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2 years ago

Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)

Mathematics

1 answer:

Kitty [74]2 years ago

6 0

Answer:

a) Empty set

b) $\{x : x \in N \text{ and } x < 13\}$

Step-by-step explanation:

Roster form is a comma separated list form of set.

a) The set of natural numbers x that satisfy x + 4 = 1.

$x + 4 = 1\\x = -3 \notin N$

Thus, x is an empty set.

b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We use x to represent this set. Now x belongs to natural number and is less than equal to 12.

Thus, it can be written as:

$\{x : x \in N \text{ and } x < 13\}$

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Compare the decimals by using the symbol < or >. a. 0.531 _____ 0.456 b. 0.63 _____ 0.47 c. 0.267 _____ 0.539 d. 0.07 ____

rodikova [14]

Answer:

0.531 > 0.456

0.63 > 0.47

0.267 < 0.539

0.07 < 0.7

Step-by-step explanation:

a. 0.531 _____ 0.456

compare the numbers from left to right

5 is greater than 4 so 0.531 greater than 0.456

0.531 > 0.456

b. 0.63 _____ 0.47

6 is greater than 4. 0.63 > 0.47

c. 0.267 _____ 0.539

2 is less than 5 . so 0.267 less than 0.539

0.267 < 0.539

d. 0.07 _____ 0.7

0 is less than 7

0.07 < 0.7

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2 years ago

According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 p

Feliz [49]

Answer:

Step-by-step explanation:

a )

sample mean = sum total of given data / no of data

= 415.35 / 20 = 20.76

To calculate the median we arrange the data in ascending order and take the average of 10 th and 11 th term .

= 20.50 + 20.72 / 2

= 20.61

b ) To calculate the 10% trimmed mean , we neglect the largest 10% and smallest 10 % data and then calculate the mean . Here we neglect the first two smallest and last two greatest

(18.92 + 19.25 ..... + 22.43 + 22.85) / 16

= 20.74

c )

We can easily plot the data on number line from 17 to 24

d )

Maximum value of data set = 23.71 and minimum value is 18.04

mean is 20.76 , median is 20.61 and trimmed mean is 20.74

They are between maximum and minimum values of given data . Hence there is no outliers .

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2 years ago

Without using a calculator, what is 30% of 546? (You can round up to avoid decimal points)

madreJ [45]

Answer:

Hey there!

We can solve this by multiplying 0.3 by 546, which is about 164.

Hope this helps :)

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2 years ago

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a photo collage consists of seven equal sized square photo arranged in a row to form a rectangle if the total area of the colleg

Keith_Richards [23]

Answer:

Step-by-step explanation:

I have attached a written explanation to help :).

Let's say each side of the square = $x$

If we put 7 squares in a row to make the rectangle,

length of the rectangle = $7x$

Area of a rectangle = length multiplied by width

Area of rectangle = $7x$ multiplied by $x$ = $7x^2$

We are also told that the total area = 567

So $7x^2 = 567$

Now solve for $x$ .

Divide both sides by 7.

$\frac{7x^2}{7} = \frac{567}{7}$

$x^2 = 81$

Then square root both sides to find $x$

$x = \sqrt{81}$ = 9

Finally, the question asks to find the length of the collage which we said was $7x$ and we know $x = 9$

Length of collage = $7x = 7$ multiplied by $9$ = ?

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2 years ago

Kim is reading a book with 380 pages. She read 20 pages each day until she reached Part 2 of the book. Part 2 of the book is 160

d1i1m1o1n [39]

If you divide 380 by 20, you get 19. To check this, multiply 20 x 19 to see 380. Hope this helps :D

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2 years ago

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