Write the answer to Kiran's question using mathematical notation. (the money kiran)

Matrices are widely used in various fields, including solving word problems in mathematics because they provide a convenient way to organize and manipulate data, making complex problem-solving more manageable.

In word problem solutions, matrices serve as valuable tools for organizing and manipulating data, simplifying complex problem-solving endeavors. For instance, when faced with a system of linear equations, matrices provide a structured representation that enables efficient computation.

Consider a word problem involving multiple variables and equations, such as determining quantities and prices of diverse items. By formulating the problem as a matrix equation and employing matrix operations like Gaussian elimination or matrix inverses, we can decipher the unknown variables and unlock solutions.

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The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

Here, we have,

given that,

We have to find which two statements about angles on a transversal crossing parallel lines contradict each other.

we know that,

If a transversal intersects or crosses parallel lines, adjacent angles are supplementary.

Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines.

now, we have,

I. ∠1 and ∠2 are same-side interior angles it can be possible.

Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.

Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary. If , then m ∠ 1 + m ∠ 2 = 180 ∘ .

so, if number-l is true, so, we get,

II. m∠1 = m∠2 may be true,

III. m∠1 + m∠2 = 90, never can be true.

so, we get,

if, l. holds then lll. contradicts that.

Hence, The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

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Answer:

Step-by-step explanation:

1. The figure  is a rectangular prism.

Formula: V = lwh

Given: 13 ft x 7ft x 9 ft

Substitute the values to the formula and solve.

V = lwh

V = 13ft(7ft)(9ft)

V = 819 ft³

2. The given figure is a triangular prism. Notice that the base forms a right triangle.

Formula: V = 1/2bhl

Given:

b = 9m

h = 12m

l = 16 m

Substitute the given values to the formula and solve.

V = 1/2(9m)(12m)(16m)

V = 864 m³

3. This is a cylinder

Formula: V = πr²h

Given:

r = 11 yd

h = 26 yd

Solve:

V = π (11yd)²(26yd)

V = 9883.45 yd³

4. The figure is a rectangular prism.

Formula: V = lwh

Given dimensions: 9m x 9m x 13.5m

Solve:

V = 9m(9m)(13.5m)

V = 1093.5 m³

5. The figure is a triangular prism

Formula: V = 1/2bhl

Given:

b = 15yd

h = 13 yd

l = 24 yd

Solve:

V = 1/2 (15yd)(13yd)(24yd)

V = 2340 yd³

In a right angled triangle, the base is 17 and the angle between base and hypotenuse is 29°, then the hypotenuse x is equal to 19.4 after rounding off to the nearest tenth.

From the given figure, we have to find the missing length x

In the figure we can see that,

For the angle, θ = 29°

Base = 17

and, hypotenuse = x

We know that by the cosine of the angle in the given triangle can be written as,

cos θ = [tex]\frac{base}{hypotenuse}[/tex]

⇒ cos 29° = [tex]\frac{17}{x}[/tex]

⇒ x = [tex]\frac{17}{cos \ 29\textdegree}[/tex]

⇒ x = 19.437

Rounding to the nearest tenth, x = 19.4

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Rational square roots: √225, √81, √576, √36, √441, √324

Irrational square roots: √300, √120, √12, √50, √200

Let's determine whether each square root is rational or irrational:

√225 = 15. This is a rational number since it can be expressed as a fraction of two integers (15 = 15/1).

√300 ≈ 17.32050808. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√120 ≈ 10.95445115. This is also an irrational number for the same reasons as above.

√81 = 9. This is a rational number since it can be expressed as a fraction of two integers (9 = 9/1).

√576 = 24. This is a rational number since it can be expressed as a fraction of two integers (24 = 24/1).

√36 = 6. This is a rational number since it can be expressed as a fraction of two integers (6 = 6/1).

√12 ≈ 3.464101615. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√441 = 21. This is a rational number since it can be expressed as a fraction of two integers (21 = 21/1).

√50 ≈ 7.071067812. This is an irrational number for the same reasons as above.

√324 = 18. This is a rational number since it can be expressed as a fraction of two integers (18 = 18/1).

√200 ≈ 14.14213562. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

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Answer:

2816 ft^3

Step-by-step explanation:

Solution Given:

Radius(r)=8ft.

Height(h)=14 ft.

Now

To find the volume of a cylinder, you can use the formula:

[tex]\boxed{\bold{Volume = \pi * r^2 * h}}[/tex]

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

[tex]Volume = \pi * r^2 * h\\Volume=3.14*8^2*14\\Volume=2816 ft^3[/tex]

The equation subject to p is P = (n - 7/2)/q.

To solve for p, we need to isolate it on one side of the equation.

Starting with:

Pq+7/2=n

Subtract 7/2 from both sides:

Pq = n - 7/2

Divide both sides by q:

P = (n - 7/2) / q

Therefore, the solution for p is:

P = (n - 7/2) / q

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Answer:

The list of rational numbers below are ordered from greatest to least.

15, 6.7, , 100%, -55%,

To determine which of the following numbers could NOT be the missing value in the list above, we need to determine the correct order of the numbers in the list.

First, we can convert the percentages to decimals:

100% = 1

-55% = -0.55

Now we can order the numbers from greatest to least:

15, 6.7, 1, -0.55, x

We know that x is a rational number, so it can be expressed as a fraction. We can eliminate answer choices C and D because they are not rational numbers.

Next, we can compare x to the other numbers in the list. We know that x must be less than 6.7, so we can eliminate answer choice A.

That leaves us with answer choice B, -2.5. This number could be the missing value in the list, so the answer is B.

Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4

The value of inverse of function is,

⇒ f ⁻¹ (x) = x² / 36

We have to given that;

Function is,

⇒ f (x) = 6√x

Now, We can find the inverse of the function is,

⇒ f (x) = 6√x

⇒ y = 6√x

Solve for x;

⇒ y/6 = √x

⇒ (y/6)² = x

⇒ x = y² / 36

⇒ f ⁻¹ (x) = x² / 36

Thus, The value of inverse of function is,

⇒ f ⁻¹ (x) = x² / 36

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Answer:

Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.

Step-by-step explanation:

To find out if the fractions are proportional, we need to check if their cross-products are equal.Cross-product of 3/5 and 9/15:

3/5 × 9/15 = (3 × 9)/(5 × 15) = 27/75We can simplify 27/75 by dividing both the numerator and denominator by their greatest common factor, which is 3:

27/75 = (3 × 9)/(3 × 25) = 9/25Therefore, the cross-product of 3/5 and 9/15 is 9/25.Since the cross-products are not equal to each other, the fractions are not proportional.

The nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².

To find the surface area (SA) of a cylinder, we need to calculate the sum of the lateral surface area (arl) and the base area (B).

The formula for the lateral surface area of a cylinder is given by:

arl = 2πrh,

where r is the radius and h is the height of the cylinder.

The formula for the base area of a cylinder is given by:

B = πr^2.

Let's calculate the values:

Given:

Height (h) = 5 cm

Radius (r) = 4 cm

First, we calculate the lateral surface area (arl):

arl = 2πrh

= 2 * 3.14159 * 4 cm * 5 cm

≈ 125.66368 cm²

Next, we calculate the base area (B):

B = πr^2

= 3.14159 * (4 cm)^2

≈ 50.26544 cm²

Finally, we find the surface area (SA):

SA = arl + B

≈ 125.66368 cm² + 50.26544 cm²

≈ 175.92912 cm²

Rounded to the nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².

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The lower quartile of the given data set is 63.

To find the lower quartile (Q1), we need to determine the value that divides the data set into the lower 25% of the values.

First, we need to sort the data set in ascending order: 61, 61, 62, 64, 66, 69, 69, 70, 72, 73, 74, 78.

Next, we calculate the position of the lower quartile using the formula: (n+1)/4, where n is the number of data points. In this case, we have 12 data points, so (12+1)/4 = 13/4 = 3.25.

Since 3.25 is not a whole number, we can find the lower quartile by taking the average of the data points at positions 3 and 4.

The data point at position 3 is 62, and the data point at position 4 is 64.

Therefore, the lower quartile (Q1) is the average of 62 and 64:

(Q1) = (62 + 64)/2 = 126/2 = 63.

Hence, the lower quartile of the given data set is 63.

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i) The capacities of different vessels which completely fill P vessel with exact number of fillings are:

(ii) The capacities of different vessels which completely fill Q vessel with exact number of fillings are:

One vessel of 18 I

Two vessels of 9 I each

Three vessels of 6 I each

Six vessels of 3 I each

Nine vessels of 2 I each

Eighteen vessels of 1 I each

(iii) The common capacities of vessels which completely fill P as well as Q vessels with exact number of fillings are:

Two vessels of 6 I each

Three vessels of 4 I each

Six vessels of 2 I each

Twelve vessels of 1 I each

(iv) The greatest capacity of vessel that completely fills P as well as Q vessels with exact number of fillings is 6 I.

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The linear function that is modeled by the given table is:

y = -4x + 7

A general linear function is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If we know two points on the line (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points on the table:

(-11, 51) and (-5.5, 29)

Then the slope is:

a = (29 - 51)/(-5.5 + 11)

a = -4

Then the linear function is:

y = -4x + b

We know that when x = -5.5, the value of y is 29

29 = -4*-5.5 + b

29 = 22 = b

29 - 22 = b

7 = b

The linear function is:

y = -4x + 7

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Answer:

D

Step-by-step explanation:

The amount that Marketing Manager earn more than a Financial Analyst over 10 years is $388,000. The Option H.

To get how much more a Marketing Manager will earn than a Financial Analyst, we have to calculate the difference in their median annual salaries and multiply by 10.

The difference in median annual salaries is:

= $115,750 - $76,950

= $38,800

The amount earned more by a Marketing Manager over 10 years is:

= $38,800 x 10

= $388,000.

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Answer: {m∠HLI = m∠ILM}

Examining the figure the option that must be true is

D. m< HLI = m< ILM

The knowledge of angle on a straight line which is 180 degrees is used here,

Using the given angles and the concept of adjacent angles we have that

angle GLH = 150 - 60 = 60

Using angles on a straight line being 180 degrees we have that

angle ILJ = 180 - 60 - 60 - 30 - 15 = 15 degrees

Using adjacent angles

angle ILM = 15 + 15 = 30 degrees

hence we can say that m< HLI = m< ILM

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The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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The profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.

The profit generated by the company manufacturing lawn mowers is the difference between the revenue and the cost, so we can subtract the cost polynomial C= 38x+300 from the revenue polynomial R= -0.5x²+91x to obtain the profit polynomial:

P(x) = R(x) - C(x)

P(x) = (-0.5x²+91x) - (38x+300)

P(x) = -0.5x² + 53x - 300

Therefore, the profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.

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The table that represents a linear function is the second table.

A linear function is written as:

y = ax + b

We can see that for each increase of 1 unit in the value of x, the value of y increases by a units.

Then we need to identify the table where the increases in the y-value are constant.

With that in mind we can discard options 1, 3 and 4.

Wher particularly options 1 and 4 show that sometimes the y-value increases and sometimes decreases, that is why we discard these.

Then the remainign option must be the correct one, which is the second option.

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The equivalent equations that have the value x = 3 are:

2 + x = 5, x + 1 = 4, and (-5) + x = -2.

Equations are considered equivalent if they have the same solution(s). In other words, if you solve each equation for the variable, you should end up with the same value(s).

Let's look at the options given:

2 + x = 5: This equation can be solved by subtracting 2 from both sides, leaving x = 3.

x + 1 = 4: This equation can be solved by subtracting 1 from both sides, leaving x = 3.

9 + x = 6: This equation can be solved by subtracting 9 from both sides, leaving x = -3.

x + (-4) = 7: This equation can be solved by adding 4 to both sides, leaving x = 11.

-5 + x = -2: This equation can be solved by adding 5 to both sides, leaving x = 3.

So, we can see that the first, second, and fifth equations are equivalent since they all simplify to x = 3. The third and fourth equations are not equivalent to any of the other equations, since they have different solutions.

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Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³

We know that the relation between one yard and one meter is:

1yd = 0.91m

Then the relation between one cubic yard and one cubic meter is:

(1yd)³ = (0.91m)³

1 yd³ = 0.83 m³

Now we can perform a change of units between the volume in yards and the volume in meters, we will get:

2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³

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Answer:

To many questions, and too many numbers

Step-by-step explanation:

Answer: 48 cm square

Step-by-step explanation:

We can first divide this shape into two rectangles, cutting it off at the 6cm line. The rectangle below has an area of 20cm square, noted by the 10 cm base and 2 cm base thickness. For the other rectangle, we can see that the height is 9cm, but since we already have done the bottom rectangle, we can subtract 2cm away from the 9cm ad get 7 cm. So the height for the top rectangle is 7cm. Then doing the same thing for the width with 10cm and 6cm gives us 4 cm. This then gives us a total of 28cm for the top and 20cm for the bottom. This combines to get us 48 cm. THE FIGURE IS NOT TO SCALE.

The zero of f is x = -2. C.

The equation of the linear function can be found using the point-slope formula:

y - y1 = m(x - x1)

m is the slope and (x1, y1) is a point on the line.

Plugging in the given values, we get:

y - 4 = 4(x + 1)

Expanding and simplifying, we get:

y = 4x + 8

The zero of f (where f(x) = y) set y = 0 and solve for x:

0 = 4x + 8

4x = -8

x = -2

The point-slope formula may be used to determine the equation of the linear function:

y - y1 = m(x - x1)

(X1, Y1) is a point on the line, and m is the slope.

With the above variables obtain:

y - 4 = 4(x + 1)

By enlarging and condensing, we obtain:

y = 4x + 8

y = 0, you may solve for x using the zero of f (where f(x) = y):

0 = 4x + 8 4x

= -8 x

= -2

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The correct option that shows the associative property is D:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

The associative property of addition says that we can perform sums in any order we want:

A + (B + C) = (A + B) + C

The option that shows this property is the one at D, where we have 3 vectors and we can select any order in which we add them, such that the sum is written as:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

That expression shows the associative property of the addition with matrices.

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The best equation that describes the lined graph is: C. y= -3x - 3

To determine the best description for the lined graph, we have to insert several values for x and see what that gives us as the value of y. After doing this, we will crosscheck against the values in the graph. First, at x = 0, the value of y = -3.

On the lined graph, we see that the values correspond. Also, at x = 1, the value of y becomes -6. On the lined graph, this also corresponds so, the selected equation matches the description of the lined graph.

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