Area Questions and Answers

Marquez owns a company that produces metal fire pits and sells them for 250 00 The company s weekly profit P x can be modeled by the function P x 0 5x 40x 300 where x is the number of 1 50 price increases for each fire pit Use the graph below to answer the question profit 1000 800 600 400 200 0 450 00 10 310 00 20 30 40 50 60 Approximately what amount should the company sell each fire pit for to maximize profit 2 points O 700 00 70 80 number of price increases

What is the volume of this figure 11 cm 5 cm 2 cm 2 cm 6 cm 4 cm cubic centimeters

Nation Australia Austria Brazil Germany India Number of States in 14 Federal Nations States Nation 6 Micronesia Nigeria Malaysia Mexico 9 26 16 29 13 31 Saint Kitts and Nevis South Sudan Sudan United States Venezuela States 4 36 2 10 17 50 23 The table above lists the number of states in each of the 14 federal nations that have subdivisions called states According to the table what is the mean number of states of these nations Round your answer to the nearest tenth

3 Given ASTU AS T U ST 10 cm S T 15 cm the perimeter of ASTU is 30 cm and the area of AS T U is 225 cm What is the area of ASTU G ed bluo Tass a 33 75 cm b 45 cm c 100 cm d 150 cm pors LOV TIS 01 JOSY 202 015161W ute elible gables sest

object Assume objects are perpendicular if they appear so

Conditional Probability Given P A 0 6 P B 0 4 P A and B 0 1 Determine P A B 0 10 0 25 0 50 0 66 P Q P A P B A

Qu Independent Events Given that events A and B are independent P A 0 80 and P A and B 0 24 what is 0 104 0 192 0 56 0 30

Question 3 In A RST what is x A B UD 3 it is not a right triangle because7 5 8 C 28 feet 10 feet 161 feet D 17 feet R 18 ft 6 ft K X 15 ft Note Figure is not drawn to scale

What is the value of a in units A 12 B 12 8 C 15 D 20 10

ansformations of the absolute valu h x x 31 2 transformations are needed in orde

What is the value of x in the following parallelogram 1 point What is mZV K Type your answer Y 12x 22 V 10x 27 7x 2 M 2x 29 L W

6 In the diagram below EF 3 5 Determine the length of DE and DF D 30 90 E

Product Type Vanilla Chocolate Total A 0 250 B 0 435 C 0 526 D 0 667 Frozen Yogurt 26 32 Flavor The incomplete table above shows the sales for a particular sweet shop by product and flavor There were 4 times as many vanilla ice creams sold as vanilla frozen yogurts and there were 6 times as many chocolate ice creams sold as chocolate frozen yogurts If there were a total of 32 frozen yogurts and 152 ice creams sold and no flavors other than vanilla and chocolate were available which of the following is closest to the probability that a randomly selected ice cream sold was vanilla Ice Cream South Sudan Sudan 152

2 A solid has a circle of radius 2 as its base All sections of the solid perpendicular to a given diameter of the base are squares as shown in the figure below 31 Find the volume of the solid TO

Matthew constructs a fence around a patch of grass in his backyard The patch has a width that is 8 feet more than 4 times the length What is the perimeter of the fence if Matthew s patch of grass has an area of 5 472 square feet A 364 feet B 376 feet C 396 feet D 400 feet

A coffee shop is filling coffee cups from an industrial urn that contains 64 gallons of coffee At most how many 16 ounce cups of coffee can be filled from the urn 1 gallon 128 ounces A 4 B 512 C 1 024 D 2 048 44 G

4 v 17 2 5t A constantly accelerating particle is moving in a straight line After t seconds the particle is moving at a velocity of v in meters per second as shown in the equation above What is t when v is 67 A 184 5 D B 67 C 33 6 D 20

2 Determine the length of and 5 3 S 60 t 4 In the given diagram determine the value of and 12 V 30 W 3 Determine the length of and A 90 60 5 In the diagram below Determine the area of C 9 X 60 B

Find the intercepts of the following equation 5x 2 4y 20 Select the correct choice below and if necessary fil OA The intercept s is are

Find the value of x so that AABC AWRY x 3 B Type your answer 2x 2 timber W 1 6 m fence 3 x 3 R 3 1 point A piece of timber leaning against a wall just touches the top of a fence as shown Find how f up the wall the timber reaches Round to the nearest tenth wall 18 Y

A right triangle is removed from a rectangle to create the shaded region shown below Find the area of the shaded region Be sure to include the correct unit in your answer If necessary refer to the list of geometry formulas 6 yd 8 yd 10 yd 12 yd alo yd 08 yd yd Start over 3

A textile manufacture is producing shirts and pants They make both in red and blue Let B represent the set of all red clothing items produced by the manufacturer and let C represent the set of all pants produced by the manufacturer If all of the clothing items below are produced by the manufacturer which could be set B C in the Blue Shirt V T Red Pants Red Shirt

1 point A Find the parametric equations for the line through the point P 4 2 3 that is perpendicular to the plane 5x 2y 4z 1 Use t as your variable t 0 should correspond to P and the velocity vector of the line should be the same as the standard normal vector of the plane X 5 y 2 Z 4 B At what point Q does this line intersect the yz plane Q

Given the graph of y 3sinx choose where the graph crosses the x axis Select one or more a None of these b 3T EN EN C d Tt

16 a In how many ways could you choose two fives one after the other from a deck of cards b In how many ways could you choose a red five and a spade one after the other c In how many ways could you choose a red five or a spade d In how many ways could you choose a red five or a heart e Explain which counting principles you could apply in parts a to d

Exponential Growth Decay Word Problems 6 You have inherited land that was purchased for 30 000 in 1960 The value of the land increased by approximately 5 per year What is the approximate value of the land in the year 2011 7 During normal breathing about 12 of the air in the lungs is replaced after one breath Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL How much of the original air is present after 240 breaths 8 An adult takes 400 mg of ibuprofen Each hour the amount of ibuprofen in the person s system decreases by about 29 How much ibuprofen is left after 6 hours 9 You deposit 1600 in a bank account Find the balance after 3 years for each of the following situations a The account pays 2 5 annual interest compounded monthly b The account pays 1 7 5 annual interest compounded quarterly c The account pays 4 annual interest compounded yearly

Farmer Ed has 2 000 meters of fencing and wants to enclose a rectangular plot that borders on a river If Farmer Ed does not fence the side along the river what is the largest area that can be enclosed The largest area that can be enclosed is 2 000 2x square meters

Graph the solution set of the inequality where 2 4x 1 4 2x 2

Find the area of the shaded region 10 units

6 Consider again the integral 1 1 1 3 3 4 x y dy dx from Question 5 You could evaluate I by direct calculation but instead you will try two different ways 6a Interpret I as a volume of a solid TCR Define the solid T using set builder notation and includ sketches in R to support your argument Compute the volume using geometry of known solids in R Do not evaluate any integrals I

Sketch the graph of f x 3 x 104 gatal 10

A rectangle is removed from a right triangle to create the shaded region shown below Find the area of the shaded region Be sur o include the correct unit in your answer f necessary refer to the list of geometry formulas 8 cm 4 cm 2 cm 10 cm 0 8 08 cm X cm cm

Clearly and neatly show all work for each problem For all calculations involving you can use the estimation of 3 14 Where needed round all final answers to one decimal place 1 An 8 1 inch tall cylindrical can has a diameter of 2 7 inches Three spherical balls are put inside each with a circumferences of 7 85 inches Find the volume of the region between the can and the balls

2x 5y 25 nx 3y p In the given system of equations n and p are constants The system has infinitely many solutions What is the value of np

Find the center of mass of the following plane region with variable density Describe the distribution of mass in the region The upper half y20 of the plate bounded by the ellipse x 36y 36 with p x y 1 y

Quadrilateral ABCD has vertices at A 2 6 B 0 0 C 6 0 and D 8 6

equation of the circle oin standard form 0 3 2 3

3 6 points Objective Solve problems involving area of a sector A 6 B C The measure of central ZABC is 90 degrees What is the area of the shaded sector 367 units 67 units 97 units 187 units

S On a windy morning a hot air balloon starts ascending and flying away from the top of a hill The altitude A in feet of the balloon hours after starting its ascent from the hill can be modeled by the function A z 162 64z 80 Part A Does the parabola open up or down Part B Identify the value of the z and y intercepts and explain their meaning in context z intercept 0 3 intercept 0 Part C When the balloon reach its maximum altitude at what height is the maximum altitude obtained feet

Consider a polynomial function whose equation is f x x x 2 x 1 a Part A 22 What degree is the function Part B Classify the degree of the function as even or odd Part C SHOW HINT b Describe the end behavior A f x 00 Asx o B f x o As x c f x As x

28 Factor the following expression 2 152 56

A sector has an area of 18 square centimeters and is defined by a circle with a radius of 4 cm determine the approximate central angle for the sector to the nearest degree Figure may not be drawn to scale 123 129 157 145 G B 18 cm x 4 cm C

O is the center of the regular nonagon below Find its perimeter Round to the nearest tenth if necessary 5 4 0

2 1 point Line v is a transversal 70 80 110 100 True Statements No Answers Chosen Possible answers Line X is parallel to Line Z Line X is parallel to Line Y Line Wis parallel to Line Y Line Wis parallel to Li Line Wis parallel to Li

What value for a makes ASTW AXYZ 3x 1 T 3x 1 Type your answer 2x 1 W x 5 Z 4x 3 4x 5 X 1 point Deshaun wants to make a triangular garden Which of the following are possible dimension 8ft by 12ft by 20ft 6ft by 6ft by 12ft 4ft by 5ft by 10ft 6ft by 8ft by 10ft

8 Why are these triangles similar P 30 20 SAS N SSS AA 1 point Why are these triangles similar M Triangles are not similar 8 SAS SSS J 30 M 130 B Triangles are not similar C 4 B

5 1 point Why are these triangles similar 3 6 AA 9 O O O O SAS AA Triangles are not similar OOC SSS 1 point Why are these triangles similar PO SAS AA SSS

Angle JKL is a straight angle The measure of angle JKM is 150 The measure of angle MKL is x What is the value of x 150 M to

23 Part A 0 A function g z is obtained by shifting the graph of the function z 2 three units left stretching the graph vertically by a factor of two reflecting that result over the z axis and then translating the graph up four units Determine the equation of the function Choose the suitable option 2 z 3 4 b None of the above 2 z 3 4 2 z 3 4 Part B The function g is now transformed 2 units up to obtain another function The equation of the function a is

14 Question 14 30 V 0 Find the product 5 7 4 31