The Expected Value to the player for one play of the game is - 7.784.
Define Expected Value.In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.
Price of raffle ticket= $10
First price= $5460
Second prize= $496
Remaining 18 prize= $100
$0 for the remaining tickets= 3500-20=3480 tickets
When winning the 1st prize, the winnings = $5460−$10=$5450.
When winning the 2nd prize, the profit= $496−$10=$486.
When winning the other 18 prizes, the profit= $100−$10=$90.
When there is no winning, the loss= $0
The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:
P(X=5450)= 1/3500
P(X= 486)= 1/3500
P(X= 90)= 18/3500
P(X= -10)= 3480/3500
The product of each alternative and its probability equals the expected value, which is added up:
E(X)= ∑ xP(x)
= 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]
= [tex]\frac{-27224}{3500}[/tex]
= - 7.784
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80 points!! PLS HELP! look at picture. this is geometry and has to do with similar triangles.
The sum of DE+FG+HI=90 if DE, FG, HI are all parallel to BC and BC=60.
What is meant by trapezium?Quadrilaterals with at least one set of parallel sides are referred to as "trapezoid" quadrilaterals. In British and other dialects of English, the word "trapezium" is used.
Euclidean geometry dictates that a trapezoid must be a convex quadrilateral. The base of the trapezoid is referred to by its parallel sides. If the other two sides are parallel, the trapezoid is a parallelogram, and there are two pairs of bases. If not, the other two sides are known as the legs (or lateral sides). Unlike the specific situations below, a scalene trapezoid is a trapezoid where none of the sides have equal lengths.
Given,
ΔABC is a scalene triangle.
And BC=60
DE, FG, HI are all parallel to BC.
From the midpoint-theorem,
DE||BC then,
DE=(1/2)BC
FG||BC
FG=(1/2)BC
HI ||BC
HI=(1/2)BC
DE+FG+HI=(1/2BC+1/2BC+1/2BC)
=(1/2(3BC))
1/2(3(60))
=90
Therefore,
The sum of DE+FG+HI=90
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consider a trial in which a jury must decide between the hypothesis that the defendant is guilty and the hypothesis that the defendant is innocent. in the framework of hypothesis testing and the u.s. legal system, which of the hypotheses should be the null hypothesis?
The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury.
Given that,
Think about a case where a jury must choose between the hypotheses that the defendant is guilty and the defendant is innocent.
We have to find which of the hypotheses ought to be the null hypothesis in the context of hypothesis testing and the American legal system.
We know that,
A jury in a trial must choose between two hypotheses. The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury. They must decide based on the information provided.
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a 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 10 feet above the ground?
If the top slips down the wall at a rate of 2 ft/s, then 3.476 ft/s fast the foot will be moving away from the wall when the top is 10 feet above the ground.
In the given question, a 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s.
We have to find how fast will the foot be moving away from the wall when the top is 10 feet above the ground.
As given, 15ft ladder dy/dt= -2y=13ft
Let the length be x and height be y
So from the Pythagorean theorem
x^2+y^2=h^2
Now apply the above formula to get the value
x^2+y^2=15^2
Take the derivative with respect to time
2x * dx/dt+2y*dy/dt=0
dx/dt= -y/x *dy/dt
When y = 13
then x^2+13^2=15^2
x = 7.48
dx/dt= -13/748 * (- 2)
dx/dt= 3.476 ft/s
Hence, if the top slips down the wall at a rate of 2 ft/s, 3.476 ft/s fast will the foot be moving away from the wall when the top is 10 feet above the ground.
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Which is the solution for the system of
linear equations graphed below?
A. (-4,3)
B. (0, 1)
C. (0, 3)
D. (-3, 4)
Answer:
D. (-3, 4)
Step-by-step explanation:
Hope it helps!
please help me now, much appreciated! I'll give brainliest if you answer!
By evaluating the piecewise function we will see that the difference is:
f(1) - f(-7) = 3
How to find f(1) - f(-7)?Here we have a piecewise function defined on the image, and we want to find the difference:
f(1) - f(-7).
First, let's find these values.
f(1) means that we need to evaluate the function in x = 1.
Notice that the second piece can be used on the domain 4 < x ≤ 1, so we need to use that part.
f(1) = -(1)^2 - 3*1
f(1) =-1 - 3 = -4
To evaluate in x = -7 we need to use the first piece of the function:
f(-7) = |-7 + 5| - 9
f(-7) = |-2| - 9 = -7
Then the difference is:
f(1) - f(-7) = -4 - (-7) = -4 + 7 = 3
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the scores on a standardized test have an average of 1200 with a standard deviation of 60. a sample of 50 scores is selected. what is the probability that the sample mean will be between 1195 and 1205? round your answer to three decimal places.
The probability that the sample mean will be between 1195 and 1205 is 0.445
What is a probability distribution?
In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.
Given, mean = [tex]\mu[/tex] = 1200
standard deviation = [tex]\sigma[/tex] = 60
n = 50
[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]
[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]
= P(-0.59 < Z <0.59 )
= P(Z <0.59 ) - P(Z <-0.59 )
Using the z table, we get
=0.7224-0.2776
=0.4448 = 0.445 ( rounded to 3 decimal places)
Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445
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Solve while using the Pythagorean theorem! Please help
Answer:
Step-by-step explanation:
a^2 +b^2 =c^2
8^2 +14^2=y^2
64+196 =y^2
260=y^2
(260)^1/2 =y
Simplified: 4^1/2 * 65^1/2= 2(65^1/2)
What type of variable is required to construct a confidence interval for a population​ proportion?.
A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes. So the correct option is D.
In the given question we have to find what type of variable is required to construct a confidence interval for a population proportion.
As we know that;
Population proportion is the percentage of the entire population that possesses the given quality (which is qualitative in nature). The confidence interval for the population proportion must thus be constructed using a qualitative variable with two possible outcomes.
So, the correct option is identified from nature of different type of the variables. A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes.
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The right question is:
What type of variable is required to construct a confidence interval for a population proportion?
A. Quantitative
B. Qualitative with any number of possible outcomes
C. Continuous
D. Qualitative with 2 possible outcomes
E. Discrete
F. Qualitative with 3 or more possible outcomes
Please show all work. Show the steps in transforming the expression on the right into the one on the left. (Verifying identities - this is precalc.)
(1+3cosx-4cos²x)/sin²x = (1-4cosx)/(1-cosx)
(1 – 3cosx – 4cos^2x) / sin^2x =
(1+cos x)(1-4cos x) /(1-cos^2 x) =
(1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] =
(1-4cos x) /(1-cos x)
Factor:
1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =
RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED
Find the complex zeros of each polynomial function. Use your results to write the polynomial as a product of linear factors. Thanks! :)
here you are the answer.
The increase in price of an article is 20% . If the new price is $150 , what was the original price?
$600 is the original price of the article if the price of an article is 20% and new price is $150
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The increase in price of an article is 20%
The new price is $150
We need to find the original price of the article.
Let 20% of x=150
20/100x=150
0.2x=150
Divide both side by 0.2
x=750
Now subtract 750 and 150 we get original price
750-150
600
Hence, $600 is the original price of the article if the price of an article is 20% and new price is $150
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29x + 3 (5 – 35x) = −119 - 9x
Answer:
The answer is x=2
Step-by-step explanation:
1. Rearrange terms-
29x + 3 ( 5 - 35x) = - 119 - 9x
29x + 3 ( - 35x + 5) = - 119 - 9x
2. Distribute-
29x + 3 ( - 35x + 5) = - 119 - 9x
29x - 105x + 15 = - 119 - 9x
3. Combine like terms-
29x - 105x + 15 = - 119 - 9x
- 76x + 15 = -119 -9x
4. Rearrange terms-
- 76x + 15 = - 119 - 9x
- 76x + 15 = - 9x - 119
5. Subtract 15 from both sides-
- 76x + 15 = - 9x - 119
- 76x +15 -15 = -9x - 119 - 15
6. Simplify-
- 76x = - 9x - 134
7. Add 9x to both sides-
- 76x + 9x = - 9x - 134 + 9x
8. simplify-
- 67x = - 134
9. Divide both sides by the same factor-
[tex]\frac{-67x}{-67} = \frac{-134}{-67}[/tex]
10. Simplify-
x = 2
compare using >, =, or <. 3 _____ -3
Answer:
=
Step-by-step explanation:
Find the cube roots of i. Round all numbers to 3 decimal places. Enter 0s or 1s in the appropriate boxes to answer 0 + i, 1+0i, etc.
The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.
In order to find the cube root of unity let us say,
x³ = 1
Solving further,
x³-1 = 0
Now,
(x-1)(x²+x+1)=0
For, x-1=0
x = 1.
And,
For, (x²+x+1)
Solving by using quadratic formula,
x = -1±√(-3)/2.
x = -1±i√3/2
x = -1+i√3/2 and,
x = -1-i√3/2
also, x = 1.
So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.
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Todd's living room is rectangular and measures 9 meters by 3 meters. Beginning in one corner, Todd walks the length of his living room and then turns and walks the width. Finally, Todd walks back to the corner he started in. How far has he walked? If necessary, round to the nearest tenth.
In MNO, O≈ N, MN = 20 and NO = 14. Find OM.
The length of OM is 20 if MN=20 and N0=14
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.
To find the length of OM
Given,
MN=20
ON=14
∠O≅∠N
Since, ∠O≅∠N
ΔMNO is isosceles triangle with
OM=MN=20
Hence, the length of OM is 20.
Therefore, The length of OM is 20 if MN=20 and N0=14
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suppose a sample of bone fossil contains 5.2% of the carbon-14 found in an equal amount of carbon in present-day bone. estimate the age of the fossil, assuming an exponential decay model. the half-life of carbon-14 is approximately 5700 years.
The age of the fossil is 24, 312 years assuming an exponential decay model.
Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:
P = 100 e^(-kt)
Where P is the remaining quantity, k is the constant of decay, and t is time.
As the half life of the carbon 14 is 5700, when 50% of the substance remains,
50 = 100 e^(-5700k)
1/2 = e^(-5700k)
In(1/2) = In(e^(-5700k))
- In (2) = -5700k
k = In(2)/5700 = 0.0001216
Since, 5.2% carbon-14 remains,
5.2 = 100 e^(-0.0001216t)
0.052 = e^(-0.0001216t)
In(0.0052) = - 0.0001216
t = In(0.052) * - 0.0001216
t ≈ 24, 312 years.
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HELP I WILL GIVE BRAINLIEST!!!
Answer:
ITS B
Step-by-step explanation:
Can you guys help me with this thanksss!!
Answer:
Step-by-step explanation:
What are you supposed to do
-0.8x - 2.14 = -6.2 all my points
Answer: 5.072
Step-by-step explanation: -0.8-2.14=-6.2
+2.14 | +2.14
-----------------------------------------------------------------------------------------------
-4.06/-0.8=5.072
Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.
The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by [tex]\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)[/tex]. Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.
The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,
Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate
The complete question is -
Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250
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. There are 976 people working in an office. On a particular day, 61
people were absent. What percentage of the workforce did not show
up for work that day?
Answer: 6.25%
Step-by-step explanation:
To find what percent 61 is of 976, we divide 61/976. This comes out to be 0.0625. Multiply by 100 to get your percentage, and it's 6.25%.
A kindergarten teacher has five books to distribute to 20 children in her class. (a) how many ways are there for her to distribute the books if they are all the same and no child gets more than one? (b) how many ways are there for her to distribute the books if they are different and no child gets more than one?
The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.
(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.
(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.
(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.
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The complete question is:
A kindergarten teacher has five books to distribute to 20 children in her class.
(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?
(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.
(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?
A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.33 degrees. The camera is 196.0 cm above the surface. How far from the camera is the rock?
The distance between the rock and the surface is 827.20 cm.
Given data,
There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.
How far is the rock from the camera?
From the given data,
tan c = AB/BC
tan 13.33° = 196/BC
BC = 196/tan 13.33°
BC = 827.20 cm
Hence, the distance between the rock and the surface is 827.20 cm.
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a cone has volume of 98cm the radius of the cone is 5.13 what is the hight of the cone
Step-by-step explanation:
v=1/3πr²h
98=1/3×22/7×(5.13)²×h
98=1/3×22/7×(27.2403)×h
98=28.537×h
h=28.537/98
h=0.291m
hope it helps. please mark brainliest
Answer:
Answer to your question is in the attachment
Lola has a collection of 432 trading cards, and Joel has a collection of 505
trading cards.
At the end of each month, Lola buys a box of 40 trading cards and Joel
buys a box of 32 trading cards.
After how many months will Lola have more trading cards than Joel?
Answer: 10 months
Step-by-step explanation:
432 + 40x >505 + 32x
40x >32x + 73
8x > 73
8x/8 > 73/8
x > 73/8 = 9.125
Round 9.125 to 10
The number of months that will take Lola to have more trading cards is obtained as 8.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The number of cards with Lola and Joel are 432 and 505 respectively.
Suppose the number of required month be x.
Then, the inequality expression can be written for the given case as,
432 + 40x > 505 + 32x
⇒ 40x - 32x > 505 - 432
⇒ 8x > 63
⇒ x > 63/8
The number of months should be an integer value.
And, the nearest integer value of the greater than 63/8 is 8.
Hence, the number of months required for the given case is 8.
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we are given a bag of 35 different colored chips. there are 20 black chips and 15 white chips. you draw 11 chips at random, what is the probability of getting 5 black chips and 6 white chips1 ?
The probability of getting 5 black chips and 6 white chips is [tex]\frac{7}{22}[/tex].
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to data in the given question,
We have the given information:
Total number of different colored chips = 35
Number of black chips = 20
Number of white chips = 15
And you draw 11 chips at random.
Now, we will calculate the probability of getting 5 black chips and 6 white chips,
[tex]P(B) = \frac{5}{20} =\frac{1}{4} \\P(W) = \frac{6}{15} =\frac{2}{5} \\P( black and white ) = \frac{\frac{1}{4}*\frac{2}{5}}{\frac{11}{35} } \\=\frac{\frac{1}{2}*\frac{1}{5}}{\frac{11}{35} }\\=\frac{1}{10}*\frac{35}{11}=\frac{7}{22}[/tex]
Therefore, the probability of getting 5 black chips and 6 white chips is 7/22.
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Combine the like terms to create an equivalent expression.
7k + 3k + 11 =
Stuck? Review related articles/videos or use a hint.
Answer:
When you combine like terms, you look for the same variable or look for constants. In this case, the same variable if 'k'. Now you add the coefficients 7 and 3, which is 10. So the expression simplifies to 10k + 11.
Hope this helps!
Answer:
10k + 11
Step-by-step explanation:
Like terms are terms that have the same amount of the same variables.
In this case, note that two of the terms have the variable "k" attached:
7k & 3k, respectively.
In this case, the question asks you to combine like terms, or to simplify the given expression:
7k + 3k + 11
(7k + 3k) + 11
10k + 11
10k + 11 is your answer.
~
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what is the formula for square of a circle?
The formula for the area of a circle is pi times the radius squared (A = π r²)
What is a circle?A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre." The line of reflection symmetry is formed by every line that passes through the circle. It also has rotational symmetry around the center for all angles.
It is a curved portion of its circumference. A semicircle is an arc that connects the endpoints of the diameter and has a measure of 180°. The circle is divided into two parts by an arc. The minor arc is the smaller part, and the major arc is the larger part.
To find the area goes thus;
Identify the radius of a circle.
Square the radius.
Multiply by pi. Pi.
In conclusion, the formula is πr².
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Complete question
what is the formula for the area of a circle?
A pharmacist asserts that more than 40% of prescribed medicines are derived from plants. They decide to test this assertion by computing the sample proportion for a random sample. The data results in a test statistic of z = 2.14 and a P- value of .0162. Test at a 5% significance level. a. State the hypotheses for their test. I b. Briefly describe what the P-value is. c. Using the test statistic, how was the P-value found? d. Based on the P-value what conclusion should the pharmacist make? In particular, do they have enough evidence in support of their claim?
We reject the null hypothesis and come to the conclusion that their argument is adequately supported.
Given that,
z = 2.14 and p value = 0.0162
a) Hypotheses are
H₀ : p≤ 0.40
H₀ : p > 0.40 (claim)
This is right tailed test.
b) p value = 0.0162
c) Test statistic Z =2.14
P(Z>2.14) = 1 - P(Z≤2.14)
= 1 - 0.98382
= 0.01618
P value ≈ 0.01618
d) P value is less than α = 5% = 0.05
So, we reject the null hypothesis and conclude that they have enough evidence in support of their claim
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