Answer: 2
Step-by-step explanation:
because the common range here is 7-13.
2 isnot in this common range so it could be identified as an outlier
19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?
Why is the following not a probability? model?
LOADING...
Click the icon to view the data table.
Determine why it is not a probability model. Choose the correct answer below.
A.
This is not a probability model because at least one probability is greater than 0.
B.
This is not a probability model because at least one probability is greater than 1.
C.
This is not a probability model because the sum of the probabilities is not 1.
D.
This is not a probability model because at least one probability is less than 0
The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.
What is probability?Probability is a measure of the probability of an event, expressed as a number between 0 and 1.
For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.
In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.
If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.
If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.
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Identify the sampling method as simple random sampling, systematic sampling, convenience sampling, or stratified sampling. A computer randomly selects 100 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor. Choose the correct sampling technique below. A. Systematic sampling B. Convenience sampling c. Simple random sampling D. Stratified sampling
The correct sampling technique for the given case is C. Simple random sampling
Each person in a population has an equal probability of being chosen to be a member of specific sample when using simple random sampling as a statistical sampling technique. With this technique, a random sample is picked at random from a wider population, giving each person a fair chance of being chosen. This indicates that there is no bias in selection process and that any person or object in overall population has same likelihood of getting chosen.
Simple random sampling is frequently employed in research investigations because it is an easy-to-use and objective sampling technique. Given that 100 names were randomly chosen from a list of all registered voters, simple random sampling is appropriate sampling technique in this particular case.
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Enzo is making a scale drawing of the rectangle below.
A rectangle has a length of 8 centimeters and width of 5 centimeters.
Enzo says that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters. Which explains whether Enzo is correct?
Enzo is correct because he used a factor of 2 to enlarge the rectangle.
Enzo is correct because he doubled one dimension and added the two lengths to get the other dimension.
Enzo is not correct because the enlarged rectangle should be 16 centimeters by 5 centimeters.
Enzo is not correct because he did not multiply the length and width by the same factor.
Answer:
Step-by-step explanation:
D is it
Write a quadratic function f whose zeros is 7
The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
(x - 7)(x - 7)
⇒ (x - 7)²
⇒ x² + 7²+ 2 × 7 × x
⇒ x² + 49 + 14x
⇒ x² + 14x + 49
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What is the value of “a”
What is the vertex form of the graph
what is the standard form of the graph
what is the factored form of the graph
The value of a is 2.
the vertex form of the graph : y = 2 ( x + 1 )² - 9,
the standard form of the graph : y = 2x² + 4x - 7,
the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The equation of the parabola in vertex form:
The vertex v is at v ( -1, -9 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )² + k
y = a ( x - (-1) )² + (-9)
substituting point ( -3, -5 ) from the graph we have:
-5 = a ( -3 + 1 )² - 9
-5 = 2a - 9
a = 2
substituting the known values to y = a ( x- h ) + k
y = 2 ( x + 1 )² - 9
the equation of the parabola in factored form
y = 2 ( x + 1) ( x + 1 ) - 9
the equation of the parabola in standard form
y = 2 ( x + 1) ( x + 1 ) - 9
y = 2 ( x² + 2x + 1 ) - 9
y = 2x² + 4x - 7
Hence, the value of a is 2
the vertex form of the graph : y = 2 ( x + 1 )² - 9
the standard form of the graph : y = 2x² + 4x - 7
the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9
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A photographer needs a frame for an 5x7 inch picture, such that the total area is 80in^2.Calculate the width of the frame.
Answer:
The width of the frame is 10 inches.
5x7 = 35
80-35 = 45
45/7 = 6.4
5 + 6.4 = 11.4
11.4 rounded down = 11
11 - 5 = 10
Width of the frame = 10 inches
srs of 25 seniors 17 respond "yes" confidence interval for true proportion of seniors which of the following conditions were not met?
The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.
To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula
CI = p ± z × sqrt((p × (1 - p)) / n)
where
p = proportion of the sample who answered "Yes"
z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)
n = sample size
Plugging in the values given in the question, we get
p = 0.54
z = 1.96
n = 1019
CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)
CI = 0.54 ± 0.030
CI = (0.51, 0.57)
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I have solved the question in general, as the given question is incomplete,
The complete question is:
Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?
A person invests 10000 dollars in a bank. The bank pays 6.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 29500 dollars?
Answer:
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, we know that P = $10,000, r = 6.5% = 0.065, and we want to find t when A = $29,500. We also know that the interest is compounded annually, so n = 1.
Substituting these values into the formula, we get:
$29,500 = $10,000(1 + 0.065/1)^(1t)
Dividing both sides by $10,000, we get:
2.95 = (1.065)^t
Taking the natural logarithm of both sides, we get:
ln(2.95) = ln(1.065)^t
Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:
ln(2.95) = t ln(1.065)
Dividing both sides by ln(1.065), we get:
t = ln(2.95)/ln(1.065) ≈ 18.2
Therefore, the person must leave the money in the bank for about 18.2 years to reach $29,500. To the nearest tenth of a year, the answer is 18.2 years.
in the right triangle what is the value of X? 30 24 X
Answer:
x = 21
Step-by-step explanation:
Given the angle measurements of two angles, we can deduce that this is a 30-60-90 triangle. The formula for side lengths of this type of triangle is given by s → s√3 → 2s with s being the shortest side (the side opposite the 30° angle).
We are looking for the side length represented by s[tex]\sqrt{3}[/tex]. We can see that the hypotenuse is represented by 2s, so...
2s = 24
s = 12
The side length of the shortest side is 12. Therefore, we can say that
x = s [tex]\sqrt{3}[/tex]
x = 12 * [tex]\sqrt{3}[/tex]
x = 20.785
The question asks for our answer to the nearest whole number, so
x = 21
Brianna Wallen lives in Denver, Colorado, where the rate of assessment is 29% of market value. The tax rate is 81.16 mills. The county tax assessor determined that the market value of her home is $438,300. What is the real estate tax on her home?
Step 1 Find the assessed value. Step 2 Express the tax rate as a decimal. Step 3 Find the real estate tax
The real estate tax on Brianna Wallen's home is $37,934.83.
What is property tax?Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.
The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.
The tax is calculated using the given formula:
Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)
Substituting the given values we have:
Tax = (0.29 x $438,300) x (81.16 / 1000)
Tax = $37,934.83
Hence, the real estate tax on Brianna Wallen's home is $37,934.83.
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you know that a pair of triangles has two pairs of congruent angles. what other information do you need to show that the triangles are congruent?
you need to know that _____ are congruent.
Answer:
You need to know that the ratio of their sides are congruent
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
15 seconds
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y=14t^2[/tex]
[tex]y=130t+1200[/tex]
They will be side by side when:
[tex]14t^2=130t+1200[/tex]
[tex]14t^2-130t-1200=0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta=(-130)^2-4(14)(-1200)=84100[/tex]
[tex]x_1=\dfrac{130+\sqrt{84100} }{28}=1.5[/tex]
[tex]x_2=\dfrac{130-\sqrt{84100} }{28}=-5.71[/tex]
Time is a non-negative measure, hence 15 seconds is correct.
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A sample of n observations is taken from a normal population. The appropriate chi-square distribution has
a. n degrees of freedom.
b. n - 1 degrees of freedom.
c. n - 2 degrees of freedom.
d. n - 3 degrees of freedom.
The variance of a sample is equal to n - 1 degrees of freedom, the appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom.
The appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom. This is because the chi-square distribution measures the variance of a population, which is the squared sum of the differences between the observed values and the expected values. Since the expected value for a sample of n observations is equal to the mean of the population, the variance of the sample is equal to the sum of the squared differences between the observed values and the mean of the population. This gives us the formula for the chi-square distribution:
Chi Square = [tex](Sum of (Observed - Mean)^2) / (Mean)[/tex]
For a sample of n observations, the mean is equal to the sum of the observations divided by n, so we can rewrite the formula as follows:
Chi Square = [tex](Sum of (Observed - (Sum of Observations/n))^2) / (Sum of Observations/n)[/tex]
Since the sum of the observations is a constant, we can move it to the other side of the equation, giving us:
We can simplify this equation further by noting that the sum of the [tex](Observed - (Sum of Observations/n))^2[/tex] terms is equal to the variance of the sample. This gives us the final equation:
Chi Square = Variance / (Sum of Observations/n)
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Imagine
X
in the below is a missing value. If I were to run a median imputer on this set of data what would the returned value be?
50,60,70,80,100,60,5000,x
(It's okay to have to look up how to do this!) An. error 80 100 70 The features in a model.... None of these answers are correct Are always functions of each other Kecp the model validation process stable Are used as proxics for y-hatfy (that is yhat divided by y) Which of the below were discussed as being problems with the hold out method for validation? Outliers can skew the result Validation is sometimes too challenging
K=3
is not sufficiently large cnough Data is not available for test and control differences. The modefis not trained on all of the day
The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.
This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.
Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.
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Complete question is:
Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)
50
An error
80
70
100
The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.
We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.
The current population of a city is 8.35 × 105 people and the city is expected to grow in population by approximately 1.6 x 10^ people next year
Answer:
Step-by-step explanation:
8.35 times 105 is 876.75
1.6 times 10 is 16
Hope this helps
A machine can dig a land of 5 bighas in 14 hours. How long will it take to dig 60 bighas of land by the same machine?
Answer168 Bighas of land.
Step-by-step explanation:
Since the machine can dig a land of five bighas in 14 hours, put it into a ration 5:14 5(land it can dig) 14(amount of hours it takes.) Have X as the time to dig 60 bighas, 60(amount of land) : x (time). The equation would be 60/x=5/14 ===> 168 bughas of land.
1. How many quilts will Sally supply at $500.00 per quilt?
2. Are any other factors besides price taken into account with the market supply schedule she has constructed?
3. Several situations are listed below that Sally has encountered in her business. Explain how each of these situations might
alter the supply of quilts.
a new sewing machine that helps her produce quilts in less time.
Sally will supply 3 quilts at $500.00 per quilt according to the market supply schedule she constructed.
What is the supply about?The market supply schedule only takes into account the price per quilt and the quantity supplied per month. Other factors such as production costs, availability of raw materials, competition, and changes in technology are not taken into account in this supply schedule.
a. If Sally purchases a new sewing machine that helps her produce quilts in less time, her production efficiency will increase. This will enable her to produce more quilts in a shorter period of time, which will result in an increase in the supply of quilts.
b. If Sally anticipates an increase in prices for quilts in three months, she may increase the quantity supplied per month in order to take advantage of the higher prices. This may result in a temporary increase in the supply of quilts.
Lastly, c. If there are twice as many quilt suppliers as there were one year ago, Sally will likely face increased competition. This may result in a decrease in sales for Sally and a decrease in the price of quilts. In order to remain competitive, Sally may need to reduce the quantity supplied per month or find ways to differentiate her quilts from those of her competitors.
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See full question below
Part One
Sally Thomas is an entrepreneur. She makes hand-made quilts and sells them at craft shows and at her home studio. Below is a market supply schedule she constructed. Answer the questions that appear below it.
Price per quilt
Quantity Supplied Per Month
$300.00
1
$400.00
2
$500.00
3
$600.00
4
$700.00
5
1. How many quilts will Sally supply at $500.00 per quilt?
3
2. Are any other factors besides price taken into account with the market supply schedule she has constructed?
Supply
3. Several situations are listed below that Sally has encountered in her business. Explain how each of these situations might alter the supply of quilts. a. Sally purchases a new sewing machine that helps her produce quilts in less time.
Sally will be able to produce more quilts in less time, increasing the supply of quilts.
b. Sally anticipates an increase in prices for quilts in three months.
Sally will increase the quantity supplied per month for three months.
c. There are twice as many quilt suppliers as there were one year ago.
Sally will likely experience a decrease in sales which in turn will result in a decrease of supply and price.
Question 6 of 10
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE AOPQ?
Check all that apply.
AA
A. AAS
B. ASA
C. LL
OD. HL
E. LA
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
what is triangle ?Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.
given
We can use the following congruence theories or postulates based on the data in the diagram:
A. ASA
B. AAS
C. LL (corresponding angles hypothesis)
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
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Jamie is going to run for
1
2
2
1
start fraction, 1, divided by, 2, end fraction of an hour at a constant rate, and they want to plan what that rate will be.
1. Write an equation that represents the distance Jamie will run in kilometers (
�
dd) at a rate of
�
rr kilometers per hour.
The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)
What is speed and velocity?Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.
The distance is calculated using the given formula:
Distance = rate (time)
Given that, the time is 1/2 hour thus:
d = r (1/2)
Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).
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Victor has been saving up money to buy the new iPhone 14 Pro Max , which retails for $ 1099 . He currently has from Lunar New Year , and started working as a tutor for $ 50 a week . The amount of money he has in his savings account can be modeled by V(w) = 50w + 500 where V(w) is the amount he has for w weeks of working as a tuto State the value of the slope and y - intercept . a b . What is the meaning of the slope and y - intercept ? How many weeks will he have to work to buy the new iPhone 14 Pro Max ?
For Victor to have enough money to purchase the new iPhone 14 Pro Max, he will need to work for roughly 12 weeks.
Is it an equation or an expression?An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign. For illustration: When you add 8 and 3, you get 11.
a) Here is the equation for Victor's savings account:
V(w) = 50w + 500
Slope (m) = 50
Y-intercept (b) = 500
b) The slope (m = 50) represents the rate at which Victor is saving money per week. For every week that he works as a tutor, he saves $50. The y-intercept (b = 500) represents the initial amount of money that Victor had saved up before he started working as a tutor.
(c)To find out how many weeks Victor will have to work to buy the new iPhone 14 Pro Max, we need to set up an equation where the amount of money he has saved up (V(w)) is equal to the price of the phone ($1099). Therefore, we can write:
50w + 500 = 1099
Subtracting 500 from both sides, we get:
50w = 599
Dividing both sides by 50, we get:
w = 11.98
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Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = x^3 - x^2 - 37x - 35 Find the real zeros of f. Select the correct choice below and; if necessary, fill in the answer box to complete your answer. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers as needed.) There are no real zeros. Use the real zeros to factor f. f(x)= (Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)
By using rational zeros theorem, we find that there are no real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, so we cannot factor f(x) over the real numbers.
To find the real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, we can use the rational zeros theorem, which states that any rational zeros of the function must have the form p/q, where p is a factor of the constant term (-35) and q is a factor of the leading coefficient (1).
The possible rational zeros of f are therefore ±1, ±5, ±7, ±35. We can then test each of these values using synthetic division or long division to see if they are zeros of the function. After testing all of the possible rational zeros, we find that none of them are actually zeros of the function.
Therefore, we can conclude that there are no real zeros of the function f(x) = x^3 - x^2 - 37x - 35.
However, we could factor it into linear and quadratic factors with complex coefficients using the complex zeros of f(x). But since the problem only asks for factoring over the real numbers, we can conclude that the factored form of f(x) is:
f(x) = x^3 - x^2 - 37x - 35 (cannot be factored over the real numbers)
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Describe the graph of y > mx, where m > 0.
Sample Response: The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.
What did you include in your response? Check all that apply.
dashed line
half plane
positive slope
origin
shading above the line
The statements below describe the graph of y > mx, where m > 0
How to describe the graph?The inequality is given as:
y > mx
Where m > 0
The inequality symbol implies that:
The graph uses a dashed lineHalf of the region is shadedThe upper part is shadedThe condition m > 0 implies that:
The graph has a positive slopeThe graph passes through the origin (0,0)Next, we assume that:
m = 5
So, we have:
y > 5x
See attachment for the graph of y > 5x
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PLEASE HELP!!!!!!!!!
△DEF is similar to △YZX
A) which side corresponds to ED? (this one is already answered)
B) write a proportion that you could use to find XZ
C) what is XZ?
Step-by-step explanation:
B) 20:23
C) 6,0375
hope this helps
At a community college, a survey was taken to determine where students study on campus. Of the 250 students surveyed, it was determined that
170 studied in the library
135 studied in the cafeteria
76 studied in both the library and the cafeteria
How many studied in library or cafeteria (including both)?
Answer:
Step-by-step explanation:
To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.
So, the number of students who studied in library or cafeteria is:
170 + 135 - 76 = 229
Therefore, 229 students studied in the library or cafeteria (including both).
Please help me answer this question ASAP!!
Will mark as brainliest if correct and 50+ points!
Answer:
See explanation below
Step-by-step explanation:
1. 12x - 18 = 6(2x -3)
2. 15x + 25 = 5(3x + 5)
3. 14x + 21 = 7(2x + 3)
4. 5x - 5 = 5(x - 1)
5. 12x - 30 = 6(2x - 5)
6. 10x + 8 = 2(5x + 4)
7. 27x + 18 = 9(3x + 2)
8. 4x - 20 = 4(x - 5)
9. 20x + 30 = 10(2x + 3)
10. 4(x + 5) = 4x + 20
11. 3(x - 2) = 3x - 6
12. 5(2x + 4) = 10x + 20
13. 5(x - 1) = 5x - 5
14. 1/2(10x + 12) = 5x + 6
15. 4(2x + 4) = 8x + 16
16. 2(5x - 2) = 10x - 4
17. 2(x - 8) = 2x - 16
18. 4(2x + 1) = 8x + 4
4.34. Find the moment-generating function of the dis- crete random variable X that has the probability distri- bution f(x) = 2 for x = 1,2,3,... 3 and use it to determine the values of m' and j'a.bol A
If the probability distribution is f(x) = 2(1/3)ˣ for x = 1,2,3,... then the moment generating function is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].
The moment generating function (MGF) of a random variable is defined as a mathematical function that is used to determine expected values of the random variable.
It is a way to characterize the entire probability distribution of the random variable by generating a sequence of moments from the function.
The probability distribution is f(x) = 2(1/3)ˣ for x = 1,2,3,... ;
The MGF will be ⇒ Mₓ(t) = [tex]\[ \sum_{x=1}^{\infty} e^{tx} .2(\frac{1}{3})^{x}[/tex]
⇒ [tex]2 \[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] ;
This expression [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] represents an infinite geometric series.
So, [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] = [tex]\frac{e^{t}/3 }{1-e^{t}/3 }[/tex] = [tex]\frac{e^{t} }{3-e^{t} }[/tex]
We get, Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].
Therefore, the Moment generating Function for the given Probability Distribution is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].
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The given question is incomplete, the complete question is
Find the moment-generating function of the discrete random variable X that has the probability distribution f(x) = 2(1/3)ˣ for x = 1,2,3,....
Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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find the following answer
The cardinality of set from the given vein diagram is found as 2.
Explain about the cardinality of set?Think about set A. The set A is said to be finite and so its cardinality is same to the amount of elements n if it includes precisely n items, where n ≥ 0. |A| stands for the cardinality of such a set A.
It turns out that there are two kinds of infinite sets that we need to determine between since one form is much "bigger" than the other. Particularly, one type is referred to as countable and the other as uncountable.
From the given figure
Set A = {8 , 8, 3, 6}
Compliment of Set B (elements not present in set B):
Set [tex]B^{c}[/tex] = {8, 8, 6(pink), 3(white)}
Thus,
(A∩ [tex]B^{c}[/tex] ) = {8, 8} (present in both set)
n (A∩ [tex]B^{c}[/tex] ) = 2 (cardinal number)
Thus, the cardinality of the set from the given vein diagram is found as 2.
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consider the funciton f given by f(t)=log49(t7). find values for a and b such that f(t)=a+logb(t).
The values for a and b such that f(t) = a + logb(t) are,
a = log(1/log(49))
b = 49
Therefor
We can start by simplifying the expression for f(t)
f(t) = log49(t7)
f(t) = log(t7)/log(49) [Using the change of base formula]
Now we can rewrite f(t) as:
f(t) = log(t)/log(b) + a [Using the logarithmic properties log(ab) = log(a) + log(b)]
Comparing this expression with f(t) = a + logb(t), we can see that:
a = log(1/log(49)) [since log(b) = 1/log(49)]
b = t
Therefore, we have
f(t) = log(t7)/log(49) = log(t)/log(b) + log(1/log(49))
= log(t)/log(49) + log(1/log(49))
= log(1/log(49)) + log(t)/log(49)
So, a = log(1/log(49)) and b = 49.
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