Elementary row operations on an augmented matrix never change the solution set of the associated linear system.

The minimum length of the other side is 3 cm.

Given that the area of the rectangle is 40 cm², and one side of the rectangle is exactly 10 cm, we can find the maximum and minimum lengths of the other side by dividing the area by the known side length.

Let's denote the length of the other side as x cm. Since the area of a rectangle is the product of its length and width, we have the equation:

10 cm \(\times\) x cm = 40 cm²

To find the maximum length, we assume that x is the largest possible value. Therefore, rounding up the result of the division:

x = 40 cm² / 10 cm

x = 4 cm

So, the maximum length of the other side is 4 cm.

For the minimum length, we assume x is the smallest possible value. Rounding down the result of the division:

x = 39 cm² / 10 cm

x = 3.9 cm

Since the length cannot be a decimal value, we round down to the nearest whole number.

Hence, the minimum length of the other side is 3 cm.

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In the short run, a decrease in market power (or monopolization) will decrease the price level. Hence option B is correct.

The ability of a corporation or group of enterprises to affect the price or quantity of goods or services in a market is referred to as market power. A company with market power has the ability to raise prices above the level of the market, which reduces consumer surplus and may result in inefficiencies. Market dominance can develop as a result of things like entry hurdles, brand awareness, or control over vital resources. In order to encourage competition and safeguard consumer welfare, governments may restrict or dissolve businesses that hold a large amount of market power. Market structure and performance are significantly impacted by market power, a major notion in industrial organisation.

This is because when a firm has market power, it can charge a higher price for its output due to its ability to restrict output and control the market. When this market power decreases, the firm loses the ability to control the price and must lower it to remain competitive. This decrease in price may also lead to an increase in output as the firm may seek to sell more units to make up for the lost revenue from lower prices.

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Answer:

90% sure it's the 4/5 x 4/5 answer. Might be wrong though.

Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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The rational roots of the given polynomial f(x)= 20x4 + x3 + 8x2 + x - 12 are x = -4/5 and x = 3/4.

All possible rational roots of f(x) are in the form p/q where p is a factor of constant term and q is the coefficient of leading term. Here, p= -12 and q= 20

Factors of -12= -/+(1,2,3,4,6,12)

Factors of 20= -/+(1,2,4,5,10,20)

So the rational roots = -/+ (1, 2, 3, 4, 6, 12)/ (1, 2, 4, 5, 10, 20)

Solving for x when f(x) = 0,

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

Equating all factors to zero, we get

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x = i, x = -i

Hence, the rational roots are x = 3/4, x = -4/5.

The given question is incomplete, the complete question is

What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?

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The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

20

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

7 x 7 = 49

7 x 10 = 70

check

49/70

49 ÷ 7 = 7

70 ÷ 7 = 10

7/10

49/70 = 7/10

The decrease in the number of pirates in the world correlates with an increase in mean global temperature is an example of a spurious correlation.

While there might be a statistical relationship between these two variables, it is not a causative one, and the correlation is likely coincidental.This is the importance of distinguishing between correlation and causation. In this case, the decrease in the number of pirates and the increase in mean global temperature are unrelated factors that happen to show a correlation when observed over time.

This is often used humorously to demonstrate the fallacy of assuming causation based solely on a correlation. It underscores the need for careful analysis and consideration of other relevant factors before making conclusions about causal relationships. In reality, factors such as greenhouse gas emissions, deforestation, and industrialization have a more significant impact on global temperature trends than the number of pirates in the world.

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The matchup are:

Individuals who possess their own piece of land and cultivate their own crops are known as farmers.

In essence,  hunter-gatherers primarily hunt for their sustenance. They possess arms and venture into the woods or fields to hunt and procure sustenance. They consume the fruits of their own labor by relying on their ability to obtain food.

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Answer:

A' (9, - 1 )

Step-by-step explanation:

Using the translation rule

(x, y ) → (x + 6, y - 3 ) , then

A (3, 2 ) → A' (3 + 6, 2 - 3 ) → A' (9, - 1 )

Percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

As given in the question,

Money spent on

Each equipment = $36

Fees = $158

Transportation = $59

Total money spent = $( 36 + 158 + 59)

                             = $253

Percent cost of the total spent on

Each equipment = (36/253) × 100

                          = 14.23%

Fees = (36/253) × 100

        = 62.45%

Transportation =(36/253) × 100

                       = 23.32%

Therefore, percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

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Answer:

yes

Step-by-step explanation:

any positive number is greater than a negative

Answer:

No Mason is not correct you would use fractions and find a common denominator such as 12 and 2/3 would be 8/12 and 3/4 would be 9/12 therefore the two ratios are not equivelent

No, the statement is not correct.

Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b

The example given here is not relevant.

This is because if 2:3 is added by 1/1

gives 3/4 or 3:4

but  3:4 cannot be more simplified.

So, let us make the equivalent denominator for both

2/3*4*4= 8/12

3/4*3/3=9/12

So, 2:3 ≠3:4

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The ROC of the volume of a cube with respect to the length of its side is s > 0. The given rate of change of volume with respect to side length does not affect the calculation of ROC.

The volume of cube is given by V = s^3, where s is the length of its side.

Taking the derivative of V with respect to s, we get:

dV/ds = 3s^2

The rate of change of volume with respect to the length of the side s is given as:

dV/ds = 8

Substituting the value of dV/ds and solving for s, we get:

8 = 3s^2

s^2 = 8/3

s = ±√(8/3)

Since the length of side of a cube cannot be negative, we take the positive root:

s = √(8/3)

The radius of convergence (ROC) of the volume is s > 0, which means the series expansion of the volume of the cube in terms of the length of its side converges for values of s greater than zero.

Therefore, the ROC is s > 0.

The rate of change of volume does not affect the change in the calculation of ROC.

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Answer:

108.00

Step-by-step explanation:

just have to multiply 4.50 x 24

Answer:

y=-2x+5

Step-by-step explanation:

First, find the slope:

m=(y2-y1)/(x2-x1)  ==> slope formula where m is the slope

(–1, 7), (1, 3)  ==> (x1=-1, y1=7), (x2=1, y2=3)

m=(3 - 7)/(1 - (-1)) ==> plugin y2=3, y1=7, x2=1, and x1=-1 into the slope formula

m=(-4)/(1 + 1)  ==> simplify

m=(-4)/2

m=-2  ==> the slope is -2

y=mx+b  ==> slope-intercept equation

3=(-2)(1)+b  ==> plugin the slope(m=-2) and point B(1, 3)  ==> (x=1, y=3)

3=-2+b  ==> solve for b

3+2=-2+2+b  ==> add 2 on both sides to isolate b

b=5  ==> simplify

y=-2x+5  ==> plugin the slope and b=5 into the equation

Answer:7200 for the first question

Step-by-step explanation: 1000

 70

Take the last digit of 70 and multiply it by all the numbers in 1000 once you got that answer take the 7 in 70 and multiply it by all the digits in 1000 as well then once you got that answer add both of your answers together and that's your answer

Answer:

Step-by-step explanation:

The most likely quantity is centimetres.

The second option can be inches.

Hope this helps

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x^3 - a^3

The above expression represent differnt of 2 cubes

This can be re- written as

(x - a)^3

(x - a) ( x ^2 + ax + a^2)

expand the bracket

x * x^2 + ax*x + x *a^2 - a * x^2 - a * ax - a * a^2

= x^3 + ax^2 + a^2x - ax^2 - a^2x - a^3

collecting the like terms

= x^3 + ax^2 - ax^2 + a^2x -a^2x - a^3

ax^2 - ax^2 = 0

a^2x - a^2x = 0

Therefore

= x^3 + 0 + 0 - a^3

= x^3 - a^3

Answer:

275.1 I'm so sorry if it is wrong dont come at me please

answer is 11

Using pythagorean theorem

{a}^{2} + {b}^{2} = {c}^{2}

c being the hypotenuse.

Plug in 60 and 61, so 60^2 + b^2 = 61^2

then square it, 60^2 = 3,600. 61^2 = 3,721.

plug those numbers in 3,600 + b^2 =3,721

to find b^2 subtract 3600 from 3721, 3,721 - 3600 = 121

then find the square root of 121, which is 11.

Answer:

20 episodes

Step-by-step explanation:

Answer:

1 ft / 0.3048 m

Step-by-step explanation:

Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well. Therefore, the correct answers are options A, B and D.

For each participant in many research, we measure more than one variable. For instance, we track rainfall and plant growth, the quantity of eggs and nesting environment, the number of young, and soil erosion and water volume. Instead of analysing each variable independently (univariate data), we collect pairs of data and try to come up with ways to characterize bivariate data, which involves measuring two variables on each individual in our sample. We start by looking for a correlation between these two variables using the data at hand.

Numerous different kinds of associations between two variables can be found using a scatterplot.

Therefore, the correct answers are options A, B and D.

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Answer: 900.24

Step-by-step explanation:

Perimeter=L•W•H

Answer:

11 + 4

Step-by-step explanation:

11 - (-4) = 11 + 4

Answer:

11 + 4

Step-by-step explanation:

11 - (-4)

11 + 4  (Since - - becomes +)

Ans 15

Answer:

2

Step-by-step explanation:

Answer:

\(2\)

Step-by-step explanation:

\(8+14-5-7+3-7-4\)

We'll Follow the PEMDAS order of operations:-

Add and subtract:-

8+14=22

\(22-5-7+3-7-4\)

22-5=17

\(17-7+3-7-4\)

17-7=10

\(10+3-7-4\)

10+3=13

\(13-7-4\)

13-7=6

\(6-4\)

\(2\)

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