Geometry B - Final Exam

Point P is a point on a circle with center point O. Point P is also a point on PQ↔, which is tangent to circle O. Which of the following describes the relationship between radius OP and tangent PQ↔?

OP¯ and PQ↔ are always perpendicular.

The probability that event A occurs is 12%. The probability that event B occurs is 15%. The probability that both events occur is 3%. What are the conditional probabilities of the two events? Are A and B independent events?

P(A I B) = 80% (wrong XXX) P(B I A) = 25 % (correct) The probability of A given B IS NOT THE SAME as the probability of A, so A and B ARE NOT independent events. (correct/ correct) ALL WRONG 0/1, NO CREDIT FOR ANSWERS

Events A and B are independent. The probability of event A occurring is 0.64. the probability of events A and B occurring together is 0.24. What is the probability of event B?

P(B)= 0.375

A survey was given to 90 high school students. They were asked if they preferred fiction or non-fiction and if they preferred indoor or outdoor activities. Partial survey results are shown in the table. What percent of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction?

P(outdoor | non−fiction)= 28%

What is the equation of a circle with a center at (4,−9) and a radius of 5?

PART A: (x−4)2+(y+9)2=25 (correct answer part a) PART B: 5 units XXX wrong part b

The table shows the dimensions and the numbers of blades of grass on four rectangular pieces of sod. Drag the pieces of sod in order from greatest to least grass density, with greatest at the top and least at the bottom.

PIECE D PIECE C PIECE A PIECE B

Today there is a 90% chance of rain, a 30% chance of thunderstorms, and a 25% chance of rain and thunderstorms together. Are the two events "rain today" and "thunderstorms today" independent events?

Since (0.9) x (0.3) is GREATER THAN 0.25, then the two events ARE NOT independent.

Use the diagram of Circle O to help you answer this question. How can the area of a sector of a circle be calculated?

The area of a circle is πr2 where r is the length of the radius. Thus, one could take the measure of the central angle in degrees and *DIVIDE THAT BY *360, then *MULTIPLY THAT RESULT BY πr2

A circle is separated into eight sectors of equal area. These eight sectors are arranged to form a shape similar to a parallelogram. The area of the circle (πr2) is equal to the area of the parallelogram (bh).

The height of the parallelogram is equal to the *RADIUS of the circle. The base of the parallelogram is equal to *HALF OF THE CIRCUMFERENCE of the circle. Therefore, the area of the circle (πr2) is equal to the *RADIUS MULTIPLIED BY HALF OF THE CURCUMFERENCE, and the circumference of the circle is equal to * 2 TIMES PI TIMES THE RADIUS.

A 30° central angle in a circle is equivalent to π/6 radians. Drag a tile to each box to correctly complete the sentence.

The length of the arc intercepted by this central angle is π/6 times the length of the RADIUS

A random sample of 500 women and 500 men who earned degrees in science and engineering (S&E) were asked if they work in an S&E occupation. The results of the survey are shown. A person from the survey is randomly selected. What is the probability of each event below? Drag tiles to the empty boxes to create your answers.

The probability that a randomly selected person works in an S&E occupation is * 245/1000 The probability that a randomly selected person is a woman and works in an S&E occupation is * 76/1000 The probability that a randomly selected person is a woman or works in an S&E occupation is * 669/1000

Line A passes through the points (−3, 2) and (−23, 54). Line B is parallel to line A and passes through the point (−8, 0). What is the equation of line B?

y = - 2.6 x -20.8

What is the equation of the line that passes through the point (1,3) and is perpendicular to the line 2x+3y=15?

y = 3/2 x + 3/2

Circle O is shown with points A, B, C, and D on Circle O If x=50, what is the value of y and the angle measurement of ∠AOB?

y= 50 m<AOB= 100 degrees

Suppose G={−5,−3,0,3,5} and J ={0,1,3,5,7} Which set represents G∩J?

{0,3,5}

GOOD LUCK (92,86%)

GOOD LUCK (26 out of 28)

There are approximately 33,600 species of fish in the world. About 32,928 species of fish come from the world's three largest oceans and of these, 23,520 species of fish come from the Pacific Ocean. What is the probability of selecting a species of fish that comes from the Pacific Ocean given that a species of fish is selected from those coming from the world's three largest oceans?

23,530/32,928

What is the area, in square units, of DEF with D (5,-1), E (1,-4), and F(-5,4) ?

25 SQUARE UNITS

The Great Pyramid of Giza has a square base. The length of each side of the base is approximately 230 meters. The height of the pyramid is approximately 147 meters. Using these dimensions, what is the volume, in cubic meters, of the pyramid? Enter a number in the box.

2592100

Point C partitions AB into two parts so that the ratio of the length of AC to the length of CB is 1:5. What are the coordinates of point C?

( -1 , -4 )

A spinner has 10 sections numbered 1 to 10. Consider the events in the table. Which pairs of events are disjoint and cannot occur at the same time? Select all that apply.

* EVENTS B and C * EVENTS A and C * EVENTS A and D

What two-dimensional cross-sections could be obtained from a right rectangular prism?

* TRIANGLE * RECTANGLE * PENTAGON * HEXAGON

What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

1.297πr3

A sandcastle can be modeled with four 6-inch-tall square prisms, one on top of the other, as shown in the figure. The base of the bottom prism has a side length of 30 inches, and the base of each of the other three prisms has a side length 7 inches less than the side length of the base of the prism below it. What is the volume of the sandcastle?

10,596 CUBIC INCHES

What is the perimeter, in units, of ^ ABC with A (-1,-6), B (7,-6), C (3,-3)?

18 UNITS

Students from Texas, New York, Washington, Florida, and Utah identified their areas of concentration at various universities. The results are listed in the table. One of these students is selected at random. What is the probability that the selected student is from Washington under the condition that the student studies history?

5/33

Consider the circle centered at point D? Angle ADC measures 108 degrees. What is the measure of angle ABC?

54

A rectangle is placed on the coordinate grid such that one side is on the x-axis and one side is on the y-axis. What 3-dimensional shape is formed by this rectangle rotating around the y-axis?

CYLINDER