The area under the curve of function f on [a, b] is the limit of both LRAMn f and RRAMn f as n approaches infinity.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The Left Riemann Sum (LRAM) and Right Riemann Sum (RRAM) of a non-negative, increasing function f on the interval [a, b] are defined as follows -
LRAMn f = (b - a)/n × [ f(a) + f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + (n-1)(b-a)/n) ]
RRAMn f = (b - a)/n × [ f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + n(b-a)/n) ]
As f is an increasing, non-negative function on [a, b], both LRAMn f and RRAMn f will be non-negative, and the area under the curve of f will also be non-negative.
Since f is increasing on [a, b], we have -
f(a) ≤ f(a + (b-a)/n) ≤ f(a + 2(b-a)/n) ≤ ... ≤ f(a + (n-1)(b-a)/n) ≤ f(b)
Therefore, LRAMn f will be less than or equal to the area under the curve of f on [a, b], which is less than or equal to RRAMn f.
That is -
LRAMn f ≤ Area under curve of f on [a, b] ≤ RRAMn f
So we can conclude that the area under the curve of f on [a, b] is bounded between LRAMn f and RRAMn f.
Therefore, as n increases, both LRAMn f and RRAMn f converge to the area under the curve of f on [a, b].
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aleks initial knowledge check
Line 1 passes through (-4,7) and (-2,2)
NEED ANSWER ASAP
Answer:
Step-by-step explanation:
Line 1: (2 - 7)/(-2 + 4) = -5/2
Line 2: (-1 + 8)/(0 + 5) = 7/5
Line 3: (8 + 2)/(-2 -2)= 10/-4 = -10/4 = -5/2
Line 1 and Line 2: Neither
Line 1 and Line 3: Parallel
Line 2 and Line 3: Neither
the roots of the equation x²-5x+3=0 are α and β. form the quadratic equation whose roots are (2α-β) and (2β-α)
The quadratic equation whose roots are (2α-β) and (2β-α) is given as follows:
y = x² - 5x - 23.02.
How to define the quadratic equation?The quadratic equation for this problem is defined as follows:
x²-5x+3=0.
The coefficients of the equation are given as follows:
a = 1, b = -5, c = 3.
Hence the discriminant of the equation is of:
D = (-5)² - 4 x 1 x 3
D = 13.
Then the roots are given as follows:
x = (5 - sqrt(13))/2 = 0.697.x = (5 + sqrt(13))/2 = 4.303.Then the roots of the second equation are given as follows:
2 x 0.697 - 4.303 = -2.91.2 x 4.303 - 0.697 = 7.91.Applying the Factor Theorem, the quadratic function is defined as a product of it's linear factors, as follows:
y = (x + 2.91)(x - 7.91)
y = x² - 5x - 23.02.
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Please help me answer this
Answer:
x = 229
Step-by-step explanation:
x = 467 - 238
x = 229
Need help with the bottom two a little confuse
Answer:
the third one
Step-by-step explanation:
the third one
Michael plants a circular garden with a diameter of 10 feet. What is the area of his garden
Answer:
The area of the garden is 78.5 square feet.
Step-by-step explanation:
Andrea tiled a rectangle 2 1/2 units by 2 1/2 units. What is the area?
The rectangle has a surface area of 6 1/4 squares.
What is a rectangle and how big is it?The territory a rectangle occupies inside its 4 corners or limits is referred to as its area. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
How come we measure area?The amount of space within a form is measured by its area. In daily life, figuring out a shape's or surface's area can be helpful. For instance, you may require know how so much paints to buy to paint a board or the amount of grass to plant on a lawn.
To find the area,
[tex]Area=lenght*width[/tex]
[tex]Area=\frac{5}{2} *\frac{5}{2}[/tex]
[tex]Area=\frac{25}{4}[/tex]
[tex]Area=6\frac{1}{4} square unit[/tex]
Therefore, the area of the rectangle is [tex]Area=6\frac{1}{4} square unit[/tex]
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Determine whether f(x)= x^2-2x-3/ x^2+3x+2 has any holes. If it does, give the coordinates.
To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:
x^2 - 2x - 3 = (x - 3)(x + 1)
And the denominator can be factored as:
x^2 + 3x + 2 = (x + 1)(x + 2)
Therefore, we can simplify the function as:
f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]
The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:
f(x) = (x - 3)/(x + 2)
Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:
f(-1) = (-1 - 3)/(-1 + 2) = -4
Therefore, the hole in the graph of the original function is located at the point (-1, -4).
The average American worker makes about 4x10^4 dollars yearly. The average professional basketball player makes about 6x10^6 dollars yearly. How many times greater is the average professional basketball player's salary than the average American worker's salary? {(WILL GIVE BRAINLIEST)}
Answer:150 times
Step-by-step explanation:
The average professional basketball player's salary is 6x10^6 dollars yearly, while the average American worker's salary is 4x10^4 dollars yearly.
To find how many times greater the average professional basketball player's salary is, we can divide the basketball player's salary by the worker's salary:
6x10^6 / 4x10^4 = (6/4)x10^(6-4) = 1.5x10^2 = 150
Therefore, the average professional basketball player's salary is 150 times greater than the average American worker's salary.
The box and whisker plot shows the scores in the science test of two classes based on the distribution of data which observation is not correct
Based on the distribution of data, the box and whisker plot displays the results of the scientific test for two classes. It is incorrect to say that both sections have the same value for the third quartile.
The formulation of partial differential equation solutions uses distribution generalized functions. The likelihood of a specific value or range of values for a variable is known as the probability distribution. Cumulative distribution function, where the likelihood of a value not exceeding a certain value depends on that value. A list of the values recorded in a sample, or a frequency distribution. In coding theory, there are two types of distribution: inner and outer. distribution of a portion of a manifold's tangent bundle.Term distribution: the state of having all members of a category present. The distributive law from elementary algebra is generalized by the property of binary operations known as distributivity. the distribution.
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An object is launched directly in the air at a speed of 16 feet per second from platform located 7 feet above the ground. The position of the object can be modeled using the function[tex]f(t)=-16^2+16t+7[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Step-by-step explanation:
To find the maximum height of the object, we need to determine the vertex of the parabolic function f(t) = 16t^2 + 16t + 7.
The vertex of a parabola in the form f(t) = at^2 + bt + c is given by (-b/2a, f(-b/2a)). In this case, a = 16, b = 16, and c = 7, so the vertex is:
(-b/2a, f(-b/2a)) = (-16/(216), f(-16/(216))) = (-1/2, f(-1/2))
To find f(-1/2), we can substitute t = -1/2 into the function:
f(-1/2) = 16(-1/2)^2 + 16(-1/2) + 7 = 8 - 8 + 7 = 7
Therefore, the vertex is at (-1/2, 7). This means that the maximum height of the object is 7 feet above the ground.
Alternatively, we could also use the fact that the maximum height occurs at the vertex of the parabola, which is the point where the derivative of the function is zero. The derivative of f(t) is:
f'(t) = 32t + 16
Setting this equal to zero and solving for t, we get:
32t + 16 = 0
t = -1/2
So the maximum height occurs at t = -1/2, which corresponds to the vertex of the parabola, and the maximum height is 7 feet.
Eighteen cyclists were each asked the number of miles they biked last week. Their responses are given below.
Answer:
You didn't give the answers
4 sec x csc x = 8 csc x
Find all solutions in the interval of [0,2pi)
Enter results in radians.
As a result, x = pi/6 is the only answer in the range [0,2pi).
What is the radian of a pi?When quantifying the angles of trigonometry or periodic functions, radians are frequently taken into account. Radians are always expressed in units of pi, with pi equivalent to either 3.14 or 22/7.
We can start by simplifying the left-hand side of the equation using the identity:
csc x = 1/sin x
4 sec x csc x = 4(1/cos x)(1/sin x) = 4/(cos x sin x)
Substituting this back into the original equation, we get:
4/(cos x sin x) = 8 csc x
Multiplying both sides by cos x sin x, we get:
4 = 8 sin x
Dividing both sides by 8, we get:
sin x = 1/2
This means that x is either pi/6 or 5pi/6, since these are the two angles in the interval [0,2pi) where sin x = 1/2.
However, we need to check if these solutions satisfy the original equation.
For x = pi/6:
4 sec x csc x = 4 sec(pi/6) csc(pi/6) = 4(2) (2/√3) = 16/√3
8 csc x = 8 csc(pi/6) = 8(2/√3) = 16/√3
So, x = pi/6 is a solution.
For x = 5pi/6:
4 sec x csc x = 4 sec(5pi/6) csc(5pi/6) = 4(-2) (-2/√3) = 16/√3
8 csc x = 8 csc(5pi/6) = 8(-2/√3) = -16/√3
So, x = 5pi/6 is not a solution.
Therefore, the only solution in the interval [0,2pi) is x = pi/6.
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Determine if the three side lengths could form a triangle 3,7,9 acute,right, or obtuse
Answer:
The triangle is acute.
Step-by-step explanation:
To determine whether the side lengths of 3, 7, and 9 can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this condition is satisfied for the given side lengths:
3 + 7 = 10 > 9, so the sum of the two smaller sides is greater than the largest side.
7 + 9 = 16 > 3, so the sum of the two smaller sides is greater than the largest side.
3 + 9 = 12 > 7, so the sum of the two smaller sides is greater than the largest side.
Since all three inequalities are true, we can conclude that the given side lengths of 3, 7, and 9 can form a triangle.
To determine whether the triangle is acute, right, or obtuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's first determine which side is the longest. Since 9 is the largest side length, it must be the hypotenuse if the triangle is right-angled.
However, using the Pythagorean theorem, we can see that:
3^2 + 7^2 = 58 < 9^2, so the triangle is not right-angled.
Therefore, the triangle must be either acute or obtuse. To determine which one, we can use the law of cosines, which states that in any triangle:
c^2 = a^2 + b^2 - 2ab*cos(C)
where a, b, and c are the side lengths, and C is the angle opposite to side c.
Let's apply this formula to the triangle with side lengths 3, 7, and 9:
9^2 = 3^2 + 7^2 - 2(3)(7)*cos(C)
81 = 58 - 42*cos(C)
cos(C) = (58 - 81)/(-42) = 0.5476
C = cos^(-1)(0.5476) = 56.69 degrees
Therefore, the largest angle in the triangle is approximately 56.69 degrees. Since this angle is less than 90 degrees, we can conclude that the triangle is acute.
Answer:
obtuse angled triangle
Step-by-step explanation:
for the sides to form a triangle
the sum of any 2 sides must be greater than the third side.
3 + 7 = 10 > 9
3 + 9 = 12 > 7
7 + 9 = 16 > 3
then the 3 sides 3 , 7 , 9 will form a triangle
given 3 sides a , b , c with c the longest side
• if a² + b² = c² ⇒ right triangle
• if a² + b² > c² ⇒ acute angled triangle
• if a² + b² < c² ⇒ obtuse angled triangle
here a = 3 , b = 7 , c = 9
a² + b² = 3² + 7² = 9 + 49 = 58
c² = 9² = 81
since a² + b² < c²
then triangle is obtuse
Plot the point (4,5) on the graph
Answer:
I don't know if this helps.
Can someone please help me? Which triangles are similar to △ABE?
Answer:
it should be DCE
Step-by-step explanation:
Since both ABE and DCE are similar because because they are both corresponding angels that are congruent. I'm sorry i couldn't think of another triangle but I'm hoping that at least helped a bit
Ethan and David are brothers. If Ethan is 3 years older than David and the sum of their ages is 17, how old is David?
Answer: 7 years old
Step-by-step explanation: The two quickest ways to solve these types of problems are by guess and check, and systems of equations. I will show you how to solve this problem with systems of equations since it is a systematic method.
We can replace the ages of Ethan and David with variables. Ethan's age is x and David's is y. Ethan is 3 years older than David and this can be represented by: y+3=x since 3 will have to be added to David's age, y to get Ethan's age, x. A second equation we can make is x+y=17 since the sum of their two ages is 17. Now we solve the system by first isolating a variable and then plugging that into the second equation.
y+3=x x is already isolated for us
x+y=17
(y+3)+y=17 We substitute x in the second equation for y+3
2y+3=17 Rearrange variables
2y=14
y=7 David's age, y, is 7.
Hope this helps!
If you wanted to take out a loan against the value of your home equity in order to help your sister through a rough patch while shes out of a job which type of home loan would make the most sense
If you are considering taking out a loan against the value of your home equity, there are several options to consider. One of the most common types of home loans for this purpose is a home equity loan or a home equity line of credit (HELOC).
What is home equity?The difference between the value of your home and the amount you owe on your mortgage is known as Home equity.
A home equity loan is a lump sum loan that allows you to borrow against the equity in your home. You receive the funds in one lump sum and then make fixed monthly payments over a set period of time, typically 5-15 years.
The interest rate on a home equity loan is generally fixed, which means that your monthly payments will remain the same throughout the life of the loan.
With a HELOC, you have access to a revolving line of credit, much like a credit card, and you only pay interest on the amount you borrow. The interest rate on a HELOC is typically variable, which means that your monthly payments may fluctuate over time.
Both home equity loans and HELOCs may make sense for helping your sister through a rough patch, as they can provide you with access to cash quickly and may offer lower interest rates than other types of loans. However, it's important to remember that both of these loans are secured by your home, which means that if you are unable to make your payments, you risk losing your home.
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Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.
Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.
To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.
Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).
Y(x=0) = 2\sX(y=-2) = -4
Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.
What are inequalities?Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The feasible area is now visible. Let's determine the vertices' coordinates.
Where the blue and green lines intersect is our first vertex.
3x + 2 = x + 4 and y = 3x + 2
3x - x = 4 - 2
y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1
(X, Y) = Vertex 1 (1,5)
The intersection of the red and green lines is at vertex #2:
y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4
2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.
(X, Y) = Vertex 2 (-3,1)
The intersection of the red and blue lines is at vertex 3:
y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1;
So, y = 3×(-1) + 2 = -3 + 2 = -1
(X, Y) = Vertex 3 (-1, -1)
Let's now modify the graph by including the supplied equation.
The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0
the gradient m = 3/5
A line can be drawn from (0,0) to (-10, -6)
Let's now examine how it would appear in the area where it is practical.
We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.
y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.
Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.
The maximum is therefore found at (x,y) = (-5/6, -1/2).
The point where the function crosses the red line now marks the minimum.
y = 3/5 × x; y = -x -2
3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.
y = 3/5 × (-5/4) = -3/4
The minimum is thus found at (x,y) = (-5/4, -3/4)
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Write a proof for this statement
Proof for the given statement is given below.
What are Vertical Angles?Vertical angles are the angles formed on two opposite sides of intersecting lines.
The measure of a pair of vertical angles are equal.
Given are two line segments intersected each other.
The line segments are KM and JN.
Consider ΔJKL and ΔLMN.
Given JL / NL = KL / ML
This means that two corresponding sides of ΔJKL and ΔLMN are proportional.
In a similar triangles, corresponding angles are equal.
So they are similar triangles.
∠JLK and ∠MLN are a pair of vertical angles.
So they are equal.
Corresponding angle of J in ΔJKL is angle N in ΔLMN.
So ∠J = ∠N
Or, ∠J ≅ ∠N
Hence it is proved.
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I’m desperate please help
On a snow day, Alexandra created two snowmen in her backyard. Snowman A
was built to a height of 52 inches and Snowman B was built to a height of 38
inches. The next day, the temperature increased and both snowmen began to
melt. At sunrise, Snowman A's height decrease by 3 inches per hour and
Snowman B's height decreased by 2 inches per hour. Let A represent the
height of Snowman A t hours after sunrise and let B represent the height of
Snowman B t hours after sunrise. Write an equation for each situation, in
terms of t, and determine the interval of time, t, when Snowman A is taller
than Snowman B.
Answer:
Step-by-step explanation: The equation should be
A = 35 - 4t
B = 50 - 7t
And, the Height = 15 inches
Calculation of the equation and height;
Since
Height of snowman A = 35 inches
Height of snowman B = 50 inches
Height decrease of snowman A = 4 inches per hour
Height decrease of snowman B = 7 inches per hour
Here, t = number of hours
So, the equation should be
A = 35 - 4t
B = 50 - 7t
Now for the same height
35 - 4t = 50 - 7t
-4t + 7t = 50 - 35
3t = 15
t = 15
So,
A = 35 - 4(5) = 35 - 20 = 15 inches
B = 50 - 7(5) = 50 - 35 = 15 inches
Rocio is planning her holiday baking. She has three recipes that use butter and needs to make sure she buys enough at the store. One recipe calls for 2½ cups, one needs cup, and one needs 1 cup. Find the total amount of butter she needs. Simplify your answer and write it as a mixed number if necessary. 4½ cups 2½ cups 53/12cups 3/4/9cups
Rocio needs a total of 137/12 cups of butter for her holiday baking.
How to find the total amount of butter she needs.Rocio needs 4½ cups, 2½ cups, and 5⅓ cups of butter for her three recipes, respectively.
We can add these amounts of butter to find the total amount:
4½ cups + 2½ cups + 5⅓ cups
= 9/2 cups + 5/2 cups + 53/12 cups (converting mixed numbers to fractions)
= 54/12 cups + 30/12 cups + 53/12 cups (finding a common denominator)
= 137/12 cups
Therefore, Rocio needs a total of 137/12 cups of butter for her holiday baking.
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Which expression is equivalent to x1/2⋅x1/3 x1/2⋅x1/3, where the expression is defined?
[tex]x^{5/6}[/tex] is value of x in expression .
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.
This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).
expression = [tex]x^{1/2} . x^{1/3}[/tex]
= [tex]x^{1/2 + 1/3}[/tex]
= [tex]x^{5/6}[/tex]
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CAN SOMEONE HELP? The answer has to be decimal.✨
The angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
We shall evaluate for the angle of elevation θ in degree, and then convert the result to radian as follows:
θ = tan⁻¹(4255/2000)
θ = 64.82482°
we multiply by π/180 to convert to radian;
θ' = 64.82482° × π/180
θ' = 1.13186 rounded to five decimal place.
Therefore, the angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.
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if tan(A) = 3/4 then sin(b) equals
The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
What is trigοnοmetry?Relatiοnships between cubic splines and mathematics When the disciplines οf astrοphysics were cοmbined, it is thοught that the subject was bοrn in the third century B.C. Precise mathematical techniques can be used tο sοlve a large number οf geοmetric equatiοns οr tο identify the οutcοmes οf calculatiοns invοlving them. The study οf the six fundamental trigοnοmetric functiοns is knοwn as trigοnοmetry. They gο by many different names and abbreviatiοns, such as sine, dispersiοn, angle, οblique, etc (csc).
Here,
cοs(b) Plus sin(b) = 1
Using the equatiοn, we can find the sοlutiοn fοr cοs(b) in terms οf sin(b):
cοs(2b) = (1 - sin(2b)) (b)
Inputting this intο the fοrmula fοr tan(b), we οbtain:
Tan is equal tο sin(b)/√(1 - sin2(b)).
When we square bοth sides and multiply by the remainder, we get:
(Tan(b)) / (1 + (Tan(b))) Equals sin2(b)
By simplifying and substituting tan(b) = sin(A)/cοs(A), we οbtain:
the fοrmula fοr sin2(b) is (sin(A))/((cοs(A))² + (sin(A))²)
Inputting the numbers we previοusly discοvered fοr sin(A) and cοs(A), we οbtain:
=> sin²(b) = (3/5)
=> sin² / ((4/5)
=> sin² + (3/5)²)
=> sin²(b) = 9/25 / (16/25 + 9/25)
=> sin²(b) = 9/25 / 25/25
=> sin²(b) = 9/25 sin(b) = +/- 3/5
Sin(b), which is pοsitive in the first regiοn, results in:
sin(b) = 3/5
As a result, sin(b) = 3/5 if tan(A) = 3/4.
Therefοre, The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
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What is the variability of the mean is 14 and the MAD is 3.2
Therefore, the estimated mean is roughly 0.154, but without more data, we are unable to calculate the SEM or group size.
Define mean.The total of all values divided by all of the values constitutes the result of a set, also called as the arithmetic mean. It is considered to be the most popular central trend indicator, and the word "mean" is commonly used to describe it. multiply the total amount of numbers in the library by the overall amount of values inside the gathering to get this result. Either original data or data that's been combined into frequency charts can be used for calculations. The average of a figure is known to as the average.
Here,
Given a normal distribution, the MAD and standard deviation (SD) are roughly inversely proportional to one another as follows:
=> MAD = 1.4826 × SD
As a result, we can calculate the standard deviation as follows:
=> SD = MAD / 1.4826
Since the MAD in this instance is provided as 3.2, we can calculate the standard deviation as follows:
=> SD ≈ 3.2 / 1.4826 ≈ 2.16
The standard error of the mean (SEM), which can be determined as follows, then provides the variability of the mean.
=> SEM ≈ SD / sqrt(n)
=> CV Equals SD/mean
To find the mean, we can change this equation as follows:
a) Mean Equals SD / CV
With the estimated numbers for SD and CV substituted, we obtain:
=> mean ≈ 2.16 / 14 ≈ 0.154
Therefore, the estimated mean is roughly 0.154, but without more data, we are unable to calculate the SEM or group size.
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Find all the missing angles in the diagram below. Explain how you used two different angle theories to find at least two missing angles.
Angles a and b are each measured at 97°, while angles c and d are each measured at 68°. Angles and lines were used to arrive at the solution.
What are lines and angles?Straight lines have careless depth and careless width. Other types of lines include those that are perpendicular, transverse, and intersecting other lines. A form is considered to have an angle if two of its rays originate from the same location.
According to the information:We are given two parallel lines so,
Angle a = 97° (Corresponding angles)
We know that angles on a straight line form a linear pair.
So,
⇒112° + d = 180°
⇒d = 68°
Angle c = 68° (Alternate interior angles)
Using angle sum property,
⇒ a + b + 68° = 180°
⇒ 97° + b + 68° = 180°
⇒ b = 15°
Hence, the missing values have been obtained.
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Write equation to represent the new function Vertically stretched by a factor of 4, then translated 3 units right.
Answer:
Suppose the original function is denoted by f(x). To represent the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right, we can use the following equation:
g(x) = 4 f(x - 3)
In this equation, f(x - 3) represents the original function f(x) translated 3 units to the right, and the multiplication by 4 stretches the function vertically by a factor of 4. Therefore, g(x) represents the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right.
Step-by-step explanation:
You need 8 feet of copper pipe for a plumbing job. You have two options.
Option 1: Pipe for $1.50 per foot and a rebate offering $2.00 off the total
Option 2: Pipe for $1.75 per foot and a coupon offering $0.25 off each foot
You find a third company that offers pipe at $1.50 less than the total cost of the better deal between Option 1 and Option 2.
What does the third company charge for the 8 feet of copper pipe?
$8.50
$10
$10.50
$12
$12.25
The charge for the third company for the 8 feet of copper pipe as required to be determined is; $8.50.
What is the charge for the 8 feet of copper pipe from the third company?As evident from the task content;
For the first company; Pipe for $1.50 per foot and a rebate offering $2.00 off the total.
Therefore, total charge is; 8(1.50) - 2 = $10.
For the second company; Pipe for $1.75 per foot and a coupon offering $0.25 off each foot.
Therefore, total charge is 8(1.75) - 8(0.25) = $12.
Hence, since the better deal is; $10.
Ultimately, the charge of the third company whose offer is; $1.50 less than the charge of the better deal is; 10 - 1.50 = $8.50.
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Question 1-16
An equation is shown.
x² + 18x + 7 = 4
Enter a number in each box to rewrite the equation into an equation of the form (x − p)² = q.
1
(x-
²=0
Answer:
Step-by-step explanation:
To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.
First, we subtract 4 from both sides of the equation:
x² + 18x + 7 - 4 = 0
Simplifying, we get:
x² + 18x + 3 = 0
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:
x² + 18x + 81 - 81 + 3 = 0
Simplifying, we get:
(x + 9)² - 78 = 0
Now, we can rewrite the equation in the desired form by adding 78 to both sides:
(x + 9)² = 78
Therefore, the values to be entered in the boxes are:
1: (x + 9)
2: 78
Jim makes $8.50 an hour. Each week, 11% of his total pay is deducted for taxes. How many hours does Jim have to work if he wants his take-home pay to be at least $300 per week? Write and solve an inequality for this situation.