Answer:
It's 1/3.
Step-by-step explanation:
Common ratio = 9/27 = 1/3.
3 / 9 = 1/3
1 / 3 = 1/3 and so on.
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
Answer:
The probability is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 175
The population proportion is p = 0.45
Generally the mean of the sampling distribution is 
Generally the standard deviation is mathematically represented as
=> 
=> 
Generally the probability of that the sample proportion of orange candies will be between 0.35 and 0.55 is
=> 
Generally 
So
=> 
From the z-table
and
So
=>
4839400 I'm not really sure but standard form is writing a number regularly ex/the standard form of four is 4
