Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
F = 3xi + 2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z = 0) by the cylinder x2 + y2 = 4
Answers
Stokes’ Theorem:Stokes’ theorem relates a surface integral of the curl of a vector field to a line integral of the vector field along the boundary of the surface. The theorem is a generalization of the Kelvin-Stokes theorem (also called the Stokes theorem for line integrals) and the divergence theorem. The integral form of the Stokes’ Theorem is stated as follows:
∫_S curl F. dS= ∫_C F. drThe circulation of the field F around the curve C in the indicated direction is given by using Stokes' Theorem.
The circulation of the field F around the curve C in the indicated direction is given by using Stokes' Theorem. Therefore,
we need to find the curl of the vector field F to find the circulation of the field F around the curve C in the indicated direction.
Calculation of Curl of Vector Field F:
Given that the vector field is F = 3xi + 2xj + 7zk.
The curl of the vector field is given by the determinant as follows:
curl F = i ( ∂(7z)/∂y − ∂(2x)/∂z ) + j ( ∂(3x)/∂z − ∂(7z)/∂x ) + k ( ∂(2x)/∂x − ∂(3x)/∂y )= i ( 0 − 0 ) − j ( 0 − 0 ) + k ( 3 − 2 )= k
Therefore, the curl of the vector field F is k.Calculation of Surface Integral:
We need to find the surface integral of the curl of the vector field F over the surface S.
The surface is given by the cap cut from the upper hemisphere x² + y² + z² = 16 (z = 0) by the cylinder x² + y² = 4, which can be written as follows: x² + y² + z² = 16, z ≥ 0 and x² + y² ≤ 4.
The unit normal vector of the surface S is given by n = - k.
The surface integral of the curl of the vector field F over the surface S is given by∫_S curl F. dS= ∫_S k . (-k) dS= - ∫_S dS= - area(S)
Now, we need to find the area of the surface S.
The surface S is the cap of the sphere x² + y² + z² = 16, z ≥ 0 cut by the cylinder x² + y² = 4.
Let’s find the projection of the curve C on the xy-plane,
which is the circle of radius 2 centered at the origin x² + y² = 4.
The curve C starts at (2,0,0), goes counterclockwise around the circle of radius 2 centered at the origin, and ends at (-2,0,0).
The curve C is the boundary of the surface S, which is the cap of the sphere x² + y² + z² = 16, z ≥ 0 cut by the cylinder x² + y² = 4.
Therefore, the area of the surface S is the area of the cap of the sphere x² + y² + z² = 16, z ≥ 0 cut by the cylinder x² + y² = 4.
The area of the cap of the sphere x² + y² + z² = 16, z ≥ 0 cut by the cylinder x² + y² = 4 is given by the formula:
A = 2π ( r ( h² + r² )^(1/2) − r² sin^(-1) ( h/r ) )where r = 2 and h = √(16 – 4) = √12 = 2√3.So, A = 2π ( 2 ( 2√3 )^(1/2) − 4 sin^(-1) ( √3/2 ) )= 4π ( √3/2 − sin^(-1) ( √3/2 ) )
Therefore, the surface integral of the curl of the vector field F over the surface S is given by∫_S curl F. dS= - area(S)= - 4π ( √3/2 − sin^(-1) ( √3/2 ) )Calculation of Line Integral:
We need to find the line integral of the vector field F along the curve C.The curve C starts at (2,0,0), goes counterclockwise around the circle of radius 2 centered at the origin, and ends at (-2,0,0).
\(The line integral of the vector field F along the curve C is given by∫_C F. dr= ∫_C ( 3xi + 2xj + 7zk ) . (dx i + dy j)= ∫_C ( 3x dx + 2y dy )= ∫_C ( 3 ( 2 cos t ) ( −sin t dt ) + 2 ( 2 sin t ) ( cos t dt ) )= ∫_C ( −6 sin t cos t + 4 sin t cos t ) dt= ∫_C −2 sin t cos t dt= [ sin^2 ( t ) ]_0^(2π)= 0\)
Therefore, the line integral of the vector field F along the curve C is zero.
Finally, we have∫_S curl F. dS= - area(S) = - 4π ( √3/2 − sin^(-1) ( √3/2 ) )= 0 + ∫_C F. dr= 0
Therefore, the circulation of the field F around the curve C in the indicated direction is zero.
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Related Questions
Solve the right triangle by finding all missing angles and sides.
Answers
Given:
There are given the right angle triangle, ABC.
Where,
\(\begin{gathered} AB=5 \\ BC=9 \\ AC=? \end{gathered}\)Explanation:
To find the missing side in the given right angle triangle, we need to use the Pythagoras theorem:
So,
From the Pythagoras theorem in triangle ABC:
\(AB^{^2}+BC^2=AC^2\)Then,
Put the all values into the above formula:
\(\begin{gathered} AB^2+BC^2=AC^2 \\ 5^2+9^2=AC^2 \\ 25+81=AC^2 \\ 106=AC^2 \end{gathered}\)Then,
\(\begin{gathered} AC^2=106 \\ AC=\sqrt{106} \\ AC=10.3 \end{gathered}\)Therefore, the side AC is 10.3:
Now,
We need to find the missing angle in the given triangle ABC:
So,
To find the angle A, we need to use the formula of tan function:
So,
\(\begin{gathered} tanA=\frac{BC}{AB} \\ tanA=\frac{9}{5} \\ tanA=1.8 \end{gathered}\)Then,
\(\begin{gathered} tanA=1.8 \\ A=tan^{-1}(1.8) \\ A=60.9 \end{gathered}\)Now,
We need to find the value of angle C:
So,
To find the angle C, we need to use the angle of triangle rule:
So,
In a right-angled triangle, the addition of the two angles is equal to the 90 degrees.
Then,
\(\angle A+\angle C=90^{\circ}\)Then,
Put the value of angle A into the above formula;
So,
\(\begin{gathered} \angle A+\angle C=90^{\circ} \\ 61^{\circ}+\angle C=90^{\circ} \\ \angle C=90^{\circ}-61^{\circ} \\ \angle C=29^{\circ} \end{gathered}\)Final answer:
Hence, the missing side and the missing angles are shown below:
\(\begin{gathered} AC=10.3 \\ \angle A=61^{\circ} \\ \angle C=29^{\circ} \end{gathered}\)
Maureen is building a playpen for her new puppy. She wants the puppy to have 28 square feet of space. Draw a picture of what the playpen might look like and label the lengths of the sides. What is the perimeter of playpen?
Answers
The perimeter of the playpen is 21 feet.
We have,
-------------------
| |
|
width |
| |
| |
-------------------
length =
Let's label the width as w and one of the lengths as l.
Then we can use the formula for the area of a rectangle to find the other length:
Area = length x width
28 = l x w
l = 28 / w
Now we can substitute this expression for l into the formula for the perimeter of a rectangle:
Perimeter = 2 x length + 2 x width
Perimeter = 2(28/w) + 2w
Perimeter = 56/w + 2w
To find the value of w that gives the minimum perimeter, we can take the derivative of this expression with respect to w, set it equal to 0, and solve for w:
dP/dw = -56/w^2 + 2 = 0
56/w^2 = 2
w^2 = 28
w = √(28) = 2 √(7)
Now we can substitute this value for w to find the corresponding length:
l = 28 / w
l = 28 / (2 √(7))
l = 14 / √(7)
So the playpen has dimensions of approximately 2 √(7) by 14/ √(7), and the perimeter is:
Perimeter = 56/w + 2w
Perimeter = 56/(2 √(7)) + 2(2 √(7))
Perimeter = 28/ √(7) + 4 √(7)
Perimeter = (28 + 28)/ √(7)
Perimeter = 56/ √(7)
Perimeter ≈ 21.21 feet
Thus,
The perimeter of the playpen is 21 feet.
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how many 99-bit strings are there that contain more ones than zeros?
Answers
There are 3,360,276 99-bit strings that contain more ones than zeros.
Consider two cases: strings with exactly 50 ones and strings with exactly 51 ones to determine the number of 99-bit strings that contain more ones than zeros.
Using the formula for combinations, we can calculate the number of 99-bit strings with exactly 50 ones as C(99, 50). This represents choosing 50 positions out of the 99 positions to place the ones.
Calculate the number of 99-bit strings with exactly 51 ones as C(99, 51), which represents choosing 51 positions out of the 99 positions for the ones.
Sum the two cases to find the total number of strings that contain more ones than zeros:
C(99, 50) + C(99, 51) = 99! / (50! × 49!) + 99! / (51! × 48!) = 3,360,276.
Therefore, there are 3,360,276 99-bit strings.
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Determine the absolute value of the complex number colon open vertical bar 6 straight i close vertical bar
Answers
Answer:
√37 ≈ 6.083
Step-by-step explanation:
You want the modulus of the complex number 6 -i.
ModulusThe modulus of a number is written using absolute value bars:
|6 -i|
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts:
|6 -i| = √(6² +(-1)²)
|6 -i| = √37 ≈ 6.083
y' +xy = 10 sinx use h=0.2 and y(0) = 0.1 estimate the value ofy(0.2) and y(0.4) using improved Euler's method .Use values inradian for trigonometric functions
Answers
Then using improved Euler's method, we estimate the value of y(0.2) to be approximately 0.299 and the value of y(0.4) to be approximately 0.748.
To use the improved Euler's method, we need to first find the values of y' at the beginning and end of each interval. Using the given equation, we have:
y' = 10 sinx - xy
Using h=0.2, we can find the values of y' at the beginning and end of the first interval as follows:
y'(0) = 10 sin(0) - (0)(0.1) = 0
y'(0.2) = 10 sin(0.2) - (0.2)(0.1) ≈ 1.994
Using the improved Euler's method, we can estimate the value of y(0.2) as follows:
y(0.1) + (h/2)(y'(0) + y'(0.2)) = 0.1 + (0.2/2)(0 + 1.994) ≈ 0.299
We can repeat this process to estimate the value of y(0.4):
y'(0.4) = 10 sin(0.4) - (0.4)(0.299) ≈ 3.636
y(0.3) + (h/2)(y'(0.2) + y'(0.4)) = 0.299 + (0.2/2)(1.994 + 3.636) ≈ 0.748
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Name the property illustrated be each statement if 8(2q +1)=4, then 2(2q+1)=1
Answers
The property by which the expression 8(2q +1)=4, becomes 2(2q+1)=1 is called the multiplication property of equality.
What is an expression?A mixture of variables,n umbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given,
8(2q +1)=4
Multiply both sides by 1/4
1/4 × 8(2q +1)= 1/4 × 4
2(2q +1)= 1
Hene the property by which the equation 8(2q +1)=4, converted into 2(2q+1)=1 called multiplication property of equality.
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What type of angles are ECH and FCG?
Answers
ECH is an acute angle.
FCG is also an acute angle.
Answer:
Vertical angles
Step-by-step explanation:
Vertical angles are angles formed by two intersecting lines, which the angles are facing the opposite direction. Also the angles are on the same vertice (point).
The daily milk production of a dairy cow is normally distributed with mean of 3500 millilitres and a standard deviation of 250 millilitres What is the probability that a cow selected at random will produce 3900 millilitres or more
Answers
The correct answer is the probability of a cow producing 3900 millilitres of milk or more is 0.0548 or 5.48%,
The given normal distribution of daily milk production of a dairy cow is given by: Mean (μ) = 3500 milliliters, and standard deviation (σ) = 250 milliliters. We have to find the probability of getting a cow that will produce milk of 3900 millilitres or more. Using standard normal distribution, we have to convert the given normal distribution to standard normal distribution using z-score z = (x - μ) / σ where x is the observed value, μ is the mean, and σ is the standard deviation.
Therefore, z-score = (3900 - 3500) / 250 = 1.6.
Hence, the probability of a cow producing 3900 millilitres of milk or more is 0.0548 or 5.48%, as we have to find the area of the curve of standard normal distribution on the right side of the value 1.6.
Hence, the area under the curve of a standard normal distribution from z-score 1.6 to the end of the distribution which is represented by the symbol “∞” will give us the probability.
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I need help with this question
Answers
The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
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For what values of k is 9x^2+k+16 a perfect square?
Answers
Answer:
24x
Step-by-step explanation:
a² ± 2ab + b² = (a ± b)²
(3x)² + k + 4² = (3x)² + 2(3x)(4) + 4²
k = 24x
Which method is best to use if one of the equations in the system is already solved for one variable?
Answers
Substitution is the best method to use when one of the equations in the system is already solved for one variable. This involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated, and then solving the resulting equation.
Substitution is the best method to use when one of the equations in the system is already solved for one variable. This method involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated. The resulting equation will have fewer variables, making it easier to solve. Additionally, this method can be used to eliminate variables from equations that cannot be solved directly. For example, if two equations are given that cannot be solved for a common variable, substitution can be used to eliminate the variable from both equations and turn them into equations in one variable. This makes it easier to solve the system of equations.
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Use the zero product property to determine the x-intercepts for the graph of the quadratic function
1. y= -x squared -7x-12
2. y= 3x squared +11x+10
Answers
Answer:
1) x-intercepts are at -3 and -4
2) x-intercepts are at 5/3 and 2
Step-by-step explanation:
1) y = -x^2 - 7x - 12 is -(x + 3) (x + 4)
2) y = 3x^2 + 11x + 10 is (3x + 5) (x + 2)
For the vector pictured below, draw a position vector with the same magnitude and direction, and draw another position.
vector that is equal in magnitude but opposite in direction. Label the vectors vand-vrespectively.
Answers
The value of diagram of another position, vector that is equal in magnitude but opposite in direction. is shown in image.
We have to given that;
For the vector pictured , draw a position vector with the same magnitude and direction, and draw another position vector that is equal in magnitude but opposite in direction.
Hence, We can draw the vector of another position, vector that is equal in magnitude but opposite in direction. is shown in image.
Thus, The image is shown in figure.
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Find y'. y=x²√6x-1 y'=0 (Type an exact answer, using radicals as needed.)
Answers
The derivative of y with respect to x, denoted as y', is equal to (3x^2 - 1)/(2√6x).
To find the derivative of y with respect to x (y'), we can use the power rule and the chain rule of differentiation. Let's break down the steps:
First, apply the power rule to differentiate x^2, which gives us 2x.
Next, we differentiate the expression √6x - 1 using the chain rule. The derivative of √6x with respect to x is (√6)/2√x, obtained by differentiating the inside function (6x) and multiplying it by the derivative of the inside function (1/2√x).
The derivative of -1 with respect to x is 0 since it is a constant.
Combining these results, we have y' = 2x * (√6)/2√x - 0 = (√6x)/(√x) = √6x.
Therefore, the derivative of y with respect to x, y', is equal to (3x^2 - 1)/(2√6x).
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Tell whether the triangles are similar. Explain. PLEASE I MEED HELP
Answers
Answer:
No
Step-by-step explanation:
The angels are not similar. The first triangle has the top corner as 36 degrees and the bottom right as 72 degrees, which matches with the second triangle. But the second triangle has 33 degrees as the top instead of 36, so the triangles are not similar.
Step-by-step explanation:
I hope it's correct thanks me nalang kung correct
Which function has a range of all real numbers greater than or equal to -4?
A. f(x) = x-4
B. f(x) = -4x
C. f(x) = (x+1)^2 - 4
D. f(x) = -|x-3|-4
Answers
Answer:
C. \(f(x)=(x+1)^2-4\)
Step-by-step explanation:
A. the graph is a straight line with slope 1. It goes up/down infinitely far so the range is all real numbers. Not A!
B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers. Not B!
D. The graph is an absolute value function y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units. So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units. The range is all real numbers less than or equal to -4.
See the attached graphs. image2 is the function in answer choice D.
who invented maths ???
Answers
Subtract.
- 3 3/8 -
7
8
Enter your answer, in simplest form, in the box.
Answers
Answer:
the answer is there
Answer:
-4 1/4Step-by-step explanation:
Let's change the mixed fraction into improper fraction. Then, subtract to get the result.
-3 3/8 - 7/8=> -27/8 - 7/8=> -34/8=> -4 2/8 = -4 1/4Hence, the solution to the problem is -4 1/4.
Solve for the remaining angles and side of the two triangles that can be created. Round to the nearest hundredth: A = 50. a 4. b = 5 Answer How to enter your answer (opens in new window) Triangle 1: (where angle B is acute): B = ___C= ___c=___ Triangle 2: (where angle B is obtuse): B = ___C =___ c=___
Answers
For Triangle 1 (where angle B is acute): B ≈ 77.58°, C ≈ 52.42°, and c ≈ 4.94.
For Triangle 2 (where angle B is obtuse): B ≈ 102.42°, C ≈ 27.58°, and c ≈ 4.94.
To solve for the remaining angles and side of the triangles, we can use the Law of Sines. Given that A = 50, a = 4, and b = 5, we can first find angle B using the sine rule: sin(B)/b = sin(A)/a. Solving for B, we have sin(B) = (b/a) * sin(A).
For Triangle 1, where angle B is acute, we have B ≈ arcsin((5/4) * sin(50°)) ≈ 77.58°. Using the fact that the sum of angles in a triangle is 180°, we can find angle C = 180° - A - B ≈ 52.42°. To find side c, we use the sine rule again: c/sin(C) = a/sin(A). Solving for c, we have c ≈ (a * sin(C))/sin(A) ≈ (4 * sin(52.42°))/sin(50°) ≈ 4.94.
For Triangle 2, where angle B is obtuse, we have B ≈ 180° - arcsin((5/4) * sin(50°)) ≈ 102.42°. Similarly, we can find angle C = 180° - A - B ≈ 27.58°. Using the sine rule, we can find side c as c ≈ (4 * sin(C))/sin(A) ≈ (4 * sin(27.58°))/sin(50°) ≈ 4.94.
These are the rounded values for the remaining angles and side of the two triangles.
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For Triangle 1 (where angle B is acute): B ≈ 77.58°, C ≈ 52.42°, and c ≈ 4.94. For Triangle 2 (where angle B is obtuse): B ≈ 102.42°, C ≈ 27.58°, and c ≈ 4.94.
To solve for the remaining angles and side of the triangles, we can use the Law of Sines. Given that A = 50, a = 4, and b = 5, we can first find angle B using the sine rule: sin(B)/b = sin(A)/a. Solving for B, we have sin(B) = (b/a) * sin(A).
For Triangle 1, where angle B is acute, we have B ≈ arcsin((5/4) * sin(50°)) ≈ 77.58°. Using the fact that the sum of angles in a triangle is 180°, we can find angle C = 180° - A - B ≈ 52.42°. To find side c, we use the sine rule again: c/sin(C) = a/sin(A). Solving for c, we have c ≈ (a * sin(C))/sin(A) ≈ (4 * sin(52.42°))/sin(50°) ≈ 4.94.
For Triangle 2, where angle B is obtuse, we have B ≈ 180° - arcsin((5/4) * sin(50°)) ≈ 102.42°. Similarly, we can find angle C = 180° - A - B ≈ 27.58°. Using the sine rule, we can find side c as c ≈ (4 * sin(C))/sin(A) ≈ (4 * sin(27.58°))/sin(50°) ≈ 4.94.
These are the rounded values for the remaining angles and side of the two triangles.
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a college reports that the average age of their students is 28 years old. is this a statistic or a parameter?
Answers
The average age of all students in the college is a parameter. A parameter describes the whole populations.
What is the difference between parameter and statistic?A parameter is a number represents all the data from a population.A statistic is a number represents the data from a sample.Tha value of parameter or statistic can be average, percentage, and others.
A college reports that the average age of their students is 28 years old.
Is this a statistic of parameter?
The college would have access to data on all students. The data of all students in the college or the entire students is called population. So, this is a parameter.
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What is the domain in interval notation of the function graphed below? Note: As x is approaching -2, the graph is getting closer and closer to a line but not touching it.
Answers
Answer:
Step-by-step explanation:
x-values approach x = -2, but do not touch the vertical line x = -2. All other x-values are permitted. Thus, the domain is (-2, infinity).
How do you find the base area of a rectangular prism when given the volume?
Answers
you can use the formula for the volume of a rectangular prism to solve for one of the dimensions of the prism (either the length, width, or height).
What is a rectangular prism?
A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a box or a cuboid. A rectangular prism has three dimensions: length, width, and height.
To find the base area of a rectangular prism when given the volume, you can use the formula for the volume of a rectangular prism and the formula for the base area of a pyramid.
The volume of a rectangular prism is given by the formula V = lwh,
where V is the volume, l is the length, w is the width, and h is the height.
The base area of a pyramid is given by the formula B = A/h,
where B is the base area, A is the total surface area of the pyramid, and h is the height of the pyramid.
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Solve \(3xlog 2+log8^x=2\)
Answers
Hello !
Answer:
\(\boxed{\sf x = \frac{1}{ log(8) } }\)
Step-by-step explanation:
We want to find the value of x that verifies the following equation :
\(\sf 3xlog 2+log(8^x)=2\)
Let's remember :
\(\sf log( {x}^{a} ) = a \times log(x) \)
We can apply this property to our equation :
\(\sf 3x log(2 ) + x log(8) = 2\)
Let's factor the left side by x :
\(\sf x(3 log(2) + log(8) ) = 2\)
We can apply the previous property to put the 3 as an exponent in the log
\(\sf x(log( {2}^{3} ) + log(8) ) = 2 \\ x( log(8 ) + log(8) ) = 2 \\ 2x log(8) = 2\)
Let's divide both sides by 2 :
\(\sf x log(8) =1\)
Finally, let's divide both sides by log(8) :
\(\boxed{\sf x = \frac{1}{ log(8) } }\)
Have a nice day ;)
Thirteen-year-old noel was taking her algebra test but was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" this is an example of?
Answers
The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.
What is the concept exhibited by the thirteen year old as given in the task content?It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".
Such concept may be attributed to Intuitive thought.
This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.
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1. Which equation below is n = 2 a solution for?
3n = 6
n-1=2
9+n=12
3+n=8
Answers
The equation 3n = 6 has a solution n = 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have to find that which equation below is n = 2 a solution.
Then substitute n = 2;
3n = 6
3(2) = 6
This equation has a solution n = 2.
2. n-1=2
Then substitute n = 2;
2 - 1 = 1
The solution of the equation is not n = 2
3. 9+n=12
Then substitute n = 2;
9 + 2 = 11
The solution of the equation is not n = 2
4. 3+n=8
Then substitute n = 2;
3 + 2 = 5
The solution of the equation is not n = 2
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Solve each triangle. Round your answers to the nearest tenth.
m∠A = 60°, m∠B = 30°, c = 30 cm
Answers
Answer:
mb = 30
Step-by-step explanation:
i got it from me school
Answer:
Angle C = 90°
a = 15sqroot3
b = 15
Step-by-step explanation:
Solve a triangle means to find all the angles and all the sides.
Angle C must be 90° because all the angles of a triangle add up to 180°.
That makes this a 30°-60°-90° triangle so there are SHORTCUTS to finding the sides so you don't have to use trig or pythagorean thm.
SHORTCUT:
The shortest side is half the longest side. (The short leg is half the hypotenuse) and/or the longest side is twice the shortest side.
SHORTCUT:
The long leg is the shortleg•sqroot3
(advanced mode: the shortleg is the longleg/sqrt3)
So for your problem, the hypotenuse is 30, so the short leg is 15. And that makes the long leg 15sqrt3. See image.
"Benny operationalizes creativity as the number of unique adjectives that participants can generate in one minute to describe a painting. Which of the following are true?(one or more correct answers)
Benny can calculate the median of this measure.
This measre has a "true zero."
Benny cannot calculate the mean of this measure.
Benny can calculate the mode of this measure.
If Participant A generates 50 adjectives, and Participant B generates 5 adjectives, then according to this measure Participant A is ten times as creative as Participant B.
"
Answers
Benny can calculate the median and mode of the measure, but cannot calculate the mean. The measure does not have a true zero. According to this measure, Participant A is not ten times as creative as Participant B.
Benny can calculate the median of this measure because the median is the middle value when the adjectives are arranged in ascending or descending order. However, Benny cannot calculate the mean because the measure does not involve a quantitative scale that can be averaged. It is based on the count of unique adjectives, which is a discrete and non-continuous variable.
The measure does not have a true zero. A true zero would imply the absence of the measured attribute, but in this case, having zero unique adjectives is still a valid response. Therefore, the absence of adjectives does not represent a complete lack of creativity.
According to this measure, Participant A generating 50 adjectives and Participant B generating 5 adjectives does not imply that Participant A is ten times as creative as Participant B. The measure only reflects the number of unique adjectives generated and does not capture the quality, depth, or originality of the descriptions. It is important to consider other factors and indicators of creativity to make a comprehensive assessment.
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how many men and women think an ergonomic consultant should evaluate their office equipment? 517 people 109 people
Answers
The number of men who think an ergonomic consultant should evaluate their office equipment is approximately 77, and the number of women who think the same is approximately 241
Based on the provided table, we can determine the number of men and women who think an ergonomic consultant should evaluate their office equipment.
From the table, we can see that:
The total number of respondents is 700.
The percentage of males who strongly agree is 30.3%, which is equivalent to 30.3% of 254 (the total number of males).
Calculating this, we get:
(30.3/100) × 254 ≈ 77.162 males.
Similarly, the percentage of females who strongly agree is 53.8%, which is equivalent to 53.8% of 446 (the total number of females).
Calculating this, we get:
(53.8/100) × 446 ≈ 240.748 females.
Therefore, the number of men who think an ergonomic consultant should evaluate their office equipment is approximately 77, and the number of women who think the same is approximately 241.
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The complete question is :
You are a human resources manager sorting through data for a report on employee satisfaction. Several employees you interviewed mentioned they were experiencing neck and back pain. They suggested the company look into having an ergonomics consultant visit the office and conduct an evaluation. You choose to use a survey to get measurable qualitative and quantitative feedback. You ask the employees to respond to the following statement: "Our company should have an ergonomic consultant conduct an evaluation of all office equipment." The following table reflects the survey results. Total Male Female Number Percent Number Percent Number Percent 30.3 53.8 4.0 10.1 1.8 100.0 254 100.0 446 100.0 39.3 16.6 8.7 25.2 10.2 135 240 18 45 235 33.5 40.3 5.7 15.5 4.9 100 Strongly agree Agree No opinion Disagree Strongly disagree Total 282 42 64 109 34 700 26 How many men and women think an ergonomic consultant should evaluate their office equipment? O 109 people O 517 people
Find the x - intercept of the graph of the equation
1) x + y = 9
2) 3x + y = 15
3) 2x + 3y = 12
4) x - y = 4
5) 4y - x = 18
6) 3y - 7x = 35
7) x - y = -1
8) 2x + 5y =14
9) 9x - 4y = 10
Help plz!!
Answers
Answer:
ugh should i drop out
Step-by-step explanation:
The answer to this question is 13x + 5y = 48. <3
The number of times a number is multiplied by itself is called