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2 answers:
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The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt
The numbers and patterns of the blocks are;
a. Patterns;
- The height of the white blocks is the Design number, while the rows are one more than the design number
- The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number
b. The function is
c. The function is
d.
e. The design chosen is <u>Design 9</u>
The number of blocks is <u>132 blocks</u>
Reasons:
The pattern of the design are;
a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks
Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks
The number of white blocks in a design, <em>n</em> is the product of <em>n</em> and (n + 1)
The number of grey blocks in a design <em>n</em>, is the product of (n + 2) and (n + 3) less the number of white blocks in the design
b. Based on the above, the function that represent the number of picture blocks in Design <em>n</em>, is therefore;
- p(n) = n·(n + 1)
c. Based on the above, the function that represent the number of border blocks in Design <em>n</em>, is therefore;
- b(n) = (n + 2)·(n + 3) - n·(n + 1)
d. The total number of blocks, t(n) = (n + 2)·(n + 3)
t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)
- t(n) = p(n) + b(n)
e. The given number of picture blocks = 90
The number of picture blocks in a design, n = n × (n + 1)
Therefore, given that the number of picture blocks is 90, we have;
90 = n × (n + 1)
n² + n - 90 = 0
(n + 10)·(n - 9) = 0
n = 9, or n = -10
Therefore, the design museum chooses is <u>Design 9</u>
The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)
Total blocks in the design the art museum choses, t(9), is given as follows;
t(9) = (9 + 2)·(9 + 3) = <u>132 blocks</u>
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Answer:
There is a 44.73% probability that all symbols are different.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
There are 26 total letters and 10 total digits.
The plate has the following format:
number, letter, letter, letter, number, number, number
Total outcomes
Each number can have 10 values.
Each letter can have 26 values.
There are four numbers and 3 letters.
So there are
possible plates
Desired outcomes
We cannot have repeated values.
So, for example, the first number can be any of the 10 digits. The second can be any of them, bar the first one. So 9 possible digits
The same logic for the letters, 26, then 25, then 24.
So there are
10*26*25*24*9*8*7 = 78624000 plates in which all symbols are different.
(a) What is the probability that all symbols are different
There is a 44.73% probability that all symbols are different.