An engineer is estimating the weight of a steel beam. The actual weight of the beam is 152 pounds. The engineer's estimate is 150 pounds.
Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.

There are 1540 ways can five members be selected for a search and rescue mission such that at least one officer is included.

What is a combination?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

Formula to calculate combination

ⁿCₓ = n!/x!(n-x)!

Here, we have

The total count of members is 14.

The total number of officers is 3.

So, the count of non-officers will be

14−3 = 11

Now, 5 members are selected including at least one officer. So, the count of officers and non-officers in the team of 5 members is as follows:

(a) 1 officer and 4 non-officers

(b) 2 officers and 3 non-officers

(c) 3 officers and 2 non-officers

To find the ways for each of the three cases above, we use combinations

ⁿCₓ = n!/x!(n-x)!

where

n: is the total count of objects and

x: is the count of selected objects.

Number of ways when 1 officer and 4 non-officers can be selected, we have possible combinations

³C₁ ×¹¹C₄ = 3!/1!(3-1)! × 11!/4!(11-4)!

              = 3!/2! ×  11!/4!(7)!

              = (3 × 2!)/ 2!  × (11×10×9×8×7!)/(4! × 7! )

             =  3 × (11×10×9×8)/(4×3×2×1)

             =  990

Number of ways when 2 officers and 3 non-officers can be selected, we have possible combinations

³C₂ ×¹¹C₃ = 3!/2!(3-2)! × 11!/3!(11-3)!

              =  3!/2! ×  11!/3!(8)!

              =  (3 × 2!)/ 2!  × (11×10×9×8!)/(3! × 8! )

               =  3 × (11×10×9)/(3×2×1)

              = 495

Number of ways when 3 officers and 2 non-officers can be selected, we have possible combinations

³C₃ ×¹¹C₂ = 3!/3!(3-3)! × 11!/2!(11-2)!

              =  1! ×  11!/2!(9)!

              = 1 × (11×10×9!)/(2! × 9! )

               = 55

The total number of ways when 5 members can be selected including at least one officer is calculated as follows:

³C₁ ×¹¹C₄+ ³C₂ ×¹¹C₃+ ³C₃ ×¹¹C₂ = 990 + 495 +55 = 1540

Hence, there are 1540 ways can five members be selected for a search and rescue mission such that at least one officer is included.

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Setting x1 to zero in the equation 2x1 + 1x2 = 30 results in the value of x2 being 30.

The given equation is 2x1 + 1x2 = 30, where x1 and x2 represent variables. To find the value of x2 when x1 is set to zero, we substitute x1 with zero in the equation.

By replacing x1 with zero, we have 2(0) + 1x2 = 30. Simplifying further, we get 0 + 1x2 = 30, which simplifies to x2 = 30.

When x1 is set to zero, the equation reduces to a simple linear equation of the form 1x2 = 30. Therefore, the value of x2 in this scenario is 30.

Setting x1 to zero effectively eliminates the contribution of x1 in the equation, allowing us to focus solely on the value of x2. In this case, when x1 is removed from the equation, x2 becomes the sole variable responsible for fulfilling the equation's requirement of equaling 30. Thus, x2 is determined to be 30.

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 If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.

  The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.

 We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.

  Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis  consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.

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The total number of gold and blue squares are 18 and 13 respectively.

Here, we are given that Megan is making a quilt from squares of material.

The quilt has 9 rows and each row has 6 squares.

There are 4 corner squares in the quilt which will be white. Around 1 corner square there will be 3 squares that share a side with the white square.

Thus, there will be a total of 12 gold square around the 4 corner squares.

Further, there are two center squares in the middle row that are white.

Around these 2 center white squares there will be 6 squares that share a side with them. Hence, these 6 square will also be gold.

Therefore, the total number of gold squares will be-

6 + 12

= 18

Now, the white squares = 4 + 6 = 10

and gold squares = 18

and the total number of squares = 9 × 6 = 54

Thus, the number of remaining squares = 54 - 18 - 10

= 26

Out of these remaining 26 squares half will be blue and half pink.

Thus, the number of blue squares will be-

26/2

= 13

Hence, we find that the total number of gold and blue squares are 18 and 13 respectively.

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Answer:

your answer is 256

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

Since you and your friend leave your house at the same time and arrive at the restaurant at the same time, the time it takes you to travel to the restaurant is the same as the time it takes your friend to travel to the restaurant.

Therefore, the value of x, which represents the number of hours since your friend left home, is also the number of hours since you left home.

Since your distance from the restaurant is given by a linear equation, we can represent your distance from the restaurant as y = mx + b, where m is the slope of the line and b is the y-intercept.

Since you are 150 miles from the restaurant when you leave home, this means that your distance from the restaurant at x = 0 is y = 150. Therefore, b = 150.

We can substitute these values into the equation y = mx + b to find the equation that represents your distance from the restaurant:

Since the time it takes you to travel to the restaurant is the same as the time it takes your friend to travel to the restaurant, we can use the equation for your friend's distance from the restaurant, which is given as y = -40x100, to find the value of m.

Substituting this equation into the equation for your distance from the restaurant, we get:

Simplifying this equation, we get:

This is the equation that represents your distance from the restaurant. It shows that as the time (x) increases, your distance from the restaurant decreases at a rate of 40 miles per hour.

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Answer:

a²+7a+10=0

(a+2)(a+5)=0

∴a+2=0

a= -2

a+5=0

a= -5

a²+6a+8=0

(a+2)(a+4)=0

∴a+2=0

a= -2

a+4=0

a= -4

a²+9a+20

(a+4)(a+5)

∴a+4=0

a= -4

a+5=0

a= -5

Step-by-step explanation:

Solution on the Math book

Answer:

No, 5 + 3(1 - x) is NOT  equivalent to 8 - 8x.

Step-by-step explanation:

To see if they are equivalent to each other, we first need to simplify the first expression:

5 + 3(1 - x)

Distribute the 3 into the parenthesis:

5 + 3 -3x

Combine like terms:

8 - 3x

No, 5 + 3(1 - x) is NOT  equivalent to 8 - 8x.

The vector makes an angle of approximately -84.29 degrees with the positive x-axis.

To find the angle that a vector from the origin to the point (1, -10) makes with the positive x-axis, we can use trigonometry.

First, we need to determine the values of the coordinates (x, y). In this case, x = 1 and y = -10.

The angle θ between the vector and the positive x-axis can be found using the Arctan function:

θ = arctan(y / x)

Substituting the values, we have:

θ = arctan((-10) / 1)

Evaluating the arctan function, we find:

θ ≈ -84.29 degrees

Therefore, the vector makes an angle of approximately -84.29 degrees with the positive x-axis.

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Answer:

3.5

Step-by-step explanation:

300÷85=3.529

so it would take him approximately 3.5 more days before he finishes the book

Answer:

Not all the means are equal.

Step-by-step explanation:

In an ANOVA table, a sum of squares for the independent variable divided by its respective degrees of freedom.

So if the omnibus null hypothesis is rejected it means that there is sufficient evidence to conclude that not all the means are equal.

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If the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

ANOVA table gives us the total sum of squares ( TSS ), the residual sum of squares ( RSS ) and the estimated sum of squares ( ESS ).

It establishes the relation that:

ESS + RSS = TSS.

If we reject the omnibus null hypothesis, then it means that:

at least one of the population means is different from at least one other population mean.

Therefore, we get that, if the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

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The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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Answer:

y = 2/3x -6

Step-by-step explanation:

slope intercept form is y = mx + b ( m is slope)

The complete question is:

We have 15 voters and four alternatives, and the individual preference lists are as follows:

Voters 1-3: a d b c

Voters 4-5: b d a c

Voters 6-7: c d a b

Voters 8-9: a d c b

Voters 10-11: b d c a

Voters 12-13: c d b a

Voters 14-15: d b a c

1) The plurality voting procedure? - Voters 1-3: a d b c

2) The Condorcet procedure? - Voters 8-9: a d c b

3) The Hare (instant runoff) system? - Voters 4-5: b d a c

4) The Borda count procedure? - Voters 8-9: a d c b

5) Sequential pairwise voting with agenda bdac? - Voters 8-9: a d c b

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Answer:

b is the answer should be

Step-by-step explanation:

2 is too long fo dat

44 is too long

134 like rlly rlly dawg way too long

4 should be it ight

Angle C is the biggest.

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

The Curved surface area of the frustum is 60π.

In geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.

The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.

The height of the large cone=√\(10^{2}\)-\(8^{2}\)

=√\(100-64\)

=6cm

The height of small cone=6×(1/2)=3cm

(The little cone's height is equal to half that of the giant cone's height.)

The arc length of the small cone=10×1/2=5cm

The curved surface area of the frustum=π×8×10-π×r×5

=80π-5rπ

r=√\(5^{2}\)-\(3^{2}\)

=√25-9

=4cm

Hence, Curved surface area of the frustum is

= 80π-5×4×π

=80π-20π

=60π

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Answer:

Bethan = 34

Jack = 30

Ruben = 33

The solution to the system is x1 = 8, x2 = 1, and x3 = -1.

To solve the systems, we will use the method of elimination. This method involves multiplying one or both equations by a constant in order to eliminate one of the variables.

First, we will eliminate x1 from the first and second equations by multiplying the first equation by -1 and then adding the two equations together:
-1(x1 - 3x2) = -1(5)
-x1 + 3x2 = -5

-x1 + x2 + 5x3 = 2
2x2 + 5x3 = -3
Next, we will eliminate x2 from the second and third equations by multiplying the second equation by -1 and then adding the two equations together:
-1(-x1 + x2 + 5x3) = -1(2)

x1 - x2 - 5x3 = -2
x2 + x3 = 0
x1 - 6x3 = -2

Finally, we will eliminate x3 from the second and third equations by multiplying the third equation by -5 and then adding the two equations together:

-5(x2 + x3) = -5(0)
-5x2 - 5x3 = 0

2x2 + 5x3 = -3
-3x2 = -3
x2 = 1

Now that we know the value of x2, we can substitute it back into the third equation to find the value of x3:
x2 + x3 = 0
1 + x3 = 0
x3 = -1
And finally, we can substitute the values of x2 and x3 back into the first equation to find the value of x1:
x1 - 3x2 = 5
x1 - 3(1) = 5
x1 = 8
So the solution to the system is x1 = 8, x2 = 1, and x3 = -1.

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The value of x is 134.

Based on the diagram, we know that lines l, m, and n are parallel. Therefore, the alternate interior angles formed by transversal line m are congruent to the corresponding alternate interior angles formed by transversal line 11:

m and 11 are alternate interior angles, so they are congruent.

Also, the corresponding angles formed by transversals line n and 11 are congruent to the corresponding corresponding angles formed by transversals line m and 35:

11 and 35 are corresponding angles, so they are congruent.

Therefore, we can set up an equation based on the fact that the sum of the measures of the angles around any point is 360 degrees:

m + x + 35 = 180

Simplifying this equation, we get:

x + m = 145

Since m and 11 are congruent, we can substitute m with 11:

x + 11 = 145

Subtracting 11 from both sides, we get:

x = 134

Therefore, the value of x is 134.

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Answer:

Exact Form: x = 10/7

                                 ______

Decimal Form: x = 1.428571

Mixed Number Form: x = 1 3/7

Hope this helps, have a nice day/night! :D

If this helped please mark this as brainliest!

Answer:

In the picture

Step-by-step explanation:

Good luck!

Answer:

Area- Measurment of the size in the flat surface of a plane (Two Dimensional)

Surface Area- Measurment of the exposed surface of a soilid shape (Three Dimensional)

(Hope that works)

Lets take a look at each of the graphs to identify the correlation.

Graph A shows a decrease in speed per time, this could be our answer.

Graph B shows an increase in speed per time, this is not our answer.

Graph C shows a constant in speed per time, this is not our answer.

Graph D is the same as Graph B but with a different starting point, this is also not our answer.

When we are approaching a stop light, we need to slow down.

This means that the only option is Graph A.

I hope this helps! :)

Answer:

graph a should be correct

Step-by-step explanation:

because the car should be slowing down not accelerating

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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The area of the surface of revolution generated by revolving the curve y = √x, 0 ≤ x ≤ 4, about the x-axis is 2π(4^(3/2) - 1)/3.

To find the area of the surface of revolution, we can use the formula for the surface area of a solid of revolution. When a curve y = f(x), 0 ≤ x ≤ b, is revolved around the x-axis, the surface area is given by:

A = 2π ∫[a,b] f(x) √(1 + (f'(x))^2) dx,

where f'(x) is the derivative of f(x).

In this case, the curve is given by y = √x and we want to revolve it about the x-axis. The limits of integration are a = 0 and b = 4. We need to find f'(x) to substitute it into the surface area formula.

Differentiating y = √x with respect to x, we have:

f'(x) = (1/2)x^(-1/2).

Now, we can substitute f(x) = √x and f'(x) = (1/2)x^(-1/2) into the surface area formula and integrate:

A = 2π ∫[0,4] √x √(1 + (1/2x^(-1/2))^2) dx

 = 2π ∫[0,4] √x √(1 + 1/(4x)) dx.

Simplifying the expression inside the square root, we have:

A = 2π ∫[0,4] √x √((4x + 1)/(4x)) dx

 = 2π ∫[0,4] √((4x^2 + x)/(4x)) dx

 = 2π ∫[0,4] √((4x^2 + x)/(4x)) dx.

To evaluate this integral, we can simplify the expression inside the square root:

A = 2π ∫[0,4] √(x + 1/4) dx

 = 2π ∫[0,4] √(4x + 1)/2 dx

 = π ∫[0,4] √(4x + 1) dx.

Now, we can use a substitution to evaluate the integral. Let u = 4x + 1, then du = 4 dx. When x = 0, u = 1, and when x = 4, u = 17. Substituting these limits and changing the limits of integration, we have:

A = π ∫[1,17] √u (1/4) du

 = (π/4) ∫[1,17] √u du.

Evaluating this integral, we have:

A = (π/4) [2/3 u^(3/2)] | from 1 to 17

 = (π/4) [(2/3)(17^(3/2)) - (2/3)(1^(3/2))]

 = (π/4) [(2/3)(289√17 - 1)].

Simplifying further, we have:

A = 2π(4^(3/2) - 1)/3.

Therefore, the area of the surface of revolution generated by revolving the curve y = √x, 0 ≤ x ≤ 4, about the x-axis is 2π(4^(3/2) - 1)/3.

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Answer:

684 cups of lemonade can be made by the parent council.

Step-by-step explanation:

1. 24 lemons per bag, with 19 bags makes for a total of 456 lemons.

2. To get the gallon amount, take 456 lemons divided by 8, which makes 57 gallons.

3. To get the amount of cups, take the number of gallons (57) and multiply by 12, which equals 684.

Answer:

20c+14

Step-by-step explanation:

To find the perimeter we have to add up all the sides

4c+6c+7+4c+6c+7

Combine light terms

20c+14

Answer:

Well your not given C so we just leave that be and we can just add up all 4 sides since perimeter means outside length total. Now when added up,

6c+7+6c+7+4c+4c= 20c+14

20c+14 is the perimeter

Answer: 180 kilometers

Step-by-step explanation:

Answer:

I think she runs 1 kilometer every 5 minutes

Step-by-step explanation:

Answer:

pi/0.25

Step-by-step explanation:

pi/0.25 = 12.5663