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For problems 8-11, write Yes or No whether each figure is a polygon. (1 point each)

The  diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.

(a) To compute the total elongation, we can use the formula:

Elongation = (P * L) / (A * E)

where P is the axial tensile load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity for the material.

Given:
P = 30,000 lb
L = 20 ft = 240 in
Diameter of the rod = 1-1/2 in

First, we need to calculate the cross-sectional area:

Area = π * (diameter/2)^2
Area = π * (1.5/2)^2
Area ≈ 1.767 in^2

Next, we need to determine the modulus of elasticity for the material. Assuming it's a standard structural steel, we can use a typical value of 29,000,000 psi.

Now we can plug the values into the formula:

Elongation = (30,000 * 240) / (1.767 * 29,000,000)
Elongation ≈ 0.2358 in

Therefore, the total elongation is approximately 0.2358 inches.

(b) If the total elongation must not exceed 0.10 inches, we need to determine the diameter of the rod that satisfies this requirement.

We can rearrange the formula for elongation to solve for the cross-sectional area:

A = (P * L) / (E * Elongation)

Using the given values:

A = (30,000 * 240) / (29,000,000 * 0.10)
A ≈ 2.069 in^2

To find the corresponding diameter, we use the formula:

Diameter = √(4 * A / π)

Diameter = √(4 * 2.069 / π)
Diameter ≈ 1.441 in

Therefore, the diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.

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Answer:

13 ft

Step-by-step explanation:

The formula to find the length of the diagonal of a rectangle =

Diagonal² = Length² + Width²

Diagonal = √Length² + Width²

Length = 12 ft

Width = 5ft

Diagonal = √12² + 5²

Diagonal = √144 + 25

Diagonal = √169

Diagonal = 13 ft

The length of the diagonal of the rectangle = 13 ft

Step-by-step explanation:

3 Area of lateral = 3 ( bh ) = 12.2 XIO +7.04X12.2 +7.04x 12.2 = 122+85.888+85.888 = 293.776

293.776 approximate to 288

Step-by-step explanation:

[tex] \frac{ - 48 + 6}{ - 7} + ( - 3)( - 4)( - 2) \\ = \frac{ - 42}{ - 7} + 12( - 2) \\ = 6 + ( - 24) \\ = 6 - 24 \\ = - 18[/tex]

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

This should help

Answer:

The car was traveling for 1.5 hours.

Step-by-step explanation:

Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.

Here wee need to find the time if the car has gone 120 kilometers.

That is

            d = 120 km

we need to find t.

            d=80t

           120 = 80 x t

The car was traveling for 1.5 hours.

Answer:

x= 24

Step-by-step explanation:

5x=20*6

x=120/5

x=24

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In a normal distribution, approximately 68% of scores fall between the z-scores of -1.00 and +1.00.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the Empirical Rule (also known as the 68-95-99.7 Rule) applies. According to this rule, approximately 68% of the data falls within one standard deviation from the mean.

Since the z-scores represent the number of standard deviations a particular value is away from the mean, a z-score of -1.00 represents one standard deviation below the mean, and a z-score of +1.00 represents one standard deviation above the mean. Therefore, using the Empirical Rule, we can conclude that approximately 68% of scores fall between these two z-scores (-1.00 and +1.00).

This percentage represents the central portion of the distribution that is within one standard deviation from the mean, providing a useful measure of the spread and concentration of data in a normal distribution.

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The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).

To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y / x)

We know that, the point is (-10, 1), we substitute the values into the formulas:

We get,

r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and

The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.

Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.

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Answer: D

Step-by-step explanation: As we can see, D is the only one that has matching inputs, but those inputs have separate outputs. If they don't have the same output, it is not a function

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Answer:

c I think but I am not sure but I hope you have a good day

Answer:

y=-2+8

Step-by-step explanation:

The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!

Group A parallelogram, Group B Quadrilateral.

Answer: Parallelogram and Quadrilateral.

The  two ways of classifying shapes are: Parallelogram and Quadrilateral.

There are different ways to classify an item.

Quadrilaterals can be known by;

It is a polygon with four sides.

Since rectangle is known to be a parallelogram that has four right angles.

A trapezoid is regarded as a quadrilateral with only one pair of parallel sides.

And Parallelograms are known to be shapes that has four sides with only two pairs of sides that are known to be parallel.

So we conclude that Group A parallelogram, and Group B Quadrilateral.

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Answer:

3n + 2

Step-by-step explanation:

−n+(−4)−(−4n)+6

-n - 4 + 4n + 6

3n + 2

Answer:

[tex]y = 0.25x + 4[/tex]

[tex](x,y) = (2,4.5)[/tex]

Step-by-step explanation:

Given

[tex]x = 2[/tex]

[tex]y = 4.5[/tex]

Required

Make up a linear function

A linear function is represented as:

[tex]y = mx + b[/tex]

Assume [tex]b = 4[/tex]

The equation becomes

[tex]y = mx + 4[/tex]

Substitute [tex]x = 2[/tex] and [tex]y = 4.5[/tex] to solve for m

[tex]4.5 = m*2 + 4[/tex]

[tex]4.5 = 2m + 4\\[/tex]

Solve for m

[tex]2m = 4.5 - 4[/tex]

[tex]2m = 0.5[/tex]

[tex]m = 0.5/2[/tex]

[tex]m = 0.25[/tex]

So, we have:

[tex]m = 0.25[/tex], [tex]b = 4[/tex], [tex]x = 2[/tex] and [tex]y = 4.5[/tex]

[tex]y = mx + b[/tex] becomes

[tex]y = 0.25x + 4[/tex]

[tex](x,y) = (2,4.5)[/tex]

*see attachment for the diagram given

Answer:

Volume of the toy = 68 in.³

Step-by-step explanation:

The equation to find the volume of the toy = volume of the wooden rectangular prism - volume of the triangular prism removed form the center

Volume of the toy = (L*W*H) - (½*bhl)

Where,

L = 8 inches

W = 3 inches

H = 3 inches

b = 1 inch

h = 1 inch

l = 8 inches

Plug in the values into the equation

Volume of the toy = (8*3*3) - (½*1*1*8)

Volume = 72 - 4

Volume of the toy = 68 in.³

Answer:

Seven cups of canned apples are required to make apple pie recipe

Step-by-step explanation:

The weight of one canned apple is 0.45 pounds

Weight of total canned apple required to make the apple pie recipe is 3 pounds.

Total number of cups of canned apples required

[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]

So approximately seven cups of canned apples are required to make apple pie recipe

Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.

Step-by-step explanation:

Answer:

The answer your looking for is, C.

The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.

In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.  

Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).

The mean turns out to be 32.25.Next, we subtract the mean from each data point:

(23 - 32.25) = -9.25

(27 - 32.25) = -5.25

(35 - 32.25) = 2.75

(44 - 32.25) = 11.75

Then, we square each of these differences:

(-9.25)² = 85.56

(-5.25)² = 27.56

(2.75)² = 7.56

(11.75)² = 138.06

Finally, we sum up these squared deviations:

85.56 + 27.56 + 7.56 + 138.06

= 212.00

Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).

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Answer:

Below :)

Step-by-step explanation:

Least/Minimum: 0

Greatest/Maximum: 6

Median: 2

Lower Quartile Range: 1

Upper Quartile Range: 3

Find median:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Find Lower Quartile:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2

Find Upper Quartile:

2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Answer:

A or D

Step-by-step explanation:

it's simple it's really easy so the answer is 2.0 1682

Answer:

bestie thats hard

Step-by-step explanation:

Answer:

D. x=-4.5

Step-by-step explanation:

Since they are both vertical angles, m∠BOD must also be equal to 30 degrees, and if you input -4.5 as x, (2 x -4.5x) + 39, that is rewritten as -9 and 39. 39 - 9 is 30 degrees.

a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

Given that,

The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that

[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]

Where m and n are real numbers.

We know that,

a. We have to prove matrix A is invertible.

For A to be invertible.

|A| ≠ 0

|A| is the determinant of the matrix A.

|A| = 2(-m) -1(0) + 0(0) = -m

Here, m is the real number.

So, |A| = -m ≠ 0

Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. We have to prove the system AX = B has no solution.

When Rank[A|B] > Rank[A]

m = 0 and n ≠ 0 has a real number

Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. We have to prove the system AX = B has an infinite number of solutions.

When m = n = 0, and Rank[A] < 3

Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. We have to prove columns of the augmented matrix (AB) are linearly independent.

When m ≠ 0 and m∈R and n= 0

Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. We have to prove the system AX = 0 has a unique solution.

When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

The equation are 2x + y = 0, -y + 3z = 0 and mz = 0

m ≠ 0 should be any real number except zero.

Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. We have to prove at least one eigenvalue of the matrix A is zero.

When λ = 2, 1, m

m = 0 then eigen value is zero

Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. We have to prove columns of the matrix A form a basis in R³.

When m ≠ 0

Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

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Answer:

x = 18

Step-by-step explanation:

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

So, 20/8 = (4x + 3)/30

8(4x + 3) = 20(30)

32x + 24 = 600

32x = 576

x = 18

Answer:

16 + 5 =21 21 is your answer

Step-by-step explanation: