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BigorU [14]
3 years ago
14

You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board wi

th T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

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Suppose that the mean and standard deviation of the scores in a Statistics exam are 75 and 9.5 respectively. What minimum score
lyudmila [28]

The mean and standard deviation of the scores are 75 and 9.5 respectively.

The z-score is a means to find the probability of getting a particular score. This is calculated to be:

z=\frac{x-\mu}{\sigma}

where x is the score, μ is the mean, and σ is the standard deviation.

To be a part of the top 2.5 percent, the probability is:

P=\frac{2.5}{100}=0.025

The z-score for this probability, that is, P

8 0
1 year ago
Anna has a 25-meter-long fence that she plans to use to enclose a rectangular garden of width w. The fencing will be placed arou
Leviafan [203]
<h3>Answer:   -2w^2 + 25w = 25    or    -2w^2 + 25w - 25 = 0</h3>

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

Explanation:

Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.

The area of the rectangle is

Area = length*width

Area = L*W

Area = (25-2w)*w

Area = 25w - 2w^2

Area = -2w^2 + 25w

Set this equal to the desired area (25 square meters) to get

-2w^2 + 25w = 25

and we can subtract 25 from both sides to get everything on one side

-2w^2 + 25w - 25 = 0

side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)

4 0
3 years ago
Read 2 more answers
What is the profitability index of an investment with cash flows in years 0 thru 4 of -340, 120, 130, 153, and 166, respectively
ki77a [65]

The profitability index of an investment with cash flows in years 0 thru 4 of -340, 120, 130, 153, and 166, respectively, and a discount rate of 16 percent is: 15%.

<h3>Profitability index</h3>

First step is to find the Net present value (NPV)  of the given cash flow using discount rate PVF 16% and PV of cash flow which in turn will give us net present value of 49.7.

Second step is to calculate the profitability index

Profitability index  = 49.7/340

Profitability index  = .15×100

Profitability index=15%

Therefore the profitability index of an investment with cash flows in years 0 thru 4 of -340, 120, 130, 153, and 166, respectively, and a discount rate of 16 percent is: 15%.

Learn more about Profitability index here:brainly.com/question/3805108

#SPJ4

3 0
1 year ago
Find the length of the third side to the nearest tenth<br> 7<br> 1
AlexFokin [52]

Answer:

10.7

Step-by-step explanation:

3 0
3 years ago
a recipe that serves 4 calls for 1 3/4 cups of tomato sauce. if jerry makes 2 1/2 time that amount, how many cups of tomato sauc
ANEK [815]

Answer:

4 3/8 cups

Step-by-step explanation:

5 0
3 years ago
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