Don Luis, el carpintero, desea construir un mueble para estantería, el cual es in- dispensable que tenga dos áreas cuadradas, donde el cuadrado mayor mida por lado, una unidad menor que el doble del largo del cuadrado menor. El área total del mueble será de 121 pies cuadrados.

The intermediate step  in the form ( x + a ) ^2 = b (x+a)  2 =b as a result of completing the square  of x² - 4x = 45 is (x- 2)² = 49

How to determine the intermediate step?

The equation is given as:

x² - 4x = 45

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add 4 to both sides of x² - 4x = 45

x² - 4x + 4= 45 + 4

This gives

x² - 4x + 4= 49

Express as perfect square

(x- 2)² = 49

Hence, the intermediate step of x² - 4x = 45 is (x- 2)² = 49

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Answer: $48.72

Step-by-step explanation:

Based on the given conditions: 58*(20%+1)*(1-30%)

Calculate: 58*1.2*0.7

Round to the nearest cent: $48.72

(an astrix (*) means to multiply)

Let the first of the two consecutive integers be n. Then the next consecutive integer is n+1.

From the given information, we can form an inequality, which is:2n + (n+1) ≥ 25

The above inequality is formed from the statement "Twice the smaller of two consecutive integers increased by the larger integer is at least 25". Now, let's solve this inequality and find the values of n that satisfy it.2n + (n+1) ≥ 25Simplifying the above inequality, we get:3n + 1 ≥ 25

Subtracting 1 from both sides, we get:3n ≥ 24

Dividing both sides by 3, we get:n ≥ 8

Hence, the first of the two consecutive integers is greater than or equal to 8.

Therefore, the two consecutive integers that satisfy the given information are 8 and 9.

Now, we need to check which of the given values, 7, 8, or 9, satisfy the above inequality. Let's check for

n=7.2n + (n+1) = 2(7) + (7+1) = 15 < 25

Therefore, n=7 is not a solution.

Let's check for n=8.2n + (n+1) = 2(8) + (8+1) = 25 ≥ 25

Therefore, n=8 is a solution. Let's check for n=9.2n + (n+1) = 2(9) + (9+1) = 28 ≥ 25

Therefore, n=9 is also a solution.

Thus, we have found that the solutions to the given problem are n=8 and n=9.

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Step-by-step explanation:

X^a times X^b = X^a + b

so 4x times 6x = 24x^(1+1)

This is based on simple ratio & scales where a figure on a scale is used to represent the true figure on another scale.

Actual length of bus = 45 ft

The scale drawing is given by;

½ inch to represent 5 ft

Simplifying this fraction gives 45 ft

4½ inches represents 45 ft

Actual length = 45 ft

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The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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5! permutation of the letters abcdefgh contains strings ab, de, and gh.

The number of permutations of 'n' objects taken 'r' at a time is determined by the following formula:

P(n,r)=n! / (n−r)!

We can also find permutation using the Selection and Formation Method:

For example:

1. Number of ways to arrange the letter SANOJ:

here number of alphabets are 5, and we have to arrange all the letter so using permutation formula:

P(5, 5 ) = 5! / (5-5)!

P(5, 5 ) = 5!                : 0! = 1

without using the formula we can simply write 5! as the answer.

Here, we have given the word, " abcdefgh "

and we have to make those arrangements in which ab, de, and gh come together:

so now, we will count ab, de, and gh as a single word.

now, we will have 5 different words/alphabet:

1 → ab

2 → c

3 → de

4 → f

5 → gh

Number of ways to arrange all the 5 words/alphabet: 5!

Hence,

5! permutation of the letters abcdefgh contains strings ab, de, and gh.

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Answer:

Step-by-step explanation:

To find the difference between the mass of the Sun and the mass of the Earth, we need to subtract the mass of the Earth from the mass of the Sun:

Mass of the Sun - Mass of the Earth = 1.989 x 10^30 kg - 5.98 x 10^24 kg

We can subtract the two values as follows:

1.989 x 10^30 kg - 5.98 x 10^24 kg = 1.989 x 10^30 kg - 0.598 x 10^30 kg

= 1.391 x 10^30 kg

Therefore, the mass of the Sun is 1.391 x 10^30 kg greater than the mass of the Earth.

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The total profit that is earned is 4512.5

100 - q = 0

q = 100

Maximization is where q = 0

MR = mc

100 - q = 5

such that q = 95

Price would be  100 -0.5(95)

= 100 - 47.5

= 52.5

Profit earned would be

= 95*52.5 -5*95

= 4512.5

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We find that the dimensions of the rectangular sheep pen are L = 100 feet and W = 260 feet.To find the dimensions of the rectangular sheep pen, we need to solve for the length and width of the pen.

Let's assume the length of the pen is L and the width is W.

We know that the area of a rectangle is calculated by multiplying the length and width: Area = Length * Width.

Given that the area of the pen must be 26000 square feet, we have the equation L * W = 26000.

We also know that we only need to build three sides of the pen, so the total length of the fence used will be the sum of the three sides: L + W + L = 2L + W.

Given that we have a total of 460 feet of fence to use, we have the equation 2L + W = 460.

Now we have a system of two equations with two variables. We can solve this system to find the values of L and W.

Using these two equations:
L * W = 26000
2L + W = 460

We can substitute the value of W from the second equation into the first equation:
L * (460 - 2L) = 26000.

By simplifying and rearranging, we get:
-2\(L^2\)+ 460L - 26000 = 0.

This equation can be solved by factoring or using the quadratic formula. After solving, we find that the dimensions of the rectangular sheep pen are L = 100 feet and W = 260 feet.

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When interpreting the expression as \((tanx)^{(sinx)\), the limit using L'Hospital's Rule is -∞ as x approaches 0+. However, when interpreting the expression as\(tan(x^{sinx})\), the limit is not well-defined due to the indeterminate form of 0^0.

To calculate the limit using L'Hospital's Rule, let's consider both interpretations of the expression and find the limits for each case:

Case 1: lim\((tanx)^{(sinx)\) as x approaches 0+

Taking the natural logarithm of the expression, we have:

\(ln[(tanx)^{(sinx)}] = sinx * ln(tanx)\)

Now, we can rewrite the expression as:

\(lim [sinx * ln(tanx)]\)as x approaches 0+

Applying L'Hospital's Rule, we differentiate the numerator and denominator:

\(lim [(cosx * ln(tanx)) + (sinx * sec^{2}(x))] / (1 / tanx)\) as x approaches 0+

Simplifying the expression:

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * tanx\) as x approaches 0+

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * (sinx / cosx)\) as x approaches 0+

\(lim [(cosx * ln(tanx) + sinx * sec^{2}(x)) / cosx] * sinx\) as x approaches 0+

\(lim [ln(tanx) + (sinx / cosx) * sec^{2}(x)] * sinx\) as x approaches 0+

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+

Since lim ln(tanx) as x approaches 0+ = -∞ and\(lim (tanx * sec^{2}(x))\) as x approaches 0+ = 0, we have:

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+ = -∞

Therefore, the limit of \((tanx)^{(sinx)\) as x approaches 0+ using L'Hospital's Rule is -∞.

Case 2: lim\(tan(x^{sinx})\)as x approaches 0+

We can rewrite the expression as:

lim\(tan(x^{(sinx)})\) as x approaches 0+

This expression does not have an indeterminate form of \(0^0\), so we do not need to use L'Hospital's Rule. Instead, we can substitute x = 0 directly into the expression:

lim \(tan(0^{(sin0)})\) as x approaches 0+

lim\(tan(0^0)\)as x approaches 0+

The value of \(0^0\) is considered an indeterminate form, so we cannot determine its value directly. The limit in this case is not well-defined.

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Answer:

80 in²

Step-by-step explanation:

8/10 = x/100

x = 80

Answer:

  height = 2/5h

Step-by-step explanation:

You want the height of a frustum if the volume of the frustum is 98/125 times the volume of the original cone, which was of height h.

Let h' represent the height of the part of the cone that is removed to leave the frustum. Then its volume (v') is ...

  v' = (volume of large cone)(1 - 98/125) = v·(27/125)

The scale factor between h' and h is ...

  (h'/h)³ = v'/v = 27/125

  h'/h = ∛(27/125) = 3/5

The height of the frustum in terms of the height of the original cone is ...

  frustum height = (height of large cone) - (height of small cone)

  frustum height = h - (3/5)h

  frustum height = 2/5h

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a) Probability of hitting the black circle is closer to zero than 1.

b) Probability of hitting the white portion is closer to 1 than 0

To get the probability of getting any point in the given image, we have to first of all find the area of the square which is:

Area of Square = 9 * 9 = 81 sq. units

Area of Circle = π * 1.5² = 7.07 Sq.units

Area of white part = 81 - 7.07

Area of white part = 73.93 Sq.units

a) Probability of hitting the black circle = 7.07/81 = 0.095

This probability is closer to zero than 1.

b) Probability of hitting the white portion = 73.93/81 = 0.9127

This probability is closer to 1 than 0

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Answer:

Using a right angled triangle if Sin A =24/25 The other side =7

therefore Cos A =7/25

However Sin is positive in the second quadrant and Cos is negative.

So there are two answers to your question 7/25 and -7/25

529

Step-by-step explanation:

Knowing the value of of  cosθ,  find out the values of the other trigonometric ratios using the trigonometric identities.

Keep in mind the fact that the angle lies in the fourth quadrant and provide the signs for the trigonometric ratios accordingly.

Now express  sin2θ,cos2θ  and  tan2θ  in terms of  sinθ,cosθ  and  tanθ,  whose values are now known, to get the required answers.

Hope this helps

It is sampled at a rate 25% higher than the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is limited to 0.1% of the peak signal amplitude.

To sketch the amplitude spectrum of g(t), we observe that sinc functions centered at 16 kHz and 10 kHz contribute amplitudes of 16x10³ and 10x10³, respectively, while the cosine component centered at 30 kHz has an amplitude of 20x10³. The horizontal axis represents the frequency (f).

The amplitude spectrum of the sampled signal, within the range -50 kHz to 30 kHz, will exhibit replicas of the original spectrum centered at multiples of the sampling frequency. The amplitudes and frequencies should be labeled according to the replicated components.

The minimum required bandwidth for binary transmission can be determined by considering the highest frequency component in g(t), which is 30 kHz. Therefore, the minimum required bandwidth will be 30 kHz.

For M-ary multi-amplitude signaling within a channel bandwidth of 50 kHz, we need to find the minimum value of M. It can be determined by comparing the available bandwidth with the required bandwidth for each amplitude component of g(t). The minimum M will be the smallest number of levels needed to represent all the significant amplitude components without violating the bandwidth constraint.

To minimize M, we need to select a pulse shape that achieves the narrowest bandwidth while maintaining an acceptable level of distortion. Different pulse shapes can be considered, such as rectangular, triangular, or raised cosine pulses.    

If a raised cosine pulse is used, the roll-off factor determines the pulse shape's bandwidth efficiency. The roll-off factor is defined as the excess bandwidth beyond the Nyquist bandwidth. The required M can be calculated based on the available channel bandwidth, the roll-off factor, and the distortion tolerance.

When using delta modulation with a sampling rate of five times the Nyquist rate, the number of levels (L) and corresponding bit rate can be determined by considering the quantization error and the maximum acceptable error in sample amplitudes. The bit rate will be determined based on the number of bits required to represent each level and the sampling rate.  

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Answer :

\(\boxed{\textsf{ The final answer is \textbf{n}$^{\textbf{3}}$ .}}\)

Step-by-step explanation:

Its given that n is the middle out of the three consecutive integers . So ,

The last integer will be :-

\(\sf\implies Last \ Integer \ = \ n - 1 \)

The next Integer will be :-

\(\sf\implies Next \ Integer \ = \ n + 1 \)

Now the Question says that the three integers are multipled to give a product . So that would be.

\(\sf\implies Product_{(three\ consecutive\ integers)}= (n-1)n(n+1) = (n^2-1)(n) = \pink{n^3-n}\)

Now thirdly it's given that n is added to the given integer . That would be ,

\(\sf\implies Adding\ n = \ n^3 - n + n = \pink{n^3} \)

Here - n and +n gets cancelled. So we are ultimately left out with n³.

Hence the final number is a cube of some number.

Answer:

D) 14.2

Step-by-step explanation:

The matrix sum A + 3B is undefined because A and 3B have different sizes. The matrix sum 4C - 2E is undefined because the number of rows in C is not equal to the number of columns in E. The matrix products DB and EB are undefined because the number of rows in D is not equal to the number of columns in B, and the number of columns in E is not equal to the number of rows in B, respectively.



The matrix operations to be computed are A + 3B, 4C - 2E, DB, and EB.

The expression A + 3B is undefined because A and 3B have different sizes. In matrix addition, the matrices being added must have the same dimensions, meaning they must have the same number of rows and columns. Since A and 3B have different sizes, their sum cannot be computed.

The expression 4C - 2E is undefined because the number of rows in C is not equal to the number of columns in E. In matrix subtraction, the matrices being subtracted must have the same dimensions. Since C and E have different dimensions, their subtraction cannot be performed.

The expression DB is undefined because the number of rows in D is not equal to the number of columns in B. In matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since the number of columns in D is not equal to the number of rows in B, their product cannot be computed.

Similarly, the expression EB is also undefined because the number of columns in E is not equal to the number of rows in B.

In summary, the matrix sum A + 3B is undefined because A and 3B have different sizes. The matrix sum 4C - 2E is undefined because the number of rows in C is not equal to the number of columns in E. The matrix products DB and EB are undefined because the number of rows in D is not equal to the number of columns in B, and the number of columns in E is not equal to the number of rows in B, respectively.


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(d) The ordered pair solution of this equation 3x/4  + 2y = 15 is (4, 6).

(e) The ordered pair solution of this equation xy ≥ 6 is (-2, -4).

The ordered pair solution of the equations is calculated by simplifying the equations as follows;

The given equations;

(d) 3x/4  + 2y = 15

(e) xy ≥ 6

(d) The solution of this equation 3x/4  + 2y = 15 is calculated as follows;

let the value of x = 4 and the value of y = 6

so we will substitute this value into the equation and check if it will be equal to 15.

(4, 6) = (3 x 4 )/4  +  2(6)

(4, 6) = 3  +  12

(4, 6) = 15

(e) The solution of this equation xy ≥ 6 is calculated as follows;

let x = -2, and let y = - 4

(-2, -4) = (-2)(-4) = 8

8 ≥ 6 (this solution is true)

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Answer:

Nash ran 6 miles and walked 20 miles.

Step-by-step explanation:

Note: Consider we need to find the number of miles he ran and the number of miles he walked in the first week.

Total distance = 26 miles every week.

Ratio of the number of miles he ran to the number of miles he walked is 3:10.

Let he ran 3x miles and walked 10 x miles. So,

Total distance = 3x+10x

\(3x+10x=26\)

\(13x=26\)

Divide both sides by 13.

\(x=2\)

The value of x is 2.

Number of miles he ran = 3(2) = 6 miles

Number of miles he walked = 10(2) = 20 miles

Therefore, Nash ran 6 miles and walked 20 miles in the first week.

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Answer:

1/25

Step-by-step explanation:

The probability of drawing a blue marble, replacing it, then drawing a yellow marble is 1/25.

Given,

A bag contains four red marbles, six green marbles, eight yellow marbles, and two blue marbles.

We need to find the probability of drawing a blue marble, replacing it, then drawing a yellow marble.

A combination is used to select required items from a set where the order of selection does not matter.

It is given by:

n^Cr = n! / r! (n-r)!

Where n = the number of elements present in a set.

Find the number of each marble.

Red marbles - 4

Green marbles - 6

Yellow marbles - 8

Blue marbles - 2

Find the probability of drawing a blue marble

P ( B ) = ^2C_1 / ^20C_1

          = (2! / 1!) / (20! / 19! 1!)

          = 2 / 20

          = 1/10

Find the probability of drawing a yellow marble

P ( Y ) = ^8C_1 / ^20C_1

          = (8! / 1! 7!) / (20! / 191 1!)

          = 8 / 20

          = 2 / 5

Find the probability of drawing a blue marble, replacing it, then drawing a yellow marble

Both the probability is independent so,

P = P ( B ) X P ( Y )

  = 1/ 10 X 2 / 5

  = 1 / 25

Thus the probability of drawing a blue marble, replacing it, then drawing a yellow marble is 1/25.

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If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Answer:

-86

Step-by-step explanation:

simplify each equation as much as possible

f(x)= 4x(2+9) add

4x(11) multiply

f(x)=44x

substitute given numbers into each equation

44(-2)=-88                3(4)-14= 12-14=-2

combine equations

-88-(-2)= -86   add since you are subtracting a negative number

Answer:

2x +23

Step-by-step explanation:

Let the required number be x

Twice of number = 2x

23 more than twice a number = 2x + 23

Answer:

2x + 23

Step-by-step explanation:

Let x be the number

I hope this helps!