Help me find the volume of the composite figure

Using it's concept, it is found that the range of the graphed function \(y = \sqrt[3]{-x -1}\) is of all real values.

The range of a function is the set that contains all possible output values for the function.

The parent function \(y = \sqrt[3]{x}\) has all real values as the range, hence any translation of the function, such as \(y = \sqrt[3]{-x -1}\), will have a range of all real values.

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If two triangles are similar, then their internal angles have the same measure.

Since the internal angles of any triangle must sum to 180º, then the angle R must have a measure of 50º and the angle A must have a measure of 50º.

Nevertheless, notice that angles C and B have a measure of 65º while the angles S and T have measures of 67º and 63º respectively.

Since not all the angles from triangle ABC match those of STR, then, these triangles are not similar.

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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The product of two linear functions having same variables will be a quadratic function where as the The product of two linear functions having different variables will be a linear function.

Linear function is the function whose degree is 1.

Degree of a function is the highest power of the variable of the function.

Let us take two examples.

1. Suppose the two linear functions are -

f(x) = 2x + 3 and g (x) = x + 5

The product of f(x) and g(x) will be

(2x + 3)(x + 5)

=2x (x + 5) + 3 (x + 5)

= 2x² + 10x + 3x + 15

= 2x² + 13x + 15

Here, f(x) and g(x) are the functions having same variables so there product is a quadratic function.

2. Suppose the two linear functions are -

f(x) = 2x + 3 and g (y) = y + 5

The product of f(x) and g(y) will be

(2x + 3)(y + 5)

=2x (y + 5) + 3 (y + 5)

= 2xy + 10x + 3y + 15

Here, f(x) and g(y) are the functions having different variables so there product is a linear function.

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Answer:

its B and A

Step-by-step explanation:

Answer:

its in between the fist and second one cuusing what is given thats what i figured out

Step-by-step explanation:

3 x 36= 108 / 3 x 15 = 45

9 x 12 = 108 / 9 x 5 = 45

6 x 18 = 108 / 6 x 7 = 42

i hope this helps :)

The nth term of the arithmetic sequence 300,250,200 is 350-50n if the common ratio is -50

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an arithmetic sequence:

300,250,200

The first term a = 300

Common difference d = 250-300 = -50

nth term:

A(n) = a + (n-1)d

A(n) = 300 + (n-1)(-50)

A(n) = 300 -50n + 50

A(n) = 350—50n

Thus, the nth term of the arithmetic sequence 300,250,200 is 350-50n if the common ratio is -50

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Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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There does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.

Given two norms, p and q, on a vector space V, we say that p is less than q, written p ≤ q, if there exists a constant C > 0 such that for all vectors v in V,

p(v) ≤ Cq(v)

Now, let's consider the three norms:

   The 1-norm: p1(v) = ∑|v_i|

   The 2-norm: p2(v) = √(∑v_i^2)

   The infinity-norm: p∞(v) = max{|v_i|}

We are given that p1(v) ≤ p2(v) for all vectors v in V and that p2(v) ≤ p∞(v) for all vectors v in V. We want to show that there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V.

Suppose for the sake of contradiction that such a constant C does exist. Then, for any non-zero vector v in V,

p∞(v) ≤ Cp1(v)

max{|v_i|} ≤ C ∑|v_i|

Since v is non-zero, there exists an index i such that |v_i| > 0. We can divide both sides of the inequality by |v_i| to get:

1 ≤ C ∑|v_j| / |v_i|

Now, since p1(v) ≤ p2(v) for all vectors v in V, we have:

p1(v) = ∑|v_j| ≤ √(∑v_j^2) = p2(v)

So, we can substitute this into the inequality above to get:

1 ≤ C √(∑v_j^2) / |v_i| = Cp2(v) / |v_i|

Finally, since p2(v) ≤ p∞(v) for all vectors v in V, we have:

p2(v) / |v_i| ≤ p∞(v) / |v_i| = 1

So, we have reached a contradiction:

1 ≤ Cp2(v) / |v_i| ≤ C

This contradicts the assumption that C > 0, so there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.

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Account balance of Ginny after withdrawal = $ 20 .

Given : Ginny's account balance before withdrawal ie . $ 40

            Her withdrawal amount ie . $ 20

To find : account balance after withdrawal

Calculation : Opening balance = $ 40 ie . initially Ginny had $ 40 .

After withdrawal ( taking out ) of $ 20 ,

Ginny has 40 - 20 = $ 20 left .

After adjustment , final amount = $ 20 .

Therefore , account balance of Ginny after withdrawal = $ 20 .

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The coordinates of R(x₂, y₂) is (6,5)

Given, the directed line segment PR is divided by point Q (0,-1) in a ratio of 4:3. point P (-8,-9)

We know the formula for section formula here

Q(x, y) = ((x₂m + x₁n)/(m + n), (y₂m + y₁n)/(m + n))

Here, (x₁, y₁) = (-8, -9)

(x,y) = (0,-1)

we have to find (x₂, y₂)

(0, -1) = ((4x₂ + (- 24))/(4+3) , (4y₂ + (- 27))/(3+4))

(0, -1) = ((4x₂ - 24)/7 , (4y₂ - 27)/7)

(4x₂ - 24)/7 = 0

4x₂ - 24 =0

4x₂ = 24

x₂ = 6

(4y₂ - 27)/7 = -1

4y₂ - 27 = -7

4y₂ = 20

y₂ = 5

Therefore, the coordinates of R(x₂, y₂) is (6,5)

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Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

For this problem, we are given the function that models the cost of producing a tractor in the function of the number of tractors built. We need to determine the number of tractors we should build to incur the minimum cost.

To solve this problem, we need to find the minimum value for the given function, which happens to be the vertex of the quadratic function. So we have:

We need to build 275 tractors.

In the standard equation for a line, y = mx + b, the variable b represents the y-intercept of the line.

The standard equation of a line is a way of representing a straight line in a two-dimensional Cartesian coordinate system. It is also called the slope-intercept form.

The slope represents the steepness of the line, while the y-intercept represents the value of y when x is equal to 0.

This form is useful for graphing lines, as well as for finding the equation of a line given its slope and y-intercept.

The y-intercept in the standard equation is the point where the line intersects the y-axis, which means it is the value of y when x = 0.

The slope of the line, represented by "m", determines how steep the line is, while the y-intercept determines where the line crosses the y-axis.

Thus, the b in the standard equation represents y-intercept of the line.

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Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Answer:

1. sinα = +2√5/5 2.  cosα = +√5/5 3. cotα = +1/2 4. secα = +√5 5. cosecα = +√5/2.

Step-by-step explanation:

1. Since tan(α) = 2 and 1 + cot²α = cosec²α

1 + 1/tan²α = 1/sin²α

1 + 1/2² = 1/sin²α

1 + 1/4 = 1/sin²α

5/4 = 1/sin²α

sinα = ±√(4/5)

sinα = ±2/√5

sinα = ±2√5/5

Since 0<α<π/2, sinα = +2√5/5

2. sin²α + cos²α = 1

(2/√5)² + cos²α = 1

4/5 + cos²α = 1

cos²α = 1 - 4/5

cos²α = 1/5

cosα = ±1/√5

cosα = ±√5/5

Since 0<α<π/2, cosα = +√5/5

3. cotα = 1/tanα = 1/2

Since 0<α<π/2, cotα = +1/2

4. secα = 1/cosα = 1/±1/√5 = ±√5

Since 0<α<π/2, secα = +√5

5. cosecα = 1/sinα = 1/±2/√5 = ±√5/2

Since 0<α<π/2, cosecα = +√5/2

Answer:

The answer; – 15

\( - 15 \: \: - 19 = - 34\)

I hope I helped you^_^

Answer:

-15

Step-by-step explanation:

34-19=15

CHECK:

-15-19=-34 (correct, and proven)

       Hence,  The solution is:  

        x   =     1

        y   =  - 2

        z   =     2

Step-by-step explanation:

        3x  +  y  =  1

        x  -  y  +  z  =  5

        3x  +  y  +  z  =  3

        x  +  y  =  -1

        x  +  y  =   -1

        3x  +  y  =  1

        x   =   1

        y  =  -2

        1   -  (-2)  +   z    =   5

        z    =   2

       Hence, The Solution is:   x  =  1,   y  =  -2,    z   =  2

I hope this helps you!

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

78.333333333

Step-by-step explanation:

Answer:

C: 90

Step-by-step explanation:

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer:

8

Step-by-step explanation:

45 points for a free movie - 25 points = 20 remaining points needed

20 / 2.5 = 8

She would need 8 visits to earn a free movie ticket.

Answer:

8

Step-by-step explanation:

25+2.5x=45

subtract 25 from each side

2.5x=20

divide both sides by 2.5

x=8

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Mr Simpson's class:

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

Answer: it’s b because if you times that by anything it will always be a product I think

Step-by-step explanation: