On Using Heron's formula, area of the triangle is 60.866 square units
Using the formula A = 1/2bh,
area of the triangle: Area = 1/2 * √170 * 9.073 ≈ 60.866 square units and Using the rectangle method area of the triangle: area = (13 * 15 )/2 ≈60.866 square units .
Method 1: Heron's Formula
Heron's formula can be used to calculate the area of a triangle given the lengths of its three sides. The formula is as follows:
[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}[/tex], where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle (s = (a+b+c)/2).
Using the coordinates of the vertices of the triangle, we can find the lengths of the sides using the distance formula:
[tex]AB = \sqrt{ ((1-(-8))^2+(-6-7)^2)} = \sqrt{170} \\AC = \sqrt{((5-(-8))^2+(9-7)^2) } = \sqrt{290}\\BC =\sqrt{((5-1)^2+(9-(-6))^2)} = \sqrt{370}[/tex]
The semi-perimeter, s, is then:
s = (AB + AC + BC)/2 = (√170 + √290 + √370)/2 ≈ 16.362
Using Heron's formula, we can then find the area of the triangle:
[tex]Area = \sqrt{s(s-AB)(s-AC)(s-BC))} \\= \sqrt{ (16.362(16.362-\sqrt{170} )(16.362-\sqrt{290} )(16.362-\sqrt{370} ))} \\= 60.866[/tex]
Method 2: Base and Altitude Method
Another way to find the area of the triangle is to use the formula A = 1/2bh, where b is the length of the base of the triangle and h is the height. We can find the length of the base by using the distance formula to calculate the distance between the points (-8,7) and (1,-6):
[tex]b =\sqrt{((1-(-8))^2+(-6-7)^2) }= \sqrt{170}[/tex]
To find the height, we need to find the equation of the line passing through (-8,7) and (1,-6), which is the same as the equation of the line passing through the midpoint of AB and C, which can be found using the midpoint formula:
Midpoint of AB: ((-8+1)/2, (7-6)/2) = (-3.5, 0.5)
Line passing through (-8,7) and (1,-6): y = (-13/9)x + (103/9)
To find the altitude, we need to find the distance from point (5,9) to this line. We can use the formula for the distance between a point and a line:
h = |(-13/9)(5) + 1(9) - (103/9)|/√((-13/9)² + 1²) ≈ 9.073
Using the formula A = 1/2bh, we can then find the area of the triangle:
Area = 1/2 * √170 * 9.073 ≈ 60.866 square units
Method 3: Rectangle Method
Another way to find the area of the triangle is to use the rectangle method. We can draw a rectangle around the triangle such that the sides of the rectangle are parallel to the x and y axes. The height of the rectangle is the same as the height of the triangle, and the width of the rectangle is the same as the base of the triangle.
We can find the dimensions of the rectangle by finding the differences between the x-coordinates and y-coordinates of the vertices:
Width: 5 - (-8) = 13
Height: 9 - (-6) =15
Using the rectangle method ,we can then find the area of the triangle:
area = (13 * 15 )/2 ≈60.866 square units
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Brian multiplies 1.098 by powers of 10.
1.098 × 101 = 10.98
1.098 × 102 = 109.8
1.098 × 103 = 1,098
1.098 × 104 = 10,980
By what power of 10 would Brian multiply 1.098 to get a product of 1,098,000?
To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to the power 6.
What is scientific notation?Powers of 10 are used in scientific notation to indicate extremely big or extremely tiny quantities. A number is written as the result of a coefficient (a number between 1 and 10) and a power of 10 when it is expressed in scientific notation. The number represented by the power of 10 is the distance the decimal point must be moved to convert a number to standard form (i.e., a number without exponents).
To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to 6.
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1. h = 1.5 inches; r = 4 inches
2. h = 4 inches; r = 3 inches
(Volume problems for pi)
V=pir *2h
The volume of the first cylinder is 75.4 cubic inches and that of the second is 113.1 cubic inches.
What is volume of cylinder?Two parallel circular bases joined by a curving lateral surface make up the three-dimensional geometric object known as a cylinder. The area of one of a cylinder's circular bases is multiplied by one of its heights to determine the cylinder's volume. In other words, V = πr²h, where V is the cylinder's volume, r is the circumference of one of its circular bases, and h is the cylinder's height.
The volume of the cylinder is given as:
V = πr²h
First cylinder with h = 1.5 inches and r = 4 inches, the volume is:
V = π(4²)(1.5)
V = 24π
V ≈ 75.4 cubic inches
For h = 4 inches and r = 3 inches, the volume is:
V = π(3²)(4)
V = 36π
V ≈ 113.1 cubic inches
Hence, the volume of the first cylinder is 75.4 cubic inches and that of the second is 113.1 cubic inches.
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The volume of the first cylinder is 75.4 cubic inches and that of the second is 113.1 cubic inches.
What is volume of cylinder?Two parallel circular bases joined by a curving lateral surface make up the three-dimensional geometric object known as a cylinder. The area of one of a cylinder's circular bases is multiplied by one of its heights to determine the cylinder's volume. In other words, V = πr²h, where V is the cylinder's volume, r is the circumference of one of its circular bases, and h is the cylinder's height.
The volume of the cylinder is given as:
[tex]V = \pi r^2h[/tex]
First cylinder with h = 1.5 inches and r = 4 inches, the volume is:
[tex]V = \pi (4^2)(1.5)[/tex]
V = 24π
V ≈ 75.4 cubic inches
For h = 4 inches and r = 3 inches, the volume is:
[tex]V = \pi (3^2)(4)[/tex]
[tex]V = 36\pi[/tex]
V ≈ 113.1 cubic inches
Hence, the volume of the first cylinder is 75.4 cubic inches and that of the second is 113.1 cubic inches.
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solve simultaneously
[tex]44 = x - y {e}^{ - 0.7} [/tex]
[tex]18 = x - y[/tex]
Step-by-step explanation:
write an equation in slope-intercept form of the line that passes through the point (2,15) and (5,21)
Answer:
y = 2x + 11
Explanation:
N/A
Graph the function by hand using the techniques you were taught in this unit: f(x) = 2sin(x)-2. Your work and explanations must use the methods taught in this class.
• Amplitude: 2
• Period: 2pi
• Midline: y = -2
• y-intercept: (0, -2)
To graph the function f(x) = 2sin(x)-2, we can start by plotting the y-intercept (0, -2).
Next, we can use the amplitude of 2 to mark the highest and lowest points of the graph. The highest point will be 2 units above the midline at y = 0, and the lowest point will be 2 units below the midline at y = -4.
To establish the period of the function, we need to identify the distance between one complete cycle of the graph. Since sine has a period of 2pi, we can see that the period of our function is also 2pi.
Starting from the y-intercept, we can mark a point on the graph that is one-quarter of the way through a cycle, at x = pi/2. The sine function will be at its maximum value of 1 at this point, so the graph will be at y = 0 + 2
Graph the image of V(
–
6,3) after a rotation 90° clockwise around the origin.
The graph of point V(-6,3) after a rotation 90° clockwise rotation around the origin is given below:
What is graph?
In mathematics, a graph is a visual representation of a set of objects, which are called vertices or nodes, connected by links or edges. A graph can be used to represent relationships or connections between objects in a clear and concise way.
To graph the image of point V(-6, 3) after a 90° clockwise rotation around the origin, we can use the following steps:
Draw the coordinate axes and plot the point V(-6, 3).Draw a perpendicular line from point V to the x-axis. This line represents the distance between the point and the x-axis.To rotate the point 90° clockwise around the origin, we need to swap the x and y coordinates and change the sign of the new x-coordinate. So, the new coordinates will be (3, 6).Plot the new point V' (3, 6) on the graph.Connect the points V and V' with a straight line to show the transformation.The graph of point V(-6, 3) and its image after a 90° clockwise rotation around the origin is shown below:
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Write 1.1 as a mixed number.
-
at bedtime, you read three books to your kids, walker, matthew, and dean. together, they have 43 books. if you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? assume they have different favorites. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
If we randomly choose three books, then the probability that the three we choose will consist of each of their favorite books is 0.000081.
The total number of books is = 43 books.
Now, 3 books have to be selected.
So, the number of ways of choosing 3 different books from the 43 books can be calculated as : ⁴³C₃ = 12341,
The number of ways that those 3 get their favourite book is = ³C₃ = 1.
The probability that 3 you choose will consist of each of their favorite books is = 1/12341
= 8.103×10⁻⁵,
= 0.000081
Therefore, the required probability is 0.000081.
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what is the measurement of the third angle of a triangle if the other two angles each measures 45 degrees?
Answer: The answer is 90!
Step-by-step explanation:
A triangle's sides have to equal 180 degrees. The other two angles measure 45 degrees + 45 degrees, which equals 90. Now all you have to do is subtract 90 from 180. This equals 90, so the answer is 90 degrees.
Whenever you do problems like this in the future, remember these steps:
Angle 1 + Angle 2
180 - Combination of Angles 1 and 2 = Answer
The reason that you subtract from 180 degrees is because a straight angle is always 180 degrees. If you need more help with problems like these, I recommend watching some tutorials!
I hope this helped you!
If the taking turns procedure takes place on this distribution of goods, who would walk away with each pile? Person A chooses first.
Pile 1
Pile 2
Pile 3
Pile 4
Pile 5
Pile 1 will go to(No answer given)
Pile 2 will go to(No answer given)
Pile 3 will go to (No answer given)
Pile 4 will go to (No answer given) + Person A views,21% 13% 22% 18% 26%
Person B views 24% 17% 14% 22% 23%
In this situation, did each person get their fair share? (No answer given)
a) Note that the distribution of piles would be:
Person A gets Pile 5
Person B gets Pile 1
Person A gets Pile 3
Person B gets Pile 4
Person A gets Pile 2.
b) No, in this situation each person did not get their fair share.
If the taking turns procedure is such that Person A chooses first and then they alternate turns, then the following would be the distribution of piles:
Person A chooses first and would likely choose Pile 5, as it has the highest percentage viewed by them.Person B chooses next and would likely choose Pile 1, as it has the highest percentage viewed by them among the remaining piles.Person A chooses next and would likely choose Pile 3, as it has the highest percentage viewed by them among the remaining piles.Person B chooses next and would likely choose Pile 4, as it has the highest percentage viewed by them among the remaining piles.Finally, Person A would choose Pile 2, as it is the only remaining pile.So the distribution of piles would be:
Person A gets Pile 5Person B gets Pile 1Person A gets Pile 3Person B gets Pile 4Person A gets Pile 2.b) No, in this situation each person did not get their fair share if the criterion for fairness is defined as each person receiving an equal share of the piles.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
Find the indicated measure in parallelogram ABCD. State which theorem you used.
AD = 23.2 (opposite side of parallelogram are equal) and ∠D = ∠B = 188 (opposite angles are equal).
Explain the features of parallelogram:Parallelograms' characteristics
The opposing sides of a parallelogram are parallel to one another.A parallelogram has equal-length opposing sides.In a parallelogram, the measurements of the opposing angles are equal.The total of all the angles of a parallelogram, like all other quadrilaterals, is 360°.From the properties of parallelogram:
AD = BC (opposite side of parallelogram are equal)
x + 21 = 12x - 1
12x - 2x = 21 + 1
10x = 22
x = 2.2
AD = x + 21 = 2.2 + 21 = 23.2
Now,
∠A + ∠D = 180° (co interior angles are supplementary)
y - 9 + y/2 = 180
2y - 18 + y = 360
y = 360 + 18
y = 378
∠D = y/2 = 378/2 = 188
∠D = ∠B = 188 (opposite angles are equal).
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Findthe
y -intercept
oftheparabola y = x2 + 2x + 10
The y -intercept of the parabola y = x^2 + 2x + 10 is (0, 10)
the y-intercept represents the value of y when x=0. In the equation y = x^2 + 2x + 10, the x^2 and 2x terms create a parabola that opens upwards. As x approaches infinity or negative infinity, the value of y also increases towards infinity.
The y-intercept of a graph is the point at which the graph crosses the y-axis, which is where x=0. To find the y-intercept of the parabola y = x^2 + 2x + 10, we substitute x=0 into the equation, which gives
y = 0^2 + 2(0) + 10
y = 10
Therefore, the y-intercept of the parabola is (0, 10), which means the graph crosses the y-axis at the point (0, 10).
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The given question is incomplete, the complete question is:
Find the y -intercept of the parabola y = x^2 + 2x + 10
Please I need help
Manuel makes bird food by mixing sunflower seeds and
corn kernels. He bought 2.5 pounds of sunflower seeds. He
also bought some corn kernels. Sunflower seeds and corn
kernels each cost $2.20 per pound. The total amount
Manuel spent on the sunflower seeds and corn kernels was
$9.35.
Enter the number of pounds of corn kernels Manuel
purchased.
Manuel purchased 1.75 pounds of corn kernels.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side
In the given question,
Let's use x to represent the number of pounds of corn kernels Manuel purchased.
We know that Manuel bought 2.5 pounds of sunflower seeds, and that both the sunflower seeds and corn kernels cost $2.20 per pound.
The total amount Manuel spent on the sunflower seeds and corn kernels was $9.35, so we can write the equation: 2.2(2.5) + 2.2x = 9.35
Simplifying the left side of the equation, we get: 5.5 + 2.2x = 9.35
Subtracting 5.5 from both sides, we get: 2.2x = 3.85
Dividing both sides by 2.2, we get: x = 1.75
Therefore, Manuel purchased 1.75 pounds of corn kernels.
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what is 500 times 500
By multiplication, 500 times 500 is 250,000 using distributive property.
What is Multiplication?Multiplication is an arithmetic operation that combines two or more quantities into a single quantity. The result of multiplication is called the product. Multiplication is usually represented by the symbol "×" or "*".
For example, the product of 3 and 4 is 12, which is written as 3 × 4 = 12 or 3 * 4 = 12. In general, to multiply two numbers a and b, we write a × b or a * b, and the result is the product of the two numbers.
Multiplication is also distributive over addition, which means that a × (b + c) = (a × b) + (a × c) for any values of a, b, and c.
We are given :
500 × 500
Using distributive property
500 × 500 = 5 × 100 × 5 × 100
= (5 × 5) × (100 × 100)
= (25) × (10000)
= 250,000
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Expand and simplify 3(3x-2)-(2x-7)
Answer:
21
Step-by-step explanation:
Answer:7x+1
Step-by-step explanation:
1). Distribute: 9x-6-2x+7
2). Combine like terms: 9x+1-2x
3). Combine like terms: 7x+1
1. Two linear equations are shown in the graph below. Enter the coordinates of these two linear
equations;
Answer:
y=-0.5x+2; y=3x-5
Step-by-step explanation:
First linear equation:
y=ax+b
A(0,2) B(4,0)
2=a*0+b
0=4*a+b
b=2
4a+b=0
4a+2=0
4a=-2
a=-0.5
y=-0.5x+2
Second linear equation:
y=cx+d
C(0,-5) D(2,1)
-5=c*0+d
1=c*2+d
d=-5
2c+d=1
2c-5=1
2c=6
c=3
y=3x-5
In analyzing hits by certain bombs in a war, an area was partitioned into 574 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 574 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Question content area bottom
Part 1
Identify the values of μ, x, and e.
x is the number of sucesses.
e = 2.71828 is the Euler number.
μ is the mean in the given interval.
The probability that a randomly selected region had exactly two hits is 0.1710.
How to identify the values of μ, x, and e and describe what each of those symbols represents?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
P(x)= (μ^x * e^-μ)/x!
Where
x is the number of sucesses
e = 2.71828 is the Euler number
μ is the mean in the given interval.
A total of 535 bombs hit the combined area of 574 regions. So the mean hits per region is:
P = 535/574 = 0.9321
Assume that we want to find the probability that a randomly selected region had exactly two hits (i.e P(x = 2)).
P(x) = (μ^x * e^-μ)/x!
P(2) = (0.9321^2 * e^-(0.9321))/2!
P(2) = 0.1710
Therefore, the probability that a randomly selected region had exactly two hits is 0.1710.
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what is 63.92/9.4 in long division explanation
In long division, 63.92/9.4 results with quotient of 6.8.
What is long division explanation?Long division is a method of dividing two numbers by repeatedly subtracting the divisor from the dividend and keeping track of the resulting quotient and remainder. This method is often used when dividing two numbers with several digits. The process of long division involves several steps that are repeated until there is no remainder left or until a desired level of precision is achieved.
In long division, the dividend is the number being divided, and the divisor is the number by which the dividend is being divided. The quotient is the result of the division, and the remainder is the amount left over after the division is complete.
006.800
94 | 639.200
−0
63
−0
639
−564
752
−752
0
Thus, In long division, 63.92/9.4 results with quotient of 6.8.
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if you have an 88, a 95, a 93, and an 80, what do you need to make on the next quiz to have a mean quiz score of 90
You would need to make a 94 on the next quiz to have a mean quiz score of 90.
If 90 is the desired mean, then you have to multiply it by the number of quizzes
5 x 90 = 450 is the total in the 5 quizzes.
Now, add the scores of the first four quizzes.
88 + 95 + 93 + 80 = 356
Then, take the amount of the 5 quizzes and subtract it from the amount of the total 4 quizzes.
450 - 356 = 94
Are these triangles similar, congruent or neither? What theorem supports your answer?
options:
Similar: SAS
Similar: AA
Similar: SSS
Congruent: ASA
Congruent: SSS
Congruent: SAS
Neither
Both of the two triangles are similar by SSS similarity postulate.
How to Identify Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.
Looking at the 2 given triangles, we can see the ratio if corresponding sides as:
39/13 = 3
39/13 = 3
21/7 = 3
Since the ratios of the corresponding sides of both triangles are the same, then they are both Similar by SSS similarity postulate.
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What type of function is a circle?
is a pineapple
Step-by-step explanation:this is becuase you should work it out youself you silly goose
Answer:
circle is not a function.
Step-by-step explanation:
there are certain rules to define a mapping as function, one of them is function should not have more than 1 value at a given x.
for illustration purpose consider the below diagram,
as you can see in the given circle at x = 2, there are two different values of y, therefore equation of circle doesn't qualify as a function. half circle can be defined as a function (by restricting the range to only positive or negative values).
Hopefully you found the answer helpful
A public opinion poll in Ohio wants to determine whether registered voters support a recent school bond. They select a simple random sample of 50
registered voters from each county in the state and ask whether they approve or disapprove of the measure.
What is the population
What is the sample
Answer:
i hope this is what you are looking for
The population is all registered voters in Ohio, and the sample is the 50 registered voters from each county in Ohio that were randomly selected
Explanation:In this case, the population refers to all registered voters in Ohio, as they are the total group being studied. The sample is the subset of the population that is being evaluated to represent the entire population. In this question, the sample is the 50 registered voters from each county in Ohio that were randomly selected for the public opinion poll.
This scenario is an example of statistical sampling, a technique used in statistics to analyze a subset of a population and extrapolate insights or findings to the entire population.
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a dataset on 91 roller coasters lists the duration of the ride in seconds in addition to the drop height in feet for some of the coasters. one coaster, the tower of terror, is unusual for having a large drop but a short ride. after setting it aside, a regression to predict duration from drop for the remaining 90 coasters has r29.4%. complete parts a through c.a) What are the variable and units in this regression? The predictor variable is ___ in units of ___ and the response variable is ___ in units of ___ b) What units does the slope have? Feet, Seconds per foot, Seconds, Feet per second. c) Is the slope probably positive or probably negative? Explain. The slope is probably ____ because ___
(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.
(b) The slope is in seconds per foot.
(c) The slope may be negative, as greater drop heights generally result in longer travel times.
(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.
(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.
(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.
Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .
The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.
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The theoretical probability of tossing two heads when tossing a pair of coins is 0.25. When the pair of coins was tossed 20 times, two heads came up only 2 times. Which procedure would result in an experimental probability that is closer to the theoretical probability?
toss the coins more than 20 times
toss the coins fewer than 20 times
count only those tosses that result in two heads or two tails
toss three coins instead of two coins
Answer:
Toss the coins more than 20 times.
Step-by-step explanation:
Toss the coins more than 20 times. The experimental probability gets closer to the theoretical probability when the sample size is larger.
You buy a circular rug with a diameter of 7 feet how much floor space for the rug cover
Step-by-step explanation:
All you need to do here is use the area of a circle equation!
So a=pi(r)^2
A=pi(7)^2
A=pi49
Area would be 49pi or about 153.938 feet^2. Hope this helps!
Answer:
The rug will cover
Step-by-step explanation:
5. discuss the effects on sample size, requirements of changing the desired confidence level, and the acceptable sampling error.
Changing any of these factors will impact the others. Increasing the sample size generally results in more accurate estimates, while increasing the desired confidence level or decreasing the acceptable sampling error requires a larger sample size.
What is sample size?Sample size refers to the number of individuals or observations included in a study or experiment. It is a crucial component of research design because it determines how much data can be collected and analyzed, as well as the precision and accuracy of the results.
What is sampling error?Sampling error is the difference between the results obtained from a sample and the results that would have been obtained if the entire population had been surveyed. It is a measure of the variability between the sample estimate and the true population parameter.
In the given question,
The sample size, desired confidence level, and acceptable sampling error are all interrelated factors in statistical sampling. Changing any of these factors will have an impact on the others.
First, let's define each factor:
Sample size: The number of individuals or items included in a sample.Confidence level: The degree of certainty that the true population parameter falls within the calculated confidence interval.Sampling error: The degree of error or variation between the sample statistic and the true population parameter.Now, let's discuss the effects of changing each factor:
Sample size: Increasing the sample size generally results in a more accurate estimate of the population parameter. This is because a larger sample size reduces the effect of random variability and increases the precision of the estimate.
Confidence level: Increasing the desired confidence level requires a larger sample size to achieve the same level of precision. This is because a higher level of confidence requires a wider confidence interval, which in turn requires more data points.
Sampling error: Decreasing the acceptable sampling error requires a larger sample size to achieve the same level of precision. This is because a smaller sampling error requires a narrower confidence interval, which in turn requires more data points.
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A country road is 27 miles long and goes all the way around a lake, connecting the six cottages that are next to the lake. Two of the cottages are 1 mile apart (along the road). Two cottages are 2 miles apart, two are 3 miles apart, two are 4 miles apart, … two are 25 miles apart, and two are 26 miles apart. How are the cottages distributed along the road?
Using probability distribution, we can distribute the cottages as the follows along the road.
Define probability distribution?An experiment's potential outcomes are broken down into a probability distribution, which indicates the relative possibility of each one happening. For the purpose of describing a probability distribution, there are two key functions.
They are the cumulative distribution function and the probability density function, sometimes known as the probability mass function.
As the distance between each cottage and its neighbour is 1, 2, 3, 4, ... 25, or 26 miles, the entire length of the road that these distances occupy must equal 27 miles. The road links the six cottages, which explains why.
The cottages 1and 2 are separated by a mile, according to one conceivable distribution.
Similarly,
Two miles separate cottages 3 and 4.
Three miles separate cottages 5 and 6.
There are 4 miles between Cottages 1 and 3.
There are 5 miles between cottages 2 and 4.
There are 6 miles between cottages 3 and 5.
There are 7 miles between cottages 4 and 6.
Twenty-five miles separate cottages 1 and 6.
There are 26 miles between cottages 2 and 5.
By flipping the order of the cottage distances, a second potential distribution can be created. Which is:
There are 26 miles between cottages 2 and 5.
Twenty-five miles separate cottages 1 and 6.
There are 7 miles between cottages 4 and 6.
There are 6 miles between cottages 3 and 5.
There are 5 miles between cottages 2 and 4.
There are 4 miles between Cottages 1 and 3.
Three miles separate cottages 5 and 6.
Two miles separate cottages 3 and 4.
Two cottages 1 and 2 are one mile apart.
These two show that there are numerous ways to arrange the distances between the cottages while still adhering to the requirement that the distances must add to 27 miles, while there may be other alternative distributions.
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These two demonstrate that there are a variety of distributions for the distances between the cottages that still adhere to the requirement that the distances sum up to 27 miles.
Define probability distribution?The probability distribution of the possible results of an experiment shows the relative likelihood of each one occurring. There are two essential functions for defining a probability distribution.
They are the probability density function, also called the probability mass function, and the cumulative distribution function.
The total length of the road that these distances fill must be 27 miles because the distance between each cottage and its neighbor is 1, 2, 3, 4,... 25, or 26 miles. The six houses are connected by a road, which explains why.
According to one possible distribution, the distance between cottages 1 and 2 is one mile.
Similarly,
Cottages 3 and 4 are separated by two kilometers.
Cottages 5 and 6 are separated by three kilometers.
The distance between Cottages 1 and 3 is 4 kilometers.
The distance between houses 2 and 4 is 5 miles.
The distance between cottages 3 and 5 is six kilometers.
The distance between cottages 4 and 6 is seven kilometers.
The distance between houses 1 and 6 is 25 miles.
The distance between houses 2 and 5 is 26 miles.
It is possible to generate a second potential distribution by flipping the order of the cottage distances. That is:
The distance between houses 2 and 5 is 26 miles.
The distance between houses 1 and 6 is 25 miles.
The distance between cottages 4 and 6 is seven kilometers.
The distance between cottages 3 and 5 is six kilometers.
The distance between houses 2 and 4 is 5 miles.
The distance between Cottages 1 and 3 is 4 kilometers.
Cottages 5 and 6 are separated by three kilometers.
Cottages 3 and 4 are separated by two kilometers.
Two cottages 1 and 2 are one mile apart.
These two demonstrate that there are a variety of distributions for the distances between the cottages that still adhere to the requirement that the distances sum up to 27 miles.
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if 1 million passengers pass through the st. louis airport with checked baggage each month, a successful six sigma program for baggage handling would result in how many passengers with misplaced luggage? group of answer choices 3.4 34 6.0 2700 6 times the monthly standard deviation of passengers
Answer: 3.4 The number of passengers with misplaced luggage if 1 million passengers pass through the St. Louis airport with checked baggage each month would be 3.4 passengers.
A six sigma program is a quality improvement methodology that uses data and statistical analysis to identify and eliminate defects in a process. Six Sigma methodologies are used to improve efficiency and minimize defects in many business processes, including baggage handling in airports.
Sigma is a term used to refer to standard deviation, which is a measure of the spread of data in a process. A six sigma program aims to reduce the standard deviation in a process to a level where there are fewer than 3.4 defects per million opportunities.
Therefore, if one million passengers pass through the St. Louis airport each month, a successful six sigma program for baggage handling would result in 3.4 passengers with misplaced luggage.
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A component with time to failure T has failure rate z(t)= 2. 0*10-6 t/hour for t>0 1) Determine the probability that the component survives 200 hours 2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours
The probability that the component survives 200 hours is approximately 0.9802. The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
What is probability?
Probability is a numerical representation of the likelihood or chance of a specific event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
To determine the probability that the component survives 200 hours, we need to calculate the survival function, which is the probability that the component lasts longer than 200 hours. We can use the formula:
[tex]$$ S(t) = e^{-\int_0^t z(u) du} $$[/tex]
where [tex]$S(t)$[/tex] is the survival function and [tex]$\int_0^t z(u) du$[/tex] is the integral of the failure rate from 0 to [tex]$t$[/tex].
In this case, the failure rate is [tex]$z(t) = 2.0\times10^{-6}t/\text{hour}$[/tex] for [tex]$t > 0$[/tex]. Integrating this from 0 to 200 gives:
[tex]$$ \int_0^{200} z(t) dt = \int_0^{200} (2.0\times10^{-6}t) dt =[/tex] [tex]\left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{200} = 0.02 $$[/tex]
Substituting this into the survival function formula gives:
[tex]$$ S(200) = e^{-\int_0^{200} z(t) dt} = e^{-0.02} \approx 0.9802 $$[/tex]
Therefore, the probability that the component survives 200 hours is approximately 0.9802.
To determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, we need to use the conditional probability formula:
[tex]$ P(T > 400|T > 200) = \frac{P(T > 400 \cap T > 200)}{P(T > 200)} $$[/tex]
We can calculate the numerator using the survival function:
[tex]$ P(T > 400 \cap T > 200) = S(400) $$[/tex]
To find [tex]$S(400)$[/tex], we need to integrate the failure rate from 0 to 400:
[tex]$$ \int_0^{400} z(t) dt = \int_0^{400} (2.0\times10^{-6}t) dt = \left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{400} = 0.16 $$[/tex]
Substituting this into the survival function formula gives:
[tex]$$ S(400) = e^{-\int_0^{400} z(t) dt} = e^{-0.16} \approx 0.8534 $$[/tex]
To find the denominator, we can use the survival function we found earlier:
[tex]$ P(T > 200) = S(200) = e^{-0.02} \approx 0.9802 $$[/tex]
Substituting these values into the conditional probability formula gives:
[tex]$ P(T > 400|T > 200) = \frac{S(400)}{S(200)} \approx \frac{0.8534}{0.9802} \approx 0.8703 $$[/tex]
Therefore, the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
1) The probability that the component survives 200 hours is approximately 0.9802.
2) The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
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Complete question:
1. A component with time to failure [tex]$\mathbf{T}$[/tex] has failure rate[tex]$z(t)=2.0*10^{-6}$[/tex]t/hour for [tex]$t \ge 0$[/tex]
1) Determine the probability that the component survives 200 hours
2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours Note that the failure rate in this problem is not constant, but a function of time [tex]${\mathbf{}}t$[/tex].
2. Consider a computer system called [tex]$3\mathrm{P2M}$[/tex] in the following figure. The system consists of three processors and two shared memories communicating over a shared bus, as shown in the following Figure. The [tex]$3\mathrm{P2M}$[/tex] system is operational as long as at least two processors can communicate with at least one of the two memories over the bus. a) Construct the fault tree model of this system b) Find all the minimal cut sets c) Assume all the components fail exponentially with the following failure rates: processors (P1, P2, P3): 0.0001/hour; memories (M1, M2): 0.0001/hour; bus: 0.000001 /hour. Find the system reliability at mission time [tex]$t=100$[/tex] hours.
if a person is making the median salary for a construction worker, they are making more than what percentage of teachers? they are making more than % of teachers.
It's difficult to provide a precise answer to this question without knowing the specific median salary for a construction worker and the median salary for teachers in the same geographic area or region.
However, according to data from the Bureau of Labor Statistics (BLS) in the United States, the median annual salary for construction workers as of May 2020 was $38,970, while the median annual salary for elementary, middle, and high school teachers was $61,660. This means that a person making the median salary for a construction worker would be making less than approximately 37% of teachers.
It's important to note that this is a general comparison and the specific salaries can vary depending on factors such as location, years of experience, education level, and job responsibilities.
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