Answer:
94.2 cm^3.
Step-by-step explanation:
Volume of a cone = 1/3πr^2h
The radius of the cone = 1/2 * 6 = 3
So here the volume is:
1/3 * π * 3^2 * 10
= 94.247
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.
Answer:
2017.
Step-by-step explanation:
The equation for the future sale of motorcycles
= 5.75(1.16)^t where t is in years
For cars it is
3.5(1.25)^t
3.5(1.25)^t > 5.75(1.16)^t
(1.25)^t > (5.75/3.5) 1.16^t
t ln 1.25 > ln 1.64286 + t ln 1.16
t ln 1.25 - t ln 1.16 > ln 1.64286
t (ln 1.25 - ln 1.16) > ln 1.64286
t > ln 1.64286 / (ln1.25 - ln 1.16)
t > 6.64 .
So the answer is in the year 2017.
Answer:
Step-by-step explanation:
Industry And logistic
Answer:
x = -4/7, y = 2/7
Step-by-step explanation:
Given: f(x) = 3x + 2 and g(x) = - 4x - 2
The point of intersection of the two functions is the point at which both functions intersect. We have to solve the functions simultaneously to get the solution.
f(x) = y = 3x + 2
y = 3x + 2 (1)
g(x) = y = -4x - 2
y = -4x - 2 (2)
Subtract equation 2 from equation 1:
0 = 7x + 4
7x = -4
x = -4/7
Put x = (-4/7) in y = 3x + 2:
y = 3(-4/7) + 2 = -12/7 + 2 = 2/7
