Answer:
its B on edg2020
Step-by-step explanation:
B: Crops in the drought-affected areas were destroyed, which led to a decreased food supply and higher food prices.
John is organizing a local event. He expects the approximate attendance for the event to be modeled by the function a(t) = -16t2 + 48t + 64, where t is time in hours. Assuming the event ends when there are no attendees, plot the domain to represent the duration of the event. line plot
Answer:
the duration of this event is 4 hours
Step-by-step explanation:
This function is a quadratic one
let Δ be the dicriminant :
a = -16b = 48c= 64 Δ = 48²-4*(-16)*64 = 6400so there are two values that satisfy -16t²+48t+64 = 0 x and y
x= (-48+80)/-16*2 = -1y= (-48-80)/-16*2= 4x<0 so w won't take it since time is a positive value here
so t = y = 4h
The average number of tunnel construction projects that take place at any one time in a certain state is 3. Find the probability of exactly five tunnel construction projects taking place in this state.
Answer: 0.1008188
Step-by-step explanation:
The question will usng the poisson distribution formula:
Given :
Mean(λ) number of occurrence in a given interval = 3
P(X=x) = Probability of exactly x occurrence in a given interval
Number of desired occurence(x) = 5
P(X=x) = [(λ^x) * (e^-λ)] / x!
Where ; e = base of natural logarithm = 2.7182818
P(X=5) = [(3^5) * (e^-3)] / 5!
P(X=5) = [(243) * (0.0497870)] / 120
P(X=5) = [12.098257] / 120
P(X=5) = 0.1008188
Answer:0.10
Step-by-step explanation:
A small regional carrier accepted 16 reservations for a particular flight with 12 seats. 8 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 48% chance, independently of each other.
A) Find the probability that overbooking occurs.
B) Find the probability that the flight has empty seats.
Answer:
a) 32.04% probability that overbooking occurs.
b) 40.79% probability that the flight has empty seats.
Step-by-step explanation:
For each booked passenger, there are only two possible outcomes. Either they arrive for the flight, or they do not arrive. The probability of a passenger arriving is independent of other passengers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Our variable of interest are the 8 reservations that went for the passengers with a 48% probability of arriving.
This means that [tex]n = 8, p = 0.48[/tex]
A) Find the probability that overbooking occurs.
12 seats, 8 of which are already occupied. So overbooking occurs if more than 4 of the reservated arrive.
[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{8,5}.(0.48)^{5}.(0.52)^{3} = 0.2006[/tex]
[tex]P(X = 6) = C_{8,6}.(0.48)^{6}.(0.52)^{2} = 0.0926[/tex]
[tex]P(X = 7) = C_{8,7}.(0.48)^{7}.(0.52)^{7} = 0.0244[/tex]
[tex]P(X = 8) = C_{8,5}.(0.48)^{8}.(0.52)^{0} = 0.0028[/tex]
[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2006 + 0.0926 + 0.0244 + 0.0028 = 0.3204[/tex]
32.04% probability that overbooking occurs.
B) Find the probability that the flight has empty seats.
Less than 4 of the booked passengers arrive.
To make it easier, i will use
[tex]P(X < 4) = 1 - (P(X = 4) + P(X > 4))[/tex]
From a), P(X > 4) = 0.3204
[tex]P(X = 4) = C_{8,4}.(0.48)^{4}.(0.52)^{4} = 0.2717[/tex]
[tex]P(X < 4) = 1 - (P(X = 4) + P(X > 4)) = 1 - (0.2717 + 0.3204) = 1 - 0.5921 = 0.4079[/tex]
40.79% probability that the flight has empty seats.
An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency
Answer:
The frequency table is shown below.
Step-by-step explanation:
The data set arranged ascending order is:
S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58, 60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}
It is asked to use the minimum value from the data set as the lower class limit for the first row.
So, the lower class limit for the first class interval is 33.
To determine the class width compute the range as follows:
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
[tex]=84-33\\=51[/tex]
The number of classes requires is 5.
The class width is:
[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]
So, the class width is 10.
The classes are:
33 - 42
43 - 52
53 - 62
63 - 72
73 - 82
83 - 92
Compute the frequencies of each class as follows:
Class Interval Values Frequency
33 - 42 33 , 34 , 39 3
43 - 52 48 , 49 , 50 3
53 - 62 53 , 54 , 55 , 56 , 58 , 58, 60 7
63 - 72 63 , 64 , 65 , 70 , 71 5
73 - 82 74 1
83 - 92 84 1
TOTAL 20
Compute the relative frequencies as follows:
Class Interval Frequency Relative Frequency
33 - 42 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
43 - 52 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
53 - 62 7 [tex]\frac{7}{20}\times 100\%=35\%[/tex]
63 - 72 5 [tex]\frac{5}{20}\times 100\%=25\%[/tex]
73 - 82 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
83 - 92 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
TOTAL 20 100%
According to insurance records, a car with a certain protection system will be recovered 87% of the time. If 600 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen?
Answer:
The mean and standard deviation of the number of cars recovered after being stolen is 522 and 8.24 respectively.
Step-by-step explanation:
We are given that according to insurance records, a car with a certain protection system will be recovered 87% of the time.
Also, 600 stolen cars are randomly selected.
Let X = Number of cars recovered after being stolen
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=01,2,3,......[/tex]
where, n = number of trials = 600 cars
r = number of success
p = probability of success which in our question is the probability
that car with a certain protection system will be recovered,
i.e. p = 87%.
So, X ~ Binom(n = 600, p = 0.87)
Now, the mean of X, E(X) = [tex]n \times p[/tex]
= [tex]600 \times 0.87[/tex] = 522
Also, the standard deviation of X, S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{600 \times 0.87 \times (1-0.87)}[/tex]
= 8.24
which of the following is the probability that a blue marble will be selected from a bag containing 9 red marbles,6 blue marbles,7green marbles, and 11 yellow marbles if one is selected randomly?
Answer:
2/11
Step-by-step explanation:
Total number of marbles: 9 + 6 + 7 + 11 = 33
Number of blue marbles: 6
p(blue marble) = 6/33 = 2/11
Answer:
Probability = 2/11Step-by-step explanation:
[tex]9- red- marbles\\6- blue- marbles\\7-green- marbles\\ 11- yellow \\Probability = \frac{Event}{Total -No -of -Possible -Outcome} \\\\\\P = \frac{6}{9+6+7+11} \\P = \frac{6}{33} \\\\P = \frac{2}{11} \\[/tex]
Someone can help me pleaseeee, for tonight with 2 or 3 will be fine
FIND THE LENGTH
Answer:
4)..21 units
5). 15 units
6). 25 units
Step-by-step explanation:
4). Since ΔABC ~ ΔDEF,
Their corresponding sides will be proportional.
[tex]\frac{AB}{DE}= \frac{BC}{EF}= \frac{AC}{DF}[/tex]
Since, [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex]
[tex]\frac{14}{42}=\frac{7}{x}[/tex]
x = [tex]\frac{42\times 7}{14}[/tex]
x = 21 units
5). Since ΔABC ~ ΔDEF,
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
[tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
[tex]\frac{6}{9}=\frac{10}{x}[/tex]
x = 15 units
6). Since ΔABC ~ ΔDEF,
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
[tex]\frac{BC}{EF}=\frac{AC}{DF}[/tex]
[tex]\frac{6}{30}=\frac{5}{x}[/tex]
x = 25 units
Jess is cutting bows of ribbon which will be used to wrap gifts. If jess needs 1 7/11 feet of ribbon to make a bow and she has 36 feet of ribbon, then how many bows can jess make?
Answer:
22
Step-by-step explanation:
You need to divide 36 ft by 1 7/11 ft, and then round down if you don't get a whole number.
[tex]\dfrac{36~ft}{1 \frac{7}{11}~ft} =[/tex]
[tex]= \dfrac{36}{\frac{18}{11}}[/tex]
[tex] = \dfrac{36}{1} \times \dfrac{11}{18} [/tex]
[tex] = \dfrac{36 \times 11}{1 \times 18} [/tex]
[tex] = 22 [/tex]
Answer: 22
The lines shown below are parallel. If the green line has a slope of -1, what is
the slope of the red line?
A. 1
6
0
B. -1
C.-2
5
D. 2
Answer:
-1
Step-by-step explanation:
Parallel lines have the same slope. If the slope of the green line is -1, the slope of the red line is -1
The slope of the red line is -1
What are parallel lines?"These are the lines in the same plane that are at equal distance from each other and never meet."
What is slope of a line?"It is the change in y coordinate with respect to the change in x coordinate."
For given question,
The red line and the green line shown in the figure are parallel lines.
The slope of the green line is -1.
We know that the slope of the parallel lines is equal.
This means the slope of red line would be -1
Therefore, the slope of the red line is -1
Learn more about slope of a line here:
https://brainly.com/question/14511992
#SPJ2
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Answer:
x = y = 26 cm; z = 13 cm
Step-by-step explanation:
We can calculate the dimensions of the square base as
∛(2·8788) = 26 cm
the height of the box will be half of 26/2 which is 13 cm.
x = y = 26 cm; z = 13 cm
then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier
area = xy +2(xz +yz)
But we were given the volume as 8788
Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then
L = xy +2(xz +yz) +λ(xyz -8788)
For x: we have
y+2z +λyz=0
For y we have
y: x +2z +λxz=0
For z we have 2x+2y +λxy=0............eqn(*)
For we have xyz -8788=0
If we simplify the partial derivative equation of y and x above then we have
λ = (y +2z)/(yz).
= 1/z +2/y............eqn(1)
λ = (x +2z)/(xz)
= 1/z +2/x.............eqn(2)
Set eqn(1 and 2) to equate we have
1/z +2/y = 1/z +2/x
x = y
From eqn(*) we can get z
λ = (2x +2y)/(xy) = 2/y +2/x
If we simplify we have
1/z +2y = 2/x +2/y
Then z = x/2
26/2 =13
Therefore,
x = y = 2z = ∛(2·8788)
X= 26
y = 26 cm
z = 13 cm
Pleaase help me..........
Answer: 12/25
Steps:
1. Turn 0.48 into 48/100
2. Divide the numerator and denominator of 48/100 by 4, which ends up as 12/25.
0.48 as a fraction is 48/100
We can simplify this fraction.
48÷2/100÷2 → 24/50
24÷2/50÷2 → 12/25
Therefore, the answer is A.
Best of Luck!
In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly. What is the average population growth per year?
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.
Simplify the expression (5j+5) – (5j+5)
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Determine the slope-intercept form of the equation of the line parallel to y = -4/3 x + 11 that passes through the point (–6, 2). y = x +
Answer: -4/3x - 6
Step-by-step explanation:
First, let's find the slope of the line
y=- -4/3x+11
As the equation is already in slope-intercept form y=mx+c ,
Slope = -4/3
Let a point (x,y) be on the new line.
By finding the slope again,
y−2/x+6= -4/3
y−2= -4/3(x+6)
y−2= -4/3x−8
y = -4/3x - 6
{x:x∈z and |x| ≤ 2}
Answer:
x={...-5,-4,-3,-2,-1,0,1,2}
Step-by-step explanation:
Integers are much like of a whole number but they include negative numbers. But doesn't include neither fractions nor decimals.Please answer this correctly without making mistakes
Answer:
Question 2
Step-by-step explanation:
2) The time when she woke up was - 3° C
During nature walk, temperature got 3° C warmer than when she woke up.
So, temperature during nature walk = - 3 + 3 = 0° C
an arithmetic series has first term 160 and common difference d . the sum of the first 25 terms of the series 3500 . find the common difference d.
Answer:
d = - [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
The sum to n terms of an arithmetic series is
[tex]S_n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 160, n = 25 and [tex]S_{25}[/tex] = 3500 , thus
[tex]\frac{25}{2}[/tex] [ (2 × 160) + 24d ] = 3500, that is
12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )
320 + 24d = 280 ( subtract 320 from both sides )
24d = - 40 ( divide both sides by 24 )
d = - [tex]\frac{40}{24}[/tex] = - [tex]\frac{5}{3}[/tex]
The Science Club has 24 members, 20 girls and 4 boys. What is the ratio of girls to boys in the Science Club?
Answer:
5:1
Step-by-step explanation:
You divide both to find a common multiple which in this case is 5
20:4 ----> (20÷4):(4×5) ----> 5:1
Hope that explains it :)
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
find the solutions to 9x^2-54x=0
Answer:
x₁ = 0
x₂ = 6
Step-by-step explanation:
9x² - 54x = 0
9x(x - 6) = 0
x(x - 6) = 0
x = 0
x - 6 = 0 → x = 6
Hope this helps! :)
Answer:
x₁ = 0
x₂ = 6
Step-by-step explanation:
9x² - 54x = 0
9x(x - 6) = 0
9x = 0 => x₁ = 0
x - 6 = 0 => x₂ = 6
The average life a manufacturer's blender is 5 years, with a standard deviation of 1 year. Assuming that the lives of these blenders follow approximately a normal distribution, find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
Answer:
55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 5, \sigma = 1, n = 9, s = \frac{1}{\sqrt{9}} = 0.3333[/tex]
Find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 4.5. So
X = 5.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.1 - 5}{0.3333}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a pvalue of 0.6179
X = 4.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.5 - 5}{0.3333}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.6179 - 0.0668 = 0.5511
55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
what is the equation of the line that is parallel to the given line and passes through the point (2, 3) ? a. x + 2y = 4 b. x + 2y = 8 c. 2x + y =4 d. 2x + y = 8
Answer:
see explanations
Step-by-step explanation:
The given blue line has a slope of m = -1/2.
The line parallel to the given line passing through point (x0,y0)=(2,3) is given by the point-slope form:
(y-y0)=m(x-x0)
substitute values
(y-3) = (-1/2)(x-2)
Expand and transpose
y = (-1/2)x + 1 + 3
y = (-1/2)x + 4 ....................(1)
We choose the second equation b. x+2y=8 and convert to slope-intercept form:
2y=-x+8
y = (-1/2)x + 4, which is exactly equation (1)
So
b. x+2y=8 is the correct answer.
Answer:
b. x + 2y = 8
Step-by-step explanation:
Which of the following best describes the algebraic expression 5(x + 2) - 3 ?
bre
Answer:
D
Step-by-step explanation:
a) Al usar un microscopio el microscopio se amplía una célula 400 veces. Escribe el factor de ampliación como cociente o como escala.
b) La imagen de una célula usando dicho microscopio mide 1,5 mm ¿ Cuánto mide la célula en la realidad?
Answer:
x = 0,00375 mm
Step-by-step explanation:
a) El factor de ampliación es 400/1 es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio
b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:
Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)
Es decir 1,5 mm ⇒ 400
x (mm) ⇒ 1 (tamaño real de la célula)
Entonces
x = 1,5 /400
x = 0,00375 mm
M/J Grade 8 Pre-Algebra-PT-FL-1205070-003
Answer:
Following are the description of the given course code:
Step-by-step explanation:
The given course code is Pre-Algebra, which is just an introduction arithmetic course programs to train high school in the Algebra 1. This course aims to strengthen required problem solving skills, datatypes, equations, as well as graphing.
In this course students start to see the "big picture" of maths but also understand that mathematical, algorithmic, and angular principles are intertwined to form a basis for higher mathematics education.The duration of this code is in year and it is divided into two levels. In this, code it includes PreK to 12 Education Courses , with the general mathematics .Answer:
A
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
What is the solution to the system of equations? please explain I really need help
Answer:
The solution is the point where the lines intersect.
The answer is (-3 , -8)
find the circumference of a circle with a diameter of 6 cm
Circumference = πd
~substitute → (π)(6 cm)
~simplify → 6π cm.
So the circumference of the circle shown here is 6π cm.
Answer:
18.85 cm
Step-by-step explanation:
The circumference of a circle has a formula.
Circumference = π × diameter
The diameter is 6 centimeters.
Circumference = π × 6
Circumference ≈ 18.85
The circumference of the circle is 18.85 centimeters.
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $800, 3 prizes of $200, 5 prizes of $50, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answer:
The expected value of this raffle if you buy 1 ticket is $0.41.
Step-by-step explanation:
The expected value of the raffle if we buy one ticket is the sum of the prizes multiplied by each of its probabilities.
This can be written as:
[tex]E(X)=\sum p_iX_i[/tex]
For example, the first prize is $800 and we have only 1 prize, that divided by the number of tickets gives us a probability of 1/5000.
If we do this with all the prizes, we can calculate the expected value of a ticket.
[tex]E(X)=\sum p_iX_i\\\\\\E(X)=\dfrac{1\cdot800+3\cdot200+5\cdot50+20\cdot20}{5000}\\\\\\E(X)=\dfrac{800+600+250+400}{5000}=\dfrac{2050}{5000}=0.41[/tex]