In reference to the question given, the mean absolute deviation of the set {6, 8, 8, 12, 16} is 2.4.
Calculating the Mean Absolute Deviation of a Set of Numbers.To find the mean absolute deviation of a set of numbers, we first need to calculate the deviations of each number from the mean of the set, then take the absolute value of each deviation, and finally calculate the average of all the absolute deviations.
To find the mean of the set {6, 8, 8, 12, 16}, we first need to calculate the mean:
mean = (6 + 8 + 8 + 12 + 16) / 5 = 10
Next, we calculate the deviations of each number from the mean:
|6 - 10| = 4
|8 - 10| = 2
|8 - 10| = 2
|12 - 10| = 2
|16 - 10| = 6
Taking the absolute value of each deviation gives us:
4, 2, 2, 2, 6
Finally, we calculate the mean of these absolute deviations:
mean absolute deviation = (4 + 2 + 2 + 2 + 6) / 5 = 2.4
Therefore, the mean absolute deviation of the set {6, 8, 8, 12, 16} is 2.4.
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a cone-shaped container is oriented with its circular base on the top and its apex at the bottom. it has a radius of 12 inches and a height of 8 inches. the cone starts filling up with water. what fraction of the volume of the cone is filled when the water reaches a height of 2 inches?
Fraction of the volume of the cone = 1/4 0r 0.25
Volume of a coneA cone is a solid that has a circular base and a single vertex.
To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:
volume = (1/3) × π × r² × h
Volume of the cone using radius 12inches and height 8inches =
(1/3) × π × 12² × 8
= 0.6981inches³
Volume of the cone using radius 12inches and height 2inches =
(1/3) × π × 12² × 2
= 0.17453inches³
in order to find the fraction filled with water, we use the
Volume of 2inches/Volume of 8 inches.
0.17453/0.6981
= 0.25 or 1/4
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Please help.
Justin initially purchased a property for $85,000. After 5 years, the property was worth $112,000. What is the average rate of change for the first 5 years? A. $2,700 per year B. $8,450 per year C. $5,400 per year D. $6,750 per year
Answer:
C. $5,400 per year.
Step-by-step explanation:
Average rate of change = ($112,000 - $85,000) / 5 = $27,000 / 5 = $5,400 per year
Which sentence BEST describes what operation should be performed to solve the equation -2j = 15?
Division by -2
Step-by-step explanation:The properties of equality allow us to manipulate equations in order to solve for a variable.
Properties of Equality
The properties of equality, also referred to as PoEs, describe how an equation can be changed while remaining true. There are numerous PoEs such as the reflexive, substitution, and addition properties of equality. However, for the purposes of this question, the most important is the division property of equality. The division property of equality states that if both sides of an equation are divided by the same number, the equation is still true. In other terms:
if a = b, then [tex]\displaystyle\frac{a}{c} =\frac{b}{c}[/tex]Solving for a Variable
To find an unknown variable, we need to isolate the variable. This means using the properties of equality and other techniques to get the variable all by itself on one side of the equation. To isolate j, we need to divide both sides of the equation by -2. This will isolate j and maintain equality as shown by the division property of equality.
[tex]\frac{-2j}{-2}= \frac{15}{-2}[/tex]j = [tex]-\frac{15}{2}[/tex]By dividing both sides by -2, we can see that j = -15/2.
what is rogerhub grade calculator
RogerHub Grade Calculator is an online tool that helps students calculate their current or predicted grades based on their assignments, tests, and exams.
The RogerHub Grade Calculator allows students to input their course information, including the grading scale, assignments, tests, and exams, along with the weights or point values for each. Once the data is entered, the calculator provides the student with their current grade in the course, as well as what they need to score on future assignments or tests to achieve a desired final grade.
This can be a useful tool for students who want to track their progress and make informed decisions about how to prioritize their studies. The calculator can be used for courses at any level, from high school to college and beyond.
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The length of this rectangle is 2 3/4 feet. The width is 8 1/2 feet. what is the area of the rectangle in sq feet
The area of the rectangle is 23.375 sq feet.
What is area of rectangle ?
The area of a rectangle is the product of its length and width. It is a measure of the region enclosed by the rectangle. In the context of geometry, the area is expressed in square units, such as square inches, square feet, or square meters.
Given by the question:
To find the area of the rectangle, we need to multiply the length and width.
Length = 2 3/4 feet = 11/4 feet
Width = 8 1/2 feet = 17/2 feet
Area = Length x Width
Area = (11/4) x (17/2)
Area = 93.5/4 sq feet
So the area of the rectangle is 23.375 sq feet (when rounded to three decimal places).
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How do you know if a midpoint Riemann sum is an overestimate or underestimate?
When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.
We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.
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The table displays data collected, in meters, from a track meet.
one third 2 4 1
7 two thirds four fifths five halves
What is the median of the data collected?
The median of the data is approximately 1.43 meters.
Describe Statistics?Brief informative coefficients known as descriptive statistics are used to sum up a particular data set, which may be a sample of a population or a representation of the complete population. Measures of central tendency and measurements of variability make up descriptive statistics (spread). The mean, median, and mode are measurements of central tendency, while the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness are measures of variability.
KEY LESSONS
The properties of a data collection are summed up or described using descriptive statistics.
Measures of central tendency, measures of variability (or spread), and measures of frequency distribution make up the three fundamental kinds of measures in descriptive statistics.
The center of the data set is described by measures of central tendency (mean, median, mode).
To find the median of a set of data, we need to first arrange the data in order from least to greatest.
2, 4, 1, 7/3, 4/5, 5/2
Next, we find the middle value(s) of the ordered data.
Since we have six values, the middle is between the 3rd and 4th values.
2, 4, 1, [7/3, 4/5], 5/2
To find the median, we take the average of the two middle values:
(7/3 + 4/5) / 2 = (35/15 + 8/15) / 2 = 43/30 ≈ 1.43
Therefore, the median of the data is approximately 1.43 meters.
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REASONING
5. The table below shows a relationship between the variables x and y. Explain why this table
does not represent a rule where y is a function of x.
y
0
5
1
7
2
9
1
3
2
8
0
2
Table A is representing a function, and Table B does not represent a function.
What is function?
Function, can be stated as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
When a Table needs to be a function, it need to satisfy following conditions (look at the .jpeg image attached with this answer):
1. condition: every image has its pre-image,
in other words, In first circle, EVERY element has to be connected with SOME of the elements in second circle
2. condition: every image has only on pre-image.
in other words, In first circle, there MUSTN'T be an element that has MORE THAN ONE connection with elements in second circle
Table A satisfies BOTH of these conditions; that is why table A is indeed a function.
Table B satisfies FIRST condition but it does not satisfy the SECOND condition, that is why it is NOT a function.
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which figure is a translation of figure A? explain
Answer:
Figure B
Step-by-step explanation:
A translation is when you move every point of a figure in the same direction and same distance. It must retain the original shape of the figure and be superimposable. Figure C is a reflection, not a translation.
Find the 7th term of the arithmetic sequence − 3 � + 5 −3x+5, 2 � + 3 2x+3, 7 � + 1 ,. . . 7x+1
The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.
What is the 7th term of the arithmetic sequence?To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:
(2x+3) - (-3x+5) = 5x - 2
This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:
a₇ = (-3x+5) + (7 - 1)(5x - 2)
Simplifying the equation:
a₇ = -3x + 5 + 30x - 12
a₇ = 27x - 7
Therefore, the 7th term of the arithmetic sequence is 27x - 7.
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Complete the table of values for the function f(x)=1/2
The table of values for the function f(x)=1/2 are shown as follow:
What is function?
A function is an expression or relationship that involves one or more variables. It has several inputs and outputs. Each input has a single output. The function describes how the inputs relate to the output.
The function f(x) = 1/2 is a horizontal line that crosses the y-axis at the point (0, 1/2). Since the value of f(x) is constant for all values of x, the table of values for this function will have the same output value of 1/2 for every input value of x.
The table of values for the function f(x)=1/2 are shown as follow:
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what does determine slope intercept form of the equation
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept of the line.
It allows for the easy representation of a linear equation in two variables, with the slope indicating how steep the line is and the y-intercept indicating where the line intersects the y-axis.
By rearranging an equation in standard form
(Ax + By = C)or point-slope form
(y - y1 = m(x - x1))we can solve for y in terms of x to convert it to slope-intercept form. This form is commonly used in applications such as graphing and predicting values on a line.
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Consider this function.
f(x) = 5x
How is function / transformed to create function g? Match each transformation of function with its description.
4
g(x)= 1/3(5)^x
g(x)=5^1/3x
g(x) = 5^3x
g(x) = 3(5)^3
horizontal stretch of a factor of 3
vertical stretch of a factor of 3
vertical compression of a factor of 1/3
horizontal compression of a factor of 1/3
Answer:
g(x) = 5^3x is a horizontal stretch of a factor of 3. g(x)= 1/3(5)^x is a vertical stretch of a factor of 3. g(x) = 5^1/3x is a vertical compression of a factor of 1/3. g(x) = 3(5)^3 is a horizontal compression of a factor of 1/3.
what information does a probability model give
A probability model gives information about the likelihood of different outcomes of a random event or experiment.
A probability model is a mathematical tool used to describe the likelihood of different outcomes in a random event or experiment. It provides information about the distribution of probabilities associated with the different possible outcomes, and can be used to make predictions about the likelihood of specific events occurring.
Probability models can be simple or complex, depending on the nature of the event or experiment being modeled, and can be used to make predictions in a wide range of fields, from finance to physics. By providing a framework for understanding the distribution of probabilities associated with different outcomes, probability models allow us to make informed decisions and assess risk in a variety of contexts.
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Find the dimensions of the cube
Answer: DBSB272 PONTA DEM
Step-by-step explanation: Find a answer
A recipe requires 1, cups of milk for every y of a cup of flour. What is the ratio of
cups of milk to one cup of flour?
Answer:
1y is your answer, 1:y
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think it could be any number only if they gave you the number for y
What is the expression for this??
By evaluating the expression in y = 5 we will see that the depth after 5 minutes is -165 ft. (or 165 feet below sea level).
What is the depth of the submarine after 5 minutes?We know that the expression:
-230 + 13*y
Represents the depth of the submarine as a function of time. Then y is the time in minutes, so we can write:
depth = -230 + 13*y
To get the depth after 5 minutes, just replace the variable y by the number 15, then you will get:
depth = -230 + 13*5
depth = -230 + 65
depth = -165
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cinco veces la edad al cuadrado de pepito, más 15, es igual a tres veces tu edad al cuadrado, más 25 años .¿ cual es la edad de pepito?
Jimena tiene 8 años de edad.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Sean , , las edades de Jimena, su padre y su madre. A continuación, traducimos cada oración relevante del enunciado a expresiones matemáticas:
(i) Si su papá tiene 27 años más que Jimena:
y = x+27 (1)
(ii) Su mamá tiene 34 años:
x = 34 (2)
(iii) La suma de las tres edades es igual a la diferencia de 10 veces la edad de Jimena, menos 3 años:
x+y+z = x-3 * 10 (3)
Al aplicar (1) y (2) en (3), tenemos la siguiente ecuación resultante:
x = 8
Jimena tiene 8 años de edad.
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How to convert 90 confidence interval?
To convert 90% confidence interval, add and subtract the margin of error from the sample mean
A 90% confidence interval is a range of values that is likely to contain the true population parameter with 90% probability. Here's how you can calculate a 90% confidence interval:
Collect a sample of data that is representative of the population
Calculate the sample mean and the sample standard deviation (s).
Determine the sample size (n).
Use a t-distribution table or calculator to find the critical t value for a 90% confidence level and (n-1) degrees of freedom.
Calculate the margin of error by multiplying the critical t value by the standard error of the mean, which is s/ [tex]\sqrt{n}[/tex].
margin of error = t-value × (s / [tex]\sqrt{n}[/tex])
Determine the upper and lower bounds of the confidence interval by adding and subtracting the margin of error from the sample mean.
Lower bound = Sample mean - margin of error
Upper bound = sample mean + margin of error
The resulting interval will be the 90% confidence interval for the population mean.
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NEED HELP ASAP WITH THIS QUESTION
Answer:
The vertical height above the runway to the nearest foot is 580 feet.
Step-by-step explanation:
The vertical height is opposite the angle 75 degrees, and the hypotenuse is 600 ft. The trigonometric function sine will be used since sine = opposite/hypotenuse and we're solving for the opposite side and have the hypotenuse.
Let x be the vertical height.
[tex]\frac{sin(75)}{1} = \frac{x}{600}[/tex]
x = sin(75) * 600
x = 579.555495773
The question is asking for the vertical height rounded to the nearest foot, which is 580.
A shipping container is in the form of a right rectangular prism, with dimensions of 35 ft by 8 ft by 7 ft 6 inches. How many cubic feet of shipped goods would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answer: Cry 8374629173
Step-by-step explanation: Cry like 2734295
Addison's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 21 regular sodas and 29 diet sodas. What percentage of the sodas served were regular?
From the given information provided, out of total sodas served, 42% of the sodas served were regular.
To find the percentage of sodas served that were regular, we need to calculate the ratio of the number of regular sodas to the total number of sodas served, and then express this ratio as a percentage.
The total number of sodas served is the sum of regular and diet sodas:
Total sodas served = 21 + 29 = 50
The number of regular sodas served is 21.
To find the percentage of sodas served that were regular, we can use the following formula:
Percentage of regular sodas = (Number of regular sodas / Total number of sodas served) x 100%
Substituting the values, we get:
Percentage of regular sodas = (21 / 50) x 100%
Percentage of regular sodas = 42%
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Calculate the value of x to one decimal place
The value of x in the triangle is 3.4 cm
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the above as a guide, we have the following:
tan(43) = 3.2/x
Make x the subject of the formula
So, we have the following representation
x = 3.2/tan(43)
Evaluate
x = 3.4
Hence, the solution is 3.4
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Select all the correct locations on the graph.
Vector u has its initial point at (5, -7) and its terminal point at (8, -9). On the graph, identify the scalar multiples of u that have a direction opposite that of u.
The scalar multiples of u that have a direction opposite that of u is -54 i + 21 j .
Initial Point of vector , u= (-7,2)= -7 i + 2 j
Terminal point of Vector , u= (11, -5)= 11 i -5 j
Vector , u= Terminal point - Initial Point
= 11 i - 5 j - (-7 i+ 2 j)
= 11 i - 5 j + 7 i - 2 j
= 18 i - 7 j
⇒Vector, v= 3 ×Direction Opposite to that of vector, u
= -3 u
= -3 × (18 i - 7 j )
= 3× (-18 i + 7 j)
= -54 i + 21 j
Hence, The scalar multiples of u that have a direction opposite that of u is -54 i + 21 j .
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What whole number is equal to the fraction 1 over 1?
Answer:
Anything.
Step-by-step explanation:
The reason why I say " anything " is because the fraction, [tex]\frac{1}{1}[/tex] is bascially representing the number 1, nothing else so you can put whatever you want, tens, hundreds, thousands, millions, and so on.
So whatever number you want to put it will always equal, [tex]\frac{1}{1}[/tex], But just remember to always put the number that you choose on top or the numerator such as the following:
[tex]\frac{4}{1}[/tex].
Thus, you answer is, anything.
Use logarithmic regression to find an equation of the form y = a + b ln(x) to model the data.
a score of x = 70 on an exam with µ = 82 and σ = 8, or a score of x = 60 on an exam with µ = 72 and σ = 12?
A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:
z = (70 - 82) / 8 = -1.5
For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:
z = (60 - 72) / 12 = -1.0
The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
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Jacque is using a soup can for a school project and wants to paint it. If the can is 13 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14 and include the top of the soup can.
826.61 cm2
494.55 cm2
390.15 cm2
144.50 cm2
The required surface area of the soup can which is in cylindrical shape and needs to be painted is approx 494.55 cm².
What is a cylinder?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 characterized as an infinitely curved surface.
Often, the bases are shaped like circles.
The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.
So, the surface area of the soup can that needs to be painted will be:
Surface area formula: 2πrh+2πr²
Now, insert values as follows:
A = 2πrh+2πr²
A = 23.14*4.5*13+2*3.14*4.5²
A = 494.8 cm²
Therefore, the required surface area of the soup can which is in cylindrical shape and needs to be painted is approx 494.55 cm².
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Correct question:
Jacque is using a soup can for a school project and wants to paint it. If the can is 13 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14 and include the top of the soup can.
A. 826.61 cm2
B. 494.55 cm2
C. 390.15 cm2
D. 144.50 cm2
Answer:
Step-by-step explanation:
answet 494.55
what is trig equation solver?
Trigonometry equation solver is used to solve mathematical expression with an equality between two elements containing unknown variables and trigonometric functions.
The relationships between the lengths and angles of triangles' sides are the subject of this area of mathematics. A trigonometric equation is one that has one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it.
A trigonometric equation is cos2 x + 5 sin x = 0, for instance. The term "solutions of the given trigonometric equation" refers to all feasible values that fulfil the given trigonometric equation.
sin²A + cos²A = 1
sec²A – tan²A = 1
cosec²A – cot²A = 1
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1. Alden took out a mortgage on his home for $275,000 for 30 years at an annual interest rate of 4%. In January, Alden paid $495 toward the principal and the rest of his mortgage payment was the interest on
the loan. How much did Aiden pay in interest for the month of January? Use the monthly mortgage payment table below.
Show your work.
A) $859.92
B) $817.91
C) $759.96
D) $805.42
So, in response to the above question, we can state that As a result, equation Alden paid interest of $816.75 for the month of January.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We must first estimate the monthly mortgage payment using the monthly mortgage payment table in order to compute the amount of interest paid for the month of January.
The table shows that the monthly payment per $1,000 borrowed for a 30-year loan at 4% interest is $4.77. So, the following formula may be used to determine Alden's mortgage payment each month:
$275,000 / $1,000 = 275
$275 x $4.77 = $1,311.75 (monthly mortgage payment) (monthly mortgage payment)
Alden's January mortgage payment included $495 towards the principle, with the balance going to interest. The amount of interest paid can be determined as follows:
$1,311.75 - $495 = $816.75
As a result, Alden paid interest of $816.75 for the month of January.
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