The solutions of the given equation are 3.16, 1, and - 1.
Solutions of equations:All numbers that make an equation true when the unknowns are eliminated from the equation are considered the solution of the equation.
For the given equation, we can find the solutions by factorizing as shown below.
Here finding the factors of the given polynomial is known as Factorizing. In other words, writing the given equation as a product of its factors.
Here we have
x⁴ - 11x² + 10 = 0
We can solve the above equation as follows
x⁴ - 11x² + 10 = 0
x⁴ - 10x² - x² + 10 = 0
Group out the like terms
x²(x² - 10) - (x² - 10) = 0
(x² - 10) (x² - 1) = 0
(x² - 10) (x - 1)(x + 1) = 0 [ ∵ (x² - 1²) = (x - 1)(x + 1) ]
x² - 10 = 0 => x = √10 = 3.16
x - 1 = 0 => x = 1
x + 1 = 0 => x = -1
Therefore,
The solutions of the given equation are 3.16, 1, and - 1.
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what is hitters data python?
In Python, the term "hitters data" refers to a dataset that details the hitting statistics of Major League Baseball (MLB) players.
It is a well-known dataset in the area of sports analytics and is frequently utilized in applications for data analysis and machine learning.
The player name, team, and different statistics like hits, runs, home runs and batting averages are often variables in the Hitters dataset. To examine player performance and spot trends or patterns in the data, the dataset may be employed.
The Hitters dataset may be imported and worked with in Python using a variety of tools, including Pandas, NumPy, and Scikit-learn. Based on Hitter's data, these libraries enable data cleansing, exploratory analysis, and the construction of predictive models.
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Turn the (a) Are they taking the test? (b) Write a letter. a lette (c) Don't make a noise. (d) Please bring some noodles. (e) Let him complete his work. (f) Does she compose poems? (g) Has she composed a song? (h) Did he To following sentences into passive voice. Opleted Linder
A cylinder has a radius of 10 m and a height of 8 m. what is the exact volume of the cylinder? responses 18π m³ 18 pi, m³ 80π m³ 80 pi, m³ 160π m³ 160 pi, m³ 800π m³
The exact volume of a cylinder with a radius of 10 m and a height of 8 m is 800π m³. This can be calculated using the formula for the volume of a cylinder, which is V = πr²h. (option 4)
In that, r is the radius and h is the height of the cylinder. In this case, r = 10 m and h = 8 m, so the volume can be calculated as V = π(10 m)²(8 m) = 800π m³.
To calculate this volume, we first use the formula for the volume of a cylinder, which states that the volume is equal to πr²h, where r is the radius and h is the height of the cylinder. In this case, the radius of the cylinder is 10 m and the height is 8 m, so the volume can be calculated as
V = π(10 m)²(8 m) = 800π m³.This is the exact volume of the cylinder.
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Complete Question:
A cylinder has a radius of 10 m and a height of 8 m. what is the exact volume of the cylinder? responses
18π m³80π m³ 160π m³ 800π m³Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4)
The directrix of the parabola defined by the equation (x+9)²= -16(y-5) is x=-16(y-5)+9.
What is equation?Equation is a physical and mathematical statement that describe physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variables may be pointed such as you energy.
The directrix of a parabola is the line which is perpendicular to the axis of symmetry and is equidistant from the focus of the parabola. In this case, the axis of symmetry is y=5 and the focus is (9,-16).
The equation of a line perpendicular to the axis of symmetry is y=mx+b where m is the slope of the line and b is the y-intercept. The slope of the line perpendicular to the axis of symmetry is given by the negative reciprocal of the slope of the axis of symmetry. The slope of the axis of symmetry is 0, so the slope of the perpendicular line is undefined.
Using the point-slope form of the equation of a line, we can represent the equation of the directrix as x=-16(y-5)+9. This is because the point (9,-16) is equidistant from the directrix, so the y-intercept of the directrix is -16(5-5)+9 = 9.
Therefore, the directrix of the parabola defined by the equation (x+9)² = -16(y-5) is x=-16(y-5)+9.
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Find the measure of x X 52 12
Round to the nearest Hundredth
Answer:
Step-by-step explanation:
Step 1: Draw a line from the vertex of the angle to the given point on the x-axis.
Step 2: Draw a line from the given point to the point on the y-axis where the angle intersects the y-axis.
Step 3: Calculate the length of the line segment created in Step 2. This will be x.
Step 4: Calculate the measure of angle 0 by using the given measure of angle and the length of x. This will be 0 degrees.
which are the top five arms exporting states in the world?
According to the Institute, the top five exporters from 2014 to 2018 were the United States, Russia, France, Germany and China, while the top five importers were Saudi Arabia, India, Egypt, Australia and Algeria. Many developed countries have domestic munitions industries to supply their armies.
The military industry, also known as defense industry, defense industry, military industry, or arms trade, is a global industry that manufactures and sells weapons and military technology. Companies in the public and private sectors conduct research and development, design, manufacture and maintenance of military equipment, equipment and facilities. Arms industry products include weapons, ammunition, weapons platforms, military communications, and other electronic products. The military industry also provides other logistical and operational support.
This was a 4.6% increase over 2017 sales, marking the fourth consecutive year of Top 100 firearm sales growth. In 2004, more than $30 billion was spent on international arms trade (this % figure does not include domestic arms sales). According to the Institute, the top five exporters from 2014-2018 were the United States, Russia, France, Germany and China, while the top five importers were Saudi Arabia, India, Egypt, Australia and Algeria.
Many developed countries have domestic munitions industries to supply their armed forces. The Small Arms Survey estimates that there are 875 million small arms in circulation worldwide, manufactured by more than 1,000 companies in approximately 100 countries.
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Wally is employed as an executive with Pay More Incorporated. To entice Wally to work for Pay More, the corporation loaned him $20,000 at the beginning of the year at a simple interest rate of 1 percent. Wally would have paid interest of $2,400 this year if the interest rate on the loan had been set at the prevailing federal interest rate.b. Assume instead that Pay More forgave the loan and interest on December 31. What amount of gross income does Wally recognize this year?
Answer:18000$
Step-by-step explanation:
What is the result 27 divided by 3 ?
Answer:
Step-by-step explanation:
27/3=9
Explain how to use the regression calculator to make a reasonable prediction
The regression calculator is a useful tool for making predictions based on historical data. This calculator is used to predict future outcomes based on past patterns.
To use the regression calculator, you must first collect the historical data that you want to use to predict the future. This can be anything from the number of sales of a product to the number of visitors to a website.
Once the data has been collected, you need to enter the regression calculator. This calculator will allow you to enter the data and then generate a regression model. This will give you a trend line that will fit the data you have entered. This trend line will allow you to predict the future outcome with some accuracy.
To make a reasonable prediction, you will need to adjust the model to ensure that the results are as accurate as possible. This is achieved by varying the parameters of the model, such as the type of regression (linear, polynomial, etc.), the number of variables and the variable boundaries. These parameters will influence the accuracy of the prediction.
Once the model is ready, predictions can be made using the trend line. The trend line will give you a prediction for the future based on the historical data entered. This will help you make informed decisions about the future.
In summary, the regression calculator is a useful tool for predicting the future based on past patterns. For best results, you should carefully adjust the model parameters to obtain an accurate trend line. This will allow you to make reasonable predictions regarding the future.
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it is assumed that approximately 15% of adults in the u.s. are left-handed. consider the probability that among 100 adults selected in the u.s., there are at least 30 who are left-handed. given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? why or why not?
The probability of at least 30 left-handed individuals in a sample of 100
What is boinomial probability ?
Binomial probability refers to the probability of a particular number of "successes" occurring in a fixed number of independent trials. In other words, it calculates the probability of a specific outcome happening a certain number of times in a given set of trials.
The binomial probability formula is:
P(X=k) = (n choose k) *[tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex]
where:
P(X=k) is the probability of getting k successes in n trials
n is the number of trials
k is the number of successes
p is the probability of success on a single trial
(n choose k) is the binomial coefficient, which represent
He probability of selecting at least 30 left-handed individuals out of a sample of 100 adults in the US can be calculated using the binomial probability formula with x counting the number who are left-handed.
However, we must be careful when applying the formula to this problem because the sample is selected without replacement. The binomial distribution assumes that each trial is independent of the others, which is not the case when sampling without replacement.
In cases where the sample size is much smaller than the population size, the effect of not replacing the selected individuals is negligible. However, when the sample size is a substantial portion of the population size, as in this case, the probability of selecting an individual who is left-handed changes after each selection. This means that the probabilities of each selection are not independent, and the binomial formula cannot be used.
Therefore, to accurately calculate the probability of at least 30 left-handed individuals in a sample of 100 adults selected in the US without replacement, we need to use a different probability distribution, such as the hypergeometric distribution.
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In the figure below, m2 = 76°. Find m< 1, m<3, m<4
Answer:*
m<1 = 76°
m<3 = 76°
m<4 = 180° - 76° = 104°
*My answer is based on the information you provided me.
Step-by-step explanation:
Unfortunately, I cannot see the figure you are referring to as you didn’t provide a picture. However, I can provide a general approach to solve this problem based on the information given.
Assuming that the figure is a diagram of intersecting lines, here's a way to find the measures of angles 1, 3, and 4:
1. Angles 2 and 3 are vertical angles, which means they have the same measure. Therefore, m<3 = 76°.
2. Angles 2 and 4 are supplementary angles, which means their measures add up to 180°. Therefore, m<4 = 180° - m<2.
3. Angles 1, 2, and 4 form a straight line, which means their measures add up to 180°. Therefore, m<1 + m<2 + m<4 = 180°.
4. Substitute the given measure of m<2 and the value of m<4 found in step 2 into the equation from step 3, and solve for m<1:
m<1 + 76° + (180° - 76°) = 180°
m<1 + 104° = 180°
m<1 = 76°
Therefore, the measures of angles 1, 3, and 4 are:
m<1 = 76°
m<3 = 76°
m<4 = 180° - 76° = 104°
Write an additional equation that will complete the system of equations with no solution, one solution, and infinitely many solutions. The equation: -6y + 5x = -18
(a) The additional equation that will complete the system of equations with no solution is -2x + 3y = 7 and 4x - 6y = -16.
(b) The additional equation that will complete the system of equations with one solution is 2x + y = 8 and 3x - 2y = 7
(b) The additional equation that will complete the system of equations with infinitely many solutions is 4x - 6y = 12 and 2x - 3y = 6
What are the additional equations required?Some additional equations that can complete systems with no solution, one solution, and infinitely many solutions:
No solution:
-2x + 3y = 7
4x - 6y = -16
One solution:
2x + y = 8
3x - 2y = 7
Infinitely many solutions:
4x - 6y = 12
2x - 3y = 6
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If your good at Geometric Congruence, please answer the questions below in the photos. Please help, thank you.
Answer:
X=22 because of the symmetrical angle so 158+158=316 and one full angle = 360 then 360-316=44 and there are two sides so 44÷2=22
Stacy has 3 collector’s cards. She receives 2 more cards each week that she volunteers
at the student center.
Let x = the number of weeks.
Let y = the number of collector’s cards.
Which equation represents the amount of cards Stacy has?
Pls help me
The equation represents the amount of cards Stacy has: y = 2x + 3
At the beginning, Stacy has 3 collector's cards. Then, for every week she volunteers at the student center, she receives 2 more cards.
Let x = the number of weeks.
y = the number of collector’s cards.
So, after x weeks, she will have received 2x more cards. Therefore, the equation that represents the amount of cards Stacy has after x weeks is:
y = 2x + 3
Where y represents the number of collector's cards and x represents the number of weeks Stacy has volunteered at the student center.
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Randall is saving money to buy a bicycle. He has 37.80 in his savings account and saves 20% of his paper route earnings each week after 10 weeks, he has 87.80 in his savings account. How much does Randall earn each week from his paper route.
Answer:
$25
Step-by-step explanation:
Let's first subtract the savings account
87.80 - 37.80 = $50
Which means after 10 weeks, she saves $50
$50/10weeks = $5/1 week
Now they save 20% of the route. Which means $5 is 20% of the route.
To get to 100% we multiply 20% by 5.
That means we multiply the $5 by 5 also, giving us $25.
Find the area of the shaded region. Round to the nearest square unit when applicable. Show appropriate work. formules, and substitutions.
The areas of the composite figures are listed below:
516 55π cm² 96 m² (29.5π + 77) m² 58 ft² 588 cm²How to determine the areas of composite figures
In this problem we need to determine the areas of composite figures, which are the result of adding and subtracting geometric figures, whose area formulas are listed below:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Circle
A = π · r²
Semicircle
A = 0.5π · r²
Quarter of a circle
A = 0.25π · r²
Square
A = l²
Where:
b - Baseh - Heightl - Side lengthr - RadiusA - AreaNow we proceed to determine the area of each figure:
Area 1
A = 30 · 20 - 6 · 14
A = 600 - 84
A = 516
Area 2
A = π · (8 cm)² - π · (3 cm)²
A = (64 - 9) · π cm²
A = 55π cm²
Area 3
A = (14 m)² - 4 · (5 m)²
A = 196 m² - 100 m²
A = 96 m²
Area 4
A = 0.5π · (7 m)² + 0.5 · (14 m) · (11 m)
A = 29.5π m² + 77 m²
A = (29.5π + 77) m²
Area 5
A = (7 ft) · (10 ft) + (3 ft) · (4 ft)
A = 70 ft² - 12 ft²
A = 58 ft²
Area 6
A = (28 cm)² - 4 · 0.25π · (14 cm)²
A = 784 cm² - 196π cm²
A = 588 cm²
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What is A divided by 6 is equal to a whole number?
Answer:
4
Step-by-step explanation:
I think and I hope I got it right sorry if I didnt
The answer I think is right is a=24
a/6=?
24/6=4
Find the coefficient of determination calculator
The coefficient of determination calculator is a tool that is used to calculate the proportion of the variation in the dependent variable that is explained by the independent variable
The coefficient of determination, also known as R-squared, is a statistical measure that ranges from 0 to 1, where 0 indicates that none of the variation in the dependent variable is explained by the independent variable, and 1 indicates that all of the variation in the dependent variable is explained by the independent variable.
To use the coefficient of determination calculator, follow these steps:
Input the data: You will need to enter the data for both the independent and dependent variables in the calculator. .
Run the calculation: Once you have input the data, the calculator will use it to calculate the coefficient of determination.
Interpret the result: The output of the calculator will be the coefficient of determination, expressed as a decimal.
It's important to note that the coefficient of determination is only meaningful for linear regression models, where the relationship between the variables is assumed to be linear.
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what is the square root of 4761
Answer: 69 (nice)
Step-by-step explanation:
ask the question: what squared equals 4761?
69 x 69 = 4761
Therefore, sqrt4761 = 69
In the figure below, m/WXY = 64°, m/XYW = 67°, and m/WZV = 77º.
What is m/ZVW?
OA. 67°
OB. 54°
OC. 77°
OD. 44°
Z
W
Note picture not drawn to scale
Which statement is correct about the F distribution? A) Cannot be negative B) Cannot be positive C) Is the same as the t distribution D) Is the same as the z distribution
Option A) "Cannot be negative" is a correct statement about the F distribution. The F distribution is a probability distribution that is used in statistical hypothesis testing to compare the variances of two populations.
The assertion "cannot be positive" about the F distribution is erroneous. The F distribution can only accept positive values and cannot accept negative values; however, it can accept values greater than zero.
"Is the same as the t distribution" is an error. When the sample size is small or the population standard deviation is unknown, the t distribution is employed for testing hypotheses regarding the population mean.
"Is the same as the z distribution" is similarly erroneous. When the population standard deviation is known and the sample size is large, the z distribution is employed as a probability distribution.
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find the Mean of Absolute Deviation of 6,8,8,12,16
In reference to the question given, the mean absolute deviation of the set {6, 8, 8, 12, 16} is 2.4.
Calculating the Mean Absolute Deviation of a Set of Numbers.To find the mean absolute deviation of a set of numbers, we first need to calculate the deviations of each number from the mean of the set, then take the absolute value of each deviation, and finally calculate the average of all the absolute deviations.
To find the mean of the set {6, 8, 8, 12, 16}, we first need to calculate the mean:
mean = (6 + 8 + 8 + 12 + 16) / 5 = 10
Next, we calculate the deviations of each number from the mean:
|6 - 10| = 4
|8 - 10| = 2
|8 - 10| = 2
|12 - 10| = 2
|16 - 10| = 6
Taking the absolute value of each deviation gives us:
4, 2, 2, 2, 6
Finally, we calculate the mean of these absolute deviations:
mean absolute deviation = (4 + 2 + 2 + 2 + 6) / 5 = 2.4
Therefore, the mean absolute deviation of the set {6, 8, 8, 12, 16} is 2.4.
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Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
Kamden guessed a star Kamden guessed not a star
Card had a star 4 2
Card didn't have a star 1 752
The two-way frequency table of column relative frequencies for Kamden is shown below.
What is a two-way frequency table?
A two-way frequency table is a table that's used to graphically the represent frequencies or relative frequencies that are associated with two categorical variables.
How to complete the two-way frequency table?
When card had a star, the relative frequency that Kamden guessed a star is given by:
F(s) = 4/5
F(s) = 0.80.
Kamden guessed not a star is given by:
F(ns) = 2/754
F(ns) = 0.002 ≈ 0.00.
When card didn't have a star, the relative frequency that Kamden guessed a star is given by:
F(s) = 1/5
F(s) = 0.20.
Kamden guessed not a star is given by:
F(ns) = 752/754
F(ns) = 0.997 ≈ 1.00.
For the total, we have:
Total of F(s) = 0.80 + 0.20
Total of F(s) = 1.00.
Total of F(ns) = 0.00 + 1.00
Total of F(ns) = 1.00.
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Complete Question:
Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it. The two-way frequency table below shows data on guess and true status of the cards the friends drew. Complete the following two-way table of column relative frequencies. (If necessary, round your answers to the nearest hundredth.)
the average american height is
According to CDC data as of 2021, the average height for adult men in the United States is around 5 feet 9 inches (69.2 inches or 175.7 cm), and the average height for adult women is around 5 feet 4 inches (64.2 inches or 162.5 cm).
Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.
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How do you find the average value of a function from a graph?
To find the average value of a function from a graph, you can follow these steps:
Determine the interval over which you want to find the average value of the function. This is usually denoted by [a, b].Use the graph of the function to determine the function values at the endpoints of the interval, f(a) and f(b).Use the formula for the average value of a function over an interval: Average value = (1 / (b - a)) * ∫(a to b) f(x) dx where ∫(a to b) f(x) dx represents the definite integral of the function over the interval [a, b].Evaluate the definite integral to find the average value of the function over the interval. Average value = (1 / (b - a)) * ∫(a to b) f(x) dxCompare the average value of the function to its values at the endpoints of the interval. If the average value is between f(a) and f(b), then the function has a horizontal line that intersects the graph at the average value.For more questions on Graphs
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what is rational roots theorem?
The Rational Roots Theorem identifies possible rational roots of a polynomial equation in terms of factors of its coefficients.
The Rational Roots Hypothesis, otherwise called the Judicious Zeros Hypothesis, is a numerical hypothesis that assists with recognizing conceivable objective foundations of a polynomial condition. In particular, that's what it expresses on the off chance that a polynomial condition with number coefficients has a sane root, that root should be of the structure p/q, where p is a variable of the consistent term and q is an element of the main coefficient.
For instance, in the event that a polynomial condition has the structure ax^3 + bx^2 + cx + d = 0, and the main coefficient an and the consistent term d are numbers, then, at that point, the conceivable sane foundations of the situation are the quantities of the structure p/q, where p is a component of d and q is a variable of a.
The Normal Roots Hypothesis is valuable in tackling polynomial conditions and deciding if they have reasonable roots.
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Use the subtraction property of equality to write 3 equations that have the same solution of x=12
The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8
How to determine the equationsThe solution to the equation is given as
x = 12
The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.
Using the above as a guide, we have the following:
x - 4 = 12 - 4 (subtract 4 from both sides)x - 5 = 12 - 5 (subtract 5 from both sides)x - 7 = 12 - 7 (subtract 7 from both sides)Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.
Hence, the solution to each of these equations is x = 12.
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Explain what the vertical line test is and how it is used.
What is the domain of the given function?
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
{x | x = –4, –1, 3, 5, 6}
{y | y = –2, 0, 1, 4, 9}
{x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
{y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
Answer:
Look below
Step-by-step explanation:
The domain of any function is the x-value in an ordered pair.
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
Let A be a matrix with linearly independent columns. Which one of these statements must be true?A. The equation Ax=b never has a solution for all b.B. The equation Ax=b always has a solution for all b.C. The equation Ax=b has a solution for all b precisely when it has more columns than rows.D. There is no easy way to tell if Ax=b has a solution for all b.E. The equation Ax=b has a solution for all b precisely when it has more rows than columns.F. The equation Ax=b has a solution for all b precisely when it is a square matrix.G. none of the above
The correct statement is B. For all b, the equation Ax=b has a solution.
Since the columns of A are linearly independent, then the matrix A has full rank, and its column space is equal to the entire vector space in which it resides. This means that for any given vector b, we can find a linear combination of the columns of A that is equal to b, and therefore the equation Ax=b has a solution for all b.
Option A is incorrect, as there may be certain b vectors for which Ax=b has a solution.
Option C is incorrect, as the equation Ax=b may have a solution even when A has fewer columns than rows.
Option D is incorrect, as we can determine whether or not the equation Ax=b has a solution for all b by checking the rank of A.
Option E is incorrect, as the equation Ax=b may have a solution even when A has more columns than rows.
Option F is incorrect, as a square matrix may or may not have linearly independent columns, and therefore may or may not have a solution for all b.
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A teacher is monitoring how often students visit the website of the course during the day. She finds the following probability distribution. Find the expected number of visits to the course website.visits(x) 0 1 2 3probability 0.45 0.35 0.15 0.050.750.250.800.85
The expected number of visits to the course website.visits(x) 0 1 23probability 0.35.
What is probability?Probability is a mathematical study of outcomes in uncertain situation it is used to describe the like would have an event occurring and it can be expressed as the number between 0 to 1 probability is used to quantify the uncertainty associated with any given event it helps us understand how likely it is that something will happen and it can be used to make prediction about futures even probability theory is it of modern statistic and is widely used in fields such as finance economics and science.
Therefore, the probability of rolling at least one 3 when rolling two six-sided dice is 2 × 1/6, or 33.3%. This is because the probability of rolling a 3 on one die is independent of the probability of rolling a 3 on the other die. This means that the probability of rolling at least one 3 is equal to the sum of the probabilities of rolling a 3 on each of the two dice (1/6 + 1/6 = 2/6). As a result, the probability of rolling at least one 3 when rolling two six-sided dice is 33.3%.
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