Light A flashes every 2 minutes while light B flashes every 7. The goal is to figure out when both lights flash at the same time and then figure out the other part later. You have to find the common multiples of 7 and 2. Meaning that you have to find out which number can they both be multiplied into. In this case, it is 14 because 7 can be multiplied by 2 to get 14 and 2 can be multiplied by 7. So if every 14 minutes they flash together at the same time, now you need to find out what time AFTER 3 will they both flash. You know that they both flashed at 1:00 so they will flash again at 1:14 and 1:28 and so on, but you need to find out when is the soonest they will flash after 3. 2 hours after the 1:00 flash will be 3:00 so that is 120 minutes. 120 minutes divided by 14 minutes comes to 8.5 but you dont need the decimal. Just simply multiply 14 by 8 and that comes to 112 minutes and if you add that to 1:00 you get 2:52. so they flashed at 2:52 so the next time they flash will be 14 minutes after 2:52. Sorry for the super long answer
Answer:
The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.
The random variable <em>X</em> is exponentially distributed with mean 7 minutes.
Then the parameter of the distribution is,
.
The probability density function of <em>X</em> is:
Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:
![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7Be%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5B-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%5D%5E%7B9%7D_%7B6%7D%5C%5C%5C%5C%3De%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%206%7D-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%209%7D%5C%5C%5C%5C%3D0.424373-0.276453%5C%5C%5C%5C%3D0.14792%5C%5C%5C%5C%5Capprox%200.148)
Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Answer:
Step-by-step explanation:
The distance d between a point (m , n ) and a line in the form
Ax + By + C = 0 , is calculated as
d = 
Here (m, n ) = (6, 2 ) and
6x - y = - 3 ( add 3 to both sides )
6x - y + 3 = 0 → A = 6, B = - 1, C = 3
d = 
= 
= 
= 
× 
= 
← cancel 37 on numerator/ denominator
=
Answer:
Width = 4 m
Length = 7 m
Step-by-step explanation:
given:
perimeter of a rectangle = 22m
L = 3 + W
perimeter = 2L + 2W
perimeter = 2 (3 + W) + 2W
22 = 6 + 2W + 2W
22 - 6 = 4W
W = 16 / 4
W = 4 m
L = 3 + W
L = 3 + 4
L = 7 m
check:
perimeter = 2L + 2W
22 = 2(7) + 2(4)
22 = 14 + 8
22 = 22 ---- OK
Answer:
4x2+5x2-2x+8x=9x2+6x
Step-by-step explanation:
