How many solutions does this equation have? -7t-6=-7t no solution one solution infinitely many solutions
The equation -7t-6=-7t has no solution.
Because when we try to isolate the variable t on one side of the equation, we end up with an equation that is not true.
Here's how we can do this:
-7t-6=-7t
First, we can add 7t to both sides of the equation:
-6=0
This equation is not true, so there are no values of t that will make this equation true. Therefore, the equation has no solution.
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1.Answer using True or False
any data set that has an approximately normal distribution, 99.7% of the data are within 3 standard deviations of the mean
a. The median is equal to the 25th percentile
b. In the sample (1.1.3.422.3.4 300.5.325.3.12.01 the sample mean is 35.89
c. 25% of the data in a sample are greater than the third quartile.
d. The mode of the sample 12.4645241) is 4 Choose The population standard deviation is 5
a. False
b. True
c. False
d. False
In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.
Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False
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1. Which method would be the best to solve the following system of equations?
Graphing
Substitution
None of these methods will work.
Elimination
(3x + 7y=-19
-3x+4y= 12
As a result, the equation system has the following solution: x = -24/5, y = -9/5.
What is an illustration of an equation?A mathematical assertion known as an equation is composed of a pair of expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of a quantity x is 7.
One of the best methods to solve the given system of equations is the elimination method.
To apply the elimination method, we need to multiply one or both equations by a suitable constant so that when we add or subtract the two equations, one of the variables is eliminated. In this case, if we multiply the first equation by 3, we get:
9x + 21y = -57
Now we can add this equation to the second equation to eliminate the x variable:
9x + 21y = -57
-3x + 4y = 12
25y = -45
Dividing both sides by 25, we get:
y = -45/25 = -9/5
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the second equation:
-3x + 4y = 12
-3x + 4(-9/5) = 12
-3x - 36/5 = 12
-3x = 12 + 36/5
-3x = 72/5
x = -24/5
As a result, the following is the system of equations' solution:
x = -24/5, y = -9/5
So the best method to solve this system of equations is the elimination method.
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Find the exact length of segment AB.
Look at triangle ABC.
18
5
O √20
O 3.6
O √13
M N
-4 -3 -2 -10
-
~ ?T
A (4,5)
B(2,2) C(4,2)
1 23 4 5
x
The exact length of segment AB is equal to: D. √13 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - 2)² + (5 - 2)²]
Distance = √[(2)² + (3)²]
Distance = √(4 + 9)
Distance = √13 units.
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Help this is urgent is a chemistry question I need help I will award brainliest
Answer:
The second answer is correct
Step-by-step explanation:
The first image shows nuclear fusion, combining two lighter nuclei to make a helium and a heavy nucleus, and the second image shows nuclear fission, taking a large unstable nucleus and turning it into two lighter nuclei.
An hour before show time, only 144 people are seated for a musical. According to ticket sales, 94% of the people have yet to arrive. How many tickets were sold for the musical?
Answer:
2400
Step-by-step explanation:
144 are seated
94% yet to arrive
6% = 144
Easy method Find the value of 1%
144/6 will be 1%
If 1% =24 then 100% will be 24x 100
Total tickets sold will be 2400
Check: 6% of 2400 is 144
Write a second equation whose graph goes thru(0,2) so the system has one solution at (4,1)
Answer:
y= -1/4x+b
Step-by-step explanation:
see image
Compare gradients
a) Complete the tables of values for the four lines: P, Q, R and S.
R y = 3x
P
४
y
y = x
x
Q y = 2x
y
-2
-2
-1
-1
0
↓↑
0
1
c) What do you notice?
1
2
-1
2
5-
b) Plot and label the lines P, Q, R and S.
4-
3-
2-
1-
0
-2-
-3-
-4
४
-5-
y
s y = x
४
y
-2
-2
-1
-1
0
O
x
1
1
2
2
White
Rose
Maths
N
Answer:
3
Step-by-step explanation:
by the help of Prashant chettri
O POLYNOMIAL AND RATIONAL FUNCTIONS Finding the asymptotes of a rational function: Constant ovel aph all vertical and horizontal asymptotes of the rational function f(x)=(5)/(3x+6)
The asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 .
To find the asymptotes of a rational function, we need to analyze the degree of the numerator and denominator, and find the values of x that make the denominator equal to zero.
First, let's find the vertical asymptotes. Vertical asymptotes occur when the denominator of a rational function is equal to zero. In this case, the denominator is 3x+6. Setting this equal to zero, we get:
3x+6=0
3x=-6
x=-2
So, the vertical asymptote is x=-2.
Next, let's find the horizontal asymptotes. Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 0 and the degree of the denominator is 1, so there is a horizontal asymptote. To find the horizontal asymptote, we need to look at the leading coefficients of the numerator and denominator. The leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 3. So, the horizontal asymptote is y=5/3.
Therefore, the asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 (vertical asymptote) and y=5/3 (horizontal asymptote).
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Which equation represents the formula for the general term, an, of an arithmetic sequence when a1=3 and a11=23
Answers:
an=3+2(n-1)
an=3+23(n-1)
an=23+10(n-1)
an=23+2(n-1)
Therefore , the solution of the given problem of arithmetic mean comes out to be option A an=3+2(n-1).
Arithmetic mean : What is it?The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.
Here,
The following is the formula for the general word "an" in an arithmetic sequence:
=> a = a1 + (n - 1)d
where the first term is denoted by a1, the term number is n, and the common difference is d.
A1 = 3 and A11 = 23 are provided. To determine the common difference, we can use the method for the eleventh term:
=> a11 = a1 + (11 - 1)d
=> 23 = 3 + 10d
=> d = 2
Inputting this number of d into the general term's formula yields the following results:
=> a = 3 + (n - 1)2
The right response is therefore: an=3+2(n-1).
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Show that d/dx (csc(x)) = −csc(x)cot(x)
d/dx (csc(x)) = d/dx 1/sin^2(x)
= (0-1) / sin^2(x)
= 1 / sin (x)
= -sin (x)
= −csc(x)cot(x)
To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.
The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:
1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)
Therefore, d/dx (csc(x)) = −csc(x)cot(x).
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Here is a regular 10-sided polygon. Work out the value of x. Show your working clearly Diagram NOT accurately drawn
Answer:
144
Step-by-step explanation:
Use algebra to determine whether or not the point (-1,6) lies on the line (-3,5)
The equation is true, the point (-1,6) does indeed lie on the line (-3,5).
The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine whether or not the point (-1,6) lies on the line (-3,5), we need to plug in the x and y values of the point into the equation of the line and see if the equation is true.
First, we need to find the slope of the line. The slope is the difference in the y values divided by the difference in the x values:
m = (5 - 6)/(-3 - (-1)) = -1/-2 = 1/2
Next, we need to find the y-intercept of the line. We can do this by plugging in one of the points and solving for b:
5 = (1/2)(-3) + b
b = 5 + (3/2) = 13/2
Now we have the equation of the line: y = (1/2)x + 13/2
Finally, we can plug in the x and y values of the point (-1,6) to see if the equation is true:
6 = (1/2)(-1) + 13/2
6 = -1/2 + 13/2
6 = 12/2
6 = 6
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ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments).
a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a ±10 percent of the population data?
b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days).
c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error?
a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.
How did we get the values?a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score for the desired confidence level (1.96 for 95% confidence level)
p = proportion of beak adjustments estimated from preliminary investigation (0.3)
E = margin of error (0.1)
Plugging in the values:
n = (1.96^2 * 0.3 * 0.7) / 0.1^2
n = 38.15
Rounding up, we need at least 39 work sampling observations.
b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.
c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:
Standard = (Total time worked / Total number of beak adjustments) * 100
For the six employees summarized in the table:
Granny:
Standard = (82 / 164) * 100
Standard = 50 hours per hundred beak adjustments
Tweety:
Standard = (80 / 161) * 100
Standard = 49.69 hours per hundred beak adjustments
Item:
Standard = (200 / 185) * 100
Standard = 108.11 hours per hundred beak adjustments
Total:
Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100
Standard = 83.56 hours per hundred beak adjustments
The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:
Standard Error = Standard Deviation / √(n)
Where:
Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))
n = sample size
Using the data provided in the table, we can calculate the standard deviation and standard error as follows:
Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))
Standard Deviation = 55.88
Standard Error = 55.88 / √(6)
Standard Error = 22.83
This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.
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The complete question goes thus:
ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99
help me with this please
Ok, ik this may be impossible without a protractor. But im Still Gonna Ask for Help…
Answer:
You must be really must to answer that paper yho
Find the value of x that makes the quadrilateral a parallelogram.
Answer: Your answer will be [tex]x=7[/tex]
If it's okay, I would like someone to talk to. My email address is jeremiah.mccrocklin06 at symbol g mail . com
Mariam wants to buy strawberries and apples to make a fruit tart. Strawberries cost $3 per pound and apples cost $3.25 per pound. How many pounds of fruit does she buy if she buys 0.5 pounds of strawberries and 3 pounds of apples? How many pounds of fruit does she buy if she buys
�
x pounds of strawberries and
�
y pounds of apples?
Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.
Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.
The arithmetic operations were used to arrive at the answer.
What do math operations entail?The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.
According to the given information:We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.
So, the total pounds of fruit bought = 0.5 + 3 = 3.5
Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits = (x + y)
Hence, the required solution has been obtained.
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Pls help! How do you write 8xy^2+1x^2-4x^2y-7y in standard form?
x² - 7y - 4x²y + 8xy² is standard form of equation.
What are equations, and what different kinds are there?
Equations can be divided into two categories: identities and conditional equations. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.
When two expressions are joined together by the equals sign ("="), the result is an equation. A mathematical statement that demonstrates the equality of two mathematical expressions is the definition of an equation.
8xy²+1x²-4x²y-7y
standard form = 8xy² + 1x² - 4x²y - 7y
= x² - 7y - 4x²y + 8xy²
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Help a girl out I need help his due for tomorrow please help guys
The function that generates the sequence 1, 2, 4, 8, ... is:
Of(x) = 2^(x-1)
We can check this by plugging in the first few values of x:
Of(1) = 2^(1-1) = 1
Of(2) = 2^(2-1) = 2
Of(3) = 2^(3-1) = 4
Of(4) = 2^(4-1) = 8
Therefore, the answer is option B.
the shorter leg of a right triangle is 7 centimeters less than the other leg. Find the length of the two legs if the hypothenuse is 13 centimeters
The lengths of the two legs are 2 centimeters and 9 centimeters.
Let's call the shorter leg of the right triangle x and the other leg y. According to the given information, we can create the following equation:
x = y - 7
Since we know that the hypothenuse is 13 centimeters, we can use the Pythagorean theorem to create another equation:
x^2 + y^2 = 13^2
Substituting the first equation into the second equation, we get:
(y - 7)^2 + y^2 = 13^2
Simplifying and rearranging terms, we get:
2y^2 - 14y - 72 = 0
Using the quadratic formula, we can solve for y:
y = (14 ± √(14^2 - 4(2)(-72))) / (2(2))
y = (14 ± √484) / 4
y = (14 ± 22) / 4
y = 9 or y = -2
Since the length of a leg cannot be negative, we reject the negative solution and take y = 9 centimeters as the length of the other leg. Then, we can use the first equation to find the length of the shorter leg:
x = 9 - 7
x = 2 centimeters
Therefore, the lengths of the two legs are 2 centimeters and 9 centimeters.
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The points I(-5,1), J(3,1), and K(-1,4) form a triangle. Find the desired slopes and lengths, then fill in the words that characterize the triangle. - slope of IJ = ____ slope of JK = ___ slope of IK= ___
- length of IJ = ___ length of JK = ___ length of IK = ___
Triangle IJK is _______ Submit Answer = √__
Triangle IJK is an isosceles triangle.
The slope of IJ is -2, the slope of JK is 1, and the slope of IK is 2. The length of IJ is 8, the length of JK is 4, and the length of IK is 6. Triangle IJK is an isosceles triangle.
√Correct
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the points A, B and C are 3 corners of a parallelogram what are the co ordinates of D
The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
It is given that:
the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.
Let D = (x, y)
Now, We know that;
The midpoint of AC = Mid-point of BD
(-2 + 5)/2 = (x + 3)/2
3 = x + 3
x = 0
(- 3+3)/2 = (y + 2)/2
y = - 2
Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).
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The current date - June 12, 2009. what date is atleast 10 years, 3 months, and 17 days after this date? A. September 18, 2021 B. September 29, 2019 C. September 18, 2019 D. September 29, 2021 E. September 18, 2009
Answer:
B
Step-by-step explanation:
now would be good please
Answer:
C, E
Step-by-step explanation:
Answer choice A implies that [tex]42 +22 \geq 50 + 27[/tex], which is false
Answer choice B implies that 50 is half of the population, however the population is 200, so it is false
Answer choice C implies that [tex]50 + 27\geq[/tex] all other combinations, which is true.
Answer choice D implies that [tex]33 + 22\leq 50[/tex], which is false
Answer choice E implies that [tex]42 \leq 22+22[/tex], which is true
So, C & E are correct
Which of the following statements can be assumed from the diagram?
The statements which can be assumed from the diagram are:
Line t and line s are perpendicularLine s is parallel to line uWhat is a Parallel Line?Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross.
Parallel curves are curves that do not touch each other or intersect and preserve a predetermined minimum distance
In simple geometry, two geometric objects are perpendicular if the intersection at the point of junction known as a foot results in right angles.
From the given image, it can be seen that
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cell selected Shade 1 5 of the grid. Click and drag to shade. What percent is equivalent to 1 5 ?
The equivalent percent of 1/5 is 20%.
To find this answer, we can convert the fraction to a decimal and then multiply by 100 to find the percent. Here are the steps:
1. Convert the fraction to a decimal: 1/5 = 0.2
2. Multiply the decimal by 100 to find the percent: 0.2 * 100 = 20%
Therefore, 1/5 is equivalent to 20%.
In terms of the shaded grid, if we were to shade 1 out of 5 squares, we would be shading 20% of the grid.
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Consider a polynomial function with real coefficients and a zero at 1+2i, what is another zero?
The answer of another zero - polynomial function with real coefficient at 1+2i is 1-2i
The other zero of the polynomial function with real coefficients and a zero at 1+2i is 1-2i.
This is because if a polynomial function with real coefficients has a complex zero,
then the conjugate of that zero is also a zero of the function. The conjugate of a complex number is obtained by changing the sign of the imaginary part.
Therefore, the conjugate of 1+2i is 1-2i. So, if 1+2i is a zero of the polynomial function, then 1-2i is also a zero of the function.
In summary, the other zero of the polynomial function with real coefficients and a zero at 1+2i is 1-2i.
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name the property the statement illustrates
Answer:
1. Transitive
2. Reflexive
3. Symmetric
4. Reflexive
5. Symmetric
6. Transitive
In a binomial situation n = 4 and p = 0.25. Determine the probabilities of the following events using the binomial formula: (Round the final answers to 4 decimal places.) a. x = 2 Probability b. x = 3 Probability c. x ≥ 2 Probability
d. x < 3 Probability
The probabilities, using the binomial distribution, are given as follows:
a. P(X = 2) = 0.2109.
b. P(X = 3) = 0.0469.
c. P(X ≥ 2) = 0.2617.
d. P(X < 3) = 0.9492.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex][tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]The parameters, and their meaning are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 4, p = 0.25.
Hence the relevant probabilities are given as follows:
P(X = 2) = 6 x 0.25² x 0.75² = 0.2109.P(X = 3) = 4 x 0.25³ x 0.75 = 0.0469.P(X = 4) = 0.25^4 = 0.0039.Then:
P(x ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2109 + 0.0469 + 0.0039 = 0.2617.
P(x < 3) = 1 - (P(X = 3) + P(X = 4)) = 1 - (0.0469 + 0.0039) = 0.9492.
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The equation of the plane passing through the origin, containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) ha
(-3x + 2y + z = 0 )
The equation of the plane passing through the origin and containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) can be found by taking the cross product of the two vectors and using the resulting vector as the normal vector of the plane. The cross product of the two vectors is given by:
\( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \times \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] = \left[\begin{array}{c}(-1)(3) - (1)(0) \\ (1)(3) - (1)(1) \\ (1)(0) - (1)(-1)\end{array}\right] = \left[\begin{array}{c}-3 \\ 2 \\ 1\end{array}\right] \)
Therefore, the equation of the plane is given by:
\( -3x + 2y + z = 0 \)
This is the equation of the plane passing through the origin and containing the two given vectors.
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