1.
Perpendicular. y=3x+4
Parallel. y=-1/3 x-8/3
2.
Perpendicular. y=-x-1
Parallel. y=x+11
3.
Perpendicular. y=7/4 x+8
Parallel. y=-7/4 x-9/7
4.
Perpendicular. y=4/5 x-3
Parallel. y=-5/4 x+35/2
yeesh, that took a while :) hope I helped!
Answer:
249.6
Step-by-step explanation:
width x height x 1/2 = area fo a triangle
12(2) x 10.4(2) x 1/2 = 249.6
I assumed this means all of the surface area. Hope this helps. Sorry if I'm wrong.
This is the concept of trigonometric identities;
To solve the expression we proceed as follows, first we simplify the question, we subtract 3 m from 135m and 96m. Our new height for London eye is 132m and Big Ben is 93 m.
speed is given by:
1 rev/min= 2pi rad/min
thus our speed will be:
1/30 rev/min
=pi/15 rad/min
Subtracting 93 m (Big Ben)- 66 m (radius of the London Eye)= 27 m
This will make right angle as:
adjacent=27 m
hypotenuse=66 m
cos x=27/66=9/22
x=arccos(9/22)
Therefore the time taken will be given by:
2 cos^-1 (9/22)* (15/pi min/rad)
N/B the 2 accounts for both up and down
thus time taken will be:
30*cos^-1(9/22)
=30cos^-1 (9/22) min
Answer:
The approximate probability that the mean of the rounded ages within 0.25 years of the mean of the true ages is P=0.766.
Step-by-step explanation:
We have a uniform distribution from which we are taking a sample of size n=48. We have to determine the sampling distribution and calculate the probability of getting a sample within 0.25 years of the mean of the true ages.
The mean of the uniform distribution is:
![\mu=\dfrac{Max+Min}{2}=\dfrac{2.5+(-2.5)}{2}=0](https://tex.z-dn.net/?f=%5Cmu%3D%5Cdfrac%7BMax%2BMin%7D%7B2%7D%3D%5Cdfrac%7B2.5%2B%28-2.5%29%7D%7B2%7D%3D0)
The standard deviation of the uniform distribution is:
![\sigma=\dfrac{Max-Min}{\sqrt{12}}=\dfrac{2.5-(-2.5)}{\sqrt{12}}=\dfrac{5}{3.46}=1.44](https://tex.z-dn.net/?f=%5Csigma%3D%5Cdfrac%7BMax-Min%7D%7B%5Csqrt%7B12%7D%7D%3D%5Cdfrac%7B2.5-%28-2.5%29%7D%7B%5Csqrt%7B12%7D%7D%3D%5Cdfrac%7B5%7D%7B3.46%7D%3D1.44)
The sampling distribution can be approximated as a normal distribution with the following parameters:
![\mu_s=\mu=0\\\\\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.44}{\sqrt{48}}=\dfrac{1.44}{6.93}=0.21](https://tex.z-dn.net/?f=%5Cmu_s%3D%5Cmu%3D0%5C%5C%5C%5C%5Csigma_s%3D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%3D%5Cdfrac%7B1.44%7D%7B%5Csqrt%7B48%7D%7D%3D%5Cdfrac%7B1.44%7D%7B6.93%7D%3D0.21)
We can now calculate the probability that the sample mean falls within 0.25 from the mean of the true ages using the z-score:
![z=\dfrac{X-\mu}{\sigma}=\dfrac{0.25-0}{0.21}=\dfrac{0.25}{0.21}=1.19\\\\\\P(|X_s-\mu|](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%3D%5Cdfrac%7B0.25-0%7D%7B0.21%7D%3D%5Cdfrac%7B0.25%7D%7B0.21%7D%3D1.19%5C%5C%5C%5C%5C%5CP%28%7CX_s-%5Cmu%7C%3C0.25%29%3DP%28%7Cz%7C%3C1.19%29%3D0.766)
Answer:
This raccoon is very cool
Step-by-step explanation: