Answer:
Power property for both
Step-by-step explanation:
The power property of logarithms says that if there is an exponent in a logarithm, then that exponent can be pulled to the front.
In the first question, 5 is at the front of the logarithm because it has been pulled from 3. If you move the 5 back to the 3, it would be 3^5, which is 243.
In the second question, 2 is at the front of the logarithm as it has been pulled from the 9. If you move the 2 back to the 9, it would be 9^2, or 81.
Example:
log10^2 would be equal to 2log10.
Answer:
144 ft
Step-by-step explanation:
The object's maximum height is the same as the y-coordinate of the vertex.
To find that, first, finds the x- coordinate(t).You can find it by: first identifying a, b and c.
Multiply the b by negative 1 or simply change its sign and divide it by 2a.
Afterward, plug the answer in the equation to find y, your answer.(ax+bx²+c=-16t²+64t+80).
Therefore, a=-6, b= 64 and c=80-64/2(-16)=-64/-32=2-16(2)²+64(2)+80=144 ft
So the maximum height of the object, when launched 64ft/sec from a platform that is 80 ft high, is 144 ft
Answer:
(a) 0.20
(b) 31%
(c) 2.52 seconds
Step-by-step explanation:
The random variable <em>Y</em> models the amount of time the subject has to wait for the light to flash.
The density curve represents that of an Uniform distribution with parameters <em>a</em> = 1 and <em>b</em> = 5.
So, 
(a)
The area under the density curve is always 1.
The length is 5 units.
Compute the height as follows:
Thus, the height of the density curve is 0.20.
(b)
Compute the value of P (Y > 3.75) as follows:
![P(Y>3.75)=\int\limits^{5}_{3.75} {\frac{1}{b-a}} \, dy \\\\=\int\limits^{5}_{3.75} {\frac{1}{5-1}} \, dy\\\\=\frac{1}{4}\times [y]^{5}_{3.75}\\\\=\frac{5-3.75}{4}\\\\=0.3125\\\\\approx 0.31](https://tex.z-dn.net/?f=P%28Y%3E3.75%29%3D%5Cint%5Climits%5E%7B5%7D_%7B3.75%7D%20%7B%5Cfrac%7B1%7D%7Bb-a%7D%7D%20%5C%2C%20dy%20%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B5%7D_%7B3.75%7D%20%7B%5Cfrac%7B1%7D%7B5-1%7D%7D%20%5C%2C%20dy%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5By%5D%5E%7B5%7D_%7B3.75%7D%5C%5C%5C%5C%3D%5Cfrac%7B5-3.75%7D%7B4%7D%5C%5C%5C%5C%3D0.3125%5C%5C%5C%5C%5Capprox%200.31)
Thus, the light will flash more than 3.75 seconds after the subject clicks "Start" 31% of the times.
(c)
Compute the 38th percentile as follows:
Thus, the 38th percentile is 2.52 seconds.
You would write the equation out as x=35x+500
You substitute x for 7 so it’s x= 35(7)+500
So the answer will be 745 dollars
