1.
The midpoint of the segment with endpoints (4, 8) and (-11, -2) is ______.
2.
The distance between the points (2,1) and (6,4) is:
3.
Write the equation of the circle with center (3, 7) and containing the point (11, 13).
4.
1.A/n _______ is the set of points in a plane such that the sum of the distances from any point on the _____ to two fixd points (the foci) is the constant sum.
2.A/n _______ is the set of points in a plane such that the difference of the distances from P to fixed points F1 and F2, the foci, is constant.
3.A/n _______ is the set of all points in a plane that are an equal distance from both a fixed point, the focus, and a fixed line, the directrix.
5.
MATCHING:
So, we've already got the equations of all the basic conics. Now for the location of the vertices, foci, and co-vertices. Y'all will now match:
For a horizontal A, vertices are (h+a, k) and (h-a, k); foci are (h+c, k) and (h-c, k); co-vertices are (h, k+b) and (h, k-b); asymptotes are y-k= (+/-)b/a(x-h)
For a horizontal B, the focus is (h+p, k), and the directrix is x=h-p
For a horizontal C, the vertices are (h+a, k) and (h-a, k); foci are (h+c, k) and (h-c, k); co-vertices are (h, k+b) and (h, k-b).
The below answers are listed as the projected guesses for A, B, and C in that order.
A.
Ellipse, Parabola, Hyperbola
B.
Hyperbola, Ellipse, Parabola
C.
Parabola, Hyperbola, Ellipse
D.
Parabola, Ellipse, Hyperbola
6.
Write an equation in standard form for the below ellipse with center (0,0):
an ellipse with vertex (0,8) and co-vertex (3,0).
No spaces, and recognize all 'squared' symbols as I have been, for instances x^{2 }is equal to x^2.
7.
Classifying Conic Sections:
B^{2}-4AC=0 in the form of Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 is a parabola.
8.
Classifying Conic Sections:
B^{2}-4AC=0 in the form of Ax^2 + Bxy + Cy^2 + Dx + Ey + F > 0 is a hyperbola.
9.
Classifying Conic Sections:
B^{2}-4AC < 0 and either B is not equal to 0 or A is not equal to C (in the form of Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0) is a circle.
A.
B.
False--- no way man, that's an ellipse!
10.
Classifying Conic Sections:
B^{2}-4AC < 0 and either B=0, and A=C (in the form of Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0) is a circle.
11.
Let's talk about nonlinear system of equations; rhar is a system in which at least one of the equations is not linear; a class of which is the conic sectiosn. You can solve these bad boys by graphing, substitution, and elimination, and the points you'll finally settle down with are the intersection points between the equations in your system. It appears that most of them are conic section and some other sort of linear or nonlinear equation.
A.
B.
C.
Oh, dear. Next is probability.
12.
Combination: order does not matter.
Permutation: order does indeed matter.
_{n}C_{r} = n! / r!(n-r)! <-- that is indeed a combination formula. Permutation's easier, do you know that one?
What is the probability of an event happening?
Answer only the second question please.
A.
B.
Number of favorable outcomes / number of outcomes in the sample space
C.
Number of possible ways to have something happen / number of ways scientists have thought smart thinkers to the moon to contemplate.
13.
Each student received a 4-digit code to use the library computers, with no digit repeated. Manu received the code 7654. What was the probability that he would receive a code of consecutive numbers?
14.
You roll a dice (basic; numbered 1-6) twice. What is the probability that you will roll one number which is a prime number (not 1), and then roll a number greater than four but less than seven?
15.
Find the probability that the red cube shows a 5 and that the sum of the red cube and the orange cube is less than or equal to 8.
16.
Inclusive events are events that have one or more outcome in common.
A simple event is an event that describes a single outcome.
A compound event is an event made up of one or more simple events.
Mutually exclusive events are events that cannot both occur in the same trial of an experiment (like rolling a 1 and a 2 on the same roll).
17.
Find the probability with a general dice of rolling at least one 4 when rolling 2 dice:
18.
Round to the second decimal place:
There are 4 students in a music-listening-to club. Each student randomly chooses an album from a list of 8 titles. What is the probability that at least 2 of the students in the group choose the same book?
19.
Find the mode and median in your lovely and very intelligent head.
Then, find the weighted average of stars for a movie.
But, ignore the category saying below 0 stars; this will involve taking 0.07 out. Keep it in mind, kay?
Round to two decimal places.
20.
Final question! *There are no binomial distributions on our final, she said so herself.
Take the data values
1, 1, 6, 4, 8, 3, 6, and 3.
Then find the standard deviation of the data.
Round to four decimal places.