2D Geometry Questions and Answers

Answer the question based on the data in the table. Hemoglobin Level Less than 25-35 years Above 35 years Total 25 years Less than 9 21 32 76 129 Between 9 and 49 52 Above 11 69 40 Total 139 128 162 429 Select the correct answer. What is the probability that a person who is above 35 years old has a hemoglobin level of 9 or above? A. 0.357 B. 0.313 C. 0.531 D. 0.343 E. 0.432

The probability of a randomly selected employee of a company being male is 60%. The probability of the employee being less than 30 years old is 70%. If the probability of the employee being less than 30 years old given that the employee is a male is 40%, what is the probability that the employee is a male, given that the employee is less than 30 years old? A. 0.34 B. 0.42 C. 0.55 D. 0.69 E. 0.71

A circle is defined by the equation given below. x² + y² - x - 2y - 11/4=0 What are the coordinates for the center of the circle and the length of the radius? A. (1/2, 1), 4 units B. (–½, −1), 2 units C. (-1/2,-1), 4 units D. (1/2, 1), 2 units

Given hexagon JKLMNO - hexagon PQRSTU, LK =15, JO=22, and QR=4, find the scale factor from JKLMNO to PQRSTU. Give your answer in decimal form rounded to the nearest hundredths. Keep in mind, is the figure getting smaller or bigger? Figures getting smaller would have a scale factor less than 1. Figures getting larger would have a scale factor greater than 1.

The general form of the equation of a circle is 7x² + 7y²-28x+42y-35 = 0. The equation of this circle in standard form is________ the centre of the circle is at the point _____and its radius is _____units

The probabilities of a positive response to two government programs from the citizens in eight cities are given in the table. City Positive Response Positive Response for Program 1 for Program 2 Atlanta 77.8% 82.1% Boston 86.4% 86.6% Chicago 65.9% 87.5% Dallas 73.8% 80.9% Houston 69.7% 79.4% Los Angeles 78.4% 88.1% Miami 82.5% 82.6% Newark 81.4% 83.3% Total 68.8% 81.7% What is the chance of a positive response for Program 2 given that the individual is from Los Angeles? A. 68.8% B. 78.4% C. 81.7% D. 88.1% E. insufficient data

Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. We also know that 8% of the yoga students study with Patrick and are female, while 66% of the students study with Carl and are female. What is the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl? A. 0.35 B. 0.56 C. 0.69 D. 0.83

Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female. The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is

A point on the line segment is chosen at random. What is the probability it is between 18 and 27?

Consider circle O. If AE=7, EC=2, and BE=4, what is ED? A. 5 B. 4.5 C. 4 D. 3.5 E. 3

Select the correct answer from the drop-down menu. The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballgame (event B) the same day is 0.61. The probability that Kate and Jane both go to the ballgame on Monday is 0.52. From the given scenario, we can conclude that events A and B are

The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Breaker's? A.0.04 B. 0.05 C. 0.15 D. 0.80

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. With reference to the figure, match the angles and arcs to their measures.

What is the equation of this circle in standard form? A. (x+5,5)²+(y + 4)² = 3.5 B. (x+ 5.5)² + (y + 4)² = 12.25 C. (x-5.5)²+(-4)² = 12.25 D. (x-5.5)² + (y-4)² = 3.5

Select the correct answer from the drop-down menu. A machine needs two of its gears replaced. You find two gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specification sheet says that the chance of gear failure is 5% after 5 years and increases to 8% after 10 years. If the gears on the machine are not linked to each other, the probability that both replacement gears will fail is____

If 21% of males and 15% of females in a given state play the guitar, what is the probability that a randomly selected subject in the state plays the guitar, given that the subject is male? A. 0.15 B. 0.21 C. 0.79 D. 0.85

Suppose you have data that shows that 12% of athletes test positive for steroids. You also know that 11% of athletes test positive for steroids and actually use steroids. What is the probability that an athlete uses steroids, given that he tests positive? A. 0.37 B. 0.43 C. 0.51 D. 0.67 E. 0.92

Here is a right pyramid with a rectangular base: What are the two shapes of cross- sections we could create by slicing the pyramid perpendicular to its base? Choose 2 answers: A Triangle B Rectangle C Trapezoid D Pentagon

Plane X contains point C. Plane Y contains points A and B How many planes exist that pass through points A, B, and C?

Prove that the involute of a circle is a constant and explain its form is it a spiral? a closed curve?

What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10 mm on each side? Round to the nearest square millimeter if necessary. A. 120 mm² B. 360 mm² C. 240 mm² D. 620 mm²

Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 9 feet long and Ariadne's shadow is 6 feet long. If Dixon is 6 feet tall, how tall is Ariadne?

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for π. A≈ 14.28 square inches, P≈ 20.56 inches A ≈33.12 square inches, P≈ 14.28 inches A≈14.28 square inches, P≈ 14.28 inches A≈ 33.12 square inches, P≈ 20.56 inches

Solve each equation with the quadratic formula. 1) 3k² - 7k-20 = 6

In the figure above, the radius of the inscribed circle is 4 inches (in.). What is the perimeter of square CABD? 8π in. 16π in. 16 in. 32 in.

Angle A and angle B are a linear pair. If m∠A =4∠B, find, m∠A and m∠B 72, 18 36, 144 18,72 144, 36

The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first the second. The figures are not drawn to scale. A. 8/3 and 10/5 B. 9/4 and 64/9 C. 9/4 and 10/5 D. 8/3 and 64/9

The complement of an angle is 53°. What is the measure of the angle? 37° 47° 127° 137°

Name the line and plane shown in the diagram. QP and plane SR line P and plane PQS PQ and plane PQS PQ and plane SP

Supplementary angles are two angles whose measures have a sum of _____. Complementary angles are two angles whose measures have a sum of_____. 180; 360 90; 180 180; 90 90; 45

Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square. 10 blocks 14 blocks 4 blocks The distance would be the same.

Find the area of a rectangle with base of 2 yd and a height of 5 ft. 10 yd2 30 ft2 30 yd2 10 ft2

Are points C, G, and H collinear or noncollinear? collinear impossible to tell noncollinear

Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by 39 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path? 168 ft 120 ft 84 ft 156 ft

Are M, N, and O collinear? If so, name the line on which they lie. No, the three points are not collinear. Yes, they lie on the line NP. Yes, they lie on the line MO. Yes, they lie on the line MP

Given the triangle find the length of side x using the Law of Sines. Round your final answer to 4 decimal places.

Find a parametrization for the following paths (a) ellipse {z € C: |z-1| + |z+1| = 4}, oriented counter-clockwise. (b) the rectangle with vertices +1+2i, oriented counter-clockwise

Given a circle of radius 13 m, find the length of the arc subtended by a central angle of 210°. Round decimals to the nearest hundredth.

What are the coordinates of point Bon AC such that AB is 3 times as long as BC?

Find the area of a parallelogram with corner points at (1,4) (4,6) (8,6) and (5.4)

3. In ΔABC, AO intersects BC at P. If |AP| = 5, |BP| = 2, and |CP| = 3, then what is b? (As usual, O is the circumcenter of ΔABC and b = |AC|.)

A moving sidewalk in an airport moves people between gates. It takes Jason's 9-year-old daughter Josie 33 sec to travel 165 ft walking with the sidewalk. It takes her 7 sec to walk 21 ft against the moving sidewalk (in the opposite direction). Find the speed of the sidewalk and find Josie's speed walking on non-moving ground. The sidewalk moves at ft/sec.

Use trigonometry and other methods to calculate and estimate the area of a region. 1) Charlie the goat is tied with a 10 meter rope to the corner of a non-rectangular building. The sides closest to him have lengths 7 meters and 12 meters. Choose a building shape and determine the area of grass that Charlie can eat. (triangle? Parallelogram? Which one is better) 2) Choose another building shape to investigate - be creative! It is unlikely that you will be able to find an exact solution - you are being asked to estimate reasonably and find a solution that makes sense.

Find the value of x in each of the following exercises:

A regular pentagon (a polygon with 5 equal sides) is inscribed in a circle of radius 12.2 cm. Find the perimeter of the pentagon.

What is the most precise name for quadrilateral ABCD with vertices A(-5,2), B(-3, 4), C(5, 4), and D(3, 2)? A. kite B. parallelogram C. rhombus D. rectangle

Two sides of a triangle for the third side measure 4 and 9. What are the possible values

Find the radius of a circle with a circumference of 287 m.

A car traveling on a 1.6° uphill grade has a grade resistance of 124 lb. Determine the weight of the car to the nearest hundred pounds. The weight of the car is approximately lb.

Solve the right triangle using the given information. a=77.9 yd, b=42.1 yd c= (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.) A=' (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.) B=' (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.)