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vichka [17]
3 years ago
6

There are 6 runners in the 100 meter race at a track meet. in how many ways can the runners be arranged

Mathematics
1 answer:
Artemon [7]3 years ago
3 0
The numbers can be arranged in 720 ways.

There are 6 people possible for the first position; 5 for the second; 4 for the third; etc.  This gives us 6! = 720.
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The number of cows on a farm increased by 60. Because of better food, the amount of milk from each cow went up from 12.8 liters
attashe74 [19]

Answer:

Step-by-step explanation:

Number of cows increased=60

Old quality of milk consumed=12.8litres

New Increase in milk consumed=15litres

Therefore the number of cows in the farm if the quality of milk is 1340litres=y

Therefore, 1cow =15litres

y cows= 1340litres

Crossmultiply:

15litres×ycows=1340litres

Make y the subject of formula

y= 1340÷15

y=89.33cows

Therefore,the number of cows on the farm if farmer gets 1340litres of milk would be 89cows.

6 0
3 years ago
Rewrite the equation by completing the square.<br>x^2-2x+1=0​
kaheart [24]

Answer:

(x - 1)² = 0

Step-by-step explanation:

Given

x² - 2x + 1 = 0 ( subtract 1 from both sides )

x² - 2x = - 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = - 1 + 1

(x - 1)² = 0

5 0
3 years ago
Which set of side lengths form a right triangle?
Reil [10]
I just took the test and the answer was D
50 in, 48 in, 14 in are the side lengths that form a right triangle
4 0
3 years ago
Read 2 more answers
The answer ............
suter [353]

Answer:

f^-1(x) = ( x + 6 )/4

Step-by-step explanation:

f(x) is the same as...y = 4x + 6....and then try to make x the subject of formula

y + 6 = 4x

x = (y + 6)/4....then when writing f^-1(x)...replace y with x

f^-1(x) = ( x + 6 )/4

3 0
3 years ago
Determine whether the set of all linear combinations of the following set of vector in R^3 is a line or a plane or all of R^3.a.
Temka [501]

Answer:

a. Line

b. Plane

c. All of R^3

Step-by-step explanation:

In order to answer this question, we need to study the linear independence between the vectors :

1 - A set of three linearly independent vectors in R^3 generates R^3.

2 - A set of two linearly independent vectors in R^3 generates a plane.

3 - A set of one vector in R^3 generates a line.

The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :

a. Let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}-2&5&-3\\6&-15&9\\-10&25&-15\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix  ⇒

\left[\begin{array}{ccc}-2&5&-3\\0&0&0\\0&0&0\end{array}\right]

We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).

We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).

At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.

b. Again, let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}1&2&0\\1&1&1\\4&5&3\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&1\\0&1&-1\\0&0&0\end{array}\right]

We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).

c. Finally :

\left[\begin{array}{ccc}0&0&3\\0&1&2\\1&1&0\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&0\\0&1&2\\0&0&3\end{array}\right]

The set is linearly independent so the set of all linear combination of the set c. is all of R^3.

4 0
2 years ago
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