Coordinate system Questions and Answers

Which of the following equations describes a circle with radius 2, centered at the point (1, 0)? Select one: (x + 1)² + y² = 4 x² + (y-1)² = 4 (x-1)² + y² = 4 (x-1)² + y² = 2

The weekly salaries (in dollars) for 8 employees of a small business are given below (Note that these are already ordered from least to greatest.) 608, 755, 781, 783, 784, 833, 883, 917 Suppose that the $608 salary changes to $832. Answer the following. (a) what happens to the mean? (b) What happens to the median?

Which equation represents the line that passes through the point (9, 4) and is perpendicular to the graph of 5x +y = 30? 5x-y=41 x-5y=-11 5x+y=49 x+5y=29

Use the fundamental Counting Principal to determine the total number of outcomes: You choose a letter from the word ZEBRA and then roll a standard die.

Which equation is perpendicular to 5x- 10y = 6 and passes through (2, 1) y= 1/2x +5 y = 1/2x -5 y=-2x+5 y = -2x - 5

What piece of information from passage 1 conflicts with the information from passage 2? A. The oceans of the world have absorbed large amounts of carbon dioxide. B. Ocean acidification is the result of carbon dioxide in the ocean waters. C. Scientists are worried that ocean acidification will affect fisheries negatively. D. The shells of many marine animals are getting thin due to ocean acidification.

Rectangular Prism 30 ft 24 ft 18 ft 27. Surface area A. 2560ft² B. 3384ft² C. 3384ft³ D.12,960 ft³

1. For the planimeter construction shown in the figure A, show that A = cs if pole is outside the area, and A=cs + II(R² + a² + 2ac) if pole is inside the area.

A bag contains 5 green, 4 red, and 3 orange marbles. Find the probability of picking 3 red marbles if each marble is returned to the bag before the next marble is picked. 1/27 1/1320 1/55 1/1728

Select the correct equation of the circle for the center and radius given. Center: (-5, 16) Radius: 2 A) (x-3)² + (+17)² = 16 B) (x-5)² + (y+16)² = C) (x+16)²+(y + 5)² = 4 D) (x+5)²+(-16)² = 4

1. Compute 15 x 182 using multiple methods and explain (6 points): a. Compute 15 x 182 with the "traditional multiplication model." Show work. b. Compute 15 x 182 with an alternate method, such as the expanded notation multiplication work. c. Explain how your two solutions show the same process involving place value.

Graph the function f(x) = 8x by moving the key points. You can only graph integer points. For example you cannot plot the point (-1,-1/4).

Determine the Frenet-Serret apparatus for the non-unit speed curve B(t) =(t, 1+t-¹,t¹t).

Convert the given rectangular coordinates into polar coordinates. (-7, 4) = ([? ], [])

Convert the given polar coordinates into rectangular coordinates. (-4,π/3) =

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. cot s=8.2042 A. 0.1213 B. 1.5911 C. 1.1619 D. 3.2629

The figure below shows contours of f(x, y) = 140ex - 100y². Find the values of f on the contours. They are equally spaced multiples of 10. Curve A: Curve B: Curve C: Curve D:

find the solution to the given system by graphing.use your own graph. y=1/3x+2 -3x+y=-3

(a) The graph of y=f(x) is shown. Draw the graph of y=2f(x). (b) The graph of y=g (x) is shown. Draw the graph of y=g (2x).

Indicate the parametric Cartesian equations of the equation circumference: x²+y²-2x+2y-7=0

Write the first six terms of the arithmetic sequence with the given property. a = 2; 5th term is 14.

1. Consider a functions g(x) = sinx and f(x) = sinx and f(x) = 5sin((x + 1)) + 16, for 0 ≤ x ≤ 10 List the four transformations that map g(x) to f(x)

Let P be the point with the spherical coordinates (p, 0, 0) =(5, π/6,π/2). The cylindrical coordinates of P are (r, θ, z)= The Cartesian coordinates of P are (x, y, z) =

Consider the trigonometric function y = 3 sin(2x + 1) - 5. Use your understanding of transformations to explain why this function contains no root. Please include a sketch in your explanation.

Write the expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. sin 5° cos 25° + cos 5° sin 25° Write the expression as the sine, cosine, or tangent of an angle. sin 5° cos 25° + cos 5° sin 25° = (Type a trigonometric expression.) Find the exact value of the expression. sin 5° cos 25° + cos 5° sin 25° = (Type an exact answer in simplified form, using radicals as needed. Rationalize the denominator if necessary.)

The length of a rectangle is three times the width. The perimeter is 49 units. Find the length.

Graph the system of inequalities. 3x + y < 2 6x + 2y > 20 Choose the graph of the solution of the system.

Graph and solve the following system. (y =4x - 9 y = -3x - 2

Match the system of equations with the type of graph. 2x -y = 3 and x + 2y = 4 x + 2y = 5 and 3x + 6y = 15 3x + y = -2 and 6x + 2y = 10

Let S be a differentiable surface with parameterization σ: R² →>> R³ (u, v)o(u, v) = (u, v, u² - v²). Find the normal, geodesic, Gaussian, mean, and principal curvatures.

How much money does an employee working for a salary of $40,000 per year get paid each week? A. $40,000 per week B. $3,333 per week C. $769 per week D. $1,538 per week

At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1-4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $20. If the coin shows heads and the die shows an even number, then you win $7. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. (c) Is this game fair? Yes No

Solve and graph the following inequality: -8x ≥ 16

A software entertainment company recently ran a holiday sale on its popular software program, Using data collected from the sale, it is possible to estimate the demand corresponding to various discounts in the price of the software Assuming that the onginal price was $38, the demand for the software can be estimated by the function q 3,371,000p 2789 where p is the price and g is the demand. Calculate and interpret the elasticity of demand What formula should be used to compute the elasticity of demand E, it g is demand at a price p? A. E= p/dp. q/dq B. E=-p/q , dq/dp C. E= p.dq D. E= q.dp

. We describe locations on the Earth using latitude and longitude 0. Using these coordinates, we describe a location A on the Earth with A = (A,A). Las Vegas, for example, has coordinates (36° N, 115° W), or (36°, -115°). Prove the distance formula cos(AB/R) = sin A sin o+cos A COSOB COS(OA - 0B), where R is the radius of the Earth. Hint: Look at AABN where N is the North pole.

Trader Joe's sold 6,425 bags of tortilla chips last month. If 5,111 of these bags were fat free, find the percent that were fat free. Round your answer to the nearest percent. % of the bags of tortilla chips sold at Trader Joe's last month where fat free.

A population numbers 13,000 organisms initially and decreases by 6% each year. Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.

Evaluating Exponential Functions In 2014 Staci invested $13,500 in a savings account for her newborn son. The account pays 2.7% interest each year. Determine the accrued value of the account in the year 2032, when her son will go to college. Round your answer the nearest cent. In the year 2032, the accrued value will be $

Round the number to 3 significant figures. 1.45| 93 Step 2: Now we need to decide if we round up or down. What is the answer rounded to three significant figures?

The population of a town increased from 3,800 people in the year 2008 to 4,750 people in 2011. Find the absolute and relative (percent) increase. Absolute increase: people Relative increase: % Round to the nearest tenth of a percent.

A company wants to decrease their energy bill by 10%. If their electric bill is currently $2,000 a month, what will their bill be if they are successful? Round your answer to the nearest dollar. $ If the company's electric bill for next month is $1840, should that be considered a success? Yes, that is a success O No, that is not a success

78% of the questions on a student's test were correct. There were 50 questions. How many of the questions were correct? A student who scored 78% on the test answered __ questions correctly.

Find the equation of the comic from the data a) Reduce the equation to its ordinary form using rotation and translation of axes b) Draw the locus Focus f(3,3) - Directive: x+3y =3 - Eccentricity e=2

Amy paid $165 for an item that was originally priced at $340. What percent of the original price did Amy pay? Round your answer to the nearest tenth of a percent. Amy paid __ % of the original price

Given the equation y =13(1.9), find each of the following. Round answers to the nearest hundredth as needed. x =-3, y = x = = I= -2, y = x = = 1, y = - x = 0, y = x = 1, y = x = 2, y = x = 3, y =

Identify which sequence of transformations could map pentagon ABCDE onto pentagon A"B"C"D"E", as shown below. (1) dilation followed by a rotation (2) translation followed by a rotation. (3) line reflection followed by a translation (4) line reflection followed by a line reflection

The function shown below is f(x). We are interested in the transformed function g(x) = -2f((x - 2)). a) Describe all the transformations g(x) has made to f(x) (shifts, stretches, etc). b) NEATLY sketch the transformed function g(z) and upload your graph as a PDF document below. You may use graph paper if you want. Be sure to label your vertical and horizontal scales so that I can tell how big your function is.

Imagine a circus tent in which the roof of the tent is shaped like a right circular cone, with the tip of the cone being the highest and center-most point of the tent. (a) The outside wall of the tent is 8 feet high. Six feet toward the center pole from the outside wall, the tent is 11 feet high. The center pole of the tent is 50 feet from the outside wall. Draw and label a picture which matches this scenario. (b) What is the slope of the line that follows the roof of the circus tent? (c) Use the slope to find the height of the tent at its center pole. (d) A rope is attached to the roof of the tent at the top of the outside wall and anchors the tent to a stake in the ground. The rope follows the line of the tent roof. How far away from the tent wall is the anchoring stake?

Simple Interest Application Simple interest is given by the formula A = P + Prt. Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Noah is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 20 years. Determine what Noah needs to deposit now in order to have a balance of $50,000 in his savings account after 20 years. Noah will have to invest $ now in order to have a balance of $50,000 in his savings account after 20 years. Round your answer to the nearest dollar.

You started this year with $384 saved and you continue to save an additional $22 per month. Write an equation to model this situation (use m for months and s for savings). Equation: