Answer: The rate of change of the distancebetween the bottom of the ladder and the wall at that instant is 6.67 meter per minute.Let us consider that distance between the top of the ladder and the ground is x meterand distance between the bottom of the ladder and the wall is y meter.So, A right angle triangle is formed.Since, the bottom of the ladder is 21 meters from the wall.So, Applying Pythagoras theorem, Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. Differentiate below equation with respect to time. Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute
Step-by-step explanation:
How many triangles can be drawn given 2 sides and a non-included angle?
Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.
What is meant by Angle ?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays known as the vertex is referred to as an angle's sides. Angles are often measured using one of two different units. The degree is the measurement unit that is most widely used. A straight angle is 90 degrees when a circle is divided into 360 equal degrees.To learn more about Angle refer to:
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If triangle LMB is dilated by a scale factor of 0.5, which of the following statements is not true?
A. Triangle LMN is similar to triangle L’M’N’.
B. Triangle L’M’N’is smaller than triangle LMN
C. The sides of triangle LMN are congruent to the sides of triangle L’M’N’.
D. The angles of triangle LMN are congruent to the angles of triangle L’M’N’.
According to the properties of geometry the correct option is C.
What is geometry?
The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.
Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.
If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.
Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.
It is given that LMN is dilated by a scale factor of 0.5.
Since scale factor is lies between 0 to 1, therefore it shows the compression.
Therefore sides of L'M'N' is smaller than LMN.
Since corresponding angles of similar figure are congruent.
So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.
Therefore option C is correct.
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What are the possible rational zeros of f X X 4 6x 3 3x 2 17x 15?
The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
Have given ,
f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex]
This is a fourth degree polynomial.
Using the rational root theorem, the possible zeros of the polynomial are the factors of 15.
We know that
Factors of 15 = ± 1, ±3, ±5, ±15
Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
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3. Write < or > for each pair of numbers.
-6.48 -6.5
5.983 5.99
3.09. 3.01
-6.48 > -6.5
5.983 < 5.99
3.09 > 3.01
Hope it helps
What does ∆ mean in calculus?
In lambda expressions and lambda (λ) phrases, the Greek letter lambda () is used to signify binding a variable in a function. You can have typed or untyped lambda calculus.
Functions can only be used in typed lambda calculus if they are able to accept the "type" of data that the input is. The Greek symbol lambda () is commonly used to represent wavelength, which is equal to the speed (v) of a wave train in a medium divided by its frequency (f): wavelength = v/f. The majority of the time, students struggle to understand calculus because they don't practice after class, can't concentrate in class, have gaps in their math knowledge, and believe it's a waste of time.
The actions you can do to make calculus simple are listed below. Calculus is the most difficult math topic, and very few students, whether in high school or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract and easier to understand because it is more concrete. The mean number of events within a particular period of time or space is denoted by the Greek letter lambda () in the Poisson distribution formula. For instance, = 0.748 floods annually.
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Correct Question:
What does λ mean in calculus?
Mathematic,Englih and Life Skill book were ditributed to 50 tudent in a cla. 22 had Mathematic book,21 Englih book and 25Life Skill book,7 had Mathematic and Englih book. Find the number of tudent who had :(a) all three book ,(b)exactly two of the book,(c)only Life Skill book
One had all three, had exactly two and 21 had life skill book according to given situation.
Define problem in mathematics.A mathematical problem is one that can be represented, examined, and potentially resolved using mathematical techniques.
Write an example of mathematical problem.Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?
Let X people have all three books then
three books=X
Math and Eng=7-X
Math and Life= 6-X
Eng and Life= 9-X
Then:
X+(7-X)+(6-X)+(9-X)+[22-(7-X)-(6-X)]+[21-(7-X)-(9-X)]+[25-(16-X)-(9-X)]=50
After simplification
X=1
(i). One had all three books
(ii) 6 had two
(iii). 21 had life skill book.
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Which of the following is a step in copying a line segment?
Copying of line segment involves 6 steps.
How to copy a line segment?Steps to copy line segment are:
1) Draw a point that will serve as the new line segment's endpoint.
2) Open the compass width from the original line segment's beginning with the compass pin in that position.
3)Place the compass pin at the new line segment's plotted point using the above-mentioned step's adjusted compass width, and then draw an arc in the area where the new line segment is to be situated.
4) Decide where the other end of the new line will be on the arc.
5) Draw a line from the location chosen in the previous step to the point designated as the start of the new line segment.
6) The original line segment's length and the length of the line depicted above are equal.
Copying of line segment involves 6 steps.
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Q Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
What is the y-intercept of the line whose equation is y =- 5x 6?
y = -(5/3)x + 4 is slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
rewrite the equation of the given line in to slope-intercept form by solving for y
3y + 5x = 6
3y = -5x + 6 (subtract 5x from both sides)
y = -(5/3)x + 2 (divide both sides by 3)
Our line is parallel to this line, so it has the same slope, and a
y-intercept of 4, so we have...
y = -(5/3)x + 4
the equation ofa line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = 1 and c = 3, hence
y = x + 3 ← is the equation of the line
*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
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solve the logarithmic equation. log 10 (x raise to power 2 - 4x )=2
Answer:
[tex]x=2+2\sqrt{ 26}[/tex]
[tex]x=2-2\sqrt{ 26}[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_{10}(x^{2}-4x)=2[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^2=x^2-4x[/tex]
[tex]\implies 100=x^2-4x[/tex]
[tex]\implies x^2-4x=100[/tex]
Add the square of half the coefficient of the term in x to both sides of the equation:
[tex]\implies x^2-4x+\left(\dfrac{-4}{2}\right)^2=100+\left(\dfrac{-4}{2}\right)^2[/tex]
[tex]\implies x^2-4x+\left(-2\right)^2=100+\left(-2}\right)^2[/tex]
[tex]\implies x^2-4x+4=100+4[/tex]
[tex]\implies x^2-4x+4=104[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex]\implies (x-2)^2=104[/tex]
Square root both sides:
[tex]\implies x-2=\pm \sqrt{104}[/tex]
[tex]\implies x-2=\pm \sqrt{4 \cdot 26}[/tex]
[tex]\implies x-2=\pm \sqrt{4} \sqrt{ 26}[/tex]
[tex]\implies x-2=\pm 2\sqrt{ 26}[/tex]
Add 2 to both sides:
[tex]\implies x=2\pm 2\sqrt{ 26}[/tex]
Therefore, the solutions are:
[tex]x=2+2\sqrt{ 26}[/tex][tex]x=2-2\sqrt{ 26}[/tex]verify the linear approximation at (0, 0). f(x, y) = y + cos2(x) ≈ 1 + 1 2 y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
In the given question, we have to verify the linear approximation at (0, 0).
f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Let f(x, y) = √(y+cos^{2}x)
f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)
f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]
f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]
f(x, y) ≈ 1+0(x-0)(1/2)(y-0)
f(x, y) ≈ 1+1/2y
Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
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The complete question is:
Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........
How do you find the missing length of a triangle on a calculator?
By using a² + b² = c² this formula we can find the missing length of a triangle.
A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.
If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:
a² + b² = c²
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:a = √(c² - b²)
If leg b is unknown, then:b = √(c² - a²)
For hypotenuse c missing, the formula is:c = √(a² + b²)
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Х
15
9
18
9
y
17
9
4
Is this relation a function?
yes
no
To be a relation of a function for every value of x there must be a single value of y thus the given relation is not a function.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given table,
At x = 9
y = 9 and y = 3
Since at a single value of x there exist two values of y thus it will not be a function.
Hence "The provided relation is not a function since there must only be one value of y for a relationship to be considered a function.".
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What is the formula of line segment?
Answer:
The length of the line segment is
d = √(x₂ - x₁)² + (y₂ - y₁)²
How do you expand a 3 term binomial?
The expanded form of a 3-term binomial is typically written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial is given by ax^2 + bx + c = a(x^2 + bx/a + c/a).
1. Take the coefficients of the binomial (which are the constants a, b and c)
2. Multiply the coefficient a with the remaining terms in the binomial (x^2 + bx + c).
3. Simplify the expression by multiplying the coefficient a with the terms (x^2 + bx/a + c/a).
4. The result is the expanded form of the 3-term binomial ax^2 + bx + c.
The expanded form of a 3-term binomial can be written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial can be obtained by multiplying the coefficient a with the remaining terms in the binomial (x^2 + bx + c) and simplifying the expression.
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How would you describe a rigid transformation?
A transformation that leaves a geometric figure's size or shape unaltered is known as a rigid transformation (also known as isometry). is a unique type of metamorphosis in which a figure's size or shape are left unaltered.
What is rigid transformations?During a rigorous alteration of the geometric object, the distance between each pair of its points is maintained. In other words, an object's size and shape are maintained through a hard transformation. For example, the rigid transformation of a triangle preserves the triangle's angles and lengths. Consider a rigid form distortion that resembles a cardboard shape.
There are translations, reflections, and isometric rotations. As a result, none of these changes have an impact on the figure's size. If neither the size nor the shape of the figures are changed, the figures are constant.
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Solve the following system of equations and show all work. y = −x2 +4y = 2x + 1
The solution to the system of equations is x = 3/2 and y = 7/4.
The given system of equations can be written as:
y = -x^2 + 4
y = 2x + 1
To solve this system of equations, we can use the substitution method. First, we'll substitute the expression for y in the second equation into the first equation. We can then solve the resulting equation for x.
In the first equation, [tex]y = -x^2 + 4[/tex] . Substituting this expression into the second equation, we get:
[tex]-x^2 + 4 = 2x + 1[/tex]
We can rearrange the terms on the left side of the equation to solve for x. To do this, we'll subtract 4 from both sides, then add x^2 to both sides:
-4 = 2x + 1 - 4
-4 + 4 = 2x + 1 - 4 + 4
0 = 2x - 3
Now, we'll divide both sides of the equation by 2 to solve for x:
0/2 = (2x - 3)/2
0 = x - 3/2
We can rearrange the terms on the right side of the equation to solve for x. To do this, we'll add 3/2 to both sides:
0 + 3/2 = x - 3/2 + 3/2
3/2 = x
Now that we have the value of x, we can substitute it into either equation to solve for y:
[tex]y = -x^2 + 4y = -(3/2)^2 + 4y = -(9/4) + 4[/tex]
y = 7/4
Therefore, the solution to the system of equations is x = 3/2 and y = 7/4.
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What are the 3 ways we can prove triangle congruence?
In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.
Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:
If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:
If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:
If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF
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y = 4/5x + 8
2x+y = -6
Plot two lines by clicking the graph.
Answer:
Just use Desmos
Step-by-step explanation:
2 1/2 divided by 4
please help asap
Answer:0.625
Step-by-step explanation:
What is the discriminant and nature of roots of 2x² 3x 5 0?
The quadratic equation [tex]2x^{2}+3x-5=0[/tex] has a discriminant of 49.
In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its classification or solution. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots include a conjugate pair of complex roots.
For an equation, [tex]ax^{2}+bx+c=0[/tex]
Discriminant, D = [tex]b^{2}-4ac[/tex]
Given in question,
[tex]2x^{2}+3x-5=0[/tex]
a = 2
b = 3
c = -5
D = [tex]3^{2}[/tex] - 4(2)(-5)
= 9 + 40
= 49
Hence, the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] is 49.
Correct Question :
What is the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] ?
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I need help at math
Answer:
The answer for the problem on the left is 70
The answer to the problem on the right is 120
Step-by-step explanation:
Left Problem:
The sum of the interior angles is 360
(n -2)180 is one formula to find the sum of the interior angles of a polygon. n stands for the number of sides
(4-2)180
2(180
360
We know three of the angles we subtract them from 360 to find the missing angle
360-60-110-120 = 70
Right Problem:
We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180. A straight line has an angle measurement of 180.
180-60 = 120
180 - 50 = 130
Now we just need to find x.
The sum of the interior angles is
(n-2) 180
(5-2)180
3(180) = 540 Subtract what we know
540 -50 - 130 - 120 = 240
The x's have the same value so 2402 is 120 .
Each x is 120
The answer to the problem on the left is 70 and the answer to the problem on the right is 120.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, angles and relative position.
Left Problem:
The sum of the interior angles is 360.
(n -2)180 is one formula to find the sum of the interior angles of a polygon. n stands for the number of sides
(4-2)180
2(180
360
We know three of the angles we subtract them from 360 to find the missing angle
360-60-110-120 = 70
Right Problem:
We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180. A straight line has an angle measurement of 180.
180-60 = 120
180 - 50 = 130
The sum of the interior angles is
(n-2) 180
(5-2)180
3(180) = 540 Subtract what we know
2x = 540 -50 - 130 - 120 = 240
x = 240 / 2 = 120
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What is the end behavior as x → − [infinity] f/x →?
Using the concept of limit, As the x tends to -infinity value, In the expression f/x, The answer is f/x tends to large(infinity) value with negative magnitude.
What do you mean by limit in mathematics?A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals. A limit describes the value that a function approaches as its inputs approach a certain value. All calculus is based on the concept of a limit.
What is the limit rule?According to product law for limits, the limit of a product of functions is equal to the sum of the limits of each individual function. The limit of a quotient of functions is equal to the quotient of the limit of each function, according to the quotient law for limits.
as [tex]\lim_{x \to \infty} \frac{f}{x}[/tex]
=f/ -infinity
=- [infinitely large value]
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Which congruence criterion do you use in the following if ∆ Abe ≅ ∆ CDB *?
The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.
To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.
In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.
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The question is -
Which congruence criterion do you use in the following? Given: EB = BD, AE = CB, ∠ A = ∠ C = 90°.
what is the slope of the line that contains the points
Answer: 0
Step-by-step explanation:
The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.
How do you solve and graph inequalities in algebra?
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.
What are the steps to graphing an inequality?The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the symbol for inequality with that for equality.
Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.
Step 4: Shading one side or area of the boundary line is the final step.
Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.
Here show an example for better understanding:
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.To know more about inequality refer to:
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What is the mean deviation of 8 9 12 15 16 20?
8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
What is the mean deviation?The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.
It is a statistical summary of statistical variability or dispersion.
So, the sum of all the values:
8 + 9 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 34 = 200
A number of observations:
= 10
Formula: Mean = (sum of all observations)/(Total number of observations)
Now, calculate using the formula as follows:
Mean = (sum of all observations)/(Total number of observations)
Mean = (200 / 10)
Mean = 20
Now, we must determine how far the provided values are from the mean.
20 - 8 = 12
20 - 9 = 11
20 - 12 = 8
20 - 15 = 5
20 - 16 = 4
20 - 20 = 0
24 - 20 = 4
30 - 20 = 10
32 - 20 = 12
34 - 20 = 14
Formula:
Mean deviation = (sum of the distance of each value from mean) / (Total number of observations.)
Sum of each value's deviation from the mean = 12 + 11 + 8 + 5 + 4 + 0 + 4 + 10 + 12 + 14 = 80
Mean deviation = 80 / 10 = 8
Therefore, 8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
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Complete question:
What is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34?
Write the equation of the line of fit.
y = 5x+20 Carlos plays the game for 25 minutes. Use the
equation of the line of fit to predict his score.
Answer:
145
Step-by-step explanation:
y = 5(25) + 20
y = 125 + 20
y = 145
Maria has ridden 44 miles of a bike course. The course is 80 miles long. What percentage of the course has Maria ridden so far?
Answer:
55percent
Step-by-step explanation:
[tex]\frac{44}{80} =0.55\\0.55x100\\55[/tex]
Does △abc appear to be the same size and shape as △xyz? explain.
Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,
The triangles ABC and XYZ are similar by SAS similarity, as,
AC = XZ = 5,
AB = YZ = 13
∠ ACB = ∠ XZY
When you translate and then rotate triangle ABC, you will get triangle XYZ.
To know more about Triangles:
brainly.com/question/16886469
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Solve for Z.
X= 2/3(Y+Z)
Answer: Z=[tex]\frac{3}{2}[/tex]x-y
Step-by-step explanation: first multiply both by the reciprocal of 2/3 to cancel it. the reciprocal of 2/3 is 3/2
x(3/2)=y+z
then to solve for x, move the to the left side by -y on both sides
you're then left with z=x(3/2)-y