The vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
What is an orthogonal vector?
An orthogonal vector is a vector that is perpendicular to another vector in a given space. In other words, two vectors are orthogonal if their dot product is equal to zero.
To find a vector orthogonal to both 2, 2, 0 and 0, 2, 5 of the form 1, we can take the cross product of the two vectors, which results in a vector that is orthogonal to both. The cross product of 2, 2, 0 and 0, 2, 5 is given by:
(2, 2, 0) x (0, 2, 5) = (20, -10, -4)
So, a vector orthogonal to both 2, 2, 0 and 0, 2, 5 is given by (20, -10, -4). We can normalize this vector by dividing it by its magnitude, which is equal to sqrt(20^2 + (-10)^2 + (-4)^2) = sqrt(444). The normalized vector will be of the form 1:
[tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
Hence, the vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex]).
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a number n to the power of n, where n is a positive integer, is called interesting. find all interesting numbers that divide 2023 to the power of 2023
4^4 and 678^678 are the only two interesting numbers that divide 2023^2023.
To find all interesting numbers that divide 2023^2023, we need to find all positive integers n such that n^n divides 2023^2023.
Since 2023^2023 = 2023 * 2023 * ... * 2023 (2023 times), we can see that the factors of 2023^2023 are simply the powers of 2023.
So, a number n^n divides 2023^2023 if and only if 2023^(n-1) divides 2023^2023. This means that n-1 must be a factor of 2023.
The factors of 2023 are 3 and 677. Therefore, the values of n that satisfy the condition are 4 (3+1) and 678 (677+1), which correspond to the interesting numbers 4^4 and 678^678. These are the only two interesting numbers that divide 2023^2023.
Therefore, 4^4 and 678^678 are the only two interesting numbers that divide 2023^2023.
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65 points
1. Find the pattern and then write a rule and an
equation that represents the pattern. Then
complete the table,
X= 0 2 10 16 20
Y= 0 1 5 8 10
Rule: Y is equal to the square root of X.
Equation: Y = √X
What is algebraic expression?
An algebraic expression is when we use b and words in solving a particular mathematical question.
In this table, the relationship between the values of X and Y appears to be Y = √X.
This can be expressed as a mathematical rule and equation as follows:
Rule: Y is equal to the square root of X.
Equation: Y = √X
We can use this rule to complete the table as following figure.
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find expressions for the real part, imaginary part, and magnitude of the function f(x) = 1/(1-ix), where x is real and I=√-1
The expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2) and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|
Given the complex function f(x) = 1/(1-ix), where I = √-1, we can find the real part, imaginary part, and magnitude as follows:
Real part: The real part of a complex number is equal to the real part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the real part of the numerator is 1. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The real part of the complex function is then given by:
Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2)
Imaginary part: The imaginary part of a complex number is equal to the imaginary part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the imaginary part of the numerator is 0. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The imaginary part of the complex function is then given by:
Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)
Magnitude: The magnitude of a complex number is equal to the square root of the sum of the squares of the real and imaginary parts. The magnitude of the complex function is then given by:
|f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|
Therefore, the expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)
and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|.
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What is the rule for the transformation above?
A.
(x' , y') = (x - 6 , y - 1)
B.
(x' , y') = (x - 6 , -y + 1)
C.
(x' , y') = (-x + 6 , -y - 1)
D.
(x' , y') = (x - 6 , y + 1)
The rule for the transformation above include the following: B. (x' , y') = (x - 6 , -y + 1).
What is a reflection?In Geometry, a reflection over the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive:
(x, y) → (x, -y)
This ultimately implies that, the parallelogram was reflected over the x-axis and then translated by 6 units to the left, and followed by a vertical translation downward by 1 unit.
(x' , y') = (x - 6 , -y + 1)
(x' , y') = (1 - 6 , -2 + 1)
(x' , y') = (-5, -1)
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the area of a right triangle is 50° one of its angle is 45° find the length of its sides and hypotenuse of triangle
If the area of the triangle is 50m² the length of it's other two sides is 10m each and hypotenuse is 14.1m
What is area of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
A right angled triangle is a triangle with 90°. Since of one of the angle is 45° , this means that the triangle is isosceles and the other two sides will be equal. This means a= b
Area of triangle = 1/2absinC
50 = 1/2 b²sin90
50× 2 = b²× 1
b² = 100
b = √ 100
b =10m
b = 10m
a= 10m
using Pythagoras theorem
c² = 10²+10²
c² =100+100
c²= 200
c =√200
c = 14.1m
therefore the measure of the other two sides is 10m each and the hypotenuse is 14.1m
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Express the solution using interval notation
The solution to the inequality 5/w > 4/45, using interval notation, is given as follows:
(-∞, 56.25).
How to obtain the interval notation?The inequality for this problem is defined as follows:
5/w > 4/45.
Applying cross multiplication, we have that the solution can be obtained as follows:
4w < 45 x 5
w < 45 x 5/4
w < 56.25.
The solution is found similarly to an equality, isolating the desired variable, and finding the desired range of values.
The solution w < 56.25 is composed by values to the left of x = 56.25 on the number line, that is, values between negative infinity and 56.25, hence the interval is given as follows:
(-∞, 56.25).
Missing InformationThe problem is incomplete, hence it was adapted to show the solution to an inequality, and then written in interval notation.
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Rani has several identical solid right circular metal cylinders of unknown base radius and height 10 cm. To find the base radius r of a cylinder, she puts them one by one into the above container half filled with water. When exactly 25 of them are put, the water reaches the level of the container being completely filled.
[tex]show \: that \: r = 5 \sqrt{ \frac{5}{\pi} } cm[/tex]
Find the value of r in centimetres to the first decimal place, by using 3.14 for the value of
[tex]\pi[/tex]
Answer:
The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.
When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.
So, 25 * πr^2 * h = V_container
Dividing both sides by 25πh gives: r^2 = V_container / (25πh)
Taking the square root of both sides gives: r = √(V_container / (25πh))
Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))
Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:
r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown
By using 3.14 for the value of π, we can calculate the value of r:
r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)
= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)
So, the base radius of the cylinder is approximately 6.3 cm.
What is the value of s?
The value of s on the right triangle is s = 4.
How to get the value of s?Here we can assume that the two triangles are similar triangles, then, the measures of the hypotenuses of the right triangles must be the same one.
Remember that the hypotenuse is the side that is opposite to the 90° angle, then we can write the equation:
s + 43 = 47
s = 47 - 43 = 4
That is the value of s.
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For question #3:A) Express the general solution of the given system of equations in terms of real-valued functions.B) Also, draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as t approachs infinity.
The solutions of the system tend towards zero, as the exponential term dominates the other terms.
The general solution of the given system of equations can be expressed as:
x(t) = c1e^(-t) + c2te^(-t)
y(t) = c3e^(-t) + c4te^(-t)
where c1, c2, c3 and c4 are constants of integration.
The direction field of the system can be drawn by plotting the slopes of the two equations at each point. The trajectories of the solutions can be sketched by plotting the solutions of the system at different points in time. As t approaches infinity, the solutions of the system tend towards zero, as the exponential term dominates the other terms.
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f(n) = 100n log n, g(n) = n (log n)2.
Functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2. A different algorithm's time complexity is represented by g(n), whereas another algorithm's time complexity is represented by F(n).
As n approaches infinity, F(n) and g(n) both expand as O(n log n), which indicates that the growth rate of the two functions is proportional to n log n as n gets very big. However, because the coefficient 100 in F(n) is smaller than the coefficient 1 in g, it develops more slowly than g(n) (n).
Hence, functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2.
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you measure the radius of a sphere as (6.20 ± 0.30) cm, and you measure its mass as (1.81 ± 0.09) kg. what is the density and uncertainty in the density of the sphere, in kilograms per cubic meter?
The density and uncertainty in the density of the sphere is (1828.28 ± 0.0984) kg/m³
The radius of a sphere is (6.20 ± 0.30) cm
Mass of the sphere is (1.81 ± 0.09) kg
We know that the formula for the density,
Density = mass/volume
d = m/V
As we know tha volume of the sphere is, [tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} \pi r^3\\\\V=\frac{4}{3} \pi (6.2\times 10^{-2})^3\\\\V=0.00099~m^3[/tex]
So, the density would be,
d = (1.81) / (0.00099)
d = 1828.28 kg/m³
We can find the uncertainty in volume as follows :
[tex]\frac{\delta V}{V}=3\frac{\delta r}{r}\\\\\frac{\delta V}{V}=3\times \frac{0.003}{0.0620} \\\\\frac{\delta V}{V}=0.0484[/tex]
and the uncertainty in the mass would be,
[tex]\frac{\delta m}{m}=\frac{0.09}{1.81} \\\\\frac{\delta m}{m}=0.05[/tex]
The uncertainty in the density of the sphere would be,
[tex]\frac{\delta d}{d}=\frac{\delta V}{V}+\frac{\delta m}{m}\\\\\frac{\delta d}{d}=0.0484+0.05\\\\\frac{\delta d}{d}=0.0984[/tex]
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Why is the symbol for standard deviation and variance the same?
The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.
Do standard deviation and standard variance equate to one another?Variance, as opposed to range and interquartile range, is a measure of dispersion that considers the spread of each data point within a data collection. In addition to the standard deviation, which is just the variance's square root, it is the measure of dispersion that is most frequently employed.Symbols,It is common to use the formula x = the mean, or average, of all the data points in the problem to represent standard deviation and variance. A single data point is denoted by X.The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.To learn more about stands for variation refer to:
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For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500. g of sulfuric acid is produced and the theoretical yield is 575 g of sulfuric acid.
A. 89.3%
B. 86.9%
C. 85.2%
D. 88.1%
The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4
is B. 86.9%
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.
Therefore, The percentage of actual yield to theoretical yield is,
= (500/575)×100%.
= 0.8695×100%.
= 86.95%.
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Hey if anybody could please give me a hand and explain this question to me and help me out that would be great
Answer:
Step-by-step explanation:
We can use similar triangles to solve this. The bigger triangle is made up of the water tower as the height and the long horizontal line as its base, and the smaller triangle fitted inside the larger is made up of the tripod of the camera as the height and the distance Brian lies on the ground beyond it as the base for that triangle. We have to add this distance to the distance of the larger triangle's base. Setting it up as a proportion:
[tex]\frac{watertower}{base} =\frac{camera}{base}[/tex]
but since everything is in different measurements, we have to sort that out first. Let's change everything to feet.
The water tower's distance is 100 yards + 2 feet 9 inches:
[tex]100yds*\frac{3ft}{1yd}=300'[/tex] and now we add in 2 feet 9 inches which is 2.75 feet to get a total of 302.75 feet from the base of the water tower to the point of the triangle. Since we have already converted Brian's distance to feet we're ready to set up the proportion:
[tex]\frac{x}{302.75} =\frac{5}{2.75}[/tex] and we cross multiply.
2.75x = 1513.75 and divide to get
x = 550.45 feet tall.
A rectangular mural measures 1 meter by 3 meters. Rebekah creates a new mural that is 0.5 meters longer. What is the perimeter of Rebekah's new mural?
The perimeter of Rebekah's new mural is 9 meters.
What is rectangular perimeter?The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
Given:
A rectangular mural measures 1 meter by 3 meters.
Rebekah creates a new mural that is 0.5 meters longer.
The perimeter of Rebekah's new mural,
= 2 (1.5 + 3)
= 9 meters.
Therefore, the perimeter is 9 meters.
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Answer:
9
Step-by-step explanation:
solve for x
8x+16 9x+11
Answer:
x = 9
Step-by-step explanation:
(8x+16) + (9x+11) = 180
17x + 27 = 180
180 - 27 = 153
17x = 153
153/17 = 9
x = 9
Answer:
To solve the equation 8x+16+9x+11=180, add 8x and 9x to both sides to get 17x+27=180. Subtract 27 from both sides to get 17x=153. Divide both sides by 17 to get x=9.
The coordinate of an object is given as a function of time by x = 4+2 - 3, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:
A. -4m/s^2
B. 4m/s^2
C. -10m/s^2
D. -13m/s62
The average acceleration over the given time interval is option C -10 m/s²
By dividing the change in velocity by the change in time, the average acceleration will be determined. Therefore, let's first determine the velocity function:
x = 4t² - 3t³
v = dx / dt
v = d( 4t² - 3t³) / dt
v = 8t - 9t²
Then,
at t = 0 sec , v = 0 m/s.
at t = 2 sec , v = 8(2) - 9(2²) = 16 - 36 = -20 m/s.
Average acceleration;
The rate of change in velocity is referred to as the average acceleration. To calculate the average acceleration of anything, we divide the change in velocity by the time since the initial measurement. A crazy ball's average acceleration, for instance, would be 20 cm/s/s if its velocity rose from 0 to 60 cm/s in 3 seconds.
avg.acc = (- 20 - 0) / (2 - 0) = -20 / 2 = -10 m/s²
That is,
-10 m/s² (option c) will be the average acceleration over the given interval.
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The given question is incomplete. Completed question is here;
The coordinates of an object is given as a function of time by x=4t^2-3t^3,where x is in meter and t is in second .what is its average acceleration over the time interval from 0 to 2 seconds
Solve the system of equations. –6x + y = –21 2x − 1 3 y = 7 What is the solution to the system of equations? (3, 3) (2, –9) infinitely many solutions no solutions
Answer:
x = 7/2
y = 0
Step-by-step explanation:
–6x + y = –21
2x − 13y = 7
Times the second equation by 3
-6x + y = -21
6x - 39y = 21
-38y = 0
y = 0
Now put -0 back for y and solve for x
-6x = -21
x = 7/2
Answer:
I think it would be infinitely many solutions
Step-by-step explanation:
I need help, can y’all explain to me how to solve it? Linear Equations
Necesito ayuda, ¿alguien puede explicarme cómo resolverla? Son ecuaciones lineales
x+y=25
2x+2y=50
The value of
x₁/x₂ = y₁/y₂ = c₁/c₂
the given lies are parallel to each other having no solution .
What are system of Equation?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are no solutions when the lines are parallel, and there are a finite number of solutions when the two equations graph as the same line.
The equation are
x + y = 25
2x + 2y = 50
The value of
x₁/x₂ = y₁/y₂ = c₁/c₂
So the given lies are parallel to each other having no solution .
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If you cannot show the triangles are congruent from the given information leave the trianglges name black and write CNBD for Cannot be Determined in place of the rule.
Step-by-step explanation:
the triangle GAS is congruent with the triangle IOL (I know, it is tempting to say OIL, but it is important to show the sequence of the corresponding corners, so G corresponds to I, A to O and S to L) by AAS (angle-angle-side) : 2 angles and a not included but corresponding side are equal between the 2 triangles.
Convert the below equation into y=mx b form 2x-y=-3
Answer: y=2x+3
Step-by-step explanation:
2x−y=−3
Step 1:
Add -2x to both sides.
2x−y+−2x=−3+−2x−y=−2x−3
Step 2: Divide both sides by -1.−y−1=−2x−3−1y=2x+3
I’m not sure how to do this
On solving the provided question, we can say that so the equation formed is 1540-6x = 236 +6 x and in 108 2/3 minutes the tanks become equal with 888 gallons each
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
when does tank 1 = tank 2 when there is 6 gpm
tank 1 = 1540
tank2 = 236
so the equation formed is
1540-6x = 236 +6 x
1304 = 12x
108 * 2/3 = x
6*108*2/3 = 652 gallons
236+652=888
1504-652=888
in 108 2/3 minutes the tanks become equal with 888 gallons each
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Can you please solve for me please?
Answer:
[tex]\boxed{\sin D = 0.39 }[/tex]
Step-by-step explanation:
DEF is a right triangle with hypotenuse = 18 and one leg = 7
The law of sines states that the ratios of the sides of a triangle to the sine of the angle opposite that side must be the same for all sides
[tex]\dfrac{18}{\sin 90} = \dfrac{7}{sin D}[/tex]
sin(90) is 1
So the above equation becomes
[tex]18 = \dfrac{7}{\sin D}[/tex]
Cross multiplying we get
[tex]\sin D = \dfrac{7}{18}\\\\\sin D = 0.3889\\[/tex]
Rounded to the nearest hundredth ( i.e. 2 decimal places):
[tex]\sin D = 0.39 \quad \quad \textrm{ANSWER}\\\\[/tex]
The price for gasoline is represented by the equation y = 2. 72x, where y represents the total price for x gallons of gasoline. Fifteen gallons of gasoline can be represented by the coordinates (15, 40. 8).
The total price is 40.8, which can be represented by the coordinates (15, 40.8).
The equation y = 2.72x can be used to calculate the price of gasoline in terms of the number of gallons purchased.
The equation y = 2.72x can be used to calculate the total price of any number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons. If we input 15 gallons into the equation, we can calculate the total price of gasoline. To do this, we must substitute 15 for x in the equation, giving us y = 2.72(15). We can then calculate the total price by multiplying 2.72 and 15, which yields 40.8. Thus, for 15 gallons of gasoline, the total price is 40.8, which can be represented by the coordinates (15, 40.8).
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A factory sampled hundreds of 9oz bags of chips off of one of their production lines to make sure the bags had the appropriate
amount of chips. They found the amount of chips to be normally distributed with = 9.12 ounces and o= .05 ounces.
PART A
Given this information, fill out the normal distribution chart below for the weight of 9oz bags of chips from this factory.
The normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
What is standard deviation?The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.
From the given samples of 9oz of chips we have the following values:
Mean = 9.12 ounces
SD = 0.05 ounces
The normal distribution of the chart below will have the following values:
The mean or the center value of the graph with the highest peak is:
Mean = 9.12
The value to the right of the mean value will be:
Mean + SD = 9.12 + 0.05 = 9.17
Mean + 2(SD) = 9.12 + 2(0.05) = 9.22
Similarly, the value to the left of the mean value will be:
Mean - SD = 9.12 - 0.05 = 9.07
Mean - 2(SD) = 9.12 - 2(SD) = 9.02
Hence, the normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
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huck can paint a fence in 5 hours. if tom helps him paint the fence they can do it in 3 hours. how long would it take for tom to paint the fence by himself? (hint: use the equation from
Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.
How long would it take for tom to paint the fence by himself?Here we will use equations of the form:
(rate at which person x paints)*(time) = 1 fence painted.
We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:
C*5 hours = 1 fence
C = (1/5) fences per hour.
And let's say that Tom's rate is T.
When they work together, the rate is:
(C + T)
And they can paint the fence in 3 hours, then:
(C + T)*3 hours = 1 fence
Replacing the value of T we will get:
( 1/5 fences per hour + T)*3 hours = 1 fence
1/5 fences per hour + T = 1/3 fences per hour.
T = (1/3 - 1/5) fences per hour
T = (5/15 - 3/15) fences per hour
T = 2/15 fences per hour.
Then Tom paints the fence in:
(15/2) hours = 7.5 hours.
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Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes fro concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for definite integral from 1 to 3 of f(x^2 + x) using 4 subintervals?a. The midpoint Riemann sum approximation underestimates the definite integral.b. The midpoint Riemann sum approximation overestimates the definite integral.c. The midpoint Riemann sum approximation cannot be determined to be an underestimate or an overestimate.
The true statement is Option B, The midpoint Riemann sum approximation overestimates the definite integral.
Given data,
In this case, since the function f changes from increasing to decreasing and the graph of f changes from concave up to concave down, we can infer that the function has a local maximum point within the interval [1, 3].
The midpoint Riemann sum approximation for the definite integral breaks the interval [1, 3] into four subintervals of equal width, and it uses the midpoint of each subinterval to approximate the value of the function within that subinterval.
Now, when the function is increasing, the midpoint Riemann sum approximation will tend to underestimate the value of the definite integral since it approximates the function using values that are smaller than the actual function values.
However, when the function changes from increasing to decreasing, the midpoint Riemann sum approximation will tend to overestimate the value of the definite integral since it approximates the function using values that are larger than the actual function values.
Hence , the midpoint Riemann sum approximation overestimates the definite integral.
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Two similar figures have a side ratio of 4:3. If the perimeter of the smaller figure is 15 units, what is perimeter of the larger figure?
Enter fractions as decimals.
The perimeter of the larger figure is: 20 units.
How to Find the Perimeter of Similar Figures?Similar figures have perimeters and side lengths that are related in such a way that, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Therefore, if x represents the perimeter of the larger figure, then:
x/15 = 4/3
Cross multiply to find x:
3x = 60
x = 60/3
x = 20
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Find the surface area of the cylinder. Round your answer to the nearest tenth.
6 ft
7 ft
Surface area of the cylinder would be 231.1 sq ft.
How do you find a surface area of a cylinder?
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
The surface area of a cylinder with height h and radius r can be found using the formula:
2πr^2 + 2πrh
Given a cylinder with height 6 ft and radius 7 ft, the surface area is:
2π * 7^2 + 2π * 7 * 6 = 147.1 + 84 = 231.1 sq ft (rounded to the nearest tenth).
Therefore, Surface area of the cylinder would be 231.1 sq ft.
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. how can the directed graph of a relation r on a finite set a be used to determine whether a relation is asymmetric?
The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.
Let the relation R R R be asymmetric. A loop in the directed graph corresponds to an ordered pair of the form ( a , a ) (a , a) (a , a). By the definition of asymmetric, the relation R R R cannot contains any ordered pairs of the form ( a , a ) (a , a) (a , a) and thus the directed graph cannot contain any loops.
They are typically represented by labeled points or small circles. We connect vertex a to vertex b with an arrow, called an edge, going from vertex a to vertex b if and only if arb. This type of graph of a relation r is called a directed graph or digraph .
It is a set where either there are many components or only the beginning or ending are provided. By n(A), we refer to the total number of components, and if n(A) is a characteristic number, then the set is constrained.
Let A be finite non-empty set.
Then the exist relation R on A which is both equivalence and order relation.
Suppose A = {[tex]a_{1} , a_{2} , a_{3} , ...... a_{n} ,[/tex]}
And, R = { [tex](a_{1} ,a_{1}) , (a_{2} ,a_{2} ) ,(a_{3} ,a_{3} )........(a_{n} ,a_{n} )[/tex] }
R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.
Then R is equivalence relation and an order relation.
Therefore,
The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.
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