What is the probability of rolling a number greater than 2 and rolling an even number on a 8 sided die

a. The domain of a function is the set of all possible values that the independent variable can take.

In this case, the independent variable is human years which takes values between 1 and 7, then the domain of the function is [1, 7].

b. The range of a function is the set of all possible values that the dependent variable can take.

In this case, the dependent variable is dog years which takes values between 15 and 44, then the range of the function is [15, 44].

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Greetings from Brasil...

First, let's make the mixed fraction improper:

- (3 3/8)

- { [(8 · 3) + 3]/8}

- { [24 + 3]/8}

- {27/8}

- (3 3/8) - (7/8)

- (27/8) - (7/8)

as the denominators are equal, we operate only with the numerators

- 34/8      simplifying

Answer:

Step-by-step explanation:

-3 3/8 - 7/8

convert -3 3/8 to improper fractions

_   27   _   7

    8            8

_   27 - 7

       8      

simplify

_   34

     8

convert to proper factions

_   17

     4

-  4 ¹/₄

Step-by-step explanation:

\( \longmapsto \rm \dfrac{6m + 7}{3m + 2} = \dfrac{5}{4} \)

By cross multiplication,

→ 4(6m + 7) = 5(3m + 2)

→ 24m + 28 = 15m + 10

→ 24m - 15m = 10 - 28

→ 9m = -18

→ m = -18 ÷ 9

→ m = -2

Value of m is -2.

The length of segment BD on the triangle is given as follows:

BD = 12.5 units.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel lines in this problem are given as follows:

BC and DE.

Then the proportional segments are given as follows:

AB and AC.

Thus the proportional relationship that relates these side lengths is given as follows:

(x - 2)/3 = (x + 3)/5.

Applying cross multiplication, the value of x is obtained as follows:

3x + 9 = 5x - 10

2x = 19

x = 19/2

x = 9.5.

Then the length of BD is obtained as follows:

BD = x + 3 = 9.5 + 3 = 12.5.

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Answer:

20

Step-by-step explanation:

We know that the diagonals are bisected, which means

2x+4 = 6x-8

Subtract 2x from each side

2x+4-2x = 6x-8-2x

4 = 4x -8

Add 8 to each side

4+8 = 4x-8+8

12 = 4x

Divide by 4

12/4 = 4x/4

3 =x

We want to know CF = DB = 2x+4 + 6x -8

CF = 8x-4

     = 8(3) -4

    = 24-4

   = 20

The Laplace transform of the solution y(t) to the given initial value problem y"+y=g(t), y(0) = -4, y'(0) = 0, where g(t) = t, t<6; 5, t>6 is represented by the function Y(s) (in terms of s).

To solve the initial value problem y"+y=g(t) with the given initial conditions, we can take the Laplace transform of both sides of the equation. This transforms the differential equation into an algebraic equation in the Laplace domain.

Applying the initial conditions to the transformed equation, we can find the Laplace transform, Y(s), of the solution y(t). The exact expression for Y(s) can be obtained by using the table of Laplace transforms and the properties of Laplace transforms.

By substituting the Laplace transform of the input function, g(t), into the transformed equation, we can solve for Y(s) in terms of the Laplace variable s.

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The standard form of the equation of an ellipse is `(x - h)^2/a^2 + (y - k)^2/b^2 = 1`, Therefore, the equation of the ellipse is `(x - 2)^2/16 + (y - 1)^2/7 = 1`

In order to find the equation of an ellipse given `v^(1)(2,-3) v^(2)(2,5)` and `foci (2,-2) f^(2) (2,4)`, we can use the following steps:

1: Determine the center of the ellipse. The midpoint of the line segment joining the foci gives us the center of the ellipse.

Therefore, the center of the ellipse is `(2,1)`.

2: Find the distance between the foci, which is `2c`.Using the distance formula, `d = sqrt((y2 - y1)^2 + (x2 - x1)^2)`, we get `d = sqrt((4 - (-2))^2 + (2 - 2)^2) = 6`.

Therefore, `2c = 6` and `c = 3`.

3: Find the distance between the center and vertex. The distance between the center and vertex is `a`.

Using the distance formula, `d = sqrt((y2 - y1)^2 + (x2 - x1)^2)`, we get `d = sqrt((5 - (-3))^2 + (2 - 2)^2) = 8`.Therefore, `a = 4`.Step 4: Find the equation of the ellipse.

The standard form of the equation of an ellipse is `(x - h)^2/a^2 + (y - k)^2/b^2 = 1`, where `(h, k)` is the center of the ellipse, `2a` is the length of the major axis, and `2b` is the length of the minor axis. Since the major axis is horizontal, `a^2 = 4^2 = 16` and `b^2 = 3^2 - 4^2 = -7`. Since `b^2` is negative, we can rewrite the equation as `(x - 2)^2/16 + (y - 1)^2/7 = 1`.

Therefore, the equation of the ellipse is `(x - 2)^2/16 + (y - 1)^2/7 = 1`

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Tom earns $32,660.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean. The mean salary is $27,800 and the standard deviation is $5400, so Tom's salary is $27,800 + 0.9 * $5400 = $32,660.

Here is a more detailed explanation of how to calculate Tom's salary:

The mean salary is $27,800.

The standard deviation is $5400.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean.

To calculate Tom's salary, we can use the following formula:

Salary = Mean + (Z-score * Standard deviation)

Substituting the known values into the formula, we get:

Salary = $27,800 + (0.9 * $5400)

Salary = $32,660

Therefore, Tom earns $32,660.

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The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = \(1\frac{1}{2}\) = 3/2

Last term an = \(2\frac{1}{2}\) = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

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Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are \(1\frac{1}{2}\), \(2\frac{1}{2}\) and 1/9 respectively, how many terms has the sequence?

The equation for the area of the rectangle is 22 = ( 3x + 1 )( 2x + 1 ), the value of x is 1.5 and the width measure 4 units.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The area of a rectangle is expressed as;

Area = length × width

From the diagram:

Area = 22 m²

Length = 3x + 1

Width = 2x + 1

a) Write the equation for the area of the rectangle:

Area = length × width

22 = ( 3x + 1 )( 2x + 1 )

b) We solve for x:

( 3x + 1 )( 2x + 1 ) = 22

Expand the bracket:

6x² + 5x + 1 = 22

6x² + 5x + 1 - 22 = 0

6x² + 5x + 21 = 0

Factor by grouping:

( 2x - 3 )( 3x + 7 ) = 0

Equate each factor to 0:

( 2x - 3 ) = 0

2x - 3 = 0

2x = 3

x = 3/2 = 1.5

Next, ( 3x + 7 ) = 0

3x + 7 = 0

3x = -7

x = -7/3

Since, we dealing with dimension, we take the positive value:

Hence, the value of x = 1.5

c) The width of the rectangle is:

Width = 2x + 1

Plug in x = 1.5

Width = 2( 1.5 ) + 1

Width = 3 + 1

Width = 4

Therefore, the width of the rectangle is 4.

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In summary, the relationships between the corresponding sides and angles of similar triangles are: Corresponding sides are proportional and congruent.

When two triangles are similar, the corresponding sides of the triangles are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is equal. Similarly, the corresponding angles of similar triangles are congruent. This means that the angles in the two triangles that correspond to each other are equal in measure.

When two triangles are similar, it means that they have the same shape but possibly different sizes. The concept of similarity implies that the corresponding sides of the triangles have the same proportional relationship.

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Answer:

her score would be -22

Step-by-step explanation:

20-42=-22

Answer:

A good chance because getting heads is most likely what you will get

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Given that:

Number of options available for transmission = 2 (Standard or Automatic)

Number of options for doors = 2 (2 doors or 4 doors)

Number of exterior colors available = 10

To find:

Total number of outcomes = ?

Solution:

First of all, let us calculate the number of outcomes for the transmission mode and number of doors options.

1. Standard - 2 doors

2. Standard - 4 doors

3. Automatic - 2 doors

4. Automatic - 4 doors

Number of outcomes possible = 4 (which is equal to number of transmission mode available multiplied by number of doors options i.e. 2\(\times 2\))

Now, these 4 will be mapped with 10 different exterior colors.

Therefore total number of outcomes possible :

Number of transmission modes \(\times\) Number of doors options  \(\times\) Number of exterior colors

2 \(\times\) 2 \(\times\) 10 = 40

The number of possible outcomes of a new car will be 40. Then the correct option is B.

A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite sample is shown as a curly bracket {..}.

A new car is available with standard or automatic transmission, two or four doors, and it is available in 10 exterior colors.

Then the number of possible outcomes will be

\(\rm Possible \ outcomes = 2*2*10\\\\Possible \ outcomes = 40\)

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Strawberries, apples, cherries, spinach, nectarines, and grape samples were positive for residues of two or more pesticides in more than 90% of the cases. The most pesticides were found in kale, collard, mustard greens, spicy peppers, and bell peppers totaling 103 and 101 pesticides, respectively.

According to the Environmental Working Group's 2022 Shoppers Guide to Pesticides in Vegetables, strawberries and spinach continue to have the highest pesticide levels of any product categories.

According to the EWG, more than 70% of non-organic vegetables contained pesticide residue. Nearly all the produce had pesticide residue levels below limits set by U.S. regulators.

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Answer:

-4

Step-by-step explanation:

Try writing the question in variable form using x as "a number"

\(\frac{1}{2} x - 3 = -5\)

add 5 to the right side of the equal sign and then do the same thing to the left of the equal sign (do the opposite of the number to both sides)

\(\frac{1}{2} x +2 = 0\)

now we kind of do the same process but with the number 2. Subtract two from the left and right side

\(\frac{1}{2}x = -2\)

now since this equation is saying "multiply one half by x" we can do the OPPOSITE so now divide one half from both sides

\(x= \frac{-2}{.5}\)

NOTICE THAT I CONVERTED 1/2 to .5 they mean the same thing

so now just divide -2 by .5

the answer is -4

The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

According to the question,

We have the following information:

A line is passing through two points (2,7) and (-4,19).

We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:

m = (y2-y1)/(x2-x1)

(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)

In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.

m = (19-7)/(-4-2)

m = 12/(-6)

m = -2

Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

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In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

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Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.

Answer:

16, OPT= 18 OPA=38

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - 5 = 2(x - 0)

y - 5 = 2x -0

y = 2x + 5

answer is D

Answer:

Step-by-step explanation:

We need to know the value of dd/dt. However, this information is not given in the problem statement. Without the value of dd/dt, we cannot determine the exact rate at which the height of the pile is increasing.

To find the rate at which the height of the pile is increasing, we need to use related rates and the formula for the volume of a cone.

Let's denote the height of the cone as h and the base diameter as d. We know that the height is twice the base diameter, so h = 2d.

The formula for the volume of a cone is given by V = (1/3)πr²h,

where r is the radius of the base. Since the base diameter is twice the radius, we can substitute r = d/2.

The rate at which gravel is being dumped into the cone is given as 30 cubic feet per minute. This means that dV/dt = 30.

We are asked to find dh/dt when the height of the pile is 10 feet, so we need to find dh/dt when h = 10.

First, we need to express the volume V in terms of h and d:

V = (1/3)π(d/2)²h

 = (1/3)π(d²/4)h

 = (1/12)πd²h

Now, we differentiate both sides of the equation with respect to time t:

dV/dt = (1/12)π(2d)(dd/dt)h + (1/12)πd²(dh/dt)

Since h = 2d, we can substitute 2d for h in the equation:

dV/dt = (1/12)π(2d)(dd/dt)(2d) + (1/12)πd²(dh/dt)

      = (1/6)πd²(dd/dt) + (1/12)πd²(dh/dt)

Now we can substitute dV/dt = 30 and h = 10 into the equation to solve for dh/dt:

30 = (1/6)πd²(dd/dt) + (1/12)πd²(dh/dt)

To find dh/dt, we need to know the value of dd/dt. However, this information is not given in the problem statement. Without the value of dd/dt, we cannot determine the exact rate at which the height of the pile is increasing.

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Answer:

4. - 11

5. 3

6. 14

7. - 60

that it is

Answer:

plug in -8 for h(x)

Step-by-step explanation:

-8=-4x-4

-4=-4x

x=1

Answer:

x=1

Step-by-step explanation:

We are looking for the input value when given an output value. We know that for any value of x, the output, or h(x) is -4x-4. Now, we are given that -4x-4 of some value x is equal to -8, so we set them equal and solve.

-4x-4=-8

-4x=-4

x=1

Answer:

12.4cm (rounded to nearest tenth)

Step-by-step explanation:

To find the length of an arc, you have to find the circumference of the full circle itself multiplied by the angle of the arc over 360°. The circumference of a circle is pi × r × 2.

Length of arc = \(\frac{90}{360}\) × 3.14 × 7.9 × 2

                      = 12.403

                      ≈ 12.4cm (rounded to nearest tenth)

Answer:

x+1=12

hope it will help you