What is the binomial expansion of (x+2y)^7

MAXImum [283]

Answer:

Step-by-step explanation:

Note that the squaring function and the square root function are inverses of one another. If we make a list of perfect squares, we get {1, 4, 9, 16, 25, ...}. Then the square roots of these numbers are {1, 2, 3, 4, 5, ... }.

Continue making a table of values to plot. The first row has x=0, y=0; this reflects that the sqrt of 0 is 0.

Fill the first (x-) column with perfect squares and the second (y-) column with the square roots of these perfect squares:

x y

0 0

1 1

4 2

9 3

and so on.

Now plot the following on the graph: (1,1), (4,2), (9,3), ....

Starting at (0,0) and moving to the right (indicating increases in x), plot these points. (You'll soon run out of room.) Draw a smooth curve from (0,0) to connect these points. The result is a graph of the square root function.

The domain of this function is "the set of all real numbers ≥0" and the range is the same: "the set of all real numbers ≥0"

4 0

3 years ago

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According to a 2018 survey by Bankrate, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose t

nalin [4]

Answer:

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they save nothing for retirement, or they save something. The probability of an adult saving nothing for retirement is independent of any other adult. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of adults in the United States save nothing for retirement (CNBC website).

This means that $p = 0.2$

Suppose that sixteen adults in the United States are selected randomly.

This means that $n = 16$

What is the probability that three or less of the selected adults have saved nothing for retirement?

This is:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{16,0}.(0.2)^{0}.(0.8)^{16} = 0.0281$

$P(X = 1) = C_{16,1}.(0.2)^{1}.(0.8)^{15} = 0.1126$

$P(X = 2) = C_{16,2}.(0.2)^{2}.(0.8)^{14} = 0.2111$

$P(X = 3) = C_{16,3}.(0.2)^{3}.(0.8)^{13} = 0.2463$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0281 + 0.1126 + 0.2111 + 0.2463 = 0.5981$

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

4 0

3 years ago

Find the probability of throwing 9 with two dice.

ololo11 [35]

Total number of possible outcomes of throwing two dice = 6×6 = 36
Number of outcomes of getting 9 i.e, (3+6),(4+5),(5+4),(6+3) = 4

$P = \frac{Number \: of \: favourable \: outcomes}{ Total \: number \: of \: possible \: outcomes}$

$P (throwing \: 9) = \frac{4}{36} = \frac{1}{9}$

6 0

3 years ago

Craig has a rectangle wooden deck that measures 799 inches by 245 inches that he wants to put a string of lights around. What le

tino4ka555 [31]

Answer:

He should buy lights that are 2088 inches long

Step-by-step explanation:

Craig has a rectangle wooden deck that measures 799 inches by 245 inches.

Let us say the length, L, is 799 inches and the breadth, B, is 245 inches.

He wants to put a string of lights around the deck.

This means that he needs to buy the length of lights that would be equal to the perimeter of the rectangular deck.

The perimeter of a rectangle is given as:

P = 2(L + B)

Hence, the length of lights he should buy is:

P = 2(799 + 245) = 2(1044)

P = 2088 inches

He should buy lights that are 2088 inches long.

5 0

3 years ago

Review the diagram of a locket in the shape of an ellipse.

Helen [10]

Answer:

B

Step-by-step explanation:

If you graph y^2/361 + x^2/169=1 you will get the same graph depicted in the equation.

8 0

3 years ago

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