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3 years ago

Which flight has the fastest average speed

Mathematics

1 answer:

Art [367]3 years ago

8 0

Answer:

Fastest wind speed ever recorded

That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976

Step-by-step explanation:

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Find the median of the data set 10,0,2, and 8

umka2103 [35]

0, 2, 8, 10
Cross out 0 and 10
Left with:
2,8
Add them
10
Divide by 2
5 is the median.

When two are left in the middle you find the mean or average of them. Basically add them together and divide by 2.

5 0

4 years ago

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(9x + 7) – (x + 3) What is the answer.

nata0808 [166]

Answer:

8x + 4

Step-by-step explanation:

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3 years ago

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For the given set, first calculate the number of subsets for the set, then calculate the

vodomira [7]

Answer:

$\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}$

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ( $N$ ) of subsets of a set containing $n$ elements: N = $2^{n}$

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = $2^{4} = 16$

(same result as using counting method)

Brief proof of formula: N = $2^{n}$

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are $n$ elements in total. => There are $2^n}$ ways to select, or in other words, there are $2^{n}$ subsets.