Choose one of the following theorems and prove it: Vertical Angles are congruent, Alternate interior angles are congruent, Corre
sponding angles are congruent. Demonstrate on a whiteboard.
(Just tell me how to write it on a whiteboard)
(Just tell me how to write it on a whiteboard)
1 answer:
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Answer:
A summary of the data is as follows;
1. Maximum = 34
2. Minimum = 24
3. The 1st quartile is 27
4. The median is or the 2nd quartile 34
5. The 3rd quartile is 33
The data is summarized in the attached box plot
Step-by-step explanation:
24, 25, 29, 30, 31, 31, 32, 34, 34
From the given data, we have the five values of a box and whisker plot as follows;
1. Maximum = 34
2. Minimum = 24
3. The 1st quartile is the term or 27
4. The median (2nd quartile) is the term or 34
5. The 3rd quartile is the term or 33
Hence the attached box plot summarizes the data.
Answer:
The probability is
Step-by-step explanation:
We can divide the amount of favourable cases by the total amount of cases.
The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8,
For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.
Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.
We can conclude that the probability for 8 rooks not being able to capture themselves is
Answer:
m∠CFD is 70°
Step-by-step explanation:
In the rhombus
- Diagonals bisect the vertex angles
- Every two adjacent angles are supplementary (their sum 180°)
Let us solve the question
∵ CDEF is a rhombus
∵ ∠E and ∠F are adjacent angles
→ By using the second property above
∴ ∠E and ∠F are supplementary
∵ The sum of the measures of the supplementary angles is 180°
∴ m∠E + m∠F = 180°
∵ m∠E = 40°
∴ 40° + m∠F = 180°
→ Subtract 40 from both sides
∵ 40 - 40 + m∠F = 180 - 40
∴ m∠F = 140°
∵ FD is a diagonal of the rhombus
→ By using the first property above
∴ FD bisects ∠F
→ That means FD divides ∠F into 2 equal angles
∴ m∠CFD = m∠EFD = m∠F
∴ m∠CFD = (140°)
∴ m∠CFD = 70°