Answer:
[tex]\frac{9(7-\sqrt{2}) }{47}[/tex]
Step-by-step explanation:
Which of the following represents the total area of the figure?
10.663 in2
24.413 in2
28.448 in2
34.335 in2
Answer:
24.413
Step-by-step explanation:
Break the shape up into 2 triangles and 1 rectangle, then add up the 3 areas.
Rectangle: 4.6 x 3.15 = 14.49
Triangle 1: 1/2(3.3)(3.15) = 5.1975
Triangle 2: 1/2(3)(6.3 - 3.15) = 4.725
Total area = 14.49 + 5.1975 + 4.725 = 24.413
Janet created a list of numbers on the board in order from greatest to least. Which list is the one that Janet could have created?
In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Without a list of options to choose from, it is difficult to determine which list Janet could have created. However, generally speaking, a list of numbers in order from greatest to least would start with the largest number and end with the smallest number.
For example:
10, 8, 5, 3, 1
In this list, 10 is the largest number and 1 is the smallest number, so it is ordered from greatest to least. Other examples could include:
-1, 2, 4, 7, 10
Therefore, In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.
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Wendell is working with the equation y=1.6^(x-1)+20 in a science class that represents the growth of a certain population of bacteria. Wendell could insert a 11 into this equation and get an answer of 129.95. So Wendell knows that after 11 days there would be a population of about 129.95 bacteria. Wendell would really love an equation that tells him the reverse of this (the inverse). Meaning Wendell could put a 129.95 into the equation and get 11 out as the answer. Create the inverse function and explain everything that you did to create this. If you simply give the correct answer without any explanation it will be marked incorrect. Three hints: It has something to do with logs. A graphical approach to this would be to graph the original, ask yourself how the "minus 1" and "plus 20" shifted the graph, and then think about how the inverse needs to adjust. An algebraic approach would be to swap the x and y values of the original and go from there. Either way, check your answer when you're done!
The inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:
f ⁻¹(x) = log₁.₆(1.6x - 32)
What is an inverse function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The output of a function is returned by the inverse function, which also returns the initial value. A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
The given function is:
[tex]f(x) = 1.6^{x-1} + 20\\[/tex]
[tex]y = 1.6^{x-1} + 20\\[/tex]
Now we are asked to find the inverse of this function.
That is, we have to write x in terms of y.
And then substitute the y back with x, to write as an inverse function
f ⁻¹(x).
[tex]y = 1.6^{x-1} + 20\\[/tex]
y - 20 = [tex]1.6^{x-1}[/tex]
y-20 = 1.6ˣ / 1.6
1.6y - 1.6 * 20 = 1.6ˣ
1.6y - 32 = 1.6ˣ
x = log₁.₆(1.6y - 32)
Therefore the inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:
f ⁻¹(x) = log₁.₆(1.6x - 32)
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(1 point) Let A be a matrix with linearly independent columns_ Which one of these statements must be true? You have only three attempts at this problem_ OA The equation Ax b has a solution for all b precisely when it has more columns than rows B. The equation Ax =b always has a solution for all b_ C. There is no easy way to tell if Ax = b has a solution for all b D: The equation Ax b has a solution for all b precisely when it has more rows than columns_ E: The equation Ax = b has a solution for all b precisely when it is a square matrix: F The equation Ax b never has a solution for all b_ none of the above
The statement that must be true is option (f) "The equation Ax = b has a solution for all b precisely when it has more columns than rows".
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
This is because if the matrix has more columns than rows, then the system of equations cannot be underdetermined, meaning that there is a unique solution for the equation.
On the other hand, if the matrix has more rows than columns, then it is possible that the equation Ax = b could have no solutions, which would mean that it is an overdetermined system.
Furthermore, if the matrix is a square matrix, then it will have the same number of rows and columns, and it is possible that the equation Ax = b could have either one solution or no solutions.
Therefore, the statement "The equation Ax = b has a solution for all b precisely when it has more columns than rows" is the only one out of the six given that must be true
Hence the option (f) is correct.
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simplify using horizontal method (2n^2+4n+4)(4n-5)
Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.
Expression : what is it?There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an expression. A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
Given :
2n² + 4n + 4
x 4n - 5
-----------
8n³ - 10n² + 16n² - 20n + 16n - 20
-----------
8n³ + 6n - 20
Thus, the simplified expression is 8n³ + 6n - 20.
Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.
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The equation f (x ) = 9000 · (0.985)t models the population of Blueville, where x represents the number of years since 2012. What is the population of Blueville in 2012?
The population of Blueville in 2012 from the exponential function is;
⇒ 9000
What is expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, We are given the equation of the function as;
⇒ f (x) = 9000(0.985)ⁿ
where;
x is the number of years since 2012
Thus, In the year 2012, it means that n will be 0,
Hence, As number of years is 0 by then we get;
f(0) = 9000(0.985)⁰
f(0) = 9000 * 1
f(0) = 9000
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How much would it cost to drive one mile based on the cos t of gas and the range of each vehicle?
The amount of money that will be used to drive only one mile by the different vehicles given above such as Deswagon and DesMobile would be =$57.35 and $56.78 respectively.
How to calculate the amount of money used by each vehicles?The total mileage that can be covered by Deswagon = 490miles.
The total cost of gas for the Deswagon = $28,100
Therefore the amount that will be paid for only one mile = X.
That is , 490 miles = $28,100
1 mile = ×
make X the subject of formula;
X = 28,100/490
= $57.35.
The total mileage that can be covered by DesMobile = 575miles.
The total cost of gas for the DesMobile = $32,650.
Therefore the amount that will be paid for only one mile = X.
That, 575 miles = $32,650
1 mile = X
Make X the subject of formula;
X = 32,650/575
X = $56.78.
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Express m in terms of e and v and find the mass of an object whose energy and speed are 1800joules and 25m/s respectively
The object has a mass of 5.76 kg.
We may represent "m" in terms of "e" (energy) and "v" (speed) using the kinetic energy formula, assuming that "m" relates to the mass of the object:
The energy an object possesses as a result of its motion is known as kinetic energy. It is described as the energy that a moving object contains as a result of its motion, which is dependent on the mass and velocity of the object.
The formula for calculating an object's kinetic energy is KE = 1/2 * m * v2.
To solve for "m," we can rearrange this formula:
m = 2 x KE /
We obtain the following by substituting the given values:
m = 2 x 1800 / 25
m = 2 x 1800 J / 625
m= 5.76 (rounded to two decimal places)
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What is the smallest angle θ1θ1 for which a laser beam will undergo total internal reflection on the hypotenuse of the glass prism in the figure? Express your answer using two significant figures.
The smallest angle θ1 for which a laser beam can undergo total internal reflection on the hypotenuse of a glass prism is 41.8°, expressed with two significant figures
The smallest angle θ1 for which a laser beam can undergo total internal reflection on the hypotenuse of a glass prism can be calculated using the law of total internal reflection. This law states that when a ray of light is incident on the surface separating two media of different refractive indices, the angle of incidence (θ1) must be greater than a certain critical angle (θc) in order for total internal reflection to occur.
Calculating the critical angle of the hypotenuse of a glass prism can be done by using Snell’s Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. In this case, the two media are air and glass, with refractive indices of 1 and 1.5 respectively.
Using Snell’s Law, we can calculate the critical angle of the hypotenuse as θc = sin⁻¹ (1/1.5) = 41.8°.
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the half-life of a radioactive kind of protactinium is 27 days. how much will be left after 54 days, if you start with 488 grams of it?
The amount having half life=27 days left after 54 days will be 122 gm.
What is a substance's half-life?
When we refer about half life, we mean the time it takes for exactly half of the radioactive material in question to decay.
More specifically, the time it takes for the radioactive material to lose exactly half of its mass.
Now,
As half-life=27 days
initial amount=488 gm
after 27 days, amount=488/2=244 gm
and after next 27 days amount=244/2
=122 gm
So, After 27+27=54 days the left substance will be 122gm of total initial amount=488gm.
hence,
The amount left after 54 days will be 122 gm.
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I need the answer noww can someone pls help me
What is the surface area of the cylinder with height 7 mi and radius 8 mi?
Answer:
surface area = 578^2
Step-by-step explanation:
SA of cylinder = 2πr^2+2πrh
r = radius (8)
h = height (7)
= 2 x π x 6^2 + 2 x π x 8 x 7
= 578.053
what is conversion horsepower to watts ?
We may use the formula 1Hp = 735Watt to convert watts to horsepower.
Watt and horsepower are both units of power.
But horsepower is a more powerful unit of power. We use horsepower to measure the power of electrical instruments such as turbines, motors, and a variety of other devices.
Thus, according to normal unit conversion rates, 1 Horsepower Equals 735 Watt.
1 Hp = 735 W
As a result, we have the conventional relationship 1Hp = 735 W. We may now simply convert any power supplied in horsepower to the unit of Watt.
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whats the answer to this and how do i solve this
Pick B. The graph's name and shape as expressed by the equation y = c is known as its constant function.
what is graph ?Theoretical physicists use graphs to graphically represent or chart facts or values in a logical way. Usually, a plot point will reveal the connection between three or more objects. A graph is a quel data structure made up of nodes, also known as triangles, and edges. The nodes, sometimes referring to as vertices, should have been joined with glue. Edges in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of advances in statistical charts, such as charts and graphs, pie charts, and line graphs. a circle logarithmic graph
given
The function illustrated is a horizontal straight line which is often represented by the equation y = c which is a constant function; consequently, the right answer is B.
By considering alternative options, we can determine that the function cannot be an identity function (since the function is not y = x), an absolute value function (because the graph is flat), or a cubic function (because the graph is flat).
Pick B. The graph's name and shape as expressed by the equation y = c is known as its constant function.
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Solve this system by the substitution method:
n = 4m
M-n=9
Answer:
Step-by-step explanation:
m
=
1
;
n
=
−
2
Explanation:
Given:
4
m
+
n
=
2
-------------------------------Equation (1)
m
−
4
n
=
9
..........................................Equation (2)
Determine the value of n
Showing every step in the first part to demonstrate method
Consider Equation (2)
Add 4n to both sides
m
−
4
n
+
4
n
=
9
+
4
n
But
4
n
−
4
n
=
0
m
=
9
+
4
n
.....................................(3)
Substitute for m in (1) using (3)
4
m
+
n
=
2
→
4
(
9
+
4
n
)
+
n
=
2
Multiply out the bracket
⇒
36
+
16
n
+
n
=
2
36
+
17
n
=
2
Subtract 36 from both sides
17
n
=
−
34
Divide both sides by 17
n
=
−
34
17
=
−
2
'.........................................................
Determine the value of m
Substitute
n
=
−
2
into (2)
m
−
4
n
=
9
→
m
−
4
(
−
2
)
=
9
m
+
8
=
9
m
=
9
−
8
m
=
1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
4
m
+
n
=
2
→
4
(
1
)
+
(
−
2
)
=
2
m
−
4
n
=
9
→
1
−
4
(
−
2
)
=
9
The fraction n/8 is between and 4/5 Write down all the possible values of n
The fraction n/8 is between 4/5 and 1. To calculate all the possible values of n, use the following equation: n = (4/5)*8 = 6.4
Since n is a fraction, the possible values are 6, 6.4, 6.8, 7.2, 7.6, 8, and 8.4.
The possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.
To find the possible values of n, we can cross-multiply and compare the fractions.
1/2 < n/8 < 4/5
Cross-multiplying gives us:
8 < 2n < 32
Dividing by 2 gives us:
4 < n < 16
The possible values of n are the integers between 4 and 16, which are 5, 6, and 7.
Therefore, the possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.
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Transcribed Image Text:Use the definition of Ax to write the matrix equation as a vector equation. 4 5 40 - 9 - 5 27 1 - 7 32 The matrix equation written as a vector equation is
The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>
A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.
In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.
To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.
The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.
Therefore, the matrix equation can be written as Ax = 40 27 32.
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What is Poke the bear in cyber security?
"Poke the bear" in cybersecurity refers to intentionally triggering a potential threat in order to test an organization's security systems and identify vulnerabilities.
In cybersecurity, "Poke the bear" means intentionally attempting to trigger a potential cyber threat in order to test an organization's security systems and identify vulnerabilities. This may involve actions such as sending a phishing email to see if employees fall for it, or attempting to breach a system in order to determine how strong its defenses are.
By proactively identifying weaknesses in their security systems, organizations can take steps to improve their cybersecurity posture and reduce the risk of a successful attack. However, "Poking the bear" should be done carefully and ethically, with appropriate permissions and safeguards in place.
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Identity the independent and dependent variables.
The equation y=12x+30 gives you the amount y (in dollars) in your savings account after x weeks. Please answer quickly!
The required in the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y, which represents the amount of money in the savings account after x weeks.
The value of y depends on the value of x, so y is dependent on x. However, the value of x does not depend on the value of y, so x is independent.
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Please help me 50 points I’ve been struggling for so long..
Clayton hiked to the bottom of El Dorado canyon and spent some time exploring when he got there. Then, he hiked back to the top. This graph shows Clayton's elevation above sea level over time.
Increasing from minute 0 to 25
True or false
Constant from minute 25 to 60
True or false
Decreasing from minute 60 to 90
True or false
I’m so lost please help
Answer
True, True, False
Step-by-step explanation:
I am not quite sure but I hope this helps in any way.
I say True to the Increasing from minute to 25 because Clayton’s time starts at 0 and the time increases to 25 minutes.
I say True because if you see the point where it shows 25 minutes and stops at 60 minutes until Clayton goes back up, it shows the line regularly occurring which would make him be constantly moving to 60 minutes. (Constant means to regularly occur)
I say false because Clayton’s time is increasing into 90 minutes, not decreasing. Also its kinda like the same concept as the Increasing from minute 0 to 25.
PLEASE HELP ME
Which is a correct classification for this triangle?
Responses
obtuse triangle
equiangular triangle
acute triangle
right triangle
Answer:
This is an obtuse triangle.
Step-by-step explanation:
Sure that are 2 acute angle but it is not acute, if it was acute, then it would have 3 acute angles. It might look like a right triangle, but the angle on the bottom left is actually past 90º. So it is an obtuse triangle. Hope this helped! Have a good day!
The scale drawing has a scale of 1inch:9 yards. What is the total area of the composite figure that the drawing represents?
The total area of the composite figure represented by the scale drawing is 2,168.1 square yards.
Describe Measurements?Measurements refer to the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others. These numerical values are expressed in units, which are standardized and accepted values used for comparison and communication.
Measurement is an essential part of science, engineering, and many other fields where precise and accurate data is required. Measurements allow us to make quantitative comparisons, analyze data, and draw conclusions.
There are different methods of measurement depending on the physical quantity being measured. For example, length can be measured using a ruler or tape measure, mass can be measured using a scale, and time can be measured using a clock or stopwatch.
It is important to note that measurements can have errors due to various factors such as limitations of the measuring instruments, environmental factors, and human error. Therefore, it is crucial to understand the limitations of the measuring instruments and to take steps to reduce errors as much as possible.
Overall, measurements are an important tool for gaining knowledge and understanding of the physical world, and they play a critical role in many aspects of our daily lives.
To find the total area of the composite figure represented by the scale drawing, we need to use the scale to convert the measurements in inches to measurements in yards, and then use these measurements to calculate the areas of the individual shapes and add them together.
Let's assume that we have labeled the various shapes in the composite figure A, B, C, and D, as shown in the scale drawing.
To convert the measurements in inches to yards, we need to divide each measurement in inches by 36 (since there are 36 inches in a yard) and then multiply by the scale factor of 9 yards per inch. This gives us the measurements in yards:
Shape A: 3 inches x 9 yards/inch = 27 yards (length), 2 inches x 9 yards/inch = 18 yards (width)
Shape B: 5 inches x 9 yards/inch = 45 yards (length), 3 inches x 9 yards/inch = 27 yards (width)
Shape C: 3 inches x 9 yards/inch = 27 yards (diameter)
Shape D: 2 inches x 9 yards/inch = 18 yards (length), 2 inches x 9 yards/inch = 18 yards (width)
Now we can calculate the areas of each shape using the appropriate formulas:
Area of Shape A: length x width = 27 yards x 18 yards = 486 square yards
Area of Shape B: length x width = 45 yards x 27 yards = 1,215 square yards
Area of Shape C: (pi x (diameter/2)^2)/4 = (pi x (27/2)^2)/4 = 143.1 square yards (using the formula for the area of a circle)
Area of Shape D: length x width = 18 yards x 18 yards = 324 square yards
Finally, we can add up the areas of all four shapes to get the total area of the composite figure:
Total area = 486 square yards + 1,215 square yards + 143.1 square yards + 324 square yards
Total area = 2,168.1 square yards
Therefore, the total area of the composite figure represented by the scale drawing is 2,168.1 square yards.
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how to convert ml to kg
To convert ml to kg we have to find the density of the liquid or the body first.
The density of the body is defined as the mass of the body per unit volume of the body.
The density of the body is the only link between mass and the volume of the body. As we know that volume and mass have different unit I.e. mass have Kg and volume have ml.
So, what we do is,
Density = Mass/volume
Now, we can inter convert them to our requirement.
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The first cup was $4.25 each refill is $2.25 and a bagel is $3.15 and got two refills and $0.50 discount how much was spent
Janes age is 10 more than three times her son's age. In two years, her age will be 12 less than the square of her son's age. What is Jane's age now?
The age of Jane is 22 years.
How to find Jane's age?Janes age is 10 more than three times her son's age. In two years, her age will be 12 less than the square of her son's age. Therefore, let's find Jane's age as follows:
Hence, using equation,
let
son's age = x
Jane age = 3x + 10
In two years,
(x + 2)² - (3x + 10 + 2) = 12
(x + 2)(x + 2) - 3x - 12 = 12
x² + 2x + 2x + 4 - 3x - 24 = 0
x² + x - 20 = 0
x² - 4x + 5x - 20 = 0
x(x - 4) + 5(x - 4) = 0
(x + 5)(x - 4) = 0
Therefore,
x = -5 and x = 4
We can only use positive numbers.
Therefore,
Jane's age = 3x + 10
Jane's age = 3(4) + 10
Jane's age = 12 + 10
Jane's age = 22
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Determine the number of rational zeros using rational zero theorem
f(x)=4x^(4)-x^(3)+3x^(2)-4x-6
The number of rational zeroes in f(x) = 4x⁴ - x³ + 3x² - 4x - 6 is 12.
What is the rational root theorem?The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.
According to the rational root theorem, the possible roots of a polynomial of degree three and above are,
± (coefficient of the last term)/(coefficient of the first terms).
Given, A polynomial function f(x) = 4x⁴ - x³ + 3x² - 4x - 6.
Now, The rational roots are ± (a₄)/(a₀).
= (± 1, ± 2, ± 3, ± 6)/(± 1, ± 2, ± 4).
Therefore, The possible number of rational zeroes is 4×3 = 12.
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What is the discount
for a retail price of $892 and a discount rate of 12%
Answer: the answer would be
$ 784.96
Step-by-step explanation:
Answer:
Step-by-step explanation:
The discount rate = 12%
The retail price= $892
The discount = the retail price*the dicount
= 12/100*892= $107.4
A line whose equation is y=3x+4 is dilated by scale factor 4 centered at (1,1). What is the linear equation of the image
Therefore , the solution of the given problem of linear equation comes out to be the linear equation of the image is y = 3x + 22.
What exactly is a linear equation?The formula y = mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.
Here,
Let's first find the coordinates of two points on the original line. We can choose any two points, but for simplicity, let's choose (0,4) and (1,7), which lie on the line y=3x+4.
The distance between these two points is:
d = √((1-0)² + (7-4)²) = √(10)
To find the new coordinates of these points after dilation, we multiply the distance by 4 and use the center of dilation (1,1) as the reference point:
New coordinates of (0,4):
x' = 1 + 4(0-1) = -3
y' = 1 + 4(4-1) = 13
New coordinates of (1,7):
x' = 1 + 4(1-1) = 1
y' = 1 + 4(7-1) = 25
So the image of the line y=3x+4 after dilation by scale factor 4 centered at (1,1) is the line passing through the points (-3,13) and (1,25). We can find the equation of this line by finding the slope and the y-intercept.
Slope:
m = (y2-y1)/(x2-x1) = (25-13)/(1-(-3)) = 12/4 = 3
Y-intercept:
y = mx + b
13 = 3(-3) + b
b = 22
Therefore, the linear equation of the image is y = 3x + 22.
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Which equation represents the relationship between Stephanie’s age and Chris’s age?
Answer:
y = x + 8 (second option)
Step-by-step explanation:
If Chris's age is x , then Stephanie who is 8 years older should be x + 8
y = x + 8
what determines which numerical measures of center and spread are appropriate for describing a given distribution of a quantitative variable? Which measures will you use in each case?
Measures of centre are used to describe the typical or average value of the data, while measures of spread describe the variability or dispersion of the data around the centre. Some common measures of centre and spread include:
Mean: the arithmetic average of the data. It is appropriate for symmetric distributions without outliers.
Median: the middle value of the data. It is appropriate for skewed distributions and distributions with outliers.
Mode: the most common value in the data. It is appropriate for distributions with a prominent peak or mode.
Range: the difference between the maximum and minimum values in the data. It is appropriate for describing the spread of the data, but it can be influenced by outliers.
Interquartile range (IQR): the range of the middle 50% of the data, from the 25th percentile (Q1) to the 75th percentile (Q3). It is appropriate for describing the spread of the data, and it is less influenced by outliers than the range.
Standard deviation: a measure of the average distance of the data from the mean. It is appropriate for symmetric distributions without outliers, and it is used to describe the spread of the data in the context of the mean.
The choice of which measures to use depends on the characteristics of the distribution and the goals of the analysis.
In general, it is important to consider multiple measures of centre and spread in order to obtain a complete understanding of the distribution of the data.
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