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polet [3.4K]
3 years ago
15

At a track meet , 10 different runners compete in the 1600m run.

Mathematics
1 answer:
Zanzabum3 years ago
4 0

Answer:

There are 3,628,800 different ways for the runners to finish.

Step-by-step explanation:

Arrangments of x elements:

The number of possible arrangments of x elements is given by the following formula:

A_{x} = x!

In this question:

10 different runners, which means that the number of different ways that there are for the runners to finish is an arrangment of 10 elements. So

A_{10} = 10! = 3628800

There are 3,628,800 different ways for the runners to finish.

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Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E
xxTIMURxx [149]

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

6 0
3 years ago
Sherita needs 1 3/5 cups of sugar. she has 8 cups of sugar. how much cups can she make?
Deffense [45]
Could you send a picture of the question
5 0
3 years ago
Read 2 more answers
1 If 2x+2 = 32, then x =​
VashaNatasha [74]
The answer would be x=15
5 0
3 years ago
Write a ratio, in the simplest form and a percent for the shaded area (there's a 5x4 box and 6 cubes are shaded)
Alexxandr [17]

Answer:

\%Percent = 30 \%

Step-by-step explanation:

Given

Shaded = 6\ cubes

Box = 5\ x\ 4

Required

Determine the percentage of the shaded cubes

First, we calculate the number of boxes:

Box = 5\ x\ 4

Express as multiplication

Box = 5\ *\ 4

Box = 20

This implies that there are 20 cubes in the box.

The percentage of the shaded cubes is:

\%Percent = \frac{Shaded}{Box} * 100\%

\%Percent = \frac{6}{20} * 100\%

\%Percent = \frac{6* 100}{20} \%

\%Percent = \frac{600}{20} \%

\%Percent = 30 \%

<em>30% were shaded</em>

5 0
2 years ago
Solve the inequality for x. Show each step of the solution.10x &gt; 2(8x – 3) – 18
Luden [163]

Answer: x<4

Given the inequality:

10x>2(8x-3)-18

We want to solve the inequality for x.

First, distribute the bracket on the right side of the inequality.

\begin{gathered} 10x>2(8x)-2(3)-18 \\ 10x>16x-6-18 \\ 10x>16x-24 \end{gathered}

Next, subtract 10x from both sides of the inequality.

\begin{gathered} 10x-10x>16x-10x-24 \\ 0>6x-24 \end{gathered}

Add 24 to both sides of the inequality.

\begin{gathered} 0+24>6x-24+24 \\ 24>6x \end{gathered}

Divide both sides of the inequality by 6.

\begin{gathered} \frac{24}{6}>\frac{6x}{6} \\ 4>x \\ \implies x

The solution to the inequality is x<4.

6 0
1 year ago
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