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3 years ago

Factor 391, 291, 387, 113, 451, 37, 411, 239, and 459 to prime factors

Mathematics

1 answer:

Zigmanuir [339]3 years ago

3 0

Answer:

391 = 17 × 23

291 = 3 × 97

387 = 3 × 3 × 43 = 3^2 × 43

113 is prime

451 = 11 × 41

37 is prime

411 = 3 × 137

239 is prime

459 = 3 × 3 × 3 × 17 = = 3^3 × 17

Step-by-step explanation:

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Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

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There are 21 ways Tim choose 2 books from the 7 recommended book

Solution:

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combinations is:

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

Substituting values in above formula, we get

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

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3 years ago

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Answer:

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Step-by-step explanation:

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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

sasho [114]

Answer is 54^2.

since there are triangles in this one, it is easier to do this. all you have to do is make boxes in and since there are angles, outside the lines. like this picture.

the orange is 1
red and dotted is 2
blue is 3
purple is 4(a regular box which should be easy to count.

all you have to do is add up all the boxes within the boundaries.
boundary 1: 12
boundary 2: 18
boundary 3: 6
boundary 4: 36

now when the boundary has a triangle in it (1, 2, & 3) divide the number you got in half or 2.
boundary 1: 6
boundary 2: 9
boundary 3: 3

the ractangle box doesn't not get divided.
boundary 1: 6
boundary 2: 9
boundary 3: 3
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add all the numbers you got now for each boundary and that would be your area squared.

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so your final answer is 54^2.

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