Answer:
0.01863, yes preference
Step-by-step explanation:
given that a class consists of 12 boys and 12 girls. The teacher picks five students to present their work to the rest of the class and says that the five students are being selected at random
Here selecting any 5 students from the group of total 24 students is combination because order does not matter.
Total no of ways of selecting any 5 from total 24 = ![24C5\\=42504](https://tex.z-dn.net/?f=24C5%5C%5C%3D42504)
No of ways of selecting only 5 girls = No of ways of selecting random 5 girls from total 12 girls
= ![12C5\\=792](https://tex.z-dn.net/?f=12C5%5C%5C%3D792)
a) the probability be that all five students
selected are girls=![\frac{792}{42504} \\=0.01863](https://tex.z-dn.net/?f=%5Cfrac%7B792%7D%7B42504%7D%20%5C%5C%3D0.01863)
b) Since the probability for selecting all girls is very small and near to 0, it is unusual to select all girls if done at random. Hence the teacher had a preference for girls.
Answer:
85
Step-by-step explanation:
Write the numbers in order
66, 72, 74, 80, 83, 87, 91, 95, 98, 99
Find the middle number
83 and 87 are in the middle, so find the mean of them. 83+87= 170
170/2 = 85.
Answer:
From the given triangle figure;
Labelled the triangle as A , B and C.
The coordinates of this triangle ABC are;
A = (1, 10) ,
B = (-2, 4)
C = (7, 4).
Given : Scale factor(k) =
and centered at point (4, -2).
The rule of dilation with
and center at point (4,-2) is:
![(x, y) \rightarrow (\frac{1}{3}(x-4)+4 , \frac{1}{3}(y+2)-2)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%20%28%5Cfrac%7B1%7D%7B3%7D%28x-4%29%2B4%20%2C%20%5Cfrac%7B1%7D%7B3%7D%28y%2B2%29-2%29)
![(x, y) \rightarrow (\frac{1}{3}x-\frac{4}{3}+4 , \frac{1}{3}y+\frac{2}{3}-2)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%20%28%5Cfrac%7B1%7D%7B3%7Dx-%5Cfrac%7B4%7D%7B3%7D%2B4%20%2C%20%5Cfrac%7B1%7D%7B3%7Dy%2B%5Cfrac%7B2%7D%7B3%7D-2%29)
or
![(x, y) \rightarrow (\frac{1}{3}x+\frac{8}{3} , \frac{1}{3}y-\frac{4}{3})](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%20%28%5Cfrac%7B1%7D%7B3%7Dx%2B%5Cfrac%7B8%7D%7B3%7D%20%2C%20%5Cfrac%7B1%7D%7B3%7Dy-%5Cfrac%7B4%7D%7B3%7D%29)
then, the dilation of the given figure are;
=
=
= A'(3 , 2)
=
=
=B'(2 , 0)
=
=
= C'(5 , 0)
The coordinates of dilation images are:
A' = (3,2) , B' = (2, 0) and C' = (5, 0)
You can see the graph of the dilated image as shown below:
Combine like terms and then simplify
This is simple. Just add the x and y values of each ordered pair to see which ones equals 2.
The answer is (-4, 6), (0, 2), (4, -2)