Answer:
![1680](https://tex.z-dn.net/?f=1680)
Step-by-step explanation:
we need a 4-digit number from the numbers
(without repetition ).
possible number at thousand place ![=8](https://tex.z-dn.net/?f=%3D8)
Possible numbers at hundred place![=8-1=7](https://tex.z-dn.net/?f=%3D8-1%3D7)
Possible numbers at
place ![=7-1=6](https://tex.z-dn.net/?f=%3D7-1%3D6)
possible number at unit place ![=6-1=5](https://tex.z-dn.net/?f=%3D6-1%3D5)
<em>So total possible numbers</em>
![=8\times7\times6\times5\\=1680](https://tex.z-dn.net/?f=%3D8%5Ctimes7%5Ctimes6%5Ctimes5%5C%5C%3D1680)
<u>Other method :</u>
We are taking
numbers out of
and here order matters so we will use permutation.
Total possible numbers ![=^8P_{4}](https://tex.z-dn.net/?f=%3D%5E8P_%7B4%7D)
![\frac{8!}{(8-4)!}\\ =\frac{8!}{4!}\\ =8\times7\times6\times5\\=1680](https://tex.z-dn.net/?f=%5Cfrac%7B8%21%7D%7B%288-4%29%21%7D%5C%5C%20%3D%5Cfrac%7B8%21%7D%7B4%21%7D%5C%5C%20%3D8%5Ctimes7%5Ctimes6%5Ctimes5%5C%5C%3D1680)
Answer:
First coin Second coin outcome
H T HT
T H TH
T T TT
Step-by-step explanation:
First coin Second coin outcome
H T HT
T H TH
T T TT
Answer:
The total cost of the crown molding is <u>$23.43</u>.
Step-by-step explanation:
Given:
Tom's dad is putting crown molding around the top of all of the walls in Tom's bedroom.
The dimensions of his bedroom are 1 3/4 and 15 3/4.
Each foot of crown molding costs $.85.
Now, to find the total cost of the crown molding.
The dimensions are:
![1\frac{3}{4}\ feet \ and\ 15\frac{3}{4} \ feet.](https://tex.z-dn.net/?f=1%5Cfrac%7B3%7D%7B4%7D%5C%20feet%20%5C%20and%5C%2015%5Cfrac%7B3%7D%7B4%7D%20%5C%20feet.)
![\frac{7}{4}\ feet\ and\ \frac{63}{4} \ feet.](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7D%5C%20feet%5C%20and%5C%20%5Cfrac%7B63%7D%7B4%7D%20%5C%20feet.)
So, to get the area of bedroom:
![\frac{7}{4} \times \frac{63}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7D%20%5Ctimes%20%5Cfrac%7B63%7D%7B4%7D)
= ![\frac{441}{16} \ feet.](https://tex.z-dn.net/?f=%5Cfrac%7B441%7D%7B16%7D%20%5C%20feet.)
<em>As given, each foot of crown molding costs $.85.</em>
Now, to get the total cost of crown molding:
![0.85\times \frac{441}{16}](https://tex.z-dn.net/?f=0.85%5Ctimes%20%5Cfrac%7B441%7D%7B16%7D)
![=\frac{374.85}{16}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B374.85%7D%7B16%7D)
![=\$23.43.](https://tex.z-dn.net/?f=%3D%5C%2423.43.)
Therefore, the total cost of the crown molding is $23.43.
Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3.
Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4.
SAS criterion for congruence
5.
Corresponding angles of congruent triangles are congruent
6.
Converse of alternate interior angle theorem
7.
Vertical angle theorem
8.
SAS criterion for congruence
9.
Converse of alternate interior angle theorem
As,
, so
as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".