In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that represents the average distance between each data point and the mean of the data set. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences. MAD is a useful measure of the variability or spread of a data set, and is often used as an alternative to the more common measure of standard deviation. Like standard deviation, MAD gives an indication of how spread out the data is, but unlike standard deviation, MAD is less sensitive to extreme values or outliers.
Here,
To find the mean absolute deviation of the data, we first need to calculate the mean (average) of the data:
Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8
Mean = 52
The mean of the data is 52.
Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is simply the absolute value of the difference between each data point and the mean:
|46 - 52| = 6
|54 - 52| = 2
|43 - 52| = 9
|57 - 52| = 5
|50 - 52| = 2
|62 - 52| = 10
|78 - 52| = 26
|42 - 52| = 10
Now, we can calculate the mean absolute deviation by taking the average of the absolute deviations:
Mean Absolute Deviation = (6 + 2 + 9 + 5 + 2 + 10 + 26 + 10) / 8
Mean Absolute Deviation = 8.5
The mean absolute deviation of the data is 8.5.
Interpretation: The mean absolute deviation represents the average distance between each data point and the mean of the data. In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units. This means that the data points are relatively spread out, with some points being much higher or lower than the mean.
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30. Mean IQ of Attorneys See the preceding exercise, in which we can assume that o = 15
for the IQ scores. Attorneys are a group with IQ scores that vary less than the IQ scores of the
general population. Find the sample size needed to estimate the mean IQ of attorneys, given that
we want 98% confidence that the sample mean is within 3 IQ points of the population mean.
Does the sample size appear to be practical?
A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
To find the sample size, we use the formula:
n = (z*σ/E)²
where n is the sample size, z is the z-score for the desired level of confidence given as 98% , σ is the population standard deviation given as 15, and E is the margin of error given as 3 IQ points.
using the above values, we get:
n = (2.33*15/3)²
n = 39.05
Therefore, we need a sample size of at least 40 attorneys to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
Whether this sample size is practical or not depends on various factors, such as the availability of attorneys with the desired characteristics, the cost and time required to collect the data, and the resources available for analysis. In general, a sample size of 40 is considered moderate to large for many applications, and it may be feasible depending on the specific context.
A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
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Solve the system of equations. 2x + 3y = 18 3x + y = 6 (9, 0) (3, 4) (1, 3) (0, 6)
X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D
To solve the system of equations:
2x + 3y = 18
3x + y = 6
We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:
To make the coefficients of x in both equations equal, multiply the second equation by two:
2(3x + y) = 2(6)
6x + 2y = 12
Now we have the system of equations:
2x + 3y = 18
6x + 2y = 12
Next, by deducting the first equation from the second equation, we can remove the y term:
(6x + 2y) - (2x + 3y) = 12 - 18
6x + 2y - 2x - 3y = -6
4x - y = -6
4x - y = -6
y = 4x + 6
At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:
2x + 3(4x + 6) = 18
2x + 12x + 18 = 18
14x + 18 = 18
14x = 0
x = 0
Replacing x = 0 in the equation y = 4x + 6 now:
y = 4(0) + 6
y = 6
Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.
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Answer:
Option D, (0,6)
Step-by-step explanation:
took the test xx
The holiday health club has reduced its annual membership by 10%. if jorge sanchez purchases a years membership and pays $270, what is the regular membership fee?
The regular membership fee of the Holiday Health Club is $300.
Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:
0.9x = 270
Solving for x, we get:
x = 270/0.9
x = 300
Hence, the regular membership fee of the Holiday Health Club is $300.
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Find the exact solutions of the equation in the interval (0, 2). (Enter your answers as a comma-separated list) 4 tan 2x - 4 cot x = 0 x= π/6 , π/2, 5π/6, 7π/6, 3π/2, 11π/6
Therefore, the solutions of tan x = -1/2 in the interval (0, 2) are:
x ≈ 2.034, 5.176
We can simplify the given equation as follows:
4 tan 2x - 4 cot x = 0
4(tan 2x - cot x) = 0
4[(2tan x)/(1 - tan^2 x) - (1)/(tan x)] = 0
Multiplying both sides by (1 - tan^2 x) * (tan x), we get:
8tan^3 x - 4tan^2 x - 8tan x + 4 = 0
Dividing both sides by 4 and rearranging, we get:
2tan^3 x - tan^2 x - 2tan x + 1 = 0
Factorizing, we get:
(tan x - 1)(2tan^2 x - tan x - 1) = 0
Using the quadratic formula to solve for the roots of 2tan^2 x - tan x - 1 = 0, we get:
tan x = [1 ± sqrt(1 + 8)] / 4 = [1 ± sqrt(9)] / 4 = 1, -1/2
Therefore, the solutions of the given equation in the interval (0, 2) are the values of x such that tan x = 1 or tan x = -1/2.
We know that tan (π/4) = 1 and tan (-π/4) = -1, so the solutions of tan x = 1 in the interval (0, 2) are:
x = π/4, 5π/4
We can find the solutions of tan x = -1/2 in the interval (0, 2) by finding the reference angle and using the signs of sine and cosine in the corresponding quadrants. We have:
tan x = -1/2
Let θ be the reference angle such that tan θ = 1/2. We know that θ is in the second or fourth quadrant.
In the second quadrant, sine is positive and cosine is negative, so we have:
sin θ = sqrt(1/(1 + tan^2 θ)) = sqrt(1/5)
cos θ = -tan θ = -1/2
Therefore, we get:
x = π - θ = π + arctan(1/2) ≈ 2.034
In the fourth quadrant, both sine and cosine are negative, so we have:
sin θ = -sqrt(1/(1 + tan^2 θ)) = -sqrt(1/5)
cos θ = -tan θ = -1/2
Therefore, we get:
x = 2π - θ = 2π + arctan(1/2) ≈ 5.176
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During the basketball game, you record the number of rebounds from missed shots for each team. (a) describe the likelihood that your team rebounds the next missed shot. (B) how many rebounds should ur team expect to have in 15 missed shots
In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15 shots is 10.5 rebounds.
Given
Number of shots missed by the given team is 7
Total number of shots fired is 10
a) Then, moving on to the first part of the question
Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.
Then,
Probability = no of shots attended / total number of shots fired
Probability = 7 /10
Then the event is likely
b) Now the second part
Then the number of rebounds the given team expect to have in the next 15 missed shots
= 7/10 ×15
= 105/10
= 10.5 rebounds
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The box-and-whisker plot shows the heights (in inches) of the players on a soccer team. What fraction of the heights are at least 68 inches?
How much of the heights are at least 68 inches?
IF the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.
Find out that how of the heights are at least 68 inches?Without seeing the box-and-whisker plot, it is difficult to determine the exact fraction of heights that are at least 68 inches. However, we can make an estimate based on the general characteristics of a box-and-whisker plot.
In a box-and-whisker plot, the "box" represents the middle 50% of the data, with the median (50th percentile) marked by a line inside the box. The "whiskers" represent the minimum and maximum values within 1.5 times the interquartile range (IQR) of the data. Any points outside the whiskers are considered outliers.
Assuming that there are no outliers in the data, we can estimate that at least 50% of the heights are above the median, which is marked by the line inside the box. If the median height is at least 68 inches, then at least 50% of the heights are at least 68 inches.
If we assume that the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.
If the median height is less than 68 inches, then we can estimate that slightly less than 50% of the heights are at least 68 inches.
In summary, without more information about the box-and-whisker plot or the data it represents, we can estimate that at least 50% of the heights are at least 68 inches.
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Simplify and evaluate
Answer:
In simplified form: 1/27
Evaluated: 0.037
Step-by-step explanation:
To simplify and evaluate 81^(-3/4), we use the rule that (a^m)^n = a^(mn) and rewrite the expression as (3^4)^(-3/4). Then, we use the rule that a^(-n) = 1/(a^n) to get:
81^(-3/4) = (3^4)^(-3/4) = 3^(-3) = 1/(3^3) = 1/27
Therefore, 81^(-3/4) simplifies to 1/27 and evaluates to 0.037
One bag of dichondra lawn food contains 30 pounds of fertilizer and its recommended coverage is 4000 square feet. if you want to cover a rectangular lawn that is 160 feet by 160 feet, how many pounds of fertilizer do you need?
To cover a rectangular lawn of 160 feet by 160 feet with dichondra lawn food, you would need 210 pounds of fertilizer.
To find the area of the rectangular lawn
Area = Length x Width
Area = 160 ft x 160 ft
Area = 25,600 sq ft
Since one bag of lawn food can cover 4000 square feet, we need to divide the total area of the lawn by the coverage of one bag
Number of bags = Total area ÷ Coverage of one bag
Number of bags = 25,600 sq ft ÷ 4000 sq ft
Number of bags = 6.4
Since we cannot buy a fraction of a bag, we need to round up to the nearest whole number of bags, which is 7.
Therefore, we need 7 bags of lawn food to cover the rectangular lawn. To find the total weight of fertilizer needed, we multiply the number of bags by the weight of one bag
Total weight of fertilizer = Number of bags x Weight of one bag
Total weight of fertilizer = 7 bags x 30 pounds/bag
Total weight of fertilizer = 210 pounds
Thus, we need 210 pounds of fertilizer to cover the rectangular lawn.
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Which polynomial does the model represent? The model shows 1 black square block, 2 white thin blocks, 1 black thin block, 1 white small square block, 3 black small blocks
The polynomial represented by the model is [tex]]x^2 - x + 2[/tex]
Based on the provided model, the polynomial represented is:
1 black square block: x^2
2 white thin blocks: -2x
1 black thin block: x
1 white small square block: -1
3 black small blocks: +3
The polynomial that the model represents is:
[tex]x^2 - 2x + x - 1 + 3[/tex]
Combining like terms, we get:
[tex]x^2 - x + 2[/tex]
So, the polynomial represented by the model is [tex]x^2 - x + 2[/tex].
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What is question asking??? All I need is one example and I get the rest I just don’t understand the assignment
It's actually asking you to find the angles within the circles and match it with the angles it's supposed to be. For example if angle COE is 90° (im taking a fake angle value), you should put arc CE <——> 90
If you are still confused and need me to do it so that you can understand what I mean, reply and I'll help you!
Answer:
See below
Step-by-step explanation:
The objective of the question has been well explained by user vaishub1101.
I am just adding an additional hint and one answer to get you going
Since you just needed one example, I am providing just that
One thing to note in the figure is that segments DEF, ACD and ABF are all tangents to the circle. This fact is important since at the point of tangency (where the tangent touches the circle), the tangent to a circle is always perpendicular to the radius.
Using this knowledge and the given angles we can compute all the other angles but not the arc length [tex]\frown \atop {CE}[/tex] since to find arc length we need the value of the radius
As an example to help you get going,
[tex]\angle{DFA} \longleftrightarrow 58^\circ[/tex]
You would drag the tile with ∠DFA to the top left box and the tile with 58° to the top right box
I am sure you can figure out the rest or else user vaishub1101 can help you out with the rest
Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or se transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.
Geometric transformations can be found in everyday life, such as moving furniture (translation), opening a door (rotation), using mirrors (reflection), zooming in and out of maps (scaling), skewing images in Photoshop (shearing), and stretching a rubber band (stretching).
Here are some examples of different types of transformations and their applications:
Translation:
Moving furniture in a room
Moving a vehicle on a map
Shifting a picture on a wall
Rotation:
Swinging a pendulum
Turning a key in a lock
Opening a door
Reflection:
Mirrors reflecting images
Water reflections of a landscape
Reflective surfaces on cars and buildings
Scaling:
Enlarging or reducing a picture on a screen
Adjusting the size of a printout
Shearing:
Skewing an image in Photoshop
Tilting a picture frame on a wall
Slanting the roof of a building for better drainage
Stretching:
Stretching a rubber band
Stretching a balloon before inflating it
Stretching a canvas for painting
These are just a few examples of the many ways geometric transformations are used in our everyday lives. By understanding these concepts, we can appreciate the beauty and functionality of the world around us.
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Jose reads his book at an average rate of
2. 5
2. 5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read
20
20 pages?
To determine how long it would take Jose to read 20 pages at his average rate, you can use a proportion.
Let x be the time in minutes it would take Jose to read 20 pages.
Then, you can set up the following proportion:
2.5 pages / 4 minutes = 20 pages / x minutes
To solve for x, you can cross-multiply:
2.5 pages * x minutes = 4 minutes * 20 pages
2.5x = 80
Finally, divide both sides by 2.5 to isolate x:
x = 32
Therefore, it would take Jose 32 minutes to read 20 pages at his average rate.
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A convention center is hosting a home show where different businesses provide information and examples for improvements that can be made to homes. The sponsors are also holding a lottery to give away $10,000 in home improvements. In a giant bin, 20 balls numbered 1 - 20 are mixed together. Then , 3 balls are selected from the bin, without replacement For $5. 00a customer can try to predict the 3 numbers that will be selected. If the order in which the numbers are selected does not matter , how many different predictions are possible for this game of chance ?
There are 1140 different predictions possible for this game of chance.
In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.
To solve this problem, we can use the formula for combinations, which is
=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]
where n is the total number of items, and x is the number of items to be selected.
In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes
=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]
Using a calculator or simplifying the equation, we get:
[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]
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Qn in attachment. ..
Answer:
pls mrk me brainliest (・(ｪ)・）
A cylinder has volume 108 cm? What is the volume of a cone with the same
radius and height? Use 3. 14 for it and be sure to add units to your answer.
The volume of the cone with the same radius and height as the cylinder is 36 cm³.
To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 108 cm^3.
So, 108 = πr^2h
To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.
V = (1/3)π( r^2 )(h)
V = (1/3)π( r^2 )(108/π)
V = (1/3)( r^2 )(108)
V = 36( r^2 )
Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³
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Which expressions are equivalent to 2(2x + 4y + x − 2y)? (1 point)
Answer:
6x + 4y
Step-by-step explanation:
2(2x + 4y + x − 2y)
= 4x + 8y + 2x - 4y
= 6x + 4y
Billy has $80 to spend. He spent $54.50 on Bruno Mars Tickets. If Stickers cost $1.34 each, what is the maximum number of Stickers he can buy? Define a variable then write and solve an inequality. Write your answer using a complete sentence.
Answer:
Billy can buy 19 or less than 19 stickers.
Step-by-step explanation:
Solving inequality:Let the unknown variable - number of stickers be 'x'.
Cost of one sticker = $1.34
Cost of 'x' stickers = 1.34 * x = 1.34x
Maximum amount that can be spent for buying stickers = 80 - 54.50
= $25.50
Inequality:
1.34x ≤ 25.50
Solving:
Divide both sides by 1.34,
[tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]
x ≤ 19.03
x ≤ 19
Billy can buy 19 or less than 19 stickers.
Ranjan is driving to Salt Lake City. His car gets 35. 5 miles per gallon of gasoline. Ranjan starts with his tank full. So far he has made two stops. Each time he stops, ranjan adds gas until his car is full again. At the first stop ranjan adds 6. 7 gallons of gas. At he second stop he adds 3. 4 gallons of gas. How many miles has ranjas drivin so far
After calculating the distance, Ranjan has driven 358.55 miles so far.
To solve this problem, we need to use the formula:
distance = fuel efficiency x fuel consumed
Let's start by calculating the total fuel consumed. At the first stop, Ranjan adds 6.7 gallons of gas, which means he consumed 6.7 gallons of gas since his tank was full at the beginning of the trip. At the second stop, he adds 3.4 gallons of gas, which means he consumed 3.4 gallons of gas between the first and second stops. Therefore, the total fuel consumed is:
6.7 + 3.4 = 10.1 gallons
Now we can calculate the distance driven using the fuel efficiency of 35.5 miles per gallon:
distance = 35.5 miles/gallon x 10.1 gallons = 358.55 miles
Therefore, Ranjan has driven 358.55 miles so far.
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What is the approximate area of the figure?
20 square meters
40 square meters
80 square meters
100 square meters
The approximate area of the figure is 40 square meters. So, the correct answer is B).
Recall the formula for the area of a kite, which is
Area = (1/2) x Base x Height
where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.
Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.
Substitute the values of the base and height into the formula for the area of a kite
Area = (1/2) x 8 meters x 10 meters
Simplify the expression by multiplying the base and height together and dividing by 2
Area = 40 square meters
Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.
Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).
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i need help fast look at photo
Step-by-step explanation:
B
26 = 13.5 + m/2.5; m = 31.25
26 = 13.5 + 31.25/2.5
26 = 13.5 + 12.5
26 = 26
15√2 = x√2please help me, how do i solve this? i'm in 9th grade and i completely forgot how to do this.
The equation 15√2 = x√2 can be solved, the value of x that satisfies the equation is 15.
To solve the equation 15√2 = x√2, you can divide both sides by √2 since the square root of 2 is a common factor on both sides of the equation. This gives:
15√2 / √2 = x√2 / √2
On the left side of the equation, the √2 and the denominator cancel out, leaving:
15
On the right side of the equation, the √2 and the denominator also cancel out, leaving:
x
So the solution to the equation is:
x = 15
Therefore, the value of x that satisfies the equation is 15.
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An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function =Cx+−0.5x2180x25,609. How many engines must be made to minimize the unit cost?
Do not round your answer.
The number of engines that must be made to minimize the unit cost are 180
How many engines must be made to minimize the unit cost?From the question, we have the following parameters that can be used in our computation:
C(x) = −0.5x² + 180x + 25,609.
Differentiate the above equation
So, we have the following representation
C'(x) = -x + 180
Set the equation to 0
So, we have the following representation
-x + 180 = 0
This gives
x = 180
Substitute x = 180 in the above equation, so, we have the following representation
C(180) = −0.5(180)² + 180(180) + 25,609
Evaluate
C(180) = 41809
Hence, the engines that must be made to minimize the unit cost are 180
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The distance between the two points M(15, a) and N(a,-5) is 20. Find the value of a.
Answer: 10
Step-by-step explanation:
just trust me
ET Previous Problem S NOX (1 point) According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 10 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mait? Such a package is shown below. Assume 7 What are the dimensions of the package of largest volume? Х х Find a formula for the volume of the parcel in terms of x and y Volume The problem statement tells us that the parcel's girth plus longth may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus longth to equal 108 inches. What equation does this produce involving randy Equation: It Solve this equation for y in terms of an Find a formula for the volume V (w) in terms of e. V(x) HH What is the domain of the function V7 Note that both and y must be positive consider how the constraint that girth plus length is 10 inches limit the possible values for Give your answer using interval notation Domain Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume Maximum Volume II Optimal dimensions = !!! andy 11
The dimensions of the package of largest volume are 18 inches by 18 inches by 36 inches. The largest possible volume is 11664 cubic inches.
How we find dimension?To find the dimensions of the package of largest volume. Let the dimensions of the square end be x, and the length of the rectangular end be y. The girth of the package is 4x, and the length is y. According to the problem statement, the girth plus length may not exceed 108 inches, so we have:
4x + y = 108We want to maximize the volume V(x,y) of the package, which is given by:
[tex]V(x,y) = x^2y[/tex]We can use the equation 4x + y = 108 to express y in terms of x:
y = 108 - 4xSubstituting this into the formula for V(x,y), we get:
[tex]V(x) = x^2(108 - 4x) = 108x^2 - 4x^3[/tex]The domain of V(x) is determined by the constraints that x and y must be positive and the girth plus length may not exceed 10 inches. Since the girth is 4x, we have:
4x + y = 108 - 3x ≤ 10Solving for x, we get:
x ≤ 32/3Since x must be positive, the domain of V(x) is:
0 < x ≤ 32/3The maximum volume and the optimal dimensions
To find the absolute maximum of V(x) on the domain 0 < x ≤ 32/3, we take the derivative of V(x) with respect to x and set it equal to zero:
[tex]V'(x) = 216x - 12x^2 = 0[/tex]
Solving for x, we get:
x = 18To confirm that this is a maximum, we take the second derivative of V(x) with respect to x:
V''(x) = 216 - 24xAt x = 18, we have V''(18) = 0, which means that the second derivative test is inconclusive. However, we can see that V(x) is increasing on the interval 0 < x < 18 and decreasing on the interval 18 < x ≤ 32/3, which means that x = 18 is indeed the absolute maximum of V(x) on the domain.
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On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).
Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?
ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS
The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU
To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.
1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)
2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)
Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:
ΔD''E''F'' ≅ ΔRSU
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Answer:
ΔDEF ≅ ΔRSU
Step-by-step explanation:
A circle is growing, its radius increasing by 5 mm per second. Find the rate at which the area is changing at the moment when the radius is 28 mm. When the radius is 28 mm, the area is changing at approximately _____.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
We are given that the radius is increasing at a rate of 5 mm per second. This means that the rate of change of the radius with respect to time is dr/dt = 5 mm/s.
To find the rate at which the area is changing, we need to find dA/dt, the derivative of the area with respect to time. We can use the chain rule to find this derivative:
dA/dt = dA/dr * dr/dt
We can find dA/dr by taking the derivative of the area formula with respect to r:
dA/dr = 2πr
Now we can substitute the values we know into the chain rule formula:
dA/dt = dA/dr * dr/dt = 2πr * 5
When the radius is 28 mm, the rate of change of the area is:
dA/dt = 2π(28) * 5 = 280π ≈ 879.64 mm^2/s
Therefore, the area is changing at a rate of approximately 879.64 mm^2/s when the radius is 28 mm.
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find the area of each polygon below b=6 h=9 ft h =10cm b = 8 h=8m b=9m
Consider a roulette wheel. Roulette wheel has 2 green slots, 18 red slots, and 18 black slots. The wheel is spun and we are interested in the number of spins before the Rth success. : Let success be landing in a green slot. Find the following probabilities. A) identity the distribution with the parameters B) the 8th success occurs on the 17th spin. C) the 13th success occurs between the 31st and the 34th spin. PLEASE SOMEONE HELP <3
A) The distribution is a negative binomial distribution with parameters r and p.
B) The probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) The probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
A) The distribution is a negative binomial distribution with parameters r = number of successes (in this case, r = 1 since we are only interested in the first success), and p = probability of success (landing in a green slot).
B) To find the probability that the 8th success occurs on the 17th spin, we use the formula for the negative binomial distribution:
P(X = k) = (k-1)C(r-1) * [tex]p^r[/tex] * [tex](1-p)^{(k-r)[/tex]
where X is the number of spins until the Rth success, k is the number of spins, and C(n,r) is the binomial coefficient (n choose r).
In this case, we want to find P(X = 17) when r = 8 and p = 2/38 (since there are 2 green slots out of 38 total slots):
P(X = 17) = (16 C 7) * (2/38)⁸ * (36/38)⁹
≈ 0.008 or 0.8%
So the probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) To find the probability that the 13th success occurs between the 31st and 34th spin, we need to find the probability of getting exactly 12 successes in the first 30 spins, followed by a success on one of the next 4 spins (31st, 32nd, 33rd, or 34th).
P(31 ≤ X ≤ 34) = P(X ≤ 34) - P(X ≤ 30)
= ∑[k=13 to 34] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex] - ∑[k=1 to 30] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex]
≈ 0.006 or 0.6%
So the probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
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A t test for a mean uses a sample of 24 observations. Find the t test statistic value that has a P-value of 0. 10 when the alternative hypothesis is (a) Ha Subscript a Ha: μ ≠0, (b) Ha: μ greater than >0, (c) Ha: mu μ<0. Find the t test statistic value when Ha: μ≠0
The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is
(a) Ha: μ ≠ 0 is ±1.711.
(b) Ha: μ > 0 is 1.319.
(c) Ha: μ < 0 is -1.319.
(d) Ha: μ ≠ 0 is ±1.711.
To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.
(a) Ha: μ ≠ 0 (two-tailed test)
The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:
t = ±1.711
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.
(b) Ha: μ > 0 (one-tailed test)
The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:
t = 1.319
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.
(c) Ha: μ < 0 (one-tailed test)
The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:
t = -1.319
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.
(d) Ha: μ ≠ 0 (two-tailed test)
To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:
t = ±1.711
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.
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please help ASAP (can give brainliest)
Answer:
134° + (2x)° = 180°
(2x)° = 46°
x = 23
So angles 1, 2, 3, and 4 all measure 23°.