Lottery: I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value. Enter each row of your table as a separate line, but don't worry too much about formatting. Tables should look similar to those given in questions 1 and 3. Don't forget to give your expected value.
Answers
To give the probability distribution, we need to calculate the probability of each possible outcome and the value of this outcome.
We have 5000 raffle, 1 will win the first prize, 2 will win the second prize, 3 will win the third prize and the rest 4994 will win no prize.
The first prize is $500, but the raffle cost $1, so the outcome is actually $499.
The second prizes are $200 each, minus the cost we have an outcome of $199.
The third prizes are $100 each, minus the cost we have an outcome of $99.
The others will not receive prizes, but they will still have the cost of $1, so the outcome is -$1.
The first prize is 1 in 5000, so the probability is 1/5000
The second prizes are 2 in 500, so the probability is 2/5000
The third prizes are 3 in 5000, so the probability is 3/5000
The lost is the rest of the 4994 in 500, so the probability is 4994/5000
So, the table for the probability distributions is:
Value gained | P(x)
$499 | 1/5000
$199 | 2/5000
$99 | 3/5000
-$1 | 4994/5000
To calculate the expected value, we multiply the value by its probability and add them:
[tex]\begin{gathered} E(x)=499\cdot\frac{1}{5000}+199\cdot\frac{2}{5000}+99\cdot\frac{3}{5000}-1\cdot\frac{4994}{5000}_{} \\ E(x)=\frac{499}{5000}+\frac{398}{5000}+\frac{297}{5000}-\frac{4994}{5000} \\ E(x)=\frac{499+398+297-4994}{5000} \\ E(x)=-\frac{3800}{5000} \\ E(x)=-0.76 \end{gathered}[/tex]So, the expected value if -$0.76.
Related Questions
The points scored on a test for a sample of 39 students are summarized in the following table
Answers
the mean score of the test for sample of 39 students is 76.92.
The data is given as:
Number of students Score of each student Total score
07 90 630
17 80 1360
11 70 770
04 60 240
The total number of students = 7 + 17 + 11 + 4
n = 39
Total scores = 630 + 1360 + 770 + 240
T = 3000
Mean score = T / n
M = 3000 / 39
M = 1000 / 13
M = 76.92
Therefore, the mean score of the test for sample of 39 students is 76.92.
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Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5 Without evaluating or graphing the functions, how do the ranges compare?
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Without evaluating or graphing the functions, it is obvious that the minimum and maximum values in the range of h(x) is greater than the minimum and maximum values in the range of g(x) by 1.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain represents the input values (x-values) to a function.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.
In conclusion, the minimum and maximum values in the range of h(x) differs from those of function g(x) by 1.
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(k²-7k+ 10) ÷ (k − 1)
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k2−7k+10
k−1
k2−5k−2k+10
k−1
k(
k2
k−
5k
k)+2(−
2k
2+
2·5
2)
k−1
Gaby's piggy bank contains quarters and nickels worth $7.50. If she has 58 coins in all, howmany of each does she have?
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let the number of quarters = x , and the number of nickels = y
quarter = $0.25 and nickel = $0.05
So, x + y = 58
x = 58 - y
and 0.25 x + 0.05 y = 7.5
so,
0.25 (58 - y) + 0.05 = 7.5
14.5 - 0.25 y + 0.05 y = 7.5
-0.2 y = -7
y = -7/-0.2 = 35
x = 58 - 35 = 23
So, the number of quarters = 23 and the number of nickels = 35
Simple calculator test - determine the angle, θ, to the nearest whole degree from each of the following:A. cos(θ) = 0.2079B. tan(θ) = 0.2126C. sin(θ) = 0.5446
Answers
Step 1
Find the value of θ using the inverse sign of all the functions.
A)
[tex]\begin{gathered} cos(\theta)=0.2079 \\ \theta=\cos^{-1}(0.2079) \\ \theta\approx78^{\circ} \end{gathered}[/tex]B)
[tex]\begin{gathered} tan(\theta)=0.2126 \\ \theta=\tan^{-1}(0.2126) \\ \theta\approx12^{\circ} \end{gathered}[/tex]C)
[tex]\begin{gathered} sin(\theta)=0.5446 \\ \theta=\sin^{-1}(0.5446) \\ \theta\approx33^{\circ} \end{gathered}[/tex]Not ConnectedThunde...lt BridgeNot Connected2 (07.01 HC)answer the following question. Find the value of sin x and cosy. What relationship do the ratios of sin x® and cos yº share?
Answers
The given triangle is a right-angled triangle.
Consider PO is Hypotenuse.
By using the Pythagoras formula, we get
[tex]PO^2=8^2+6^2[/tex][tex]PO^2=64+36[/tex][tex]PO^2=100=10^2[/tex][tex]PO=10[/tex]Consider the angle x:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =6 and Hypotenuse=10, we get
[tex]\sin x^o=\frac{6}{10}[/tex][tex]\sin x^o=\frac{3}{5}[/tex][tex]\text{Use sin }36.869=\frac{3}{5}[/tex][tex]\sin x^o=\sin 36.869[/tex][tex]x^o=37[/tex]Consider the angle y:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =8 and Hypotenuse=10, we get
[tex]\sin y^o=\frac{8}{10}[/tex][tex]\sin y^o=\frac{4}{5}[/tex][tex]\text{Use }\sin 53.13^{}=\frac{4}{5}[/tex][tex]\sin y^o=\sin \text{ 53.13}[/tex][tex]y^o=53^{}[/tex]Hence the required values are
[tex]x^o=37^o[/tex][tex]y^o=53^o[/tex]Solve by using substitution.=−3−3=−4−5
Answers
hdhduxhx, this is the solution to the exercise:
Multiplying by -1 the second equation, we have:
y = -3x - 3
-y = 4x + 5
____________
0 = x + 2
x = -2
_____________
Now we can solve for y in the first equation, this way:
y = - 3x - 3
y = -3 (-2) - 3
y = 6 - 3
y = 3
____________
Finally, let's prove that x = -2 and y = 3 is correct for the second equation, as follows:
y = -4x - 5
3 = -4 (-2) - 5
3 = 8 - 5
3 = 3
___________
We proved that x = -2 and y = 3 is correct.
claudia earns overtime pay when she works more then 40 hours in a week how many hours of overtime pay did she work for the week of march 4march 4-10march 4 -- 8.5march 5 -- offmarch 6 -- 9.25march 7 -- 8.75march 8 -- 10march 9 -- offmarch 10 -- 7.75A.44.25B. 40.0C. 4.25D. 2.25
Answers
She earns overtime pay when she works more than 40 hours in one week . The number of overtime pay she works for the weeks of march 4 can be calculated below
[tex]\begin{gathered} \text{total hour worked =}8.5\text{ +9.25+8.75+10+7.75=}44.25 \\ \text{The number of overtime pay for the w}eek\text{ of march 4 is 44.25} \end{gathered}[/tex]Consider the quadratic function.What are the x-intercepts and y-intercept?What is the equation of the axis of symmetry?What are the coordinates of the vertex?Graph the function on the coordinate plane. Include the axis of symmetry.
Answers
Kindly check below
1) Let's do it in parts.
a) We can find the x-intercepts by using the factor zero property from each factor. Like this:
[tex]\begin{gathered} -(x+4)=0\Rightarrow-x-4=0\Rightarrow-x=4\Rightarrow x=-4 \\ (x-1)=0\Rightarrow x=1 \end{gathered}[/tex]The best way to find the y-intercept with this factored form is by plugging into that equation x=0
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ y=-\left(x+4\right)\left(x-1\right) \\ y=-(0+4)(0-1) \\ y=-(4)(-1) \\ y=4 \end{gathered}[/tex]b) Expanding those factors by distributing them (FOIL) we can find this:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(x)=-\left(xx+x\left(-1\right)+4x+4\left(-1\right)\right) \\ f(x)=-x^2-3x+4 \end{gathered}[/tex]So now, let's find the x-coordinate of the vertex V(h,k):
[tex]\begin{gathered} h=\frac{-b}{2a}=\frac{-(-3)}{2(-1)}=\frac{3}{-2}=-\frac{3}{2} \\ Axis\:of\:symmetry:x=-3/2 \end{gathered}[/tex]c) The coordinates of the vertex can be found by plugging the x-coordinate into the quadratic function. This way:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(-\frac{3}{2})=-(-\frac{3}{2}+4)(-\frac{3}{2}-1)=\frac{25}{4} \\ \\ V(-\frac{3}{2},\frac{25}{4}) \end{gathered}[/tex]d) Finally, we can plot that function by setting a table:
So plotting these points (-2,6),(-1,6), (0,4), (1,0),(2,-6) and opening down the parabola for a is -1 we can plot this:
7. The manager of a local restaurant has found that his cost function for producing coffee is C(x) = .097x, where C(x) is the total cost in dollars of producing x cups. (He is ignoring the cost of the coffeepot and the cost labor.) Find the total cost of producing the following numbers of cups of coffee. (a) 1000 cups (b) 1001 cups (c) What is the marginal cost for any cup? Let C(x) be the total cost in dollars to manufacture x items. Find the average cost in exercises 8 and 9.
Answers
To solve for the total cost of producing the following numbers of cups of coffee:
[tex]\begin{gathered} C(x)=0.097x \\ \end{gathered}[/tex]where
[tex]\begin{gathered} x=nu\text{mber of cups of coff}e \\ C(x)=total\text{ cost }in\text{ dollars of producing x cups} \end{gathered}[/tex](a) The total cost of producing 1000 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1000 \\ C(x)=1000(0.097)=\text{ \$97} \end{gathered}[/tex](b) The total cost of producing 1001 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1001 \\ C(x)=1001(0.097)=\text{ \$97}.097 \end{gathered}[/tex](c) The marginal cost for any cup = $0.097
marginal cost can be found by taking the derivative of the function
[tex]\begin{gathered} C(x)=0.097x \\ C^1(x)=0.097=\text{ \$0.097} \end{gathered}[/tex]will you kindly assist me pls. work math step by step answer in numbers pls. to work how you got the answer
Answers
Translating for numbers, we have:
[tex]\frac{1}{5}=0,2\rightarrow3\frac{1}{5}=3,2[/tex]This way, we can make what follows:
[tex]Day_1+Day_2=3\frac{1}{5}+4=3,2+4=7,2_{}[/tex]Calculating now the amount is needed to complete the 9 miles:
[tex]Day_3=9-7,2\text{ = 1,8}[/tex]--------------------------------------------------------------------------------------------------------
And from here, the solution with the fractions.
We can start with the sum of what Shelly has biked in the first two days:
[tex]Day_1+Day_2=3\frac{1}{5}+4=7\frac{1}{5}_{}[/tex]This is the amount of mile she has already biked. But we know she needs to complete all the 9 miles in the third day. So, the difference from 9 and the amount she already did is the amount she needs to bike in the third day.
[tex]\text{Day}_3\text{ = 9 - 7}\frac{1}{5}\text{ = 1}\frac{4}{5}[/tex]The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 43.9 metérs, how wide must it be? The airplane wing must be ____ meters wide. (Round to the nearest hundredth.)
Answers
To compute the width of the wing, we can use the next proportion
[tex]\frac{9\text{ meters long}}{43.9\text{ meters long}}=\frac{1\text{ meter wide}}{x\text{ meters wide}}[/tex]Solving for x,
[tex]\begin{gathered} 9\cdot x=1\cdot43.9 \\ x=\frac{43.9}{9} \\ x=4.88 \end{gathered}[/tex]The airplane wing must be 4.88 meters wide.
The probability that VSU and KSU both win a basketball game in the same week is 47%. Theprobability that VSU wins is 50%. What is the probability that KSU will win given that VSUhas already won?
Answers
EXPLANATION
Let the probability that KSU will win a game be Pr(A), and let the probability that VSU wins be Pr(B). Therefore;
[tex]\begin{gathered} Pr(A\cap B)=0.47 \\ Pr(B)=0.5 \end{gathered}[/tex]We can then use the conditional probability formula below.
[tex]Pr(A|B)=\frac{Pr(A\cap B)}{Pr(B)}[/tex]Therefore, the probability that KSU will win given that VSU has already won becomes
[tex]Pr(A|B)=\frac{0.47}{0.50}=0.94[/tex]Answer: 0.94
- 16m’n-(-25m’n)+(-7m’n)Which of the following is equivalent to the expression above?
Answers
As a rule , - times - = + and - times + = -
[tex]\begin{gathered} -16m^2n-(-25m^2n)+(-7m^2n\text{ ) } \\ =-16m^2n+25m^2n-7m^2n\text{ ( based on the rule above )} \\ =+9m^2n-7m^2n\text{ ( -16 + 25 = + 9 )} \\ =+2m^2n \end{gathered}[/tex]Therefore the correct answer to the question is 2m squared n
whats the variance and the standard deviation of the data set 6,9,2,5,4,10,3,12,2,7,7,8
Answers
Given:
6,9,2,5,4,10,3,12,2,7,7,8
Required:
To find the variation and standard deviation of the given data set.
Explanation:
Now variation is
[tex]s^2=\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{n-1}[/tex]The numerator in the above is sum of the square of the given data.
Therefore,
[tex]\begin{gathered} =(6-6.25)^2+(9-6.25)^2+(2-6.25)^2+(5-6.25)^2+(4-6.25)^2+(10-6.25)^2+ \\ (3-6.25)^2+(12-6.25)^2+(2-6.25)^2+(7-6.25)^2+(7-6.25)^2+(8-6.25)^2 \end{gathered}[/tex][tex]\begin{gathered} s^2=\frac{112.25}{12-1} \\ \\ =\frac{112.25}{11} \\ \\ =10.2045 \end{gathered}[/tex]Final Answer:
[tex]10.2045[/tex]3. The difference of two-thirds of a number x and6 is at least -24. Which inequality represents allpossible values for x?
Answers
We will solve as follows:
The expression represented in the text is:
[tex]\frac{2}{3}x-6\ge-24[/tex]Now, we solve for x:
[tex]\Rightarrow\frac{2}{3}x\ge-18\Rightarrow2x\ge-54[/tex][tex]\Rightarrow x\ge-27[/tex]So, the solution is x >= 27. [Option D]
Thinking: Two students were having a discussion. They stated:“Since we factored f(x) = 2x2 + 3x + 1 into (2x+1)(x+1) we could say this:If we let h(x) = 2x + 1 and g(x) = x + 1, then we can say f(x) = h(x)g(x)” Howmight you verify their statement?
Answers
Given:
If we let h(x) = 2x + 1 and g(x) = x + 1 and
[tex]f(x)=2x^2+3x+1[/tex]Required:
How might you verify their statement?
Explanation:
We have h(x) and g(x)
[tex]\begin{gathered} =h(x)g(x) \\ =(2x+1)(x+1) \\ =2x^2+2x+x+1 \\ 2x^2+3x+1=f(x) \\ f(x)=h(x)g(x) \end{gathered}[/tex]Answer:
Hence, verified the statement.
Instructions: varies indirectly with . If =7 when =−4, find when =2. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).
Answers
y varies directly as x
This can be written mathematically as:
y = kx
If y = 7, x = -4
Solve for the constant k
7 = -4k
k = -7/4
The equation is:
y = -7/4 x
When x = 2
substitute x =2 anto the equatio n y = -7/4 x
[tex]\begin{gathered} y=-\frac{7}{4}\times2 \\ \\ y=-\frac{7}{2} \end{gathered}[/tex]in the diagram pq and St find the slope of st
Answers
1) Looking at that diagram, we can see that Point S shares the same x-coordinate from point Q since they are on the same Vertical Line. So, it's safe to say that the x-coordinate of Point S is x=-2
2) And point S is at the same horizontal axis of point P. So for the same principle, we can say that the y-coordinate of point S is y=4
S(-2,4)
3) So let's find the Fourth point of that figure, so let's find the slope of PQ
[tex]\begin{gathered} m_{PQ}=\frac{4-1}{1-(-2)}=\frac{3}{-1+2}=\frac{3}{3}=1 \\ \\ m_{ST}=-1 \end{gathered}[/tex]Since PQ is perpendicular to ST then the slope is the opposite reciprocal of 1, i.e. -1
Han spent a total of $221.76, before tax, on bags of chips for the basketball team, and each bag cost $3.52. What is the total number of bags of chips that Han bought?
Answers
Given:
a.) Han spent a total of $221.76, before tax, on bags of chips for the basketball team.
b.) Each bag cost $3.52.
Let's determine the number of bags of chips bought.
[tex]\text{ No. of bags of chips bought = }\frac{\text{ Total cost}}{\text{ Price of each bag}}[/tex][tex]\text{ = }\frac{\text{ 221.76}}{\text{ 3.52}}[/tex][tex]\text{ = 63}[/tex]Therefore, Han bought 63 bags of chips for the basketball team.
The answer is 63.
the sum of 2 numbers is 75. the second number is 3 less than twice the first. find the numbers
Answers
SOLUTION
Let one of the numbers be x
Using the statement: The second number is 3 less than twice the first
Then the second number is
[tex]2x-3[/tex]Since, the sum of 2 numbers is 75
It follows:
[tex]x+2x-3=75[/tex]Solve for x
[tex]\begin{gathered} 3x=75+3 \\ 3x=78 \\ x=\frac{78}{3} \\ x=26 \end{gathered}[/tex]Therefore the first number is 24
The second number is
[tex]\begin{gathered} 2(26)-3 \\ =49 \end{gathered}[/tex]therefore the numbers are 49 and 26.
I'll send you the pic
Answers
1. 5 (3) = 15
2. 4 (8) = 32
3. 6 (3/2) = 9
4. 12 ( ) = ?
Gifty works out that the material for a dress cost R dollar per meter and 3 meters are required for the dress. Acessories cost $50.00. what is the total amount of money Gifty will need to spend on the dress in terms of R? If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
Answers
We are given that
Cost of dress per meter = $R
Total cost of dress = $ 3R
Cost of Acessories = $50
We want to find:
Part A
The total amount of money Gifty will need to spend on the dress in terms of R
To find the total amount, we just add up
Let T denotes the total amount of money
[tex]\begin{gathered} T=3R+50 \\ \end{gathered}[/tex]Thus, the total amount is $ (3R + 50)
Part B
If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
We only need to equate T to 4000 and solve for R
[tex]\begin{gathered} T=4000 \\ 3R+50=4000 \\ 3R=4000-50 \\ 3R=3950 \\ R=\frac{3950}{3} \\ R=1316.666667 \\ R=1316.67\text{ (to 2 decimal places)} \end{gathered}[/tex]Thus, the maximum value of R is $1316.67
Angel is at a birthday party. There are 12 cupcakes where some are blue and some are green. Out of There are 8 green cupcakes. Express the number of blue cupcakes as a decimal
Answers
12 cupcakes
8 green cupcakes
To find the number of blue cupcakes subtract the green cupcakes (8) to the total cupcakes:
12 -8 = 4 blue cupcakes
To express as a decimal, divide the number of blue cupcakes by the total number of cupcakes:
4/12 = 0.33333
Look at the models below. DO Tell whether each statement is True or False. equivalent to į because à has 2 times as many shaded parts and 2 times as many equal parts as True False 3 b. , is equivalent to because has 2 times as many parts shaded and 2 more equal parts than True 0 False 4 is equivalent to because both models have i shaded part True False d. is equivalent to because á has 2 + 6 = 8 equal parts. True False
Answers
a.
Since:
[tex]\frac{1}{3}\equiv\frac{2}{2}\times\frac{1}{3}=\frac{2}{6}[/tex]The statement is true
b.
Since:
[tex]\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}\ne\frac{2}{6}[/tex]The statement is false
c.
Since:
[tex]\frac{1}{4}\equiv\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}[/tex]The statement is true.
d.
Since:
[tex]\begin{gathered} \frac{2}{6}=\frac{1}{3} \\ \frac{2}{8}=\frac{1}{4} \\ \frac{1}{4}\ne\frac{1}{3} \end{gathered}[/tex]The statement is false.
Latrice eamns 5 points for each question she answers correctly. Her grade, g is described by g = 5c, where c is the number of questions answered correctly. What is the dependent variable-Number of points per question-total grade-number of questions missed-number of questions right
Answers
The equation that describe's Latrice grade is given by:
g = 5c
g represen
what scale factor or multiplier of the dilation below
Answers
Given:
The triangle ABC is similar to the triangle A'B'C'
So, the corresponding sides are proportions
So, the factor of dilation will be:
[tex]\frac{A^{\prime}B^{\prime}}{AB}=\frac{8}{12}=\frac{2}{3}[/tex]so, the answer will be 2/3
what is the value of x would make lines l and m parrallel
Answers
We know that if l and m are parallel there might be some angles that are equal to others:
Alternate interior angles
The angles closed by a blue circle are alternate interior angles, then they should be equal if l||m.
Vertcial angles
The angles closed by an orange circle are vertical angles, because they are opposite to each other on two crossed lines.
Now, we know two angles of the triangle of the middle:
We know that the addition of all the inner angles of a triangle is 180º. This is:
50º + 55º + xº = 180º
↓
105º + xº = 180º
Now, we can find x:
105º + xº = 180º
↓
xº = 180º - 105º
xº = 75º
Answer: xº = 75ºWhat are the coordinates of point P on the directed line segment from R to Q such that 5 Pis 6 the length of the line segment from R to Q? Round to the nearest tenth, if necessary. A (-3.5, 2.3 ) B. (3.5, -2.3 ) C. (-3, 2) D. (3, 2)
Answers
Answer
Option A is correct.
P(x, y) = (-3.5, 2.3)
Explanation
Mathematically, if a point P(x, y) divides the coordinates R(x₁, y₁) and Q(x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question,
R(x₁, y₁) and Q(x₂, y₂) = R (4, -1) and Q (-5, 3)
m:n = 5:1 (5/6 of a distance divides the two parts of the distance into 5/6 and 1/6, hence, the ratio is 5:1)
x₂ = -5
x₁ = 4
y₂ = 3
y₁ = -1
m = 5
n = 1
x = [(mx₂ + nx₁)/(m + n)]
x = [(5×-5 + 1×4)/(5 + 1)]
x = [(-25 + 4)/(5 + 1)]
x = (-21/6)
x = -3.5
y = [(my₂ + ny₁)/(m + n)]
y = [(5×3 + 1×-1)/(5 + 1)]
y = [(15 - 1)/(5 + 1)]
y = (14/6)
y = 2.3
P(x, y) = (-3.5, 2.3)
Hope this Helps!!!
Which values has three significant figures?14001001101.22310
Answers
a) 1400 has 2 significant figures, zeros are no consider as significant figures
b) 1001 has 4 significant figures, zeros in between two nonzero numbers are significant figures
c) 101.2 has 4 significant figures, zeros in between two nonzero numbers are significant figures. Nonzero number are significant figures
d) 2310 has three significant figures. 2,3 and 1 are significant figures.