Answer:
56 is the answer to your question
Answer:
D. A translation 2 units down followed by a 270-degree counterclockwise rotation about the origin
Step-by-step explanation:
The given triangle has vertices at R(3,4), S(1,1), and T(5,1)
Translating the the vertices down by 2 units, we apply the rule;
![(x,y)\to (x,y-2)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28x%2Cy-2%29)
![\implies (3,4)\to (3,2)](https://tex.z-dn.net/?f=%5Cimplies%20%283%2C4%29%5Cto%20%283%2C2%29)
![\implies (1,1)\to (1,-1)](https://tex.z-dn.net/?f=%5Cimplies%20%281%2C1%29%5Cto%20%281%2C-1%29)
![\implies (5,1)\to (5,-1)](https://tex.z-dn.net/?f=%5Cimplies%20%285%2C1%29%5Cto%20%285%2C-1%29)
Rotating the resulting vertices through an angle 270 degrees counterclockwise, we apply the rule:
![(x,y)\to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28x%2C-y%29)
![\implies (3,2)\to R'(2,-3)](https://tex.z-dn.net/?f=%5Cimplies%20%283%2C2%29%5Cto%20R%27%282%2C-3%29)
![\implies (1,-1)\to S'(-1,-1)](https://tex.z-dn.net/?f=%5Cimplies%20%281%2C-1%29%5Cto%20S%27%28-1%2C-1%29)
![\implies (5,-1)\to T'(-1,-5)](https://tex.z-dn.net/?f=%5Cimplies%20%285%2C-1%29%5Cto%20T%27%28-1%2C-5%29)
Therefore the correct choice is D.
Answer:
(a) See attachment for tree diagram
(b) 24 possible outcomes
Step-by-step explanation:
Given
![Urn\ 1 = \{B_1, R_1, R_2, R_3\}](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%20%5C%7BB_1%2C%20R_1%2C%20R_2%2C%20R_3%5C%7D)
![Urn\ 2 = \{R_4, R_5, B_2, B_3\}](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%20%5C%7BR_4%2C%20R_5%2C%20B_2%2C%20B_3%5C%7D)
Solving (a): A possibility tree
If urn 1 is selected, the following selection exists:
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
If urn 2 is selected, the following selection exists:
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
<em>See attachment for possibility tree</em>
Solving (b): The total number of outcome
<u>For urn 1</u>
There are 4 balls in urn 1
![n = \{B_1,R_1,R_2,R_3\}](https://tex.z-dn.net/?f=n%20%3D%20%5C%7BB_1%2CR_1%2CR_2%2CR_3%5C%7D)
Each of the balls has 3 subsets. i.e.
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
So, the selection is:
![Urn\ 1 = 4 * 3](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%204%20%2A%203)
![Urn\ 1 = 12](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%2012)
<u>For urn 2</u>
There are 4 balls in urn 2
![n = \{B_2,B_3,R_4,R_5\}](https://tex.z-dn.net/?f=n%20%3D%20%5C%7BB_2%2CB_3%2CR_4%2CR_5%5C%7D)
Each of the balls has 3 subsets. i.e.
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
So, the selection is:
![Urn\ 2 = 4 * 3](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%204%20%2A%203)
![Urn\ 2 = 12](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%2012)
Total number of outcomes is:
![Total = Urn\ 1 + Urn\ 2](https://tex.z-dn.net/?f=Total%20%3D%20Urn%5C%201%20%2B%20Urn%5C%202)
![Total = 12 + 12](https://tex.z-dn.net/?f=Total%20%3D%2012%20%2B%2012)
![Total = 24](https://tex.z-dn.net/?f=Total%20%3D%2024)
25 percent of people had pasta.
First add 450 and 150 (which equals 600)
Next divide 600 by 150 (which equals 4)
Which means 150 is a fourth of six hundred, and a fourth is 25 percent.
Which leads to my answer of 25 percent
Answer:
325 km
Step-by-step explanation:
Given the scale :
1 : 4 ,000, 000
1cm measure in map = 4000000 on the ground
From the map :
Distance between Leeds and London = 8.125 cm
The actual distance on ground can be calculated thus :
1cm = 4,000,000
8.125cm = x
Cross multiply
x = 32500000 cm
Converting to kilometers :
1 km = 100,000 cm
x = 32500000
Cross multiply
100,000x = 32500000
x = 32500000 / 100000
x = 325
Hence, actual distance between Leeds and London is 325 km