On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).
Which statement is true regarding the functions on the graph?

The Laplace transformation is:

                 \(L [f(t)] = \frac{5 - 8e^{-7s} }{2}\)

Rewriting the f in terms of the unit step function:

\(\left \{ {{y=5} for 0\leq t\leq 7 \atop {x=-3}for t\geq 7} \right.\)

⇒ f(t) = 5[u(t) - u (t-7)] - 3u(t -7 )

         = 5u(t) - 8u (t-7)

Unit Step Function:

The unit step function, also known as the Heaviside function, is known in engineering applications as a function that can describe the switching process mathematically. We often encounter functions whose values ​​change rapidly over a certain time unit t.

where,

u(t) = \(\left \{ {{y=1 for t\geq 0} \atop {x=0 for t < 0}} \right.\)

Recall the time-shifting property of the Laplace transform:

    L{u(t - c) f( t - c)}

= \(e^{-es} L{f(t)}\)

Laplace Transformation:

In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that transforms a function of real variables (usually t in the time domain) into a function is. Complex variable (complex frequency domain, also called s-domain or s-plane). As transformations are tools for solving differential equations, they have many applications in science and engineering. In particular, it converts ordinary differential equations to algebraic equations and converts convolutions to multiplications.

and the Laplace transform of a constant function,

L[k] = k/s

So we have

L[f(t)] = L[5u(t) - 8u (t-7)]

        =  \(5[L_{1} ] - 8e^{-7s} L[1]\)

Therefore,

\(L [f(t)] = \frac{5 - 8e^{-7s} }{2}\)

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Answer:

m=3

Step-by-step explanation:

9m-19=8.

9m=27. Add 18 on both sides

m=3 divide by 9 on both sides

Hope this helps plz mark brainliest :D  

Answer:

3 = m

Step-by-step explanation:

9m - 19 = 8

      +19 +19

9m = 27

9 divided by 9 is m

27 divided by 9 is 3

The volume of a box is the amount of space in it.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using imperial or SI-derived units, such as the cubic meter and liter. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. No object in the dimensions of zero, one, or two has volume; in the dimensions of four and above, the hypervolume is a concept similar to the standard volume.

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Step-by-step explanation:

the gradient of the line = 2 units/ 3 units = 2/3

Answer: 1/9

Step-by-step explanation: 9(1/3)^5-1, which is  9(1/3)^4.

Solve and you get 1/9.

Answer:

to examine the ratio y/x (instead of x/y). If the x and y coordinates form proportional relationships, then there is some non-changing number (a constant) that when multiplied times x will create y. In this example, that number is 3 (y = 3x), and is called the constant of proportionality.

Step-by-step explanation:

Answer:

In a graph the line must pass through the origin and it has to be a straight line,

In an table the y over x has to be the same for each one

The measure of the angle in degrees is 12.87°.Given that the circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 78.03 cm long.1/360th of the circumference of the circle is 0.51 cm long.

The circumference C is given by the formula :C = 2πr Where r is the radius of the circle.1/360th of the circumference of the circle is 0.51 cm long, thus the circumference is 360 times greater, that isC = 360 × 0.51

= 183.6 cmTherefore,

2πr = 183.6 cm So ,

r = 183.6/

2π= 29.2 cm.

Now, we can use the formula below to find the measure of the angle θ:78.03 = θ/360° × 2π × 29.2θ/

360° = 78.03/(2π × 29.2)θ/

360° =

0.1383θ =

0.1383 × 360°θ = 49.79°Therefore, the measure of the angle in degrees is 49.79° rounded to 2 decimal places. Therefore, the measure of the angle in degrees is 12.87°.

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The population size of mantis shrimp will be approximately 266 individuals after 5 years.

The intrinsic rate of increase is an essential concept in population biology. It is the rate at which a population is growing at a particular moment in time. The population size after a particular period can be calculated using the intrinsic rate of increase with the help of this formula:

Nt = N0e^(rt)

where Nt is the future population size, N0 is the initial population size, r is the intrinsic rate of increase, and t is the time in years.

The population size of mantis shrimp is 475 individuals and the intrinsic rate of increase is -0.10.

We can calculate the population size after 5 years using the above formula as follows:

Nt = N0e^(rt)

Nt = 475 * e^(-0.10 * 5)

Nt = 475 * e^(-0.50)

Nt ≈ 266

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The height of the sun flower after w weeks is 25 + 3w inches and the height of flower after 9 weeks is 52 inches.

At the beginning of spring, Sophia planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall.

The sunflower then began to grow at a rate of 3 inches per week.

The height of the flowers after w weeks can be calculated using the equation below:

height of flower after w weeks = 25 + 3w

The height of the flower after 9 weeks can be calculated as follows:

height of flower after 9 weeks = 25 + 3(9)

height of flower after 9 weeks = 25 + 27

height of flower after 9 weeks = 52 inches

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L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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The height of the right-angle triangle will be 13.3 units. Then the correct option is B.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as,

H² = P² + B²

A right triangle with legs of length 7 inches and a hypotenuse of 15 inches. Then the height is given as,

15² = h² + 7²

225 = h² + 49

h² = 225 - 49

h² = 176

h = 13.266

h ≈ 13.3 units

The height of the right-angle triangle will be 13.3 units. Then the correct option is B.

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The probability of producing at least 232,000 barrels is 0.5.

The standard normal distribution table, also known as the z-table, is a table that provides the probabilities for a standard normal distribution, which has a mean of 0 and a standard deviation of 1.

The table lists the probabilities for values of the standard normal distribution between -3.49 and 3.49, in increments of 0.01.

Here we have

Daily output of marathon's garyville, louisiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels.

Since the daily output of the refinery is normally distributed,

we can use the standard normal distribution to calculate the probability of producing at least 232,000 barrels.

First, we need to standardize the value using the formula:

=> z = (x - μ) /σ

where:

x = value we want to calculate the probability for (232,000 barrels)

μ = mean (232,000 barrels)

σ = standard deviation (7,000 barrels)

=> z = (232000 - 232000) / 7000 = 0

Next, we look up the probability of producing at least 0 standard deviations from the mean in the standard normal distribution table.

This value is 0.5.

Therefore,

The probability of producing at least 232,000 barrels is 0.5.

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Answer:

first the primerter then the area

Step-by-step explanation:

Answer:

The height of the cone is simple... here are the steps

Step-by-step explanation:

V= 1/3πr²h

V would be 1,398

π would be 3.14

r² 9.2x9.2

so the new equation is 1,398=1/3(3.14)(84.64)h

Now to get h all by itself multiply all in the equation... after divide by 1/3

1,398= whatever number xh

Now divide that whatever number by 1,398 and you find the height.

Hope this helps.

Answer:

16%

Step-by-step explanation:

The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

None of the statements A, B, or C can be determined to be true based on the given information. we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

To determine which statement is true, let's analyze the given information.  We have:

P(B) = 4/1

P(A∪B) = 2/1

P(A|B) = 3/2

Let's evaluate each statement:

A) P(A) = 3/1

This statement is not directly supported by the given information. We cannot determine the value of P(A) solely based on the provided probabilities.

B) P(A∩B) = 12/1

This statement is also not supported by the given information. We do not have enough information to determine the value of P(A∩B).

C) P(B|A) = 5/1

This statement is not supported by the given information. We do not have any direct information about P(B|A), so we cannot determine its value.

D) A and B are not independent.

To determine whether A and B are independent, we can check if P(A∩B) = P(A) * P(B). However, as mentioned earlier, we do not have enough information to determine the value of P(A∩B). Therefore, we cannot conclude whether A and B are independent based on the given information.

In summary, none of the statements A, B, or C can be determined to be true based on the given information. The only conclusion we can draw is that we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

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Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line

m = \(\frac{-3=0}{2-0}\) = - \(\frac{3}{2}\)

Since the line crosses the y- axis at (0, 0 ) ⇒ b = 0

y = - \(\frac{3}{2}\) x ← equation of line

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:

8 buses

Step-by-step explanation:

Find the total number of people going on the trip by adding the number of students and the number of chaperones:

Total number of people = Number of students + Number of chaperones

= 324 + 32

= 356

Divide the total number of people by the capacity of each bus to find the number of buses needed:

Number of buses needed = Total number of people / Bus capacity

= 356 / 48

≈ 7.42

Since we cannot have a fraction of a bus, we must round up to the nearest whole number, which means we need 8 buses.

The remainder of the division, 0.42, represents the fraction of a bus that would be needed to transport the remaining people if we had more than 8 buses available. In this case, since we do not have a fraction of a bus, we round up to the next whole number.

Answer:

x = 8

y = 21

Step-by-step explanation:

The angle (7x + 12)° and the angle (12x-28)° are alternate interior angles and so has got the same measurement

7x + 12 = 12x - 28

12 + 28 = 12x - 7x

40 = 5x divide both sides by 5

8 = x

The sum of angle (12x - 28)° and (9y - 77)° must be equal because they make a straight line with the measure of 180°

12x - 28 + 9y - 77 = 180 we already found the value of x as 8 so let's rewrite the equation

12 × 8 - 28 + 9y - 77 = 180

96 - 28 - 77 = 180 add like terms

9y - 9 = 180

9y = 189 divide both sides by 9

y = 21

Answer:

approximately 4.36

Step-by-step explanation:

Simplify the expressions inside the parentheses first:

(10 + 43 - 5) = 48

(6 + 5) = 11

48 divided by 11 = 4.36 (rounded to two decimal places)

Therefore, (10 + 43 - 5) divided by (6 + 5) is equal to approximately 4.36.

The population of interest in this study is all births in southern California between the years 1989 and 1993. The sample in this study is 143,196 births for which length of gestation data and air pollution exposure during gestation were collected.

The results of this study cannot be generalized to the entire population of births in southern California beyond the years 1989 to 1993. However, the findings of the study can still provide valuable insights into the relationship between air pollutants and preterm births in this specific population and time period. It is also important to note that this study alone cannot establish causal relationships between air pollutants and preterm births, as other factors may contribute to preterm births that were not measured or accounted for in this study. Further research and analysis would be needed to establish causal relationships.

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Simple random sampling is a frequently chosen for its simplicity and periodicity.

What is frequently ?

Frequently refers to something that happens or occurs often or many times. It is an adverb that describes the regularity of an action or event, indicating that it happens with a high frequency or on a regular basis.

Simple random sampling is a random sampling technique that is frequently chosen by researchers for its simplicity and its periodic quality. This technique involves randomly selecting a sample from a larger population, with each individual in the population having an equal chance of being selected. Simple random sampling is considered to be an unbiased and efficient method for selecting a representative sample, and it is often used as a benchmark for comparing other sampling methods.

Simple random sampling is a frequently chosen for its simplicity and periodicity.

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Answer:

m<K = 51°

m<L = 78°

m<M = 51°

Step-by-step explanation:

Base angles of an isosceles ∆ are equal to each other, therefore,

m<M = m<K

Substitute

3x + 36 = 4x + 31

Collect like terms and solve for x

3x - 4x = -36 + 31

-x = -5

Divide both sides by -1

x = 5

Let's find each degree measure using the value of x

m<K = 4x + 31

Plug in the value of x

m<K = 4(5) + 31

m<K = 20 + 31

m<K = 51°

m<M = 3x + 36

= 3(5) + 36

= 15 + 36

m<M = 51°

m<L = 180° - (m<M + m<K) (sum of triangle theorem)

Substitute

m<L = 180 - (51 + 51)

m<L = 78°

Answer:

A”(-3, -18) B” (0, -27) C” (-12, -30)

Step-by-step explanation:

Two transformations have been listed beneath the graph. Complete them in order to get the solution.

The first transformation is a translation. A translation involves moving the shape across the graph without altering its form. To receive the coordinates for this. Add the <-3, -8> given to coordinates A, B, and C. Which should result in the following: A (-1, -6) B (0, -9) C (-4, -10)

Now complete the second transformation, which is a dilation. Dilations happen when a shape is either made smaller or larger by a set number. To complete the second transformation: take the number given: “3” and multiply each number in the coordinate sets you got after the first transformation by this number.

Which should result in: A”(-3, -18) B” (0, -27) C” (-12, -30)

Answer:

13/8 45/3/8  7 7/8

Step-by-step explanation:

Answer:

You're mean should be 34.

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms.

Hope this helps.