The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube? 6 cubic feet 18 cubic feet 54 cubic feet 72 cubic feet

Answer:

3x, -2x

Step-by-step explanation:

they both have x as a variable

Answer:

3x, -2x

Step-by-step explanation:

Thus, we can find nonzero matrices a, b, and c such that ac = bc and a is not equal to b by using the distributive property of matrix multiplication. One example of such matrices is provided above.

The problem statement requires us to find three matrices - a, b, and c, such that their product ac is equal to bc but a is not equal to b. To solve this problem, we need to use the properties of matrix multiplication. One such property is the distributive property, which states that a(b + c) = ab + ac, where a, b, and c are matrices.

Let's assume that a, b, and c are all 2x2 matrices. One example of such matrices could be:

a = [1 0]
   [0 2]

b = [2 0]
   [0 1]

c = [1 2]
   [3 4]

Using these matrices, we can verify that ac = bc, as follows:

ac = [1 0]  [1 2] = [1 2]
    [0 2]  [3 4]   [6 8]

bc = [2 0]  [1 2] = [2 4]
    [0 1]  [3 4]   [3 4]

As we can see, both products result in the same matrix. However, a and b are not equal, as a(1,1) = 1 and b(1,1) = 2. Therefore, we have found an example of three nonzero matrices such that ac = bc but a is not equal to b.

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If we contrast the different parts, x1 = 3 2 = y1 and x2 = 4 4 = y2 are the results.

To show that preferences represented by min{x₁, x₂} satisfy monotonicity but not strong monotonicity, we need to demonstrate two things:

Preferences satisfy monotonicity: If xᵢ ≥ yᵢ for all i, then x ≽ y, and if xᵢ > yᵢ for all i, then x ≻ y.

Preferences do not satisfy strong monotonicity: There exist x and y such that xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.

Let's address each of these points:

Monotonicity:

Suppose x and y are two bundles such that xᵢ ≥ yᵢ for all i. We need to show that x ≽ y and x ≻ y.

First, note that min{x₁, x₂} represents the minimum value between x₁ and x₂, and the same applies to y₁ and y₂.

Since x₁ ≥ y₁ and x₂ ≥ y₂, we can conclude that min{x₁, x₂} ≥ min{y₁, y₂}.

Therefore, x ≽ y, indicating that if all components of x are greater than or equal to the corresponding components of y, then x is weakly preferred to y.

However, if x₁ > y₁ and x₂ > y₂, then min{x₁, x₂} > min{y₁, y₂}. Hence, x ≻ y, indicating that if all components of x are strictly greater than the corresponding components of y, then x is strictly preferred to y.

Thus, preferences represented by min{x₁, x₂} satisfy monotonicity.

Strong Monotonicity:

To show that preferences represented by min{x₁, x₂} do not satisfy strong monotonicity, we need to provide an example of x and y such that xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.

Consider the following bundles:

x = (3, 4)

y = (2, 4)

In this case, x₁ > y₁ and x₂ = y₂, so x ≻ y.

However,Thus, xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.If we compare the individual components, x₁ = 3 ≥ 2 = y₁ and x₂ = 4 ≥ 4 = y₂.

Therefore, preferences represented by min{x₁, x₂} satisfy monotonicity but not strong monotonicity.

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Answer:

No

Step-by-step explanation:

It is not properly done.

Answer:

32

Step-by-step explanation:

NBC+ABN=ABC

x=9

2(9)+14=32

The 140 towns are named pleasant hill are there in the united states.

What is towns?

Towns and semi-dense areas having a population of at least 5,000 people and grid cells with at least 300 people per km2 density; and. Most rural areas are made up of low-density grid cells.

As given, Midway is the name of 252 towns in the united states pleasant hill occurs 5/9 times.

So,

\(252(\frac{5}{9} ) = 28(5) = 140\)

Therefore, 140 towns are named pleasant hill are there in the united states.

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Answer:

Approximate volume of ice cream = 3.03 inches

Step-by-step explanation:

Given - An empty ice cream cone has a height of 3.02 inches and a radius

of 0.98 inches.

To find - What is the approximate volume of ice cream it will  hold within the cone  ?

Proof -

We know that,

Volume of the cone = \(\frac{1}{3}\pi r^{2}h\)

where

r is the radius of the cone

h is the height of the cone

Here,

Given that,

r = 0.98 inches

h = 3.02 inches

So,

Volume = \(\frac{1}{3}\pi r^{2}h\)

             = \(\frac{1}{3}(3.14) (0.98)^{2}(3.02)\)         ( Consider the value of \(\pi\) = 3.14)

             = 3.0373

∴ we get

Approximate volume of ice cream = 3.03 inches

So,

The correct option is - G. 3 in 3

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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Answer:

28/5

Step-by-step explanation:

\(f(x) = 5x - 3 = 25 \)

\(5x = 25 + 3\)

\(5x = 28\)

\(x = \frac{28}{5} \)

I think this is the answer

The solution to the system of equations is (4, 3). This means that when x = 4 and y = 3, both equations are true.

What is the system of equations?

A system of equations is a set of two or more equations that are solved simultaneously for their unknown variables. The goal of solving a system of equations is to find the values of the unknown variables that make all the equations in the system true at the same time. A solution to a system of equations is an ordered pair of values that satisfies all the equations in the system.

To solve a system of equations, we need to find the values of x and y that make both equations true at the same time.

The first equation is: y = -1/4(3x - 36)

The second equation is: y = -1/2x + 8

To find the solution, we can set the two equations equal to each other and solve for x:

-1/4(3x - 36) = -1/2x + 8

Expanding the first equation:

-3/4x + 9 = -1/2x + 8

Adding 1/2x to both sides:

-1/4x + 9 = 8

Subtracting 9 from both sides:

-1/4x = -1

Multiplying both sides by -4:

x = 4

Now that we know x = 4, we can substitute it into either equation to find y:

y = -1/4(3x - 36)

y = -1/4(3 * 4 - 36)

y = -1/4(-12)

y = 3

Hence, The solution to the system of equations is (4, 3). This means that when x = 4 and y = 3, both equations are true.

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The sum of all repetitions performed multiplied by the resistances used during a strength-training session is the workload.

To find the sum of all repetitions performed multiplied by the resistances used during a strength-training session, you would need to calculate the total workload.

This can be done by multiplying the number of repetitions for each exercise by the resistance used for that exercise, and then adding up the results for all exercises performed during the session.

For example, if you did 10 reps of bench press with 100 pounds, 8 reps of bicep curls with 50 pounds, and 12 reps of squats with 150 pounds, the total workload would be (10 x 100) + (8 x 50) + (12 x 150) = 2,600 pounds. This number represents the total amount of weight lifted during the session and can be used to track progress and adjust future workouts.

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Answer:

43.4 m²

Step-by-step explanation:

side 1= 4+7 m=11m

side 2=3m

height = 6.2 m

we have

the area of the trapezoid = \(\frac{1}{2} height*(side1+side2)\)

=\(\frac{1}{2} *6.2*(11+3)\)

=\(\frac{1}{2} *6.2*14\)

=43.4  m²

Answer:

the second choice

Step-by-step explanation:

3.1 is to the left of 3.4 on the number line, therefore it is smaller

Answer:

Step-by-step explanation:

f/4-5=-9

f-4*5/4=-9

f-20/4=-9

f-20=-9*4

f-20=-36

f=-36+20

f=-16

Answer:

f/4 - 5 = -9

f-20/4=-9

f-20=-9×4

f-20=-36

f=-36+20

f=-16

Answer:

y = 1/2 x+4

Step-by-step explanation:

Slope intercept form is y = mx+b, where m equals the slope and b is the y-intercept.

The slope can be calculated using the formula \(m = \frac{y_{1}-y_{2} }{x_{1}-x_{2} }\).

I'll be plugging in (2,5) and (4,6) to calculate the slope.

m = (6-5)/(4-2) = 1/2

The y-intercept is the y-coordinate of where the line meets the y-axis. In the graph, you can see that the line intersects with the y-axis at (0,4). The y-coordinate of (0,4) is 4, so therefore it is the y-intercept.

Plugin m = 1/2 and b = 4 into the slope-intercept formula (y = mx+b), and you get y = 1/2 x+4

Answer:

x=6

Step-by-step explanation:

We can use ratios to solve

18              4x+6

--------- = -------------

24               40

Using cross products to solve

18*40 = 24 * (4x+6)

720 = 24*(4x+6)

Divide each side by 24

720/24 = 24/24 (4x+6)

30 = 4x+6

Subtract 6 from each side

30-6 = 4x+6-6

24 = 4x

Divide each side by 4

24/4 = 4x/4

6 = x

Given:

A homogeneous system of linear equations Ax= 0 is given.

If the determinant of A is 0 then Ax = 0 has infinitely many solutions.

If the determinant is zero that means the matrix A is not invertible.

That implies there exists a non zero x such that Ax=0 that is,

Then by linearity of A, every scalar multiple of x is mapped to zero by A.

Therefore, the system yields an infinite number of solutions.

Therefore, the statement is a true statement.

Answer:

2/7

Step-by-step explanation:

There are 7 days in a week, and 2 days start with the letter T.

Histogram is a visual representation of data distribution and a stem and leaf plot provide individual values in a set.

Pros of a histogram:

Cons of a histogram:

Pros of a stem-and-leaf plot:

Cons of a stem-and-leaf plot:

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We can see that the marginal product of labor column for each worker can be filled with the calculated values of the marginal product of labor (MPL).

In the given problem, we are provided with the output data of a pizza-making firm. We have to fill in the blanks to complete the marginal product of labor column for each worker.

Let us first define Marginal Product of Labor:

Marginal product of labor (MPL) is the additional output produced by an extra unit of labor added, keeping all other inputs constant. It is calculated as the change in total output divided by the change in labor.

Let us now calculate the marginal product of labor (MPL) of the given workers: We are given the following data:

Labor Output Marginal Product of Labor (Number of Workers) (Pizzas) (Pizzas) \(0 0 - 1 50 50 2 90 40 3 120 30 4 140 20 5 150 10\)

To calculate the marginal product of labor, we need to calculate the additional output produced by an extra unit of labor added. So, we can calculate the marginal product of labor for each worker by subtracting the output of the previous worker from the current worker's output.

Therefore, the marginal product of labor for each worker is as follows:

1st worker = 50 - 0 = 50 pizzas 2nd worker = 90 - 50 = 40 pizzas 3rd worker = 120 - 90 = 30 pizzas 4th worker = 140 - 120 = 20 pizzas 5th worker = 150 - 140 = 10 pizzas

Thus, we can see that the marginal product of labor column for each worker can be filled with the calculated values of the marginal product of labor (MPL).

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The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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Answer:

Given:

radius of bigger half circle[R]=(7+7+14)/2=14cm

radius of smaller half circle [r]=14/2=7cm

Area of shaded region =1/2[πR² -πr²]

=1/2×22/7×[14²-7²]=231cm²

Area of shaded region=231cm²

The value of the expression (7 - 1/4 × ✓16)² + (2 - 5)² is 45.

Based on the information given, the expression will be:

(7 - 1/4 × ✓16)² + (2 - 5)²

= (7 - 1)² + (-3)²

= 6² + 3²

= 36 + 9

= 45

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Answer:

edit the question clearly

Answer:

Domain: {-3, -2, 0, 2}
Range: {5, 4, 9}

This is a function.

The relation is not linear.

Step-by-step explanation:

I didn't know which one you wanted so I put what I knew.

Have a great day thx for your inquiry :)

Range of the value of the game played:To get the range of the value of the game played, we have to find the minimum and maximum possible scores. Minimum score of the game: The minimum score is when both teams play their strongest defense strategy.

For Letran, their strongest defense strategy is the Man-to-man defense and for Mapua, their strongest defense strategy is the Half-court Press defense.Using these defense strategies, Letran can get a score of 45 and Mapua can get a score of 30.Thus, the minimum possible score is 45 + 30 = 75.Maximum score of the game: The maximum score is when both teams play their weakest defense strategy.

For Letran, their weakest defense strategy is the Press defense and for Mapua, their weakest defense strategy is the Man-to-man defense.Using these defense strategies, Letran can get a score of 55 and Mapua can get a score of 40.Thus, the maximum possible score is 55 + 40 = 95.Therefore, the range of the value of the game played is 75 to 95.b) To find the defense strategy in which Letran is weak, we have to see which defense strategy allows Mapua to get the highest score.

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