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If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.

The volume of the cone can be described as the measure of a 3-D space occupied by matter.

The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,

v = πr²h / 3

As the radius of the cone = 7 inches

Height of the cone = 28 inches

v = π(7)²28 / 3

v = (π)(49)(28) / 3

v = (π)(1372) / 3

As π = 3.14

v = (3.14)(1372) / 3

v = 4308.08 / 3

v = 1436.02 ≈ 1436 cubic inches

Hence, 1436 cubic inches of sand is calculated to fit inside the cone.

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Answer:

A. Slope = 4 and y-intercept  = 3

Answer:

slope ab- 5

slope dc- -1/5

slope bc- 2/3

slope ad- 2/3

last one is- only one pair of opposite sides is parallel

Step-by-step explanation:

Answer:

5

-1/5

2/3

2/3

only one pair of opposite sides is parallel

Next Question

bisects each other

(2,2)

have the same mid point

Last Question

4/3

4/3

5

5

The maximum sum of the products taken two at a time is 180, and this can be achieved by choosing 60, 60, and 60 as the three numbers.

In order to write the number 180 as a sum of three numbers so that the sum of the products taken two at a time is a maximum, one way to do it is to use the formula:

\((x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz)\)

Let the three numbers be x, y, and z.

Then the product of the numbers taken two at a time is: \(xy + xz + yz\)

If we want to maximize the sum of the products taken two at a time, we need to maximize \(xy + xz + yz\).

In the formula: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz)\)

We can see that the first three terms on the right-hand side are fixed since they depend on x, y, and z. Therefore, to maximize the sum of the products taken two at a time, we need to maximize 2(xy + xz + yz). Since we have the number 180, we can let: \(x + y + z = 180\)

Then, we need to maximize: 2(xy + xz + yz) Using calculus, we can find that the maximum value of 2(xy + xz + yz) is attained when: \(x = y = z = 60\)

Therefore, the three numbers that can be used to write the number 180 as a sum of three numbers so that the sum of the products taken two at a time is a maximum are: 60, 60, 60.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

The other base of the trapezoid is 8 units long.

Let's denote the other base of the trapezoid as 'x'. The formula for calculating the area of a trapezoid is given by A = (1/2)(b1 + b2)h, where b1 and b2 represent the lengths of the bases and 'h' represents the height. We are given that the length of one base (b1) is 10 units, the height (h) is 4 units, and the area (A) is 36 square units.

Using the formula for the area, we can plug in the given values: 36 = (1/2)(10 + x)(4). Simplifying the equation, we get 36 = (5 + 0.5x)(4). Further simplification yields 36 = 20 + 2x. By subtracting 20 from both sides of the equation, we obtain 16 = 2x. Dividing both sides by 2 gives us x = 8.

Therefore, the other base of the trapezoid is 8 units long.

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Answer:

The choice B.

\(x > 4 \\ x < - 1\)

I hope I helped you^_^

In Matlab, you can find the inverse of a matrix using the "inv" function. This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.

Suppose you have a matrix "A", and you want to find its inverse. You can do this by typing:

B = inv(A);

This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.

Note that calculating the inverse of a matrix can be computationally expensive and should be avoided if possible. In some cases, it may be more efficient to use other methods, such as solving a system of linear equations using the backslash operator.

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Answer:

DUNNN DUNNNNNN DUNNNNNNNN

Step-by-step explanation:

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

The distance covered is 36 km and the original rate is 4 km/hr

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

Let speed be y and distance be x

The equation of time is

time = x/y

So, we have the following equations

x/(y + 1/2) = x/y - 1

x/(y - 1) = x/y + 3

So, we have

x/y - x/(y + 1/2) = 1

x/(y - 1) - x/y = 3

When solved graphically, we have

x = 36 and y = 4

This means that

The distance covered is 36 km and the speed is 4 km/hr

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Answer:

t=11/6

u=1/9

Step-by-step explanation:

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

Let's denote the amount of money Blake invests at 4% interest as "x" (in dollars) and the amount he invests at 5% interest as "11000 - x" (since the total investment is $11,000).

To earn interest, we can use the formula: Interest = Principal × Rate × Time

For the 4% interest account, the interest earned is:

0.04x × 1 (1 year) = 0.04x

For the 5% interest account, the interest earned is:

0.05(11000 - x) × 1 (1 year) = 550 - 0.05x

According to the problem, the total interest earned is $490. Therefore, we can set up the equation:

0.04x + (550 - 0.05x) = 490

Simplifying the equation:

0.04x + 550 - 0.05x = 490

-0.01x + 550 = 490

-0.01x = -60

x = 6000

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

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Answer:

Step-by-step explanation:

Comment

The surface area for a sphere is 4 pi * r^2

Givens

Surface Area X = 1808.64

Surface Area T = 452.16

Solution

Sphere X

Surface Area = 4 pi r^2

Surface Area X = 4 * 3.14

1808.64 = 12.56 * r^2                          Divide both sides by 12.56

1808.64/12.56 = 12.56 r^2/12.56

r^2 = 144                                              Take the square root of both sides

√^2  = √144

r = 12

Sphere T

Surface Area = 4 pi r^2

452.16  = 12.56 r^2                              Divide by 12.56

452.16 / 12.56 = 12.56 r^2/12.56

r^2 = 36                                                Take √ of both sides

√r^2 = √36

r = 6

Conclusion

radius x: radius T :: 12/6

radius x: radius T :: 2/1    

The volume of the solid B is 22,680/3 cubic units.

The base of the solid is the circle x^2 + y^2 = 361, which has radius 19. The equilateral triangles are perpendicular to the x-axis, and their height is equal to the radius of the circle. The area of an equilateral triangle is sqrt(3)/4 * s^2, where s is the side length. The side length of the equilateral triangle is equal to the radius of the circle, so the area of each triangle is sqrt(3)/4 * 19^2 = 361 * sqrt(3)/4. The volume of the solid is the area of each triangle multiplied by the height of the triangle, which is 19 * 361 * sqrt(3)/4 = 22,680/3 cubic units.

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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By the symmetric property of congruence is  ∠FSJ ≅∠UPR.

It is required to find the solution.

Symmetry is defined as a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half. A 2D shape is symmetrical if a line can be drawn through it and either side is a reflection of the other.

Given:

The symmetric property is if y = x then x = y. The order of what is on the left or right side of the equation does not matter. It's like saying 2+3 = 5 is the same as 5 = 2+3.

According to given question we have,

This idea can be extended to congruences because congruent angles have the same measure.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

So, ∠UPR ≅∠FSJ, then ∠FSJ ≅∠UPR.

Therefore, by the symmetric property of congruence is  ∠FSJ ≅∠UPR.

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Answer:

I think the IQR is 100

Step-by-step explanation:

You would have to find the first and third quartiles first. After that you would subtract the third quartile by the first to get the IQR

The magnitude of the vector will be 6.7. The correct option is A.

A two-dimensional object with both magnitude and direction is a vector. A directed line segment can be used to graphically represent a vector.

Given that the vector is 3i + 6j. The magnitude of the vector is calculated as:-

V = √ ( a² + b² )

V = √ ( 3² + 6² )

V = √ ( 9 + 36 )

V = √45

V = 6.7

The value of the magnitude of the vector will be equal to 6.7. Option A is correct.

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Answer:

6.7

Step-by-step explanation:

Use the origin as the initial point. Then, <3, 6>

is the terminal point.

To find the magnitude, use the Distance Formula.

|<3, 6>|=(3−0)2+(6−0)2−−−−−−−−−−−−−−−√

=9+36−−−−−√

=45−−√

≈6.7

There are different ways to estimate a variable. The sample mean is a point estimate of the population mean for the variable of interest.

A point estimate is known to be the value of a sample statistic that is often applied as one estimate of a specific population parameter.

The sample mean is defined simply as a form of average value seen in a sample. A sample is known to be the little portion of a whole.

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\(The \: \: \: \: approximate \\ value \: \: \: \: for \: \: \: \: 683 \\ divided \: \: \: \: by \: \: \: \: 19 \\ is \: \: \: \: option \: \: \: \: D. 36

\)

Answer:

its 36

Step-by-step explanation:

if u divide 683 by 19 uu would get a decimal so u round it and it gives u 36

To know the minimum rotation we have to do to map the figure onto itself, we just divide 360° by the total number of sides

So, every rotation that can be divide by 40 would be the answer, let's divide

Answer:

2(4)-3+5

Step-by-step explanation:

8-3+5

13-3

10

Answer:

i would say a

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(4) = -1

g(4) = -2

(f + g)(4) = f(4) + g(4) = -3

Hope that helps!

Answer:f(4) = -1g(4) = -2(f + g)(4) = f(4) + g(4) = -3

Step-by-step explanation:

The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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