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alina1380 [7]
3 years ago
9

Skylar is arranging 8 objects on a shelf. How many different ways can she arrange them? How can I figure this out using the form

ula for combinations?
Mathematics
1 answer:
Aneli [31]3 years ago
4 0

Personally, I never bothered learning the formula. 
When I run into a problem like this, I look at it this way: 
(I learned this method from my high school math teacher,
Mr. H. Carlisle Taylor, in 1956.  It not only works, but I can
even understand it !)

The first object can be any one of the 8 .  For each of those ...
The 2nd object can be any one of the other 7.  For each of those ...
The 3rd object can be any one of the other 6 .  For each of those ...
The 4th object can be any one of the other 5 .  For each of those ...
The 5th object can be any one of the other 4 .  For each of those ...
The 6th object can be any one of the other 3 .  For each of those ...
The 7th object can be any one of the other 2 .  For each of those ...
The 8th object has to be the 1 that's left.

Total number of possible ways to line them up is

                 (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) =  40,320 ways .

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the sum of three consecutive even integers is 36. Let X represent the first integer, x + 2 represent the second integer, and x +
ozzi

Answer:

see explanation

Step-by-step explanation:

Sum the 3 consecutive integers and equate to 36

x + x + 2 + x + 4 = 36

3x + 6 = 36 ( subtract 6 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

The 3 consecutive integers are

10, 10 + 2, 10 + 4, that is

10, 12, 14

7 0
3 years ago
A perfume company claims that the mean weight of ther new perfume is at least 8.9 fluid oz. Express the null hypothesis and the
zlopas [31]

Answer:

H0: mu = 8.9 fl oz.\\\\

Ha: mu ≠8.9 fluid oz

Step-by-step explanation:

Given that A perfume company claims that the mean weight of ther new perfume is at least 8.9 fluid oz

For testing this claim, in Statistics we perform a certain measures called hypothesis testing.

For this first step is to create null and alternate hypothesis.

Normally null hypothesis would have some statistic = something

Here we want to test the mean weight of perfume

Hence null hypothesis would be

H0: mu = 8.9 fl oz.

Alternate hypothesis would be opposite of this claim

i.e.

Ha: mu ≠8.9 fluid oz

Hence answer is

H0: mu = 8.9 fl oz.\\\\

Ha: mu ≠8.9 fluid oz

6 0
3 years ago
What are the coordinates of the point on the directed line segment from (-6, -6)(−6,−6) to (9, -1)(9,−1) that partitions the seg
GrogVix [38]

Answer:

(0, -4)

Step-by-step explanation:

The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)

The ratio the required point partitions the line = 2 to 3

The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;

\left(\dfrac{a}{a + b} \times (x_1 - x_2)+ x_1, \ \dfrac{a}{a + b} \times (y_1 - y_2)+ y_1 \right)

Therefore, the required point is located as follows;

\left(\dfrac{2}{2 + 3} \times (9 - (-6))+ (-6), \ \dfrac{2}{2 + 3}\times (-1 - (-6))+ (-6) \right) = (0, -4)

The coordinates of the point is (0, -4)

6 0
3 years ago
Irene wants to list the factors for 88. She
Paladinen [302]

Almost; she's just missing 1, since 1*88 = 88.

3 0
3 years ago
The number of points in the first five games of the basketball season are listed below. What is the mean number of points scored
Fudgin [204]

Answer: 29

Step-by-step explanation:

7 0
3 years ago
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