Data from 14 cities were combined for a 20-year period, and the 280 city-years included a total of 193 homicides. After finding the mean number of homicides per city-year, find the probability
that a randomly selected city-year has the following numbers of homicides. Then compare the actual results to those expected by using the Poison probabilities.
Homicides each city-year
a.0
b.
c. 2
d.:
3
e.
D
Next
Actual results
138
100
35
5
2
Answers
1. The probabilities of Poison distribution are: \(P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012\). \(P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447\). \(P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189\).
What is Poisson distribution?The Poisson distribution is a discrete probability distribution that defines the number of events that take place during a specific period of time or space, provided that they do so independently of one another and at a certain average rate. Siméon Denis Poisson, a French mathematician, invented it in the early 19th century to simulate the occurrence of uncommon events, such as horse kick fatalities in the Prussian army. He gave it his name.
The mean or expected value of the number of occurrences in the interval is represented by the Poisson distribution's single parameter, indicated by the Greek letter lambda.
The Poisson distribution is given as:
\(P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x!\)
Now,
a. For P(0) we have:
λ = (total number of homicides) / (total number of city-years)
= 193 / 280 = 0.689
Substituting the values of λ = 0.689 and x = 0 we have:
\(P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012\)
b. For P(1), we can plug in λ = 0.689 and x = 1 :
\(P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447\)
c. For P(2), we can plug in λ = 0.689 and x = 2:
\(P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189\)
d. For P(3), we can plug in λ = 0.689 and x = 3:
\(P(3) = (e^{(-0.689)} * 0.689^3) / 3! = 0.0272\)
e. P(4), we can plug in λ = 0.689 and x = 4:
\(P(4) = (e^{(-0.689)} * 0.689^4) / 4! = 0.0047\)
2 ) The comparison for the actual and distributed values is:
Expected 0 homicides: 0.5012 * 280 ≈ 140.35
Expected 1 homicide: 0.3447 * 280 ≈ 96.72
Expected 2 homicides: 0.1189 * 280 ≈ 33.32
Expected 3 homicides: 0.0272 * 280 ≈ 7.62
Expected 4 homicides: 0.0047 * 280 ≈ 1.31
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Related Questions
Graph the linear
equation.
Find three
points
that solve the equation, then plot
on the graph.
3x - 4y = -18
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph has a slope of 3/4, so it is convenient to choose x-values that are 4 units apart. Three points are shown in the table and on the graph.
Calculate the constant of proportionality, k, for the given table.
Answers
Answer:
k = y/x
Step-by-step explanation:
1/5, 2/10, 3/15 . . . all equal to 1/5 which is what the value of k is; 'k' stands for constant of proportionality
HELPPPP PLEASEEEE!!!!
Answers
Answer: 5, 30, 15
Step-by-step explanation:
y =3x
y is x multiplied by 3
15 divided by 3 is 5
10 multiplied by 3 is 30
45 divided by 3 is 15
Write an equation for the line parallel to the line -7x - 7y= 7 through the point (-1,2)
Answers
Answer:
\(y=-x+1\)
Step-by-step explanation:
Slope-Intercept Formula:It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:
\(-7x-7y=7\)
add 7x to both sides:
\(-7y=7x+7\)
Divide both sides by -7
\(y=-x-1\)
Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:
\(y=-x+b\text{ where b }\ne -1\)
We're given the point (-1, 2) and we can use it to solve for that "b" value.
We plug in -1 as x and 2 as y
\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)
Now we just plug this into the general equation to get: \(y=-x+1\)
100 POINTS!!! And BRAINLIEST
Select the correct option for each
cos(-25°) = _____.
cos 115°
cos 25°
sin 25°
-cos 335°
sin(-136°) = _____.
sin (-316)°
-sin 44°
-sin 316°
-cos 44°
tan(-212°) = _____.
-cot 32°
tan 32°
cot 32°
-tan 32°
cot(-315°) = _____.
cot (-45)°
cot 135°
cot 45°
-cot 45°
Answers
Using equivalent angles, the correct options are given as follows:
cos(-25°) = cos(25º).sin(-136º) = -sin(44º).tan(-212º) = -tan(32º).cot(-315º) = cot(45º).Cos(-25º)Negative 25 degrees is on the fourth quadrant, with the positive angle measure being given by:
360 - 25 = 335º.
The equivalent angle on the first quadrant is of 360º - 335º = 25º, and the cosine on the first quadrant is positive, just like in the fourth, hence:
cos(-25°) = cos(25º).
Sin(-136º)The positive angle measure is given as follows:
360 - 136 = 224º.
Which is on the third quadrant, in which both the sine and the cosine are negative.
The equivalent angle on the first quadrant is given as follows:
224º - 180º = 44º.
Hence the expression is:
sin(-136º) = -sin(44º).
Tan(-212º)The positive angle measure is given as follows:
360 - 212 = 148º.
Which is on the second quadrant, in which the tangent is negative.
The equivalent angle on the first quadrant is given as follows:
180º - 148º = 32º.
Hence the expression is:
tan(-212º) = -tan(32º).
Cot (-315º)The positive angle is given as follows:
360 - 315 = 45º.
Which is already on the first quadrant, hence the expression is given as follows:
cot(-315º) = cot(45º).
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359
110"
350
Triangle A
Triangle B
Given the triangles above, what is the measure, in degrees, of angle x?
Answers
i think the answer is 35° because the triangles are congruent to each other
Which statements about the factors of the terms in the expression 20a+15ab+ 24b are true? Select three options.
The factors common to 20a and 15ab are 1,5, a, and b.
The factors common to 20a and 15ab are 1, 5, and als
The factors common to 20a and 24b are 1, 2, and 4
The GCF of the expression is ab
The GCF of the expression is 1
Answers
Answer:
B, C, EStep-by-step explanation:
Given the expression:
20a + 15ab + 24bAnswer options:
The factors common to 20a and 15ab are 1,5, a, and b
False. b is not a common factorThe factors common to 20a and 15ab are 1, 5, and a
TrueThe factors common to 20a and 24b are 1, 2, and 4
TrueThe GCF of the expression is ab
False. ab is a factor of one of the terms only.The GCF of the expression is 1
Trueone card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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2x - 7 + 3x = 4x + 2 need help with this one
Answers
Answer:
x = 9
Step-by-step explanation:
To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:
Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:
2x + 3x - 4x = 2 + 7
Simplifying the left side: x = 9
Simplify the right side of the equation:
x = 9
Therefore, the solution to the equation is x = 9.
Identify the vertex, intercepts and whether of the graph of the function below opens up or down. Type your answers as a point (x,y). If an intercept does not exist type "none". If more than one intercept exists you can type either intercept.f(x)= -|x-1|-2 Vertex = Answerx intercept = Answery intercept = Answergraph opens Answer
Answers
Vertex = (1, -2)
x - intercept = None
y-intercept = (0, -3)
Graph opens down
Explanation:The given absolute value function is:
f(x) = -|x - 1| - 2
Generally, an absolute value function is of the form:
f(x) = a|x - h| + k
where the vertex is (h, k)
Comparing the given function with the general absolute value function:
a = -1, h = 1, k = -2
Therefore, the vertex, (h, k) = (1, -2)
To find the x-intercept, substitute f(x) = 0 into the function
0 = -|x - 1| - 2
-|x - 1| = 2
|x - 1| = -2
There are no real roots for this equation. Therefore, there is no x-intercept
The x-intercept = None
To find the y-intercept, substitute x = 0 into the function
f(x) = -|0 - 1| - 2
f(x) = -|-1| - 2
f(x) = -1 - 2
f(x) = -3
The y-intercept = (0, -3)
Since a = -1 (that is, negative), the graph opens down
Use the tangent to find the unknown side lengths.
Answers
Answer:
4.076
Step-by-step explanation:
tan27°= |AC|/8
8*tan27°= 4.076
Use the tangent to find the unknown side lengths.
This is the answer
Ac= 4.07
Ab=8.97
Choose the best estimate for the quotient.
27.2/178.6
A) 5
B) 6
C) 50
D) 60
Answers
Answer:
B
Step-by-step :
The quotient is 6.5 so the estimate is closest to 6.
Select the correct answer.
What is the solution to the equation? √x + 2 = x
Neeeed helppp
Answers
Answer:
\(x=4\)
Step-by-step explanation:
\(\sqrt{x}+2=x \\ \\ \sqrt{x}=x-2 \\ \\ x=x^2-4x+4 \\ \\ x^2-5x+4=0 \\ \\ (x-4)(x-1)=0 \\ \\ x=1,4\)
Upon substituting these solutions back into the original equation, only \(x=4\) is a solution.
The solution to the equation is x = -1 and x = 2
What is a equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
The equation given is
\(\sqrt{x + 2} = x\)
Squaring both the sides
x + 2 = x²
x² - x - 2 = 0
(x + 1)(x - 2)
x = -1
x = 2
The solution of the equation \(\sqrt{x + 2} = x\) is x = -1 and x = 2
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(a) simplify.
(I) 3a–5b–a+2b
Answers
Answer:2a-3b
Step-by-step explanation:
collect by terms- 3a -a = 2a
-5b + 2b = -3b
Answer:
2a-3b
Step-by-step explanation:
=3a-5b-a+2b
=2a-5b+2b
=2a-3b
What interest rate would be necessary to obtain $6,500 in 8 years if $5,000 is the amount of the original investment and the interest is compounded yearly?
Answers
The formular is
\(A=P(1+\frac{r}{n})^{nt}\)\(6500=5000(1+\frac{r}{1})^{1\times8}\)\(\frac{6500}{5000}=(1+r)^8\)\(1.3=(1+r)^8\)\(1.3^{\frac{1}{8}}=(1+r)^{8\times\frac{1}{8}}\)\(1.3^{0.125}=1+r\)\(1.0333=\text{ 1+r}\)subtract 1 from bothside
\(r\text{ = 0.0333}\)R = 0.0333 x 100% = 3.33%
i cannot figure this out for the life of me. any help?
Find f(3) for the
piece-wise function.
f(x) =
x+1
X
if x > 0
if x ≤ 0
f(3) = [?]
Answers
Answer:
f(3) = 3 + 1 = 4
Step-by-step explanation:
Since 3 > 0, we need to focus on the part of the function where x > 0. So:
f(3) = 3 + 1 = 4.
what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answers
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
Solve |x-5| > -2. Write your solution in interval notation.
Answers
Answer:
(−∞,∞)
Step-by-step explanation:
Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.
All real numbers
So, the answer is (−∞,∞)
Simplify each and write it as a mix number
12/14
27/90
Answers
Step-by-step explanation:
Divide 12/14 by 2:
\(\frac{12 \div 2}{14 \div 2} =\frac{6}{7}\)
Simplified. Can't be a mixed number, less than 1.
Divide 27/90 by 9:
\(\frac{27 \div 9}{90 \div 9} =\frac{3}{10}\)
Simplified. Can't be a mixed number, less than 1.
Find the area of the shaded regions. Give your answer as a completely simplified
exact value in terms of π (no approximations).
Answers
The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle in which the shaded region is shown.
The radius of the small circle r = 3 cm
The radius of the large circle R = 3+4 = 7 cm
The area of the shaded region:
= area of the large circle sector - an area of the small circle sector
= (120/360)[π7²] - (120/360)[π3²]
= 49π/3 - 3π
= 40π/3 square cm or
= 13.34π square cm
Thus, the area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
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4 - (18) + 5 please help
Answers
Answer:
-9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
PEMDAS
4-18= -14
-14+5 = -9
Which variable expression represents the word phrase?
the sum of 12 and the quotient of 9 and a number
12−(9÷y)
9 + (12 ÷ y)
12 + (9 ÷ y)
12−9y
Answers
Answer:
Answer is 12+(9÷y)
Hope this helps
which of the following describes the correct process for solving the equation 3x+6=21 and arrives at the correct solution?
Answers
To solve the equation 3x + 6 = 21, follow the following steps.
Step 1: Collect like terms
"6" crosses the equality sign to the right and becomes "-6"
3x = 21 - 6
Step 2: Simplify the expression in step 1
Note that 21 - 6 = 15
The equation becomes:
3x = 15
Step 3: Divide both sides 3
The equation becomes
3x / 3 = 15/3
x = 5
Determine whether each quadrilateral is a parallelogram. Justify your answers.
And
Explain why the quadrilateral with the given vertices is a parallelogram. Use the indicated theorem.
Answers
The given quadrilaterals, 1 and 2, are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.
3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.
4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.
What is the proof for the parallelograms?3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:
Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:
AB = √((7 - 0)² + (1 - 0)²) = √50
BC = √((5 - 7)² + (6 - 1)²) = √29
CD = √((-2 - 5)² + (5 - 6)²) =√50
DA = √((0 - (-2))² + (0 - 5)²) = √29
We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.
Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:
Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:
Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5
Slope of RS = (4 - 3) / (4 - (-1)) = 1/5
Slope of QR = (4 - 1) / (4 - 3) = 3
Slope of SP = (3 - 0) / (-1 - (-2)) = 3
The lengths of opposite sides can be calculated using the distance formula:
PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26
RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3
QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10
SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10
We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.
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What is the volume of the rectangular prism shown?
Answers
Answer:
18 3/64
Step-by-step explanation:
i did test trust me
Rewriting 3x^2=6x and solving with rewritten
Answers
Answer:
x = 0 , x = 2
Step-by-step explanation:
3x² = 6x ( subtract 6x from both sides )
3x² - 6x = 0 ← factor out 3x from each term
3x(x - 2) = 0
equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 2 = 0 ( add 2 to both sides )
x = 2
solutions are x = 0 , x = 2
X,(x-36) What is the value of x
Answers
The value of x is 63
How to determine the valueTo determine the value of the variable, we have that;
Angles at a point is equal to 360 degreesComplementary angles are defined as angles that sum up to 90 degreesSupplementary angles are defined as angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesFrom the information given, we have that;
x and x - 36 are complementary angles
Now, equate the angles to 90 degrees, we have;
x + x - 36= 90
collect the like terms, we get;
2x = 90 + 36
add the terms
2x =1 26
Divide by the coefficient
x = 63
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Complete question:
The angles X,(x-36) are complementary. What is the value of x
Help please need ASAP
Answers
Answer:
Step-by-step explanat
126
612
126
Suppose that $2000 is invested at an interest rate of 4.75% per year, compounded continuously. After how many years will the initial investment be doubled?
Answers
Answer: it will take approximately 14.62 years for the initial investment to double at an interest rate of 4.75% per year, compounded continuously.
Step-by-step explanation: Given an investment of $2000 at a continuously compounded interest rate of 4.75%, the balance in the account can be calculated using the following mathematical expression after t years:
The aforementioned equation, A = P * e^(rt), denotes the relationship between the accrued amount (A) and the principal amount (P), compounded continuously at a fixed annual rate of interest (r) over a specific time period (t), as governed by the mathematical constant "e."
In the context of financial calculations, the symbol 'P' denotes the initial capital investment. The interest rate, represented by the variable 'r', is expressed in the form of a decimal. Additionally, 'e' is the mathematical constant, roughly equivalent to 2.71828. Finally, 't' refers to the duration of the investment, measured in years.
In order to determine the duration of time required for the investment to achieve a twofold increase, it is necessary to solve the corresponding equation:
The equation expressed as 2P = P * e^(rt) can be restated more formally as follows. Given a principal investment amount represented by P and a rate of return indicated by r, compounded over time t, the equation can be expressed as the product of P and the exponential function of e^(rt), yielding twice the initial investment amount.
The variable 2P represents the monetary value acquired through doubling the initial investment.
Upon division of both sides by P, the resulting expression is as follows:
The equation 2 equals the exponential function of the base e raised to the power of the product of r and t.
By applying the natural logarithm function to both expressions, the resultant outcome is:
The natural logarithm of 2 can be represented as rt, where r denotes the logarithmic base and t denotes the logarithm of the argument, in accordance with the conventions of academic mathematical writing.
Upon resolving for the variable t, an outcome is yielded:
The mathematical expression t = ln(2) / r can be written in a formal academic style as follows: The equation determines the relationship between time t and the rate of decay r, where t is equal to the natural logarithm of 2 divided by r.
Upon substitution of the provided values, the resultant output is:
The calculated value of the variable t, representing the length of time in years, is approximately equal to 14.62 years, obtained through the algebraic manipulation of the natural logarithmic function of 2 divided by the constant value of 0.0475.
Find the slope of the line described in the table.
A. m = 0
B. m = 1
C. m = 2
D. m = 3
E. m = 4
Answers
Answer:
m = 3
Step-by-step explanation:
