approximation to the solution rounded to six decimal places.

Graph the linear equation by finding and plotting its intercepts. 9x - 4y = 36

Solve the given equation or inequality graphically. (a) x²= 6 - 7x (Enter your answers as a comma-separated list.) (b) -x² ≥ 6-7x (Enter your answer using interval notation.)