Matemáticas
4. Javier pagó $92 por 5 libretas y 3 lápices. Laura compró 2 libretas y 6 lápices, y pagó $56, ¿cuál es el
precio de cada libreta y de cada lápiz

(a) Taking the Laplace transform of the given differential equation, we get Y(s) + 4Y(s) = (1 - e^(-2s))/s + (2 - e^(-5s))/s + 9.

(b) Solving the algebraic equation, we get Y(s) = [(1 - e^(-2s))/s + (2 - e^(-5s))/s + 9]/(s + 4).

(c) Taking the inverse Laplace transform, we get the solution y(t) = 3 - e^(-4t) + 2u(t-2) - u(t-5), where u(t) is the unit step function.

(a) Taking the Laplace transform of the differential equation, we get:

L(y′) + 4L(y) = L{0u(t) + 1u(t-2) + 1u(t-5)}

where L{0u(t)} = 0, L{1u(t-2)} = e^(-2s)/s, and L{1u(t-5)} = e^(-5s)/s. Applying the Laplace transform to the differential equation gives:

sY(s) - y(0) + 4Y(s) = (1 - e^(-2s))/s + (2 - e^(-5s))/s + 9

Substituting y(0) = 9 and rearranging, we get:

Y(s) + 4Y(s) = (1 - e^(-2s))/s + (2 - e^(-5s))/s + 9

(b) Solving for Y(s), we get:

Y(s) = [(1 - e^(-2s))/s + (2 - e^(-5s))/s + 9]/(s + 4)

(c) Taking the inverse Laplace transform of Y(s), we get:

y(t) = L^{-1}(Y(s)) = L^{-1}\left(\frac{(1 - e^{-2s}) + (2 - e^{-5s}) + 9s}{s(s + 4)}\right)

Using partial fraction decomposition, we can rewrite Y(s) as:

Y(s) = \frac{1}{s+4} - \frac{e^{-2s}}{s+4} + \frac{2}{s} - \frac{2e^{-5s}}{s}

Taking the inverse Laplace transform of each term, we get:

y(t) = 3 - e^{-4t} + 2u(t-2) - u(t-5)

where u(t) is the unit step function. Thus, the solution to the differential equation is y(t) = 3 - e^(-4t) + 2u(t-2) - u(t-5).

For more questions like Differential equation click the link below:

https://brainly.com/question/14598404

#SPJ11

Answer:

The answer is 10

Step-by-step explanation:

To get this you will make the improper fraction into a fraction and then turn that into decimal form

\(4 \frac{1}{8} = 4\)

and

\(5 \frac{6}{10} = 6\)

That is how you find the estimated answer

Hope this Helped

Step-by-step explanation:

I hope this answer is helpful ):

the parameter declaration int* a can be used to declare an array of integers passed to a function is True.

The parameter declaration "int* a" can be used to declare a pointer to an integer in a function. This pointer can then be used to refer to an array of integers that is passed to the function.

In C and C++, arrays are passed to functions by passing a pointer to the first element of the array. Therefore, using "int* a" as a parameter declaration allows the function to access the array using pointer arithmetic.

what is parameter?

In general, a parameter is a quantity or value that is used to define or describe a system or process. The term is used in many different fields, such as mathematics, physics, engineering, statistics, and computer science.

In mathematics, a parameter typically refers to a variable that is fixed in a particular problem or equation, but whose value can vary in different situations. For example, in the equation of a line y = mx + b, m and b are parameters that determine the slope and intercept of the line, respectively.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

Therefore, the value of x is x = -2 / m + 3.

Supporting Answer: We have to find the equation of the line that passes through the point (3, 7) and has a slope of m. We use the point-slope form of the equation of the line, which is :y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. Thus, the equation of the line is: y - 7 = m(x - 3). Now, we are given that point A(x, 5) lies on the line. Hence, we substitute y = 5 and solve for x:x - 3 = (5 - 7) / mx - 3 = -2 / mmx = -2 / m + 3.

Equations act as a scale of balance. If you've ever seen a balancing scale, you know that it needs to have an equal amount of weight on both sides in order to be deemed "balanced". The scale will tip to one side if we just add weight to one side, and the two sides will no longer be equally weighted. Equations use the same reasoning. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

Know more about equation here:

https://brainly.com/question/29657992

#SPJ11

Answer:

25

Step-by-step explanation:

The n th term of an AP is

\(a_{n}\) = a₁ + (n- 1)d

where a₁ is the first term and d the common difference

Here d = 5, then

a₁₈ = a₁ + 17d = a₁ + 85

a₁₃ = a₁ + 12d = a₁ + 60

Thus

a₁₈ - a₁₃

= a₁ + 85 - a₁ - 60

= 25

Kendra has 15 nickels and 23 quarters.

To solve this problem, we need to set up a system of linear equations to represent the given information. We can let x be the number of nickels that Kendra has, and y be the number of quarters. We can then write the following system of equations:

x + y = 38

y = x + 8

To solve for x and y, we can substitute the second equation into the first equation to eliminate y:

x + (x + 8) = 38

2x + 8 = 38

2x = 30

x = 15

Substituting this value back into the second equation gives us y = 15 + 8 = 23. Therefore, Kendra has 15 nickels and 23 quarters.

To learn more about linear equations, visit:

brainly.com/question/11897796

#SPJ4

Answer:

this answer is simply exponential growth also you did not put in a graph so i have to kind of improvise here  also this choice SHOULD be the answer: 92 mil, 139 mil, 186 mil, 233 mil, 280 mil

i did the math and this is what i got unless i did something wrong but either way hope this helps lol

Step-by-step explanation:

The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.

Let's consider the following interpretation:

Domain of discourse: {1, 2}

A(x): x is even

B(x): x is odd

Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).

However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.

Learn more about domain here:

https://brainly.com/question/28135761

#SPJ11

-0.85714285714

Just divide 12 by -14

The mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

The sample distribution of the proportions is used to measure the proportion with which success is achieved. The chance of an event taking place is the proportion computed by dividing the number of successes by the size of the sample.

Given that, You intend to draw a random sample of size n = 580 from a population whose parameter is p = 0.31, we are asked to find the mean of the distribution of sample proportions and standard deviation of the distribution of sample proportions.

Under the sampling distribution of the proportions, the mean and standard deviation are calculated by :

a) The mean is given as ;

μ = nP

Where, n is the sample size

P is the population proportion

Therefore,

μ = 580(0.31)

μ = 179.8

b) The standard deviation is given as follows :

δ = \(\sqrt{\frac{P(1-P)}{n} }\)

δ = \(\sqrt{\frac{0.31(1-0.31)}{580} }\)

δ = 0.019

Hence, the mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

Learn more about sample distribution of the proportions, click;

https://brainly.com/question/30004083

#SPJ1

Answer:

1.cannot

2.can

3.cannot

4.can

Step-by-step explanation:

it's actually quite simple. if the angles add up to 180°, it is a triangle. so if they don't, then its not a triangle.

21+28+41= 90 -> not a triangle

65+45+70=180 -> triangle

48+52+54=154 -> not a triangle

16+40+124=180 -> triangle

The area of the four triangles is 208 square units and the area of a larger square is 441 square units.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

The area of one triangle = (1/2)(8)(13) = 52 square units

The area of four triangles = 208 square units

The area of a larger square = 441 square units

c² = 233

a² + b² = 233

a² + b² = c²

Thus, the area of the four triangles is 208 square units and the area of a larger square is 441 square units.

Learn more about Pythagoras' theorem here:

https://brainly.com/question/21511305

#SPJ1

To find the equation of a line parallel to 5x – 7y – 12 = 0 and passing through the point (-14, -4), follow these steps:

Determine the slope of the given line.

Rearrange the equation in the form y = mx + b, where m represents the slope.

In this case, we have -7y = -5x + 12, which gives y = (5/7)x – 12/7. The slope of the given line is 5/7.

Since parallel lines have the same slope, the line we are looking for will also have a slope of 5/7.

Use the point-slope form of the equation, which is y – y₁ = m(x – x₁), where (x₁, y₁) represents the given point (-14, -4).

Substitute the values into the point-slope form. The equation becomes y – (-4) = (5/7)(x – (-14)).

Simplify the equation.
This gives y + 4 = (5/7)(x + 14).

Therefore, the equation of the line parallel to 5x – 7y – 12 = 0 and passing through the point (-14, -4) is y + 4 = (5/7)(x + 14).

To find the equation of a line perpendicular to 11x – 7y – 54 = 0 and passing through the point (-44, -5), follow these steps:

Determine the slope of the given line.

Rearrange the equation in the form y = mx + b.

In this case, we have -7y = -11x + 54, which gives y = (11/7)x – 54/7. The slope of the given line is 11/7.

Perpendicular lines have negative reciprocal slopes.
Find the negative reciprocal of the slope of the given line.

In this case, the negative reciprocal is -7/11.

Use the point-slope form of the equation, y – y₁ = m(x – x₁), where (x₁, y₁) represents the given point (-44, -5).

Substitute the values into the point-slope form.

The equation becomes y – (-5) = (-7/11)(x – (-44)).

Simplify the equation.

This gives y + 5 = (-7/11)(x + 44).

Therefore, the equation of the line perpendicular to 11x – 7y – 54 = 0 and passing through the point (-44, -5) is y + 5 = (-7/11)(x + 44).


Learn more about point-slope form here : brainly.com/question/29503162

#SPJ11

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

Read moe on circumference here https://brainly.com/question/27447563

#SPJ1

Answer:

The card was worth $160.

Step-by-step explanation:

It is given that:

Percent of gift card used = 42%

Cost of groceries = $67.20

Let,

x be the total amount on gift card.

42% of x = 67.20

\(\frac{42}{100}x=67.20\)

0.42x = 67.20

\(\frac{0.42x}{0.42}=\frac{67.20}{0.42}\\x=160\)

Therefore,

The card was worth $160.

Step-by-step explanation:

x^2+9x<-20

x^2+9x+20<0

( x+5)(x+4)<0

x+5<0,x+4<0

x<-4 (because x<-5 is extraneous solution)

Answer:

The function rule is: \(y = -3x-5\)

Step-by-step explanation:

Using the given input/output values, we can take two pairs of input-output values for finding the rule.

The function is a linear function as the input and output are changing linearly.

Required pairs are:

(1,-8)  and (2, -11)

The general rule for linear function is:

\(y = mx+b\)

m is the slope of the function calculated using the formula

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Putting the values

\(m = \frac{-11+8}{2-1}\\m = \frac{-3}{1}\\m = -3\)

Putting in equation

\(y = -3x+b\)

To find the value of b, putting (1,-8) in the equation

\(-8 = -3(1) +b\\-8 = -3+b\\-8+3 = b\\b = -5\)

Putting the values

\(y = -3x-5\)

Hence,

The function rule is: \(y = -3x-5\)

T/F Solution that can be analytically obtained but is not an actual answer to the equation often due to restrictions in the type of function such as a negative in the log

This statement is true.

Because, Sometimes, when solving an equation using analytical methods, we may arrive at a solution that is mathematically correct but is not a valid answer due to the restrictions in the type of function used.

For example, if a negative value appears in the logarithmic function, the solution may not be valid because the logarithmic function is only defined for positive values.

In such cases, we need to go back and recheck our work and take into account the restrictions of the function to arrive at a valid solution.

Sometimes when solving an equation analytically, the resulting solution may not be a valid answer due to restrictions in the domain of the function.

For example, if we solve an equation involving a logarithmic function, we may end up with a negative value inside the logarithm, which is not defined for real numbers. In such cases, the solution obtained analytically is not a valid answer to the equation.

Another example is when solving for the roots of a quadratic equation using the quadratic formula, we may obtain complex solutions even though we are only interested in real solutions.

Thus, it is important to always check the solutions obtained to ensure that they satisfy any domain or range restrictions of the functions involved in the equation.

For similar question on analytically.

https://brainly.com/question/29179937

#SPJ11

452.39 cubic feet equals V. (rounded to two decimal places) . The skateboard pool's volume is therefore roughly 452.39 cubic feet.

Volume is a unit used to describe how much space a three-dimensional object or region takes up in space. It is a physical measure that expresses how much room a substance or thing takes up. Depending on the measurement method being used, there may be a difference in the unit of volume measurement. The unit of volume, for instance, is the cubic meter (m3) in the International System of Units (SI), as opposed to the cubic feet (ft3) or cubic inches (in3) used in the United States.

given

The following formula can be used to determine a hemisphere's volume:

\(V = (2/3) * \pi * r^3\)

where r is the hemisphere's radius.

The skateboard pool's radius is specified as 6 feet, and we are tasked with determining the hemisphere's approximate capacity. We can simplify the formula by substituting these values into it:

\(V = (2/3) * 3.14 * 6^3\)

V = (2/3) * 3.14 * 216

452.39 cubic feet equals V. (rounded to two decimal places) . The skateboard pool's volume is therefore roughly 452.39 cubic feet.

To know more about volume visit :-

https://brainly.com/question/1578538

#SPJ1

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

To learn more about median click here: brainly.com/question/300591

#SPJ11

Answer: 20 feet

Step-by-step explanation:

This represents a right angled triangle with the length of the slide being the hypotenuse, the height of the ladder being the height of the triangle and the distance from the base of the ladder being the length.

Solve with Pythagoras rule:

c² = a² + b²

c = hypotenuse

a= length

b = height

29² = 21² + b²

841 = 441 + b²

b² = 841 - 441

b² = 400

b = √400

b = 20 feet

Step-by-step explanation:

there are some tricks involved that your teacher tries to "play" with you.

overall, the question is, how much money is in the account after 2 years, when the originated deposit amount was $15,000, and its interest rate is 8% per year (!). and the interest is compounded (applied) quarterly (= 4 times a year).

the table tells us the multiplication factor FVIF for the original deposit to calculate the balance after n "applications" of the interest rate i.

in other words :

new balance = deposit × FVIF(i, n)

and the paid interest is simply

interest = new balance - deposit =

= deposit × (FVIF(i, n) - 1)

now, the tricks here are :

2 years quarterly means 2×4 = 8 interest application periods.

interest rate = 8% per year = 8/4 = 2% per quarter (interest application period).

so, we have to look in the table for the entry at

8 periods at 2% = 1.1717

the amount (balance) after 2 years is then

15,000 × 1.1717 = $17,575.50

the interest earned is then

17,575.50 - 15,000 = $2,575.50

Answer:

Draw your y and x axis , the y axis is going to be a vertical line while the x axis is going to be a horizontal line

Answer:

290

Step-by-step explanation:

Let the number of time the standard version was downloaded be "x", then the number of times the high-quality version was downloaded will be "4x".

The total MB downloaded for standard will be 2.1x, and the total MB downloaded for high-quality will be (4x*4.1)=16.4x.

So we have

\(2.1x+16.4x=5365\\18.5x=5365\\x=290\)

So there were 290 downloads of the standard version.

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

Learn more about polynomial function here

https://brainly.com/question/1550346

#SPJ4

Answer:

Add them up so ur answer can be right

The probability that a randomly selected plant will be erroneously detected is found to be 0.02965 = 2.965% using the provided percentages.

The symbol % and, less frequently, the abbreviation 'pct' may be used to indicate that a number is a percentage. Latin gave us the word percentage, which means "out of one hundred." Consequently, you can think of each "whole" as being divided into 100 equal parts, each of which is one percent.

given

The proportions of an inaccurate detection are as follows:

2% of 3.5% (have the protein).

3% of 96.5%(do not have the protein)

p = 0.02965

The likelihood of erroneously detecting a randomly selected plant is 0.02965, or 2.965%.

To know more about percentage visit :-

https://brainly.com/question/16797504

#SPJ4