The table shows the average temperature, in degrees Celsius, in Jacob's city over a period of five months: Month 1 2 3 4 5 Temperature 5 7.2 9.4 11.6 13.8 Did the temperature in Jacob's city increase linearly or exponentially? Linearly, because the table shows a constant percentage increase in temperature each month Exponentially, because the table shows a constant percentage increase in temperature each month Linearly, because the table shows that the temperature increased by the same amount each month Exponentially, because the table shows that the temperature increased by the same amount each month

The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer: 1/5

Step-by-step explanation:

Answer:

\({ \sf{ \frac{1}{5} }} \\ \)

Step-by-step explanation:

\({ \sf{ \frac{2 \div 2}{10 \div 2} \equiv \frac{1}{5} }} \\ \)

The work required to stretch the spring from 7 cm to 15 cm past equilibrium is 0.268 J (joules).

What is work?

Work is a physical quantity that measures the amount of energy transferred to or from an object due to the application of a force over a displacement. It is the product of the magnitude of the force applied to an object and the distance over which the force is exerted.

The work done to stretch or compress a spring can be calculated using the formula: W = (1/2) * k * Δx².

Given that the spring constant (k) is 140 kg/s² and the displacement (Δx) is 15 cm - 7 cm = 8 cm = 0.08 m, we can substitute these values into the formula:

W = (1/2) * 140 kg/s² * (0.08 m²)

W = 0.5 * 140 kg/s² * 0.0064 m²

W = 0.448 J

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The regression line is a line that best fits through a set of data points. It is used to make predictions about the values of y for a given x-value, as well as to determine the strength of a linear association between two variables.

The formula for calculating the regression line is y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y intercept. The regression line is a line that best fits through a set of data points. It is used to make predictions about the values of y for a given x-value, as well as to determine the strength of a linear association between two variables. The calculation involves finding the slope of the line, which can be done by calculating the difference in y-values divided by the difference in x-values for two points on the line, and then finding the y-intercept, which is done by plugging in the slope and one of the points into the equation y = mx + b. This equation can then be used to predict the value of y for any given x-value.

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Arc length formula is L = ∫a^b √[1 + (dy/dx)^2] dx . The arc length of a curve is the length of the curve between two points, and it can be calculated using the arc length formula in calculus.

The arc length formula can be used to find the length of a curve in terms of the function that describes the curve.

The arc length formula is given by:

L = ∫a^b √[1 + (dy/dx)^2] dx

where L is the arc length of the curve, a and b are the endpoints of the curve, dy/dx is the derivative of the function that describes the curve with respect to x, and ∫ represents the integral of the function over the interval from a to b.

To use the formula, we first find the derivative of the function that describes the curve, dy/dx. Then we plug this expression into the arc length formula and integrate the expression over the interval from a to b to find the arc length of the curve.

The arc length formula is useful in many applications, such as physics, engineering, and geometry, and it allows us to find the length of a curve even when it is not a straight line.

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La ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x. Y el precio en euros de 10 dólares es de 12 €.

La ecuación de la recta que nos da el precio en euros, y, de x dólares se puede hallar utilizando la fórmula de la pendiente de una recta, que es m = (y2 - y1) / (x2 - x1). En este caso, los puntos dados son (3, 3.6) y (7, 8.4).

Primero, calculamos la pendiente de la recta:
m = (8.4 - 3.6) / (7 - 3)

m = 4.8 / 4

m = 1.2

Luego, utilizamos la fórmula de la ecuación de la recta, y = mx + b, para encontrar el valor de b. Podemos utilizar cualquiera de los puntos dados para esto. Usaremos el punto (3, 3.6).

3.6 = 1.2(3) + b
3.6 = 3.6 + b
b = 0

Por lo tanto, la ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x.

Esta ecuación nos da el precio en euros, y, de x dólares. Si queremos encontrar el precio en euros de una cierta cantidad de dólares, simplemente sustituimos el valor de x en la ecuación y resolvemos para y. Por ejemplo, si queremos encontrar el precio en euros de 10 dólares, sustituimos x = 10 en la ecuación:

y = 1.2(10) = 12

Por lo tanto, el precio en euros de 10 dólares es de 12 €.

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Answer:

91.67%

Step-by-step explanation:

find diff between 12 and 23 as a number

divide that number from step on by 12  

multiply the result from step 2 by 100

Answer: p=4

Step-by-step explanation:

The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Given:

Prime numbers can be expressed as a sum and difference of 2 prime numbers.

To find:

The prime numbers that can be expressed as a sum and difference of 2 prime numbers.

Solution:

Prime numbers are the positive integers which are greater than 1, divisible by only 1 and itself.

Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19,... .

Only 2 is the even prime number.

The sum and difference of two odd integers is always an even number. So, we need to take one even prime number and one odd prime number to add and subtract the numbers to get a prime number.

\(2+3=5\)

\(7-2=5\)

Therefore, 5 is the only prime number that can be expressed as a sum and difference of 2 prime numbers.

The probability of obtaining less than 2 heads is 1/2.

To compute the probability of obtaining less than 2 heads when tossing 3 coins, with one of the coins having a head on both sides, we can consider the different outcomes and their probabilities.

Let's analyze the possible outcomes:

No heads (0 heads):

In this case, all three coins must show tails. The probability of getting tails on a fair coin is 1/2, so the probability of no heads is \((1/2)^{3}\) = 1/8.

One head:

There are three possible scenarios for this outcome:

a) First coin shows heads, the other two show tails.

b) Second coin shows heads, the other two show tails.

c) Third coin (the one with two heads) shows heads, the other two show tails.

The probability of getting heads on a fair coin is 1/2, so the probability for each of these scenarios is \((1/2)^{2}\) * (1/2) = 1/8. Since there are three possible scenarios, the total probability for one head is 3 * (1/8) = 3/8.

To obtain the probability of obtaining less than 2 heads, we add the probabilities of the two cases discussed above:

P(less than 2 heads) = P(0 heads) + P(1 head) = 1/8 + 3/8 = 4/8 = 1/2.

Therefore, the probability of obtaining less than 2 heads when tossing 3 coins, with one of the coins having a head on both sides, is 1/2.

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We have:

h(x) = f(x) - g(x) = 8x^2 - 3x^4

Taking the derivative, we get:

h'(x) = 16x - 12x^3

Thus, h'(-1) = 16 - 12(-1)^3 = 16 + 12 = 28.

Therefore, h'(-1) = 28.

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The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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Answer:

Step-by-step explanation:

Since mean is the average number of students, the formula for calculating the mean attendance of students is expressed as;

Mean = total number of student/sample size

\(\overline x = \frac{\sum Xi}{N}\)

Given mean = 20

Since the question talks about the first four meetings, the sample size = 4

\(20 = \frac{\sum Xi}{4}\\ \\\sum Xi = 20 * 4\\\\\sum Xi = 80\)

Since the sum total of students for the first four meetings is 80, hence the number of students who attended the meeting is greater than 20

The tree diagram illustrates the probabilities associated with different combinations of weather patterns and seasons of the year. The tree diagram is a visual representation that presents the probabilities of various outcomes resulting from the combination of weather patterns and seasons of the year.

It is a useful tool for understanding the likelihood of specific events occurring based on different factors.

The diagram is structured hierarchically, with the weather patterns forming the first level and the seasons of the year forming the second level. Each branch represents a specific combination, and the probability associated with that combination is indicated on the branch.

By analyzing the diagram, one can observe how the probabilities change depending on the weather patterns and seasons. For instance, certain weather patterns may be more prevalent during specific seasons, resulting in higher probabilities for certain combinations.

Overall, the tree diagram serves as a visual aid to comprehend the probabilities associated with simple events combining weather patterns and seasons of the year, enabling a better understanding of the likelihood of different outcomes based on these factors.

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Answer:

x = 67.5

Step-by-step explanation:

90 + x + 3x = 360            

90 + 4x = 360

4x = 360 - 90

4x = 270

x = 270 / 4

x = 67.5

Hope it helps!!!

The number we are looking for is x - 6.

To determine the number that, when subtracted from x, results in 6, we can set up the equation:

x - y = 6

Here, y represents the unknown number we are trying to find. To isolate y, we can rearrange the equation:

y = x - 6

Therefore, the number we are looking for is x - 6.

It's important to note that in mathematics, without specific values or additional information about x, we cannot determine a unique solution. The expression "6 - xx - 66 + x6 - ( x - 6)" you provided is not clear and does not allow us to solve for x or the unknown number directly. If you have specific values or additional context, please provide them, and I'll be glad to assist you further.

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A scientific hypothesis is a proposed explanation or prediction based on limited evidence or prior knowledge, which is subject to further investigation and testing.

A guess is a speculative, unsupported statement without any logical basis, whereas a hypothesis is an educated assumption derived from existing knowledge, observations, or theories. Unlike a guess, a hypothesis is testable and can be supported or refuted by evidence gathered through scientific methods.

Scientists need a hypothesis to provide a framework for their research and guide their investigations. It helps them define the specific question they want to answer and provides a starting point for designing experiments or making observations. By formulating a hypothesis, scientists can systematically evaluate and analyze data, ultimately leading to a deeper understanding of the phenomenon under investigation.

There are indeed scientific hypotheses that cannot be directly tested or proven due to practical or ethical constraints. For example, hypotheses related to historical events that occurred in the distant past may not have accessible evidence for direct testing. Additionally, some questions related to consciousness, subjective experiences, or philosophical concepts may lie beyond the scope of scientific inquiry, as they may not be objectively measurable or observable.

While science has its limitations, it is a powerful tool for investigating and understanding the natural world. However, there are questions that fall outside the realm of scientific inquiry and require other methods of investigation, such as philosophical or ethical considerations.

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Answer:

yes sssssssssssssssssss

Given:

The area of the blue rug is:

And the area of the red rug is :

So, the area of both of them is the sum of the given areas:

So, the total area =

so, the area of the new rug in factored form = 2 ( 9x + 4 )

Answer:

Is: {(-1,3), (4, 2), (-1, 5)}

Step-by-step explanation:

Because the domain have 2 numbers are the same which is (-1) so that's not a function

Answer:

The answer is the last one (-1,3), (4,2), (-1,5) Hope this helps!

option b is the correct answer

The solution to the system of equations is x = -( 1/3 ) and y = -( 4/3 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the system of equations be A and B

Now , the first equation is

y = 4x   be equation (1)

And , the second equation is

y = x - 1   be equation (2)

Substituting the value of y in equation (1) , we get

4x = x - 1

Subtracting x on both sides of the equation , we get

3x = -1

Divide by 3 on both sides of the equation , we get

x = -1/3

Substituting the value of x in equation (1) , we get

y = -4/3

Hence , the equations are solved

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Answer:

6^5 or 7776

Step-by-step explanation:

6^5 because 6 is multiplied with 6, 5 times. So, it is 6^5.

We can also simplify this number.

=> 6 x 6 x 6 x 6 x 6

=> 36 x 36 x 6

=> 36 x 216

=> 7776

The best fit for the function 5n is c. Linear.

A linear function is a function whose graph is a straight line. The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept. In the given function, 5n, the slope is 5 and the y-intercept is 0. Therefore, the function is a linear function.

An exponential function is a function whose growth rate is proportional to the size of the function. The general form of an exponential function is f(x) = a*b^x, where a is a constant and b is the base. The given function, 5n, does not fit this form, so it is not an exponential function.

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, and a_0 are constants. The given function, 5n, does not fit this form, so it is not a polynomial function.

Therefore, the correct answer is c. Linear.

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The surface area of the rectangular prism with the given length, width, and height is 1,872 square inches.

What is a rectangular prism?

A rectangular prism is simply a three-dimensional solid shape with six faces that are rectangles.

The surface area of a rectangular prism is the sum of the areas of all the faces.

The surface area of a rectangular prism is expressed as:

S.A = 2( wl + hl + hw )

where,

w is the width,

l is the length,

and h is the height;

Thus; A = 2( (24× 18) + (12×18) + (12× 24)

            = 2 ( 432 + 216 + 288 )

            = 2 × 936

            = 1,872 sq inches

Therefore, the surface area of the rectangular prism with the given length, width, and height is 1,872 square inches.

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Answer:

N = 34

Step-by-step explanation:

METHOD I

(hit and trial)

The given two ratios have to be equal.

This means, 24 : N must break down to 12 : 17 after dividing it by some common factor.

The common factor here is 2.

Since,

12 × 2 = 24

17 × 2 = 34

\( \boxed{\mathsf{ \underline{N \: must \: be \: 34}}}\)

(after dividing the first ratio by 2(common factor) we get the second ratio. Meaning that they become equivalent as required by the question).

METHOD II

(mathematical approach)

Ratios can be written in form of fractions as:

\( \boxed{ \mathsf{ \frac{24}{N} = \frac{12}{17} }}\)

Cross multiplying:

\( \implies \mathsf{24 \times 17 = 12 \times N }\)

taking 12 to the denominator:

\( \implies \mathsf{ \frac{24 \times 17 }{12} = N }\)

24 and 12 gets canceled and 2 takes up their spot

(why?

=> 24 ÷ 12 = 2)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{ N = 34 } \)

\( \implies \mathsf{ N = 34} \)

Answer:

Step-by-step explanation: