Answer:
a person who fortells an event is called
Find the volume of the cylinder shown. Use 3.14
3.14
for pi. Round your answer to the nearest tenth.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [1 h 2 -5 20 - 12] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix is the augmented matrix of a consistent linear system if ht -9 (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) C. The matrix is the augmented matrix of a consistent linear system for every value of h. D. The matrix is not the augmented matrix of a consistent linear system for any value of h.
C. The matrix is the augmented matrix of a consistent linear system for every value of h.
What is augmented matrix ?
An augmented matrix is one that is created by joining the columns of two matrices.
The augmented matrix of a consistent linear system can have any value in the last column, as long as it corresponds to a valid solution of the system of linear equations.
The presence of a non-zero value in the last column simply indicates that the system has a unique solution, while a zero value in the last column indicates that the system is either inconsistent or has infinitely many solutions.
In this case, the value of h does not affect the consistency of the system.
Hence, The matrix is the augmented matrix of a consistent linear system for every value of h.
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Serenity wants to ride her bicycle 35. 8 miles this week. She has already ridden 17
miles. If she rides for 4 more days, what is the average number of miles she would
have to ride each day to meet her goal?
Answer:
4.7 miles per day
Step-by-step explanation:
35.8 - 17 = 18.8 miles
So, she needs to ride 18.8 miles in 4days
18.8 divided by 4 = 4.7 miles per day
So, she needs to ride 4.7 miles each day to meet her goal.
what conic section is described by the equation 4x2 3xy 5y2 x y = 0?
An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. The conic's shape is fixed because the equation also contains a constant.
An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. A constant in the equation, 4x2 + 3xy + 5y2 - x - y = 0, shows that the conic's shape is fixed. The equation is neither a parabola nor a hyperbola because it lacks any x or y terms. The equation therefore describes an ellipse. An oval-shaped closed curve known as an ellipse is produced when a plane and a cone intersect. The foci, or the two places at which the ellipse is symmetric, serve as its two defining points. The standard form of an ellipse, which is centred at the origin and contains the equation A(x2) + B(xy) + C(y2) + D(x) + E(y) + F = 0, is described by the equation provided. In this case, the constants are A=4, B=3, C=5, D=1, and E=1, and F=0. The major axis to minor axis ratio in the equation is 4:5, describing a moderately flattened ellipse. The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.
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if f (x) = startfraction x over x squared minus 9 endfraction, which table identifies the increasing and decreasing behavior of the function on the intervals (−[infinity], −3), (–3, 3), and (3, [infinity])?
The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:
On the interval (-∞, -3), f(x) is increasing.
On the interval (-3, 0), f(x) is decreasing.
On the interval (0, 3), f(x) is increasing.
On the interval (3, ∞), f(x) is decreasing.
We have,
To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.
Taking the derivative of f(x) with respect to x and simplifying, we have:
[tex]f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2[/tex]
To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.
For the interval (-∞, -3):
Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.
Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.
Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).
For the interval (-3, 3):
Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.
Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.
Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).
For the interval (3, ∞):
Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.
Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.
Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).
Thus,
The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:
On the interval (-∞, -3), f(x) is increasing.
On the interval (-3, 0), f(x) is decreasing.
On the interval (0, 3), f(x) is increasing.
On the interval (3, ∞), f(x) is decreasing.
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What is the mean for the answers
A: Range is 4
Range is from the smallest to the greatest so 10 - 6 = 4.
B: There are 5 students in the groups.
Five marks, five students.
C: Mean is 8.
The mean is to add all the marks 6 + 7 + 8 + 9 + 10 = 40. Then, divide by the numbers. There are 5 numbers so, 40 ÷ 5 = 8.
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Shirley is building a shed. The length is 2x + 3 feet long and the width is x + 1 feet long
1) what is the perimeter of the shed
2) what is the area of the shed
Please help I really want to go to sleep please
The perimeter is 6x + 8 feet and the area is (2x^2 + 5x + 3) square feet
How to determine the perimeter and the areaThe perimeter of a rectangle is equal to the sum of the lengths of all four sides.
The length of the shed is 2x + 3 feet, and the width is x + 1 feet, so the perimeter of the shed is:
2 * (2x + 3) + 2 * (x + 1) = 4x + 6 + 2x + 2 = 6x + 8 feet
The area of a rectangle is equal to the product of its length and width.
So, the area of Shirley's shed is:
(2x + 3) * (x + 1) = (2x^2 + 5x + 3) square feet
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A math test has 40 questions. A student answers 85% of the questions correctly. How many questions did the student answer correctly? Enter your answer in the box. questions
34 questions was answered correctly by the student, while 6 questions were incorrect
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
A math test has 40 questions. A student answers 85% of the questions correctly.
Number of questions answered correctly = 85% of total questions = 0.85 * 40 questions = 34 questions
Number of questions not answered correctly = 40 - 34 = 6 questions
34 questions was answered correctly by the student.
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The amounts of time Chauni spent writing a certain number of songs are graphed below.
If Chauni continues to write songs at the same rate, how many songs will she have written in 60 days?
Worth 10 points
Responses
18 songs
18 songs
20 songs
20 songs
24 songs
24 songs
30 songs
30 songs
Answer:
Step-by-step explanation:
18
Tony rounded each of the numbers and to the nearest hundred. Which choice correctly compares the rounded numbers?.
To the nearest hundred, Tony rounded the figures 1183 and 1145.
What is meant by place values?Our entire number system is built on place value. In this system, a digit's position within a number affects its value. The placements of the digits make the numbers 42,316 and 61,432 distinct from one another.
Place value is the value that a digit in a number represents based on where it appears in the number.
In order to round the number to the nearest hundred, look at the digit after the tens place.
In the hundreds place, we add one if the number in the tens place is greater than or equal to 5.
We replace the remaining digits with 0 if the number in the tens place is less than 5.
1200 is the result of rounding 1183 to the nearest tenth (8 in this case).
1145 is rounded to 1100 because there are four tens places in it.
The complete question is;
Tony rounded each of the numbers 1183 and 1145 to the nearest hundred. Which choice correctly compares the rounded numbers
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if jacques sells 32,000 baskets at the highest price consumers are willing to pay according to the demand curve, his average revenue will be $ per basket.
Jacques' average revenue per basket is $ per basket.
Average revenue (AR) is calculated by dividing total revenue (TR) by total quantity sold (Q).
Therefore, AR = TR/Q
Given that Jacques sells 32,000 baskets and the highest price consumers are willing to pay according to the demand curve, his total revenue (TR) is unknown.
However, we can calculate his average revenue (AR) by dividing his total revenue (TR) by the quantity sold (Q).
AR = TR/32,000
Therefore, Jacques' average revenue per basket is $ per basket.
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Complete question:How much average revenue will Jacques make if he sells 32,000 baskets at the highest price consumers are willing to pay according to the demand curve?
subtract (2x^2-3x+5)-(3x^2-4x+7)
Answer:
−x^2+x−2
Step-by-step explanation:
Imagine you have a bond with ten years left until maturity, a face value of $1000 and a 4% coupon rate. Interest rates recently rose to 6% and you want to figure out how it might impact the price of your bond. How much would this bond pay you back in principal at the end of the 10 years?
The bond would pay back its face value of $1000 at the end of the 10 years.
How to determine the amount to pay backThe face value of the bond is the amount the bond will be worth when it matures, and it is also known as the "par value" or the "principal amount."
In this case, the face value of the bond is $1000, so at the end of the 10 years, the bond will pay back $1000 in principal to the bondholder.
The coupon rate, which is 4% in this case, determines the amount of the annual interest payment that the bondholder will receive.
Therefore, regardless of the changes in interest rates, the bond will pay back its face value of $1000 at the end of the 10 years.
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An engineer is designing a fuel tank in the shape of a cylinder. The tank must have a volume of 3,500 cubic inches. The height of the cylinder must be twice the radius. What is the approximate radius of the cylinder?.
An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.
Volume:
V = πr²h
Height:
h = 2r
V = πr²h
V= πr²(2r)
V= 2πr³
And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:
V= πr²h
3500 = 3.14 x 2 x (r)³
r = 8.2 inch
The cylinder's approximate radius must be 8.2 inches.
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.
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Can someone please answer this
The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Let the angle be 'x'. Then the equation is given as,
x + 13° = 71°
x = 71° - 13°
x = 58°
The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.
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PLEASE HELP ASAPP!!!
The value of investment at maturity is $15094.
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
a=9000
r= 0.09
t=6
y=a(1+r)ᵗ
=> y=9000(1+0.09)⁶
=> y= 9000(1.09)⁶
=> y= 15093.900
Rounded to whole number : $15094
The value of investment at maturity is $15094
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Meagan gets a third of the money that her family earns selling cookies, and the amount that she gets can be shown with the expression m
3
. What is the meaning of the variable m in the expression?
Answer: the meaning of the variable m is Meagan, M is a shortened version to show that 3 is how much money she has.
Step-by-step explanation:
hope this helps ^^
Evaluate the integral. (Use C for the constant of integration.) ∫15sin3(x)cos2(x)dx∫15sin3(x)cos2(x)dx
The result of the original integral is:
∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C
What is the integration?
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
The integral of the product of sine and cosine functions can be evaluated using the identity:
sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))
Therefore, we can rewrite the integrand as:
15sin3(x)cos2(x) = (15/2)sin(3x + 2x) + (15/2)sin(3x - 2x)
Now, we can integrate each of the two terms separately:
∫(15/2)sin(3x + 2x)dx = (15/2)cos(3x + 2x) + C
∫(15/2)sin(3x - 2x)dx = (15/2)cos(3x - 2x) + C
Therefore, the result of the original integral is:
∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C
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Exponential Functions
In the exponential function y = 3 × q⁵ the starting value is 3.
What is an exponential function?The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
Given is an exponential function is -
y = 3 × q⁵
The exponential function is written in the form abˣ.
Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.
So, the initial or starting value in function y = 3 × q⁵ is -
a = 3
Hence, the starting value is 3.
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In the three topics we have discussed: circle, ellipse, and parabola, choose one of them. Look around your place and look for something that relates to the topic you have chosen. You may draw or capture it and put it on a short size of bond paper. Write 3-5 sentences that serve as your explanation. Make sure your output is creative and the text or words are readable. PLEASE ANSER
An element around me that has one of the aforementioned shapes is a ball.
What geometric shapes are around us?One of the geometric shapes around me is a basketball. This has a completely spherical shape that from any perspective looks circular.
This ball is orange in color and due to its circular or sphere shape it can roll on the floor. Additionally, this ball has the property of deforming when it hits the ground and bounces.
Additionally, with this ball we can make parabolic shots to score it on a basketball court.
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As many as 49 million Bison used to roam the Great Plains of the United States. When the
American settlers started hunting them for fur, meat and political purposes their survival rate
dropped to 0.81. How many million would have remained after 9 years of hunting?
Answer:
7.35 million
Step-by-step explanation:
49*0.81^9 =7.35 million
TRUE/FALSE. if january has 31 days, then 7 is an even number.
Answer: False
Step-by-step explanation:
7 is not an even number, and it never will be.
Even though january has 31 days, 7 is an odd number.
False. 7 is an odd number. This is because an even number is a number which can be divided by 2 without a remainder. 7 cannot be divided by 2 without a remainder, so it is an odd number.
To calculate this, we can use the remainder operator. This operator is represented by the percentage sign (%). When using this operator, the result is the remainder of a division operation. For example, if we divide 7 by 2, the result is 3 with a remainder of 1. If we write this as an equation, it will be 7 % 2 = 1. This means that 7 is not evenly divisible by 2, and is thus an odd number.
Therefore, even though january has 31 days, 7 is an odd number.
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Define response variable. Choose the correct answer below.
A.The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
B.The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
C.An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
D.The variable whose effect on the response variable is to be assessed by the experimenter
Response variable defined with:
B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.
Define Response VariableOption B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.
On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.
Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.
The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.
The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.
Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.
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The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: , , , , , , , , and. A. Compute the range and interquartile range. Range Interquartile range b. Compute the sample mean, sample variance, and sample standard deviation (to 2 decimals). Sample mean Sample variance Sample standard deviation c. A sample of air quality index readings for Anaheim provided a sample mean of , a sample variance of , and a sample standard deviation of. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics
The values mean, variance and standard deviation for Pomona and Anaheim are compared to identify the deviation in the air quality level.
The air quality index values for various area of southern California. Here the random variable (X) represents the air quality index values for Pomona.
From the given information the data values are 28, 42, 58, 48, 45, 55, 60, 49 and 50
Range = max. value - min.value
= 60 - 28 = 32
mean for air quality index for Pomona = x'
= sum of the values/total no.of samples
= (∑Xi )/ (n)
= 435/9 = 48.33
sample variance , ∑(Xi - x')/ n-1 = 92.75
standard deviation is the sq.root of variance , i.e √92.75
= 11.66
Use mean 48.3, variance 136 and standard deviation 11.66 to compare with the air quality in Pomona and Anaheim.
The air quality index reading for Pomona mean is equal to Anaheim. That is, The Pomona mean (48.3) is equal to the Anaheim mean (48.3).
The variance and sample standard deviation for Anaheim are 136 and 11.66, respectively.
The variance and sample standard deviation for Pomona are 92.75 and 9.63, respectively.
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A set of scores ranges from a high of X = 75 to a low of X = 23. If the bottom interval in a frequency table is 18-23, what is the top interval?
The top interval in a frequency table for a set of scores ranging from a high of X = 75 to a low of X = 23 would be 73-75.
This is because the bottom interval is 18-23, and the intervals in a frequency table are generally of equal size. This means that the highest interval must be of a similar size, and would thus be 73-75. The purpose of a frequency table is to show how often values from a numerical data set occur.
The data is usually divided into intervals of equal size, such as the 18-23 interval mentioned in this scenario. The intervals are usually calculated by subtracting the lowest value from the highest value, and then dividing the result by the number of intervals desired. In this case, the highest interval must be of equal size to the 18-23 interval, resulting in a range of 73-75.
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Sketch the graph of y = |x + 3| and evaluate the area under the curve y = |x + 3| above x - axis and between x = - 6 to x = 0 .
The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.
What is the area under the curve?
The area under a curve refers to the area between a curve and the -axis. This area could be entirely above the -axis, entirely below the -axis, or a combination of above and below the -axis. In calculus, the area under a curve is a visual representation of an integral.
The graph of y = |x + 3| is a piecewise linear function that starts at (3,0), increases linearly as x decreases to -3, reaches a maximum value of 3 at x = -3, and then decreases linearly as x decreases further to -6. The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 can be calculated by finding the area of two triangular regions. One triangular region is formed by the line y = x + 3 from x = -6 to x = -3 and the x-axis, and the other triangular region is formed by the line y = -(x + 3) from x = -3 to x = 0 and the x-axis. The area of each triangular region can be calculated using the formula 1/2 * base * height, and the total area is the sum of the areas of the two triangular regions.
So, The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation of the circle,
x² + (y – 3)² = 36.
The correct option is A.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
A circle that has a diameter of 12 units and a center that lies on the y-axis.
That means, radius = 6.
And h = 0.
From the given choices:
Now, the equation of the circle,
x² + (y – 3)² = 36.
Therefore, x² + (y – 3)² = 36 is the equation.
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For f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x, find the
following:
a) (f + h)(x)
b) (f - h)(x)
c) (fg)(x)
d) (fh)(x)
e) (f/g)(x)
The values of the composite functions are
a) (f + h)(x) = 2x³ - 9x - 2b) (f - h)(x) = 2x³ - 11x + 8c) (fg)(x) = 16x³ - 20x + 3d) (fh)(x) = 2(x - 5)³ - 10(x - 5) + 3 e) (f/g)(x) = (2x³ - 10x + 3)/(2x)How to evaluate the composite functionsFrom the question, we have the following functions that can be used in our computation:
f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x
Using the above as a guide, we have the following:
a) (f + h)(x) = 2x³ - 10x + 3 + x - 5 = 2x³ - 9x - 2
b) (f - h)(x) = 2x³ - 10x + 3 - x + 5 = 2x³ - 11x + 8
c) (fg)(x) = f(g(x)) = f(2x) = 2(2x)³ - 10(2x) + 3 = 16x³ - 20x + 3
d) (fh)(x) = f(h(x)) = f(x - 5) = 2(x - 5)³ - 10(x - 5) + 3
e) (f/g)(x) = f(x)/g(x) = (2x³ - 10x + 3)/(2x)
The above are the values of the composite functions
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g-filling machines at jelly belly. the variance in a production process is an important measure of the quality of the process. a large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. jelly belly candy company is testing two machines that use different technologies to fill three pound bags of jelly beans. the file bags contains a sample of data on the weights of bags (in pounds) filled by each machine. conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. use a .05 level of significance. what is your conclusion? which machine, if either, provides the greater opportunity for quality improvements?
There is sufficient evidence to support the claim of a greater variance for machine 1
Given two data sets, n1=25 and n2=22, their means are calculated as x1=3.3284 and x2=3.2782 respectively. The variance for each data set is calculated as s1=0.2211 and s2=0.0768 respectively.
The null hypothesis is that the variance of data set 1 (s1) is less than or equal to the variance of data set 2 (s2), while the alternative hypothesis is that the variance of data set 1 is greater than the variance of data set 2.
The test statistic F is calculated as the ratio of the variance of data set 1 squared to the variance of data set 2 squared, resulting in a value of 8.288.
The P-value is calculated as the probability of obtaining the value of the test statistic, or a more extreme value, which is less than 0.01.
Therefore, based on the significance level, the null hypothesis is rejected and the alternative hypothesis is accepted.
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There is sufficient evidence to support the claim of a greater variance for machine 1
Given two data sets, n1=25 and n2=22, their means are calculated as x1=3.3284 and x2=3.2782 respectively. The variance for each data set is calculated as s1=0.2211 and s2=0.0768 respectively.
The null hypothesis is that the variance of data set 1 (s1) is less than or equal to the variance of data set 2 (s2), while the alternative hypothesis is that the variance of data set 1 is greater than the variance of data set 2.
The test statistic F is calculated as the ratio of the variance of data set 1 squared to the variance of data set 2 squared, resulting in a value of 8.288.
The P-value is calculated as the probability of obtaining the value of the test statistic, or a more extreme value, which is less than 0.01.
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HELP FIND X & Y!!! NEED ASAP! (FOR 100 POINTS!)
[tex]\huge\begin{array}{ccc}x=1;&y=\frac{\sqrt3}{2}\end{array}[/tex]
The triangle with angles 30°, 60° and 90°.
Look at the picture.
We have:
[tex]a=\dfrac{1}{2}\\\\2a=x\\\\a\sqrt3=y[/tex]
Therefore:
[tex]x=2\cdot\dfrac{1}{2}\to\boxed{x=1}\\\\y=\dfrac{1}{2}\cdot\sqrt3\to\boxed{y=\dfrac{\sqrt3}{2}}[/tex]