Four students are competing in a race. In how many different combinations could the four students place in the race?

1 answer:

4 0

"Combinations" isn't really the right word, because a combination doesn't take order of elements into account, and the outcome of a race certainly does depend on order. "Permutations" would be the correct term.

If 4 students are competing, then the race has

4! = 4 • 3 • 2 • 1 = 24

possible outcomes.

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Simplified form of expression 125 2/3

masha68 [24]

Answer:

377/3

Step-by-step explanation:

In general if we have a fraction ( mixed) as ,

$a\dfrac{c}{d}$

Then the improper fraction will be ,

Improper fraction :-

$\dfrac{ d\times a + c}{d}$

Using this concept we have ,

→ 125 ⅔

→ 125 × 3 + 2 / 3

→ 375 + 2/3

→ 377/3

<h3>Hence the simplified form of the expression is 377/3 .</h3>

3 0

2 years ago

A furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requir

miskamm [114]

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

16 chairs; 24 tables
Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608
15 chairs; 18 tables
Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480
12 chairs; 28 tables
Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636
18 chairs; 20 tables
Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

15 x 65 + 18 x 90 = X
975 + 1,620 = X
2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

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8 0

1 year ago

Geometry PEOPLE HELP

White raven [17]

Answer: second option.

Step-by-step explanation:

Given the transformation $T:(x,y)$ → $(x-5,y+3)$

You must substitute the x-coordinate of the point A (which is $x=2$ ) and the y-coordinate of the point A (which is $y=-1$ ) into $(x-5,y+3)$ to find the x-coordinate and the y-coordinate of the image of the point A.