The sphere has a radius of 5 cm. What is the volume?
2 answers:
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Answer:
Answer:
Permutation:
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Formula:
Example:
Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.
Combination:
In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.
Formula:
Example:
Combination: Picking a team of 3 people from a group of 10.
C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.
Probability:
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Formula:
Conditional Probability P(A | B) = P(A∩B) / P(B)
Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)
Example:
Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.
Answer:
C, E
Step-by-step explanation:
As a rule, these ballistic motion equations are only applicable for heights above the final resting place. Usually, that is the ground (h=0). Time is always measured as a non-negative quantity beginning at the time of launch.
The function is meaningless after the time the object comes to rest on the ground, so the domain of the function extends from 0 until that time.
These considerations allow us to evaluate the offered statements.
A. The domain never includes negative values. (A is not a true statement)
B. The heights are the same at times that are symmetrical around the time of the maximum height. Here, that time is about 1.9 seconds, not 1.5 seconds, so the heights will be different at 1 and 2 seconds after launch. (B is not a true statement)
C. The graph of the function shows the height reaches 0 at about 4.06 seconds, a little after 4 seconds. (C is true)
D. Based on our answer to C, we know t=10 is outside the domain of the function. (D is not a true statement)
E. The value of the function is 20 when t=0, so the function tells us the orange is 20 feet above the ground when it is launched. (E is true)
The true statements are C and E.
