Answer:
0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Over a long period of time, an average of 14 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives in a particular one second period.
Each minute has 60 seconds, so 
Either no particle arrives, or at least one does. The sum of the probabilities of these events is decimal 1. So
We want 
. So
In which
0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.
Answer:
Step-by-step explanation:
Explanation:
Start by writing out your starting expression
x
2
−
5
x
2
+
5
x
−
14
−
x
+
3
x
+
7
Next, factor the denominator of the first fraction
x
2
+
5
x
−
14
x
2
+
7
x
−
2
x
−
14
x
(
x
−
2
)
+
7
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
Your expression is thus equivalent to
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
x
+
3
x
+
7
Since you have to subtract two fractions, you need to find the commonon denominator first. To do that, multiply the second fraction by
x
−
2
x
−
2
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
(
x
+
3
)
⋅
(
x
−
2
)
(
x
−
2
)
⋅
(
x
+
7
)
This will get you
x
2
−
5
−
(
x
+
3
)
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
x
2
−
5
−
x
2
−
x
+
6
(
x
−
2
)
(
x
+
7
)
=
1
−
x
(
x
−
2
)
(
x
+
7
)
Answer:
The shape is translated four units left, and 2 units up, therefore the answer would be x=-4 and y=+2
Answer:
6 papayas and 11 pineapples
Step-by-step explanation:
So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.
So, papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.
lets try 8 papayas, and 9 Pineapples.
$2.50 x 8 = $20.00 total on Papayas
$3.00 x 9 = $27.00 total on Pineapples.
That would only be $47 spent total.
Lets try 10 papayas and 7 pineapples.
$2.50 x 10 = $25.00
$3.00 x 7 = $21.00
That would only be a total of $26 spent.
Lets try 6 papayas and 11 pineapples.
$2.50 x 6 = $15.00
$3.00 x 11 = $33.00
This would be a total of $48 spent.
