Math Questions

(a) The diameter of Uranus at its equator is approximately 5.11 x 10 kilometers. Write this number in standard notation. (b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.0000835 meters. Write this number in scientific notation.

The line y = x makes a 45° angle with the y-axis. What angle does the line y = x + 5 make with the y-axis? What angle would the line y = x + 5 make with any vertical line? Justify your answer.

(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 7.68 x 10 -4 meters. Write this number in standard notation. (b) The diameter of Mars at its equator is approximately 6790 kilometers. Write this number in scientific notation.

Graph the solution to the following system of inequalities. 2x+5y>-20 -2x+7y<-21 Then give the coordinates of one point in the solution set.

Sharon works as a sales associate and earns all of her salary in commission. a) Last month, she had sales that totaled $24,000. However, when she received her paycheck, she saw that she had received $33,000 in commission. Why must this be an error? b) Human Resources caught the error. Sharon was supposed to receive $3300 in commission. What is Sharon's commission rate? c) The next month Sharon received $2200 in commission. What was the amount of her sales that month?

Using rectangles each of whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of the following function, using first two and then four rectangles. f(x)= 5/x between x = 2 and x = 6 Using two rectangles, the estimate for the area under the curve is (Round to three decimal places as needed.)

Bubba is saving up money for a down payment on a condominium. He currently has $2535, but knows he can get a loan at a lower interest rate if he can put down $3303. If he invests the $2535 in an account that earns 4.2 % annually, compounded quarterly, how long will it take Bubba to accumulate the $33037 Round your answer to two decimal places. If necessary.

Graph the system below and write its solution. 3x+y=-3 y=-1/2x+2

(a) The signal from a certain satellite takes approximately 0.0078 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of South America is approximately 6.89 x 106 square miles. Write this number in standard notation.

Solve the inequality: 2x +5 <8 The answer as an inequality: The answer in interval notation: The answer on a number line: 5

A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population grow to P(t) = (976)3 t4. where t represents the number of years from the time of introduction. Step 2 of 2: How long will it take for the population to reach 26352 deer, according to this model?

A company sells x ribbon winders per year at $p per ribbon winder. The demand function for ribbon winders is given by p = 250 - 0.04x. Determine the elasticity of demand when the price is $75 apiece. Round your answer to the nearest hundredth. 0.21 0.22 0.23 0.24

A company finds the demand x, in thousands, for their kites to be x = 400 - p² at a price of p dollars. Find the elasticity of demand when the price is $4. Write your answer to two decimal places and start with 0 if your answer is between 1 and 0 or 1 and 0.

Aurelia needs to drive 280 miles. If she drives at a rate of 65 miles per hour, to the nearest tenth of an hour, how long will the trip take?

Graph the system below and write its solution. 6x-2y=-6 y=3x+3

Chester hopes to earn $1500 in interest in 3.3 years time from $15,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot. A. 40 feet B. 80 feet C. 117 feet D. 160 feet

The half-life of gold-194 is approximately 1.6 days. How much of a 15 gram sample of gold-194 would remain after 4 days? Round to three decimal places.

Billy said that the depreciation value S(in dollars) of his upgraded Rav4 after t years can be modeled by S(t) = 28000 (0.8)t. What is the rate of depreciation after 1 year? Write your answer to two decimal places. Billy said that the depreciation value S(in dollars) of his upgraded Rav4 after t years can be modeled by S(t) = 28000 (0.8)t. What is the rate of depreciation after 5 years? Write your answer to two decimal places.

5y3 = -2(5-x) Step 2 of 2: Find the equation of the line which passes through the point (-10,- 11) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.

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.