the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544
We can use the central limit theorem to approximate the distribution of the sample mean. Since the sample size is large (n=100), the sample mean follows approximately a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (i.e., 2.5/sqrt(100) = 0.25).
Let X be the sample mean, then we want to find P(|X - μ| ≤ 0.5), where μ is the population mean.
Using the standard normal distribution, we can standardize X as follows:
Z = (X - μ) / (σ / sqrt(n)) = (X - μ) / 0.25
So we want to find P(|Z| ≤ 2), where Z follows a standard normal distribution.
Using a standard normal distribution table or calculator, we find that P(|Z| ≤ 2) = 0.9544.
Therefore, the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544
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d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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Select the correct answer. Simon used these steps to solve an equation: Step 1: -6(x + 7) = 2(x − 11) Step 2: -6x − 42 = 2x − 22 Step 3: -8x − 42 = -22 Step 4: -8x = 20 Which property did he use to get from step 3 to step 4? A. addition property of equality B. distributive property C. subtraction property of equality D. transitive property
Answer: A - addition property of equality
Explanation: because -8x - 42 = -22
+42 +42
____________
-8x = 20
__ __
-8 -8
x = -2.5
Helppp.. also show work pls
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Lily has a box of candies.
5
6
of the candies are pink.
1
2
of the pink candies are round.
What fraction of the candies are pink and round?
Answer:
1/12
Step-by-step explanation:
Out of the total number of candies, 1/2 of the pink candies are round.
To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:
pink candies = 5/6
round candies among the pink ones = 1/5
Therefore, the fraction of candies that are pink and round is:
(5/6) x (1/2) x 1/5 = 1/12
So, 1/12 of the candies are pink and round.
The transformation shown is a translation.
IN
True
False
****
True, the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.
what is a triangle?
A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry.
The image shows a transformation where the figure has been moved to a different position while maintaining its size and shape. This type of transformation is called a translation, which involves sliding an object in a particular direction without changing its size or shape.
To perform a translation, we need to know how far the object has been moved horizontally and vertically. In the image, we can see that the blue triangle has been moved 2 units to the right and 3 units up. We can represent this translation using vector notation, where the vector (2, 3) represents the horizontal and vertical distances that the triangle has been moved.
Therefore, true the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.
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Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.
The expression for the total amount of shoes for both people is 4X + 2.
What is another word for total cost?As a result, total cost is the sum of fixed and variable costs, or TC = FC + VC = Kr+Lw.
Say Person 1 owns X pairs of shoes. So, Person 2 has two to three times as much as Person 1. This can be said as follows:
Person 2 possesses at least two more than three times Person 1's amount, so Person 2's amount is equal to 3X + 2.
By simply adding Person 1's and Person 2's shoe counts, we can determine the total number of shoes for both individuals, which results in:
Total equals the sum of the amounts given by Persons 1 and 2.
When we replace the value of Person 2's contribution, we obtain:
Amount total = X + (3X + 2)
If we simplify, we get:
Total = 4X plus 2
Hence, 4X + 2 is the total number of shoes for both individuals.
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The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
The equation of g(x) in vertex form include the following: C. g(x) = (x + 3)² - 2.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:
y = a(x - h)² + k
y = (x - (-3))² + (-2)
y = g(x) = (x + 3)² - 2
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nug
What the answer to this problem?
The coordinates of point Q in the parallelogram is (2b + 2a,2c)
1)How to determine the coordinates of Q?The coordinates are given as:
P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)
The parallelogram form of the object indicates that the distances PQ and RS are equal.
The distance RS is calculated as:
RS = ( 2a - 0, 0)
This gives
RS = (2a, 0)
Coordinate Q is calculated as:
Q = P + RS
This gives
Q = (2b,2c) + (2a,0)
Evaluate the sum
Q = (2b + 2a,2c)
Hence, the coordinates of point Q is (2b + 2a,2c)
2)To prove: SQ and PR bisect each otherMidpoint of SQ=(b+ a ,c)
Midpoint of PR=(a+ b, c)
hence, SQ and PR bisect each other.
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Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes. with the valley floor. If necessary, round to the nearest degree.
The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
What is grade?The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.
To find the angle we use the trigonometric functions:
tan(θ) = grade = rise/run
Given that, the grade of the incline is 78%, then grade = 0.78.
θ = arctan(0.78) ≈ 38.7 degrees.
Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
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e ABC be similar to RST. Find both missing sides t and s.
B
A
5
4
3
R
S
S
9
T
According to the solution we have come to find that, The missing sides are t=ST=9 and s=RT=12.
what is right angle triangle?
A right angle triangle, also known as a right triangle, is a triangle that has one angle measuring 90 degrees, which is also known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is a fundamental property of right triangles. Right triangles are important in mathematics and physics, and they have many applications in geometry, trigonometry, and calculus.
We can use the fact that the two triangles are similar to set up a proportion and solve for the missing sides.
AB/RS = BC/ST = AC/RT
Substituting the given values:
5/RS = 3/9 = 4/s
Solving for RS:
RS = (5/3) * 9 = 15
Solving for RT:
RT = (4/5) * 15 = 12
Therefore, the missing sides are t=ST=9 and s=RT=12.
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Sam, Larry, and Howard have contracted to paint a large room in a house. After calculating all the material costs, which are to be paid by the homeowner, they decide that $270 would be a fair price for the 16 hours it will take to prepare, paint, and clean up. Each of the men decides that $15.00 an hour is a fair wage for the job. If three-quarters of the work will be done by Larry, how much will Larry be paid for his work on the job?
Answer:
180 dollars
Step-by-step explanation:
270 for 16 hours = 16.875 dollars for each hour
15.00 an hour will be paid to larry
larry is doing 3/4 of those 16 hours
12 hours
15 x 12
larry gets 180 dollars for 12 hours of work
hope this helps x
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
What is variability?
To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.
To calculate the range, we subtract the smallest value from the largest value:
Largest value: 58
Smallest value: 10
Range = Largest value - Smallest value = 58 - 10 = 48
Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
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Assume that Canada imports more goods and services than it exports. Which of the following is true of the Canadian balance of payments accounts??
The correct answer is C. Could you please explain in detail why the trade balance must be negative, and why A and E is wrong. Thx!!!25. Assume that Canada imports more goods and services than it exports. Which of the following is true of the Canadian balance of payments accounts? (A) The current account balance must be negative. (B) The current account balance must be positive (C) The trade balance must be negative. (D) The financial account (formerly called capital account) balance must be negative (E) The financial account (formerly called capital account) balance must be positive
The trade balance must be negative.
If Canada imports more goods and services than it exports, the trade balance must be negative.
Here's a step-by-step explanation of why this is true and why options A and E are wrong:
1. The trade balance is calculated as the value of exports minus the value of imports. If imports are greater than exports, the trade balance will be negative (C). This m that Canada is seen spending more on goods and services from other countries than it is receiving from the sale of its own goods and services to other countries.
2. The current account balance includes the trade balance, but also considers other transactions such as income from investments and transfers like foreign aid. While it is possible that a negative trade balance could be offset by other positive inflows, we do not have enough information to determine whether the current account balance must be negative (A) or positive (B). Therefore, we cannot definitively say that A or B is true.
3. The financial account (formerly called capital account) balance records the net change in ownership of financial assets, such as stocks and bonds, between a country and the rest of the world. A negative financial account balance means that a country's residents are purchasing more foreign assets than foreign residents are purchasing of that country's assets. A positive financial account balance means the opposite. Since we only have information about the trade balance and not the financial transactions, we cannot determine whether the financial account balance must be negative (D) or positive (E).
Based on the information given, we can only conclude that the trade balance must be negative (C) if Canada imports more goods and services than it exports.
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what is the dimension of the solution space if you have 3 linearly independent equations in 5 unknowns?
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2. This is because, when solving a system of equations, the number of equations must match the number of unknowns; otherwise, it is impossible to solve. In this case, the number of equations (3) is less than the number of unknowns (5), meaning that the system is underdetermined. This means that there are infinite solutions, and the dimension of the solution space is 2 (the number of free variables).
In other words, the solution space is a two-dimensional plane where each point represents a possible solution to the system of equations. As the equations are linear, the solution space forms a linear subspace, which means that it is a flat surface.
It is also important to note that the linear independence of the equations is crucial to this solution. If the equations are dependent, then the solution space can have a dimension of 1, 0, or even a negative number. So, the dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
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Please help!!!
Question below!!
1. Dilation is the process of enlarging or shrinking a figure or shape by a scale factor.
2. Reflection is the process of flipping a figure or shape over an axis. In this example, A'B'C' is reflected over the x-axis.
3. A pair of triangles that are congruent are triangles with the same size and shape.
4. A pair of triangles that are similar are triangles with the same shape but different sizes.
What is dilation?Dilation is a mathematical operation used to expand or contract a shape. It involves multiplying every point in the shape by a given scale factor. The scale factor determines how much the shape is changed. The result is a line segment twice the length of the original.
1. In this example, triangle ABC is dilated by a factor of 2 about the point (-1,4). This means that all points on the triangle ABC will be multiplied by the scale factor 2. So the coordinates of point A will become (N-1,6) x 2 = (-2,12), point B will become (-4,5) x 2 = (-8,10) and point C will become (-4,0) x 2 = (-8,0). The new triangle created by the dilation is A'B'C'.
2. This means that the x-coordinates of the points remain the same, but the y-coordinates are multiplied by -1. So the coordinates of point A' will become (-2,12) x -1 = (-2,-12), point B' will become (-8,10) x -1 = (-8,-10) and point C' will become (-8,0) x -1 = (-8,0). The new triangle created by the reflection is ABC'.
3. A pair of triangles that are congruent are triangles with the same size and shape. In other words, the sides and angles of the two triangles are all equal.
4. A pair of triangles that are similar are triangles with the same shape but different sizes. In other words, the angles of the two triangles are equal, but the sides are not necessarily the same length.
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the variable socioeconomic status ranges from upper class to lower class and is an example of the select one: a. nominal level of measurement b. ordinal level of measurement c. interval-ratio level of measurement d. ratio level of measurement
The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)
Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.
Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.
However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.
Hence option (c) is correct.
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1. The orthocenter is outside the triangle. 2. An altitude is the same line segment as an angle bisector. 3. If the perpendicular bisector of one side of a triangle intersects the opposite vertex, then the triangle is isosceles
The solution of the match is
(1) Orthocenter (C) The point at which the altitudes of a triangle
meet.
(2) Centroid (D) The point at which the medians of a triangle
meet.
(3) Circumcenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(4) Incentre (B) The point at which the three angle bisectors
of a triangle meet.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.
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Complete Question:
Match the following.
(1) Orthocenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(2) Centroid (B) The point at which the three angle bisectors of
a triangle meet.
(3) Circumcenter (C) The point at which the altitudes of a triangle
meet.
(4) Incentre (D) The point at which the medians of a triangle
meet.
Rewrite the expression 2(10+12) using the distributive property of multiplication over addition
The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.
The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c
a( b + c ) = ab + ac
Using this property, we can rewrite the expression 2(10+12) as
2( 10 + 12 ) = 2(10) + 2(12)
Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:
2(10+12) = 20 + 24
Simplifying further, we get
2(10+12) = 44
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Which system has exactly one solution?
A.(y + 4x = -2
y = -4x + 5
B. (6x + 3y = -1
2x + y = 4
C. y = 4x - 5
{ y = -x-5
D.3x - = 2
{y-4 = 3(x-2)
The system of equations that has only one solution is the one where the equations have different slopes, it is the one in option C.
y = 4x - 5
y = -x - 5
Which system of equations has only one solution?A system of linear equations will have only one solution always that the lines are neither parallel nor the same line.
So, one way to check this, is to write both lines in the slope intercept form, and check that the two lines have different slopes.
For example, the first option will give.
y = -4x - 2
y = -4x + 5
These are parallel (same slope different intercept), then this systm has no solutions.
The correct option will be C, where the system is:
y = 4x - 5
y = -x - 5
The slopes are different.
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What is the exact value of sin(cos^-1 (√2/2)) + tan^-1 (sin(π/2))
[tex]\qquad \qquad \textit{Inverse Trigonometric Identities} \\\\ \begin{array}{cccl} Function&Domain&Range\\[-0.5em] \hrulefill&\hrulefill&\hrulefill\\ y=cos^{-1}(\theta)&-1 ~\le~ \theta ~\le~ 1& 0 ~\le~ y ~\le~ \pi \\\\ y=tan^{-1}(\theta)&-\infty ~\le~ \theta ~\le~ +\infty &-\frac{\pi}{2} ~\le~ y ~\le~ \frac{\pi}{2} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \theta \hspace{5em}\stackrel{\textit{so we can say}}{cos(\theta )=-\cfrac{\sqrt{2}}{2}} \\\\\\ \theta =cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \stackrel{ \textit{on the II Quadrant} }{\theta =\cfrac{3\pi }{4}} \\\\[-0.35em] ~\dotfill\\\\ sin\left[ cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right) \right]\implies sin\left( \cfrac{3\pi }{4} \right)\implies \boxed{\cfrac{\sqrt{2}}{2}}[/tex]
now let's find the angle for the inverse tangent
[tex]sin\left( \cfrac{\pi }{2} \right)\implies 1\hspace{5em}\stackrel{\textit{so we can say}}{tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]}\implies tan^{-1}(1) \stackrel{ \textit{on the I Quadrant} }{\implies\boxed{\cfrac{\pi }{4}}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left[ cos^{-1}\left( -\frac{\sqrt{2}}{2} \right) \right]~~ + ~~tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]\implies \cfrac{\sqrt{2}}{2}~~ + ~~\cfrac{\pi }{4} \implies \boxed{\cfrac{2\sqrt{2}+\pi }{4}}[/tex]
for the sine function we end up in the II Quadrant because the inverse cosine function range is constrained to the I and II Quadrants only, so our angle comes from that range.
Likewise, our angle from the inverse tangent comes from the I Quadrant, because inverse tangent range is only I and IV Quadrants.
Which of the following graphs is described by the function below?
[tex]y=x^{2} -6x-7[/tex]
A.) Graph A
B.) Graph B
C.) Graph C
D.) Graph D
The given function [tex]y=x^2 - 6x - 7[/tex] describes the graph A.
What is function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.
We can solve this Function by substituting the 0 for Y.
To find the value of x when y is equal to 0, we can substitute 0 for y in the equation and solve for x:
[tex]0 = x^2 - 6x - 7[/tex]
To solve for x, we can use the quadratic formula:
x = (-b ± [tex]\sqrt{(b^2 - 4ac)}[/tex]) / 2a
In this case, a = 1, b = -6, and c = -7. Substituting these values into the formula, we get:
x = (-(-6) ± [tex]\sqrt {((-6)^2 - 4(1)(-7)}[/tex])) / 2(1)
Simplifying:
x = (6 ± [tex]\sqrt{64}[/tex]) / 2
x = (6 ± 8) / 2
x = 7 or x = -1
Therefore, when y is equal to 0, x can be either 7 or -1.
Therefore the given function describes the graph A.
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which of the following is not a characteristic of the normal probability distribution? 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
The false statement regarding the normal distribution is given as follows:
99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The percentage of scores within 1 standard deviation of the mean is obtained considering that:
The p-value of Z = 1 is of 0.8413.The p-value of Z = -1 is of 0.1587.Hence the percentage is given as follows:
84.13 - 15.87 = 68.26%, which is different of 99.72%.
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The correct answer is that all of the following are characteristics of the normal probability distribution as given below.
What is a probability?A subfield of statistics known as probability studies random events and their likelihood of happening.
The statement "99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean" is actually a characteristic of the normal probability distribution.
The correct answer is that all of the following are characteristics of the normal probability distribution:
It is a continuous probability distribution, which means that it can take on any value within a certain range.It is symmetric around its mean.It is described by two parameters: its mean and standard deviation.The area under the curve of the probability density function is equal to 1.A large proportion (68.27%) of the data falls within one standard deviation of the mean, an even larger proportion (95.45%) falls within two standard deviations of the mean, and an even larger proportion (99.73%) falls within three standard deviations of the mean.To know more about probability, visit:
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write down a model that allows the variance of u to differ between men and women. the variance should not depend on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u
To write a model that allows the variance of u to differ between men and women, the best option is to use the heteroscedasticity model. This model will enable the variances to differ between the genders without depending on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u, Where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model. However, this model does not allow the variance of u to differ between men and women.
To achieve this, we need to modify the model to allow the variance of u to differ between men and women. This can be done by using the weighted regression model. The model will be as follows: y = b0 + b1x1 + b2x2 + u, where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model.
The weights can be represented as: wi = 1/σ^2i, where: wi = weight for observation, iσi = standard deviation of the ith observation. This model will allow the variance of u to differ between men and women without depending on other factors.
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an endangered species has a population of 5000. scientists estimate that the stock is decreasing at 3% per year. at this rate, approximately how many years will it be before 60% of the species remains?
It will take approximately 23.1 years for 60% population of the species to remain, assuming that the decrease rate remains constant over time.
We can utilize the exponential decay formula, which is given by, to respond to this question.
[tex]N(t) = N0 * e^(-rt) (-rt)[/tex]
N(t) is the population at time t, where N(t) is the population at time t, t is the time in years, and r is the yearly growth rate (or in this example, the annual drop rate).
Assuming that t is the number of years it will take for 60% of the species to survive, let's divide the drop rate by 100 to convert it from a percentage to a decimal. As a result, we have:
[tex]N(t) = 5000 * e^(-0.03t) \s0.6 * 5000 = 3000[/tex]
Given that N(t) is equal to 3000, we can solve for t by using the following method:
[tex]3000 = 5000 * e^(-0.03t) (-0.03t)\\t = ln(0.6) / -0.03 0.6 = e(-0.03t) ln(0.6) = -0.03t[/tex]
Calculating the answer, we obtain:
t = 23.1
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Can someone pls help me with this
A. The equation of the line that passes through the point (4,3) and has a slope of -5/2 is y = (-5/2)x + 13.
B. The x-intercept of the equation is x = 26/5 or 5.2
How to Find the Equation of a Line?A. To find the equation of a line that passes through the point (4,3) and has a slope of -5/2, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the given point.
Substituting the values, we get:
y - 3 = (-5/2)(x - 4)
Expanding the right side:
y - 3 = (-5/2)x + 10
Adding 3 to both sides:
y = (-5/2)x + 13
B. To find the x-intercept of this equation, we need to set y = 0 and solve for x:
0 = (-5/2)x + 13
Multiplying both sides by -2/5:
0 = x - (26/5)
Adding (26/5) to both sides:
x = 26/5
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Juan has a large bag of rice that he placed in three different containers. He put 3.253.25 pounds into the first container. He put three times as much into the second container. He put twice as much into the third container as he put into the second container.
What is the weight in pounds of the rice in the second container and the third container?
Answer:
he puts 3.354.235 pounds in it
Step-by-step explanation:
because the synapses hypural torminal that's the only answer that make since.
Gillian spends a third of her pocket money on snacks and a quarter of it on bus fare. How much money did she remain with?
Gillian pocket money is x, then Gillian has [tex]5/12x[/tex]left after spending on snacks and bus fare.
How to find the spending ?The term "spending" refers to the act of spending money to buy goods or services. It is the act of exchanging money for something, usually a product, service, or experience. Buying groceries, paying for transportation, or purchasing clothing are all examples of spending. To avoid debt and achieve your financial goals, it is critical to manage your spending wisely in personal finance.
If Gillian spends one-third of her pocket money on snacks and one-quarter on bus fare, she spends 7/12 of her pocket money on snacks and bus fare.
This means she only has [tex]1 - 7/12 = 5/12[/tex] of her pocket money remaining.
As a result, if her pocket money is x, she has 5/12x left after paying for snacks and bus fare.
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when researching a population where it is impossible or impractical to compile a list of the elements, which sampling technique is appropriate to use?
When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique
Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.
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You are the site engineer in charge of the operation of a set micro gas turbines in a factory. The correct operation of the turbines is an important factor in maintaining the energy supply for the machinery. Past experience indicates that there is a 98% chance that a turbine will operate normally in any particular day.
To ensure that a faulty turbine is identified and replaced, you order a test that measures the efficiency of each turbine and use that measure as an indication of possible problems in the turbine.
The test method is not perfect: the probability that a normally operating turbine will pass the test is 0.97 and the probability that a faulty turbine passes the test is 0.01.
The outcomes of the tests are statistically independent.
Suppose that one of the turbines fails the test, what is the probability of that turbine being faulty?
Answer:
about 0.40
Step-by-step explanation:
You have ...
probability of operating normally = 0.98probability a normally operating turbine passes the test = 0.97probability a faulty turbine passes the test = 0.01and you want to know the probability a turbine is faulty if it fails the test.
Test failureThe probability a turbine will fail the test is the sum of the probabilities a good turbine will fail, and that a bad turbine will fail.
p(good & fail) = p(good)×p(good fails) = 0.98×(1 -0.97) = 0.0294
p(bad & fail) = p(bad fails)×p(bad) = (1 -0.01)×(1 -0.98) = 0.0198
Then the probability a tested turbine will fail is ...
p(fail) = p(good & fail) +p(bad & fail) = 0.0294 +0.0198 = 0.0492
Conditional probabilityThe probability that a turbine is faulty given that it failed the test is ...
p(bad | failed) = p(bad & fail)/p(fail) = 0.0198/0.0492 ≈ 0.4024
The probability a turbine is faulty if it fails the test is about 0.40.
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How do I solve these equations in the best way an 8th grader can?
Answer:
1) x= 2
Step-by-step explanation: