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3 years ago

How many three letter arrangements can be made from the letters of COMPLEXITY?*

Mathematics

1 answer:

Natali [406]3 years ago

5 0

Answer:

720 arrangements

Step-by-step explanation:

We have three spaces that we want to fill with any letter from "complexity":

__ __ __

For the first space, we have 10 letters to choose from (there are 10 letters in the word "complexity"). For the second space, since we have already used up one letter for the first space, we have 9 letters remaining to choose from. Similarly, we only have 8 letters remaining to choose from for the last space.

Now, we multiply them all together: 10 * 9 * 8 = 720 arrangements.

Note that we multiply instead of add. This is because for any letter we place in space 1, it can be paired with any of the 9 letters for space 2 and any of the 8 letters for space 3.

Hope this helps!

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cassie tells rita she will meet her in 15 to 20 minutes. If t represents the time that cassie meets rita how can you express thi

Mila [183]

Answer:

Step-by-step explanation:

Express this time interval in set notation:

15 ≤ t ≤ 20

This says that the waiting time will be between 15 and 20 minutes.

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3 years ago

Two jet planes simultaneously started travelling in opposite directions from the same airport. Four hours later they were 3800 m

alexira [117]

Answer:

Step-by-step explanation:

let the speed of one plane=x

speed of other plane=x+80

time=4 hrs

then 4x+4(x+80)=3800

4x+4x+320=3800

8x=3800-320

or 8x=3480

x=435

speed of one plane=435 m/h

speed of other plane=435+80=515 m/h

Let he walks x hrs

then he take a taxi for 2-x hrs

4x+(2-x)50=31

4x+100-50x=31

-46x=-69

$x=\frac{-69}{-46}=\frac{3}{2}$

so he walks 3/2 hrs=1.5 hrs

travels by taxi=2-1.5=0.5 hrs

distance traveled by taxi=0.5×50=25 miles

8 0

3 years ago

What is the solution to the inequality?<br> −6x+5>−1

Bogdan [553]

Answer:

$\boxed{x$

Step-by-step explanation:

$-6x+5>-1\qquad\text{subtract 5 from both sides}\\\\-6x>-6\qquad\text{change the signs}\\\\6x$

3 0

3 years ago

Sue initially has 5 hours of pop music and 4 hours of classical music in her collection. Every month onwards, the hours of pop m

Snezhnost [94]

<h2>Answer</h2>

f(x) = 5(1.25)x + 4

<h2>Explanation</h2>

To solve this, we are going to use the standard exponential equation:

$f(x)=a(1+b)^x$

where

$a$ is the initial amount

$b$ is the growth rate in decimal form

$x$ is the time (in months for our case)

Since the hours of classic music remain constant, we just need to add them at the end. We know form our problem that Sue initially has 5 hours of pop, so $a=5$ ; we also know that every month onward, the hours of pop music in her collection is 25% more than what she had the previous month, so $b=\frac{25}{100} =0.25$ . Now let's replace the values in our function: