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Tems11 [23]
3 years ago
15

Select the correct answer.

Mathematics
1 answer:
Mice21 [21]3 years ago
8 0

Answer:

n = 11

Step-by-step explanation:

Perimeter =  sum of all the sides

n + n - 3 + 2(n-2) = 37 units

n + n - 3 + 2n - 4 = 37             {Combine like terms}

n + n + 2n - 3 - 4  = 37

                 4n - 7 = 37

                       4n= 37 + 7

                       4n = 44

                         n = 44/4

n = 11

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A 5×6 rectangular grid with unit cells is given. Let A(0, 0) and B(5, 6) be the bottom-left corner and top-right corner, respect
harina [27]

Answer:

462 paths from A to B

Step-by-step explanation:

The question is incomplete. However, a possible question is to determine the number of possible paths on the grid map.

The first step is to represent the grid map itself. (See attachment 1)

From the question, we understand that:

  • Only right movement is allowed in the horizontal direction
  • Only up movement is allowed in the vertical direction

There are a several number of ways to navigate through. However, one possible way is in attachment 2

In attachment 2,

  • R represents the right movement
  • U represents the up movement

And we have:

R = 5     and    U = 6

The number of possible paths (N) is then calculated as:

N = \frac{(N + U)!}{N!U!}

Substitute values for N and U

N = \frac{(5 + 6)!}{5!6!}

N = \frac{11!}{5!6!}

N = \frac{39916800}{120 * 720}

N = \frac{39916800}{86400}

N = 462

<em>Hence, there are 462 possible paths from A to B</em>

4 0
3 years ago
It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next lay
Hitman42 [59]

Answer:

Yes all of the logs can be used in such a grouping.

We'll have <u>19 logs</u> in the bottom row (and have 19 rows)

========================================================

Explanation:

Let n be the number of layers. Let T(n) represent how many logs there are total.

  • If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.
  • If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.
  • If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.
  • Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10
  • Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15

This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula

T(n) = 0.5*n*(n+1)

---------------

For example, let's say we wanted to find how many logs there were in the fifth layer

T(n) = 0.5*n*(n+1)

T(5) = 0.5*5*(5+1)

T(5) = 15

This matches from earlier.

The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.

-------------------

T(n) = 0.5*n*(n+1)

190 = 0.5*n*(n+1)

190*2 = n(n+1)

380 = n^2+n

0 = n^2+n-380

n^2+n-180 = 0

Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.

If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.

----------

Check:

1+2+3+4+5+6+7+8+9+10 = 55

11+12+13+14+15+16+17+18+19 = 135

55+135 = 190

Or you could say,

T(n) = 0.5*n*(n+1)

T(19) = 0.5*19*(19+1)

T(19) = 190

Either way, the answer is confirmed.

8 0
2 years ago
What is the next sequence 1/2, 1/2, 3/8, 1/4, 5/32
NemiM [27]
1/8 is tha answer............
5 0
3 years ago
A barbeque restaurant serves four meats brisket chicken ribs and turkey how many two meat combo can be served for the luncheon p
Gnesinka [82]

Answer:

2

Step-by-step explanation:

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3 years ago
Mrs. Saunders bought a 19 pound turkey for Thanksgiving. The total cost of the
Luda [366]

Answer:

$1.35 per pound

Step-by-step explanation:

25.65/19=1.35

7 0
2 years ago
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