please answer the following questions
26.If a pebble is dropped into a pond in the sape of an ellipse at the coation of one cofuse the waves will converge at the location of the other focus. If the pong had a major axis of 20 feet and a minor axis of 16 feet how far apart are the foci?
12 feet
24feet
36 feet
6 feet
27. What are the foci of the hyperbola with equation 16y^2 - 9x^2 = 144
(0,±25)
(±5,0)
(±25,0)
(0,±5)
28. Find an equation that models a hyperbolic lens with a =12 inches and foci that are 26 inches apart. Assume that the center of a hyperbola is the origin and the transverse axis is vertical.
x62/144 - y^2/169 = 1
y^2/144 - x^2/25 = 1
x^2/144 - y^2/676 = 1
y^2/169 - x^2/25 = 1
29. There are 12 students in a social studies class. 3 students will be selected to present their term project today. In how many different orders can three students be selected?
1,320
220
504
36
30. What is the theoretical probability of rolling a sum of 6 on one roll of two standard number cubes?
1/9
5/36
1/12
1/6
31. Garrett throws a dart at a circular dartboard. The dart board has a radius of 16 inches and the bulls eye in the center of the dartboard has a radius of 6 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull's eye.
37.5%
26.7%
7.1%
14.1%
32. You roll a standard, six-sided number cube. What is the probability of rolling a prime number or number greater than 3?
2/3
5/6
1
1/3
26. 24 feet
27. (±5,0)
28. y^2/169 - x^2/144 = 1
29. 220
30. 1/9
31. 7.1%
32. 2/3
33. The table shows the results of survey of college students. Find the probability that a student's first class of the day is humanities class, given the student is female.
Male Female
Humanaties 70 80
Science 50 80
other 60 70
0.533
0.615
0.348
0.538
34. The test scores for a math class are shown below.
81, 84, 82, 93, 81, 85, 95, 89, 86, 94
What are the mean, median, and mode of the data set.
35. The test scores for a math class are shown below.
81, 84, 82, 93, 81, 85, 95, 89, 86, 94
What is the standard deviation of the data set? Round your answer to the nearest tenth
4.9
5.5
5.3
5.1
36. Amanda surveyed 20 juniors and seniors at Delmar High school to find the number of hours per week they spend working at part-time jobs. Her results are shown below.
Juniors- 20, 10, 20, 10, 15, 0, 0, 10, 20, 15
Seniors 20, 20, 10, 20, 0, 0, 0, 10, 0, 10
Which statement about the data is true.
A. The range of hours worked is the same or juniors and seniors
B. The mean, median, and mode for the juniors surveyed fall within a 3-hours range
C. The mean number of hours worked by the seniors surveyed is 12
D. The mean number of hours worked is the same for juniors and seniors.
37. Stillwater juniors High divides students into teams taught by a group of teachers. The table shows the number of students in each team.
The principal uses a computer to randomly select the name of the student from all the students in the school. With the computer program, it is possible to draw the name of the same student twice. If the principle selects the name of a student from the Acers on the first try what is the probability she draw the name of a student from the Acers on the second try?
Team Number Of Students
Acers 78
blazers 80
outbacks 83
Quasars 77
Voyagers 88
total 400
1/78
38/399
19/100
39/200
33. 0.615
34. Mean = 87.1, Median = 85.5, Mode = 81
35. 5.3
36. D. The mean number of hours worked is the same for juniors and seniors.
37. 77/400 or 0.1925
37. Stillwater juniors High divides students into teams taught by a group of teachers. The table shows the number of students in each team.
The principal uses a computer to randomly select the name of the student from all the students in the school. With the computer program, it is possible to draw the name of the same student twice. If the principle selects the name of a student from the Acers on the first try what is the probability she draw the name of a student from the Acers on the second try?
Team Number Of Students
Acers 78
blazers 80
outbacks 83
Quasars 77
Voyagers 88
total 400
1/78
38/399
19/100
39/200
The correct answer is 1/77. When a student from the Acers team is selected on the first try, there are 77 students left in the team out of 399 total students remaining. Therefore, the probability of drawing another student from the Acers team on the second try is 1/77.
that's incorrect it has to be one of the choices given
In that case, the closest answer is 1/78, although it is not exact. If the principle selects a student from the Acers team on the first try, there are 78 students in that team out of 400 total students. If the same student is allowed to be selected again, there are still 78 students in the Acers team, but now there are 399 total students to choose from. Therefore, the probability of drawing the same student from the Acers team on the second try is 1/78.
Which cosine Function has a maximum of 0.5, a minimum of -0.5 and a peiod of 2π/3?
A y= cos 2∅/3
B y=2 cos 3∅
C y=2 cos ∅/3
D y=0.5 cos 3∅
The correct answer is C.
To verify, we can use the amplitude formula for cosine functions:
Amplitude = (maximum - minimum)/2
Plugging in the given values, we have:
Amplitude = (0.5 - (-0.5))/2 = 1
The general form of a cosine function with amplitude 1 and period 2π/3 is:
y = A cos (2π/3)(x - h) + k
where A is the amplitude, h is the horizontal shift, and k is the vertical shift.
To get a maximum of 0.5 and a minimum of -0.5, we need to set k = 0.5 and h = π/3 or -π/3 (so that the maximum and minimum happen at x = 0).
Thus, we have:
y = cos (2π/3)(x - π/3)
or
y = cos (2π/3)(x + π/3)
Both equations are equivalent and correspond to the answer choice C, y = 2 cos ∅/3.
Sure! I'll answer each question and also explain how to arrive at the answer.
26. The distance between the foci of an ellipse can be found using the formula c = √(a^2 - b^2), where a is the major axis and b is the minor axis. In this case, a = 20 ft and b = 16 ft. Plugging these values into the formula, we get c = √(20^2 - 16^2) = √(400 - 256) = √144 = 12 ft. Therefore, the foci are 12 feet apart. The answer is 12 feet.
27. The equation of the hyperbola is given as 16y^2 - 9x^2 = 144, which is in the standard form (y^2/a^2) - (x^2/b^2) = 1. Comparing this with the standard form, we have a^2 = 144/16 = 9 and b^2 = 144/9 = 16. Therefore, a = 3 and b = 4. The foci of the hyperbola are given by (∓√(a^2 + b^2), 0). Plugging in the values, we get (∓√(3^2 + 4^2), 0) = (∓√(9 + 16), 0) = (∓√25, 0) = (∓5, 0). Therefore, the foci are (0, ±5). The answer is (0, ±5).
28. The equation of a hyperbola with a vertical transverse axis and centered at the origin is given by (x^2/a^2) - (y^2/b^2) = 1, where a is the distance from the center to the vertex. In this case, a = 12 inches and the foci are 26 inches apart. The distance between the foci is given by c = √(a^2 + b^2), where c is the distance between the foci. Plugging in the values, we get 26 = √(12^2 + b^2). Squaring both sides and solving for b^2, we get b^2 = 26^2 - 12^2 = 676 - 144 = 532. Therefore, b = √532. The equation of the hyperbola is then (x^2/144) - (y^2/532) = 1. The answer is x^2/144 - y^2/532 = 1.
29. To find the number of different orders in which 3 students can be selected out of 12, we use the formula for combinations. The number of combinations is given by nCr = n! / (r! * (n-r)!), where n is the total number of students and r is the number of students being selected. Plugging in the values, we get 12! / (3! * (12-3)!) = 12! / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220. Therefore, there are 220 different orders in which three students can be selected. The answer is 220.
30. The theoretical probability of rolling a sum of 6 on two standard number cubes can be found by counting the number of favorable outcomes (rolling a sum of 6) and dividing it by the total number of possible outcomes (36). We can find the favorable outcomes by listing all the possible combinations that sum up to 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). Therefore, there are 5 favorable outcomes. The probability is then 5/36. The answer is 5/36.
31. The probability of hitting the bull's eye on the dartboard can be found by dividing the area of the bull's eye by the area of the entire dartboard. The area of a circle is given by the formula A = πr^2, where r is the radius. The area of the bull's eye is therefore π(6^2) = 36π. The area of the whole dartboard is π(16^2) = 256π. Dividing the area of the bull's eye by the area of the whole dartboard and converting it to a percentage, we get (36π / 256π) * 100 = (36/256) * 100 = 14.1%. Therefore, the probability of hitting the bull's eye is 14.1%. The answer is 14.1%.
32. To find the probability of rolling a prime number or a number greater than 3 on a standard, six-sided cube, we first need to determine the favorable outcomes. The prime numbers on a standard cube are 2, 3, and 5. Numbers greater than 3 are 4, 5, and 6. Therefore, the favorable outcomes are 2, 3, 4, 5, and 6, which is a total of 5 numbers. The total number of possible outcomes is 6 (since there are 6 sides on the cube). Therefore, the probability is 5/6. The answer is 5/6.