Answer:
8th grade!
Step-by-step explanation:
Answer: 0.9738
Step-by-step explanation:
We assume that the scores follows a normal distribution.
Let
denotes the class average .
As per given we have,
![\mu=76\ \ \&\ \ \sigma=12](https://tex.z-dn.net/?f=%5Cmu%3D76%5C%20%5C%20%5C%26%5C%20%5C%20%5Csigma%3D12)
Sample size : n= 12
The probability that a class of 15 students will have a class average greater than 70 on Professor Elderman’s final exam will be :
![P(\overline{x}>70)=1-P(\overline{x}](https://tex.z-dn.net/?f=P%28%5Coverline%7Bx%7D%3E70%29%3D1-P%28%5Coverline%7Bx%7D%3C70%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%3C%5Cdfrac%7B70-76%7D%7B%5Cdfrac%7B12%7D%7B%5Csqrt%7B15%7D%7D%7D%29%5C%5C%5C%5C%5Capprox1-P%28z%3C-1.94%29%5C%20%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%20%3D1-%281-P%28z%3C1.94%29%29%5C%20%5C%20%5B%5Cbecause%20P%28Z%3C-z%29%3D1-P%28Z%3Cz%29%5D%5C%5C%5C%5C%3D1-1%2BP%28z%3C1.94%29%5C%5C%5C%5C%3D0%2B0.9738%3D0.9738%5C%20%5C%20%5Ctext%7B%5BBy%20z-table%5D%7D)
Hence, the correct answer = 0.9738
Answer:
B
Step-by-step explanation:
Answer:
Part 7) ![AB=27\ units](https://tex.z-dn.net/?f=AB%3D27%5C%20units)
Part 8) ![x=1.7\ units](https://tex.z-dn.net/?f=x%3D1.7%5C%20units)
Step-by-step explanation:
Part 7) Find the length of AB
we know that
The<u><em> two tangent theorem</em></u> states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same
so
In this problem, applying the two tangent theorem
AB=BC
substitute the given values
![15x-3=10x+7](https://tex.z-dn.net/?f=15x-3%3D10x%2B7)
solve for x
![15x-10x=7+3\\5x=10\\x=2](https://tex.z-dn.net/?f=15x-10x%3D7%2B3%5C%5C5x%3D10%5C%5Cx%3D2)
Find the length of AB
![AB=15x-3](https://tex.z-dn.net/?f=AB%3D15x-3)
substitute the value of x
![AB=15(2)-3=27\ units](https://tex.z-dn.net/?f=AB%3D15%282%29-3%3D27%5C%20units)
Part 8) we know that
If CD is tangent to circle E at point C
then
Line segment CD is perpendicular to line segment EC (radius) and CDE is a right triangle
so
Applying the Pythagorean Theorem in the right triangle CDE
![DE^2=CD^2+EC^2](https://tex.z-dn.net/?f=DE%5E2%3DCD%5E2%2BEC%5E2)
substitute the given values
![2^2=x^2+1^2](https://tex.z-dn.net/?f=2%5E2%3Dx%5E2%2B1%5E2)
solve for x
![4=x^2+1\\x^2=3\\x=1.7\ units](https://tex.z-dn.net/?f=4%3Dx%5E2%2B1%5C%5Cx%5E2%3D3%5C%5Cx%3D1.7%5C%20units)