What is the volume of this composite solid? 5 m 6 m 9 m 12 m​

The simplified exponential expression is given as follows:

[tex]21^6[/tex]

The exponential expression in the context of this problem is defined as follows:

[tex]\frac{21^3 \times 21^5}{21^2}[/tex]

First we look at the numerator, when we have two terms with the same base and different exponents multiplying, we keep the base and add the exponents, hence:

21^3 x 21^5 = 21^8

Now we have the following division operation:

21^8/21^2.

When we have two terms with the same base and different exponents dividing themselves, we keep the base and subtract the exponents, hence:

21^(8 - 2) = 21^6.

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Answer:

3 and -16

Step-by-step explanation:

To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48

We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:

3 x (-16) = -48

Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.

Answer: -3, 16

Step-by-step explanation:

option D 20  is correct answer .the perimeter of polygon XYDB is 20.

what is  polygon ?

A polygon is a closed geometric shape made up of straight line segments connected end-to-end. It is a two-dimensional figure that has three or more sides and angles. Polygons can be classified according to the number of sides

In the given question,

To find the perimeter of polygon XYDB, we need to add up the lengths of all its sides. Since all side lengths are given as 5, we can simply multiply 5 by the number of sides to get the perimeter.

Polygon XYDB has four sides, so the perimeter is:

Perimeter = 4 × 5 = 20

Therefore, the perimeter of polygon XYDB is 20.

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Answer:

D. 20 cm

Step-by-step explanation:

Answer:

Summer for 9th Graders: 0.14

Fall for 10th Graders: 0.15

Spring overall total: 0.36

Summer overall total: 0.22

Fall overall total: 0.33

Winter overall total: 0.09

Step-by-step explanation:

Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.

However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency

Answer:

3,4,5 is the answer

Step-by-step explanation:

for the explanation using pythagoras theoem

[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]

may you give me branliest as you promised

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

As the counselor recommends that the client reconsider marrying her fiancé based on his belief discretion, this is an example of harmful use of bias.

The counselor's personal beliefs against interfaith marriages are influencing their professional advice, which can be harmful to the client's well-being and may even violate ethical guidelines for mental health professionals.

The counselor should provide unbiased and objective guidance to the client based on their specific needs and circumstances, rather than imposing their own beliefs or values onto the client's decision-making process.

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Answer:

[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]

[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]

[tex]4b - 32 = 12[/tex]

[tex]4b = 44[/tex]

[tex]b = 11[/tex]

For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.

Answer:

24

Step-by-step explanation:

Answer:

A. $24

Step-by-step explanation:

Given:

Solve for average tip:

Answer:

Thus, the waiter's average tip per table is $24.

The answer is A.

Arun's purple paint will be redder.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.

Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:

7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.

Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:

3 / (2 + 3) × 100% = 60%.

Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.

Therefore, the answer is Arun's purple paint will be redder.

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Answer:

To determine the line of reflection if the image of Y, Y′, is at (-6, -1), we need to find the perpendicular bisector of the line segment connecting Y and Y′. This perpendicular bisector will be the line of reflection.

The midpoint of the line segment YY′ is:

[(6 + (-6))/2, (-1 + (-1))/2] = (0, -1)

The slope of the line segment YY′ is:

(-1 - (-1))/(-6 - 6) = 0/(-12) = 0

Since the slope of YY′ is 0, the perpendicular bisector of YY′ is a vertical line passing through its midpoint (0, -1), which is the y-axis. Therefore, the line of reflection is the y-axis.

Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.

What is selling price?

Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.

If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.

Let P be the original selling price of the dress. Then:

0.3P = $104.98

Solving for P, we get:

P = $104.98 / 0.3

P = $349.93

Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.

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Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)

A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.

In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.

For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.

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In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

To read the time on an analogue clock, look in the direction its hands are pointing. The current hour is indicated by the smallest hand, the current minute by the largest hand, and the current second by the thinnest hand.

There are 24 hours in a day, and the hour hand completes two full rotations of the clock because the numbers on the dial only go up to 12. once, from noon to midnight, and once, from midnight to noon.

Given data:

Current time on clock = 1:00

Hour hand at 1 .

Minute hand at 12.

Number of hours must pass for the hands to form a straight angle:

When

minute hand is at 12 and hour hand will be at 6.

Number of hours = 6: 00 - 1: 00

Number of hours = 5 hours

Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

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None of the given numbers make the equation 8/y² + 2 true.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.

Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.

Substituting y=1 would give us:

8/1² + 2 = 8 + 2 = 10

So, 1 is not the answer.

Substituting y=2 would give us:

8/2² + 2 = 8/4 + 2 = 2 + 2 = 4

So, 2 is not the answer.

Substituting y=3 would give us:

8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888

So, 3 is not the answer.

Substituting y=4 would give us:

8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5

So, 4 is not the answer.

Therefore, none of the given numbers make the equation 8/y² + 2 true.

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the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h

what is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid

In the given question,

To find the area of a trapezoid, we use the formula:

A = (1/2) * (b₁ + b₂) * h

where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).

In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.

Using the Pythagorean theorem, we can find the length of the altitude:

a² + (b₁ - b₂)² = (2a)²

Simplifying and solving for a, we get:

a² + (b₁- b₂)² = 4a²

3a² = (b₁ - b₂)²

a = (1/√3) * |b₁ - b₂|

Since we know that the sum of the non-parallel sides is 10 km, we can write:

b₁ + b₂ = 10

Let's assume that b1 is the longer base, so we can write:

b₁ = 8 km

b₂ = 10 - b₁ = 2 km

Substituting these values into the formula for the altitude, we get:

a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km

Now we can use the formula for the area of a trapezoid to find the area:

A = (1/2) * (b1 + b2) * h

A = (1/2) * (8 + 2) * 2√3

A = 10√3 km²

Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).

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The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .

A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.

The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.

A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

In the given equation y = x²  + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.

Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.

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The complete question is :

Which statement explains the type of function that is represented by the equation y=x² +9?

A The function is linear because it contains more than one term.

B) The function is linear because the variable x is raised to the second power.

C) The function is nonlinear because it contains more than one term.

D) The function is nonlinear because the variable x is raised to the second power.

Step-by-step explanation:

36^3/4   *    36 ^-1/4    =   36 ^( 3/4 - 1/4 )  =  36 ^1/2 = sqrt (36 ) = 6

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

The equation of the circle with center (3,6) and tangent to the x-axis is (x - 3)² + 36 = r²

In mathematics, a tangent is a straight line that touches a curve or surface at a single point and is perpendicular to the radius or line that passes through that point. The point of contact between the tangent and the curve or surface is called the point of tangency.

In geometry, the tangent to a circle is a straight line that intersects the circle at exactly one point. This point is called the point of tangency, and the tangent is perpendicular to the radius of the circle at that point.

The tangent is an important concept in calculus, where it is used to define the derivative of a function. The derivative of a function f(x) at a point x=a is defined as the slope of the tangent line to the graph of f(x) at the point (a, f(a)). This slope measures the rate at which the function is changing at that point.

If an equation is tangent to the x-axis, this means that it only intersects the x-axis at one point, which has a y-coordinate of zero. So, we need to write an equation of a circle with center (3,6) that intersects the x-axis at one point with a y-coordinate of zero.

Let the radius of the circle be r. Since the center of the circle is (3,6), the equation of the circle can be written in the form:

(x - 3)² + (y - 6)² = r²

Since the circle is tangent to the x-axis, we know that it intersects the x-axis at (x,0), where x is a point on the x-axis. Substituting y=0, we get:

(x - 3)² + (0 - 6)² = r²

Simplifying this equation, we get:

(x - 3)² + 36 = r²

So, the equation of the circle with center (3,6) and tangent to the x-axis is:

(x - 3)² + 36 = r²

Note that there are many possible values for r that would satisfy this equation, since we haven't specified the size of the circle. We only know that it is tangent to the x-axis and has center (3,6).

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The complete question is :

How do you write an equation with center (3,6), tangent to the x-axis?

Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

There are 52 quarters and 15 half-dollars

Let's represent the number of half-dollars as "x" and the number of quarters as "y".

From the problem statement, we know that:

x + y = 67 (because there are a total of 67 coins)

y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)

We can use substitution to solve for x:

x + (3x + 7) = 67

4x + 7 = 67

4x = 60

x = 15

So there are 15 half-dollars. We can use this to find the number of quarters:

y = 3x + 7

y = 3(15) + 7

y = 52

So there are 52 quarters.

Therefore, there are 52 quarters and 15 half-dollars.

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Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

What is the unit price?

In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.

According to given information

a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:

y - 0 = (-2/9)x

y = (-2/9)x

Substituting x = 18n, where n is the number of $18 price increases, we have:

y = (-2/9)(18n) = -4n

Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:

p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),

where q0 is the quantity of gaming systems sold at the original price of $180.

b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:

R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q

c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:

R'(q) = 9q - 9q0/2 = 0

q = q0/2

Substituting q = q0/2 into the revenue equation, we have:

R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)

R(q0/2) = (9/8)*q0^2 + (45/2)*q0

To find the corresponding price, we can use the expression for p(q) found in part (a):

p(q0/2) = 180 + (9/2)(q0/2 - q0)

p(q0/2) = 135

Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

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Answer: less than

Step-by-step explanation:

Answer:

at 6 pm

Step-by-step explanation:

I'm 99.9% sure that it's correct, please tell me if I'm wrong

Answer:

27.78%

Step-by-step explanation:

To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.

Total spending = food + rent + other + fun

Total spending = $400 + $500 + $600 + $300

Total spending = $1800

So, the percentage of the total spending that is on rent is:

($500 / $1800) x 100% = 27.78%

Therefore, approximately 27.78% of the total spending is on rent.