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3 years ago

In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 5 at a time?

2 answers:

4 0

This is a permutation problem in which you are to arrange the objects and the order doesn't matter. You can easily calculate it using your scientific calculator. Just use the formula nPr, where n is the total number of objects taken r at a time.

PAYMENT = 7 letters => 7P5 = 2520
There are 2,520 ways

For butterfly, its quite tricky because there are two letters. Oder does matter here, since no matter which t comes first, that is still the same. So, this is what you do:

BUTTERFLY = 9 letters
9P5 ÷ 2! => since there are two same letters
15120 ÷ 2 = 7560
There are 7560 ways.

LenKa [72]3 years ago

4 0

PAYMENT be arranged letters are taken 5 times then total 35 letters
BUTTERFLY be arranged letters are taken 5 times then total 45 letters

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Carbon-14 has a half-life of 5730 years. In a plant fossil, you find that the 14C has decayed to 1/8.00 of the original amount.

drek231 [11]

Note that 8.00 = (2.00)^3, that implies that a decay to 1/8.00 means that the Carbon-14 has passed 3 half-life. (1 to decay to 1/2, other to decay to 1/4, and other to decay to 1/8). And, three half-life is 3 * 5730 years = 17,920 years. So,<span> the answer is that the plant was alive 17,920 years.</span>

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3 years ago

PLEASE i need help

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1. 8^3 * 8^2, 8^5, and (2^3)^5
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3 years ago

Given the function defined in the table below, find the average rate of

Savatey [412]

Answer:

The average rate of change from 2 < x < 3 is -3.

Step-by-step explanation:

f(2) = 13

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3 years ago

A rectangular swimming pool is 25 ft long and 20 1/2 ft wide, and it must be filled to a depth of 4 1/2 ft. One cubic foot of wa

bazaltina [42]

ANSWER

307½ gallons of water

EXPLANATION

The volume of the rectangular swimming pool is

$V = l \times w \times h$

where l=25ft and w=20½ ft.

when it is filled to a depth of 4½ ft ,then the height is , h=4½ ft.

We substitute these values into the formula to get:

$V = 25\times 20.5\times 4.5$

$V = 2306.25 {ft}^{3}$

If one cubic foot of water is 7½ gallons, then 2306.25 cubic feet will be

$\frac{2306.25}{7.5} = 307.5gallons$

We need 307.5 gallons of water to fill the pool.

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3 years ago

Jackson is building a bookshelf and has a piece of wood that is 5/8 long. He needs to cut pieces that are 1/16 foot long. How ma

Genrish500 [490]

Answer:

<h2>6 is the Answer.</h2>

Step-by-step explanation:

A fraction consists of two parts the top number and the bottom one.

Think of the top number as the count and the bottom as the size indicator. So you have:

countsize indicator −−−−−−−−−−→proper names numeratordenominator

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider the action example of dividing 3 into 6.

We can do this division directly because their size indicators are the same. That is, we have: 61÷31. People do not normally write it this way but it is correct.

To directly divide the counts the size indicator must be the same

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So we need to see how many of 18 will fit into 34

We can not do this directly in one operation as the size indicators are not the same.

Lets make the size indicators (denominators) the same

Multiply by 1 and you do not change the value but

1 comes in many forms.

[34×1]÷18 → [34×22]÷18

[3×24×2]÷18 → 68÷18

Now that the size indicators (denominators) are the same we can just divide the counts (numerators)

countsize indicator→[68÷18]=6÷1=6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I could explain more showing the connection between this and the shortcut method but what I have shown you will do for now.

6 0

2 years ago