1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5
Answer:
P(0) = 0.6825
P(1) = 0.2607
Step-by-step explanation:
From the given information, the number of homicide is 107 and the total number of homicides per city –year is 280.
Let us denote the number of homicides per city-year as X.
The mean value, X is calculated as:
\begin{array}{c}\\{\rm{Mean}} = \frac{{107}}{{280}}\\\\ = 0.382\\\end{array}
Mean= 107/280 = 0.382
The mean number of homicides per city- year \left( {\lambda = \mu } \right)(λ=μ) is 0.382.
a. The probability that zero homicides is obtained is as below:
\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}
P(X=0) = e −0.382 (0.382)⁰/1
= (0.6825)(1)
/1
P(X=0) = 0.6825
Thus, the probability that zero homicides P(0) is 0.6825.
b. The probability that one homicides is obtained is as below:
\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}
P(X=1) = e −0.382 (0.382)¹/1
= (0.6825)(0.382)/1
P(X=1) = 0.2607
Thus, the probability that zero homicides P(0) is 0.2607.
Answer: Ball's kinetic energy became potential energy
Step-by-step explanation:
There are no options attached but this should be along the lines of what happened.
Kinetic energy refers to energy that an object has as a result of it moving whilst potential energy is the opposite and is energy that an object stores within itself due to several factors whilst it is not in motion.
The ball was initially in motion which means that it had kinetic energy but as the ball was slowing down, this energy was gradually converted to potential energy until the balls came to a standstill.
Answer:
y=2x+3
Step-by-step explanation:the rise over run is 2/1 indicating that the slope is 2. the line also passes through 3 which means the y intercept is 3.
