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1 year ago

31 cars are in a race. In how many different ways can cars finish in order in the top 4 positions?

Mathematics

1 answer:

cupoosta [38]1 year ago

8 0

Answer:

755,160 ways

Explanation:

We're told that 31 cars are in a race.

Considering the order in which the cars can finish in the top 4 positions, any of the 31 cars can finish in the first position, any of the remaining 30 cars can finish in the second position, any of the remaining 29 cars can finish in the third position and any of the remaining 28 cars can finish in the fourth position, so the different numbers of ways can be determined as seen below;

$31\times30\times29\times28=755,160\text{ ways}$

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Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this set listed in increasing order). a) {

Irina-Kira [14]

Answer:

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

Step-by-step explanation:

in matrix, arrays are placed in rows , which represents the horizontal sides from left to right, while arrays in the column are placed vertically from top to bottom. Here, we placed the arrays in a 4x4 matrix

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

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3 years ago

(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent

laiz [17]

Answer:

$12.50 \space\ h = 2500.75$

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

$\boxed {12.50 \times h = 2500.75}$

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = $\frac{2500.75}{12.50}$

= 200.6 hours

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1 year ago

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What type of triangle has side lengths 4, 4/15, and 16?

zvonat [6]

Answer:

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2 years ago

Find the perimeter pf a rectangular parking lot that has a width of 3x+2 and a length of 5x-7.*

uranmaximum [27]

Answer:

Perimeter is 16x - 10

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3 years ago

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vesna_86 [32]

Answer:

see explanation

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In 13 - 17

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r² - 25

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3 years ago

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