Answer:
a) z* = -1.97
b) z* = -2.33
c) z* = -1.65
d) z* = 2.04
e) z* = 2.33
f) z* = -1.25.
Step-by-step explanation:
Z-score:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
a. P(z < z*) = 0.0244
We have to look at the ztable, and find z which has a pvalue of 0.0244. So it is z* = -1.97
b. P(z < z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 0.0098. So it is z* = -2.33
c. P(z < z*) = 0.0496
We have to look at the ztable, and find z which has a pvalue of 0.0496. So it is z* = -1.65
d. P(z > z*) = 0.0204
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0204 = 0.9796. So z* = 2.04
e. P(z > z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0098 = 0.9902. So z* = 2.33
(f) P(z > z* or z < -z*) = 0.201
This is z which has a pvalue of 0.201/2 = 0.1055. So it is z* = -1.25.
Answer:
The scale of a model train is 1 inch to 13.5 feet. One of the cars of the model train is 5 inches long. What is the length, in feet, of the actual train car?
Algebra
Step-by-step explanation:
I need this answer too, did you figure it out?
Volume = 4 * 4 * 7 = 112 cm^3 Answer
Answer:
C
Step-by-step explanation:
Remember that if s(t) is a position function then:
is the velocity function and
is the acceleration function.
So, to find the acceleration, we need to solve for the second derivative of our original function. Our original function is:
So, let's take the first derivative first with respect to t:
![\frac{d}{dt}[s(t)]=\frac{d}{dt}[t^2+4t+10]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5Bs%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%2B4t%2B10%5D)
Expand on the right:
![s'(t)=\frac{d}{dt}[t^2]+\frac{d}{dt}[4t]+\frac{d}{dt}[10]](https://tex.z-dn.net/?f=s%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B4t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B10%5D)
Use the power rule. Remember that the derivative of a constant is 0. So, our derivative is:
This is also our velocity function.
To find acceleration, we want to second derivative. So, let's take the derivative of both sides again:
![\frac{d}{dt}[s'(t)]=\frac{d}{dt}[2t+4]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5Bs%27%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B2t%2B4%5D)
Again, expand the right:
![s''(t)=\frac{d}{dt}[2t]+\frac{d}{dt}[4]](https://tex.z-dn.net/?f=s%27%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B2t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B4%5D)
Power rule. This yields:
So, our answer is C.
And we're done!
