Answer:
The scale factor is 2/3.
Step-by-step explanation:
Given data,
The given image is (6,9)
The image after dilation is (4,6)
The scale factor is calculated by dividing the resultant image by the initial image.
For example, if the initial dimensions are (x1, y1) and the final dimensions are (x2,y2). The scale factor is calculated using x2/x1 = y2/y1 = Scale Factor
In our scenario,
x1 = 6
x2 = 4
y1 = 9
y2 = 6
Scale Factor = x2/x1
=> 4/6
=> 2/3
Similarly for y axis,
Scale Factor = y2/y1
=> 6/9
=> 2/3
Therefore, the scale factor is 2/3.
Rewrite the square root of X as X^ 1/2. Then take the derivative. Since 1/3 is a constant with respect to X you can pull that out. So, you should have
1/3 d/dx [ (2x^2-x^5)/3x^1/2].
Then factor x^2 out of 2x^2-x^5.
Then by using the negative exponent rule you should have
1/3 d/dx [ x^2(2-x^3)x^-1/2 ]
Then multiply x^2 by x ^-1/2 by adding the exponents.
1/3 d/dx [ x^3/2 (2-x^3)]
Then differentiate.
You should get x^1/2 - (3x^7/2)/2.
I hope that helps.
Answer:
240 texts
Step-by-step explanation:

Answer:
The confidence interval for the proportion of production lines that caused defects is (0.07, 0.09).
Step-by-step explanation:
A confidence interval for a population proportion is a function of the sample proportion and the margin of error.
The interval has two bounds, a lower bound and an upper bound.
The lower bound is the sample proportion subtracted by the margin of error.
The upper bound is the margin of error added to the sample proportion.
In this problem, we have that:
Sample proportion 0.08
Margin of error 0.01
0.08 - 0.01 = 0.07
0.08 + 0.01 = 0.09
The confidence interval for the proportion of production lines that caused defects is (0.07, 0.09).