1. Find the volume of the cylinder. Round to the
nearest hundredths.
5 CM
0.75 CM

The value of the median of the trapezoid is, 14 units

In the given diagram a trapezoid has been given with two bases,

AB = 7 units and CD = 21 units

We have to find, the median of the trapezoid.

Since, We know that median of a trapezoid is half of the sum of bases.

So, We get;

median of ABCD = 1/2 (AB + CD)

                                = 1/2 ( 7 + 21 )

                                = 1/2 ( 28 )

                                = 14 units.

Thus,. The value of the median of the trapezoid is, 14 units

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The Range of a generic Exponential Equation such as 5³ uis y>0.

The range of a generic exponential equation such as 5³ depends on the specific form of the equation.

However, based on the given options, the correct answer would be:

y > 0

The range of exponential functions with a positive base (such as 5³) is always greater than zero.

This means that the output values (y) of the function will be positive for all possible input values (x).

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Answer:8π

Step-by-step explanation:

To find the area of the circle circumscribed about an isosceles right triangle, we first need to determine the length of the hypotenuse of the triangle.

Given that the area of the isosceles right triangle is 8, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

Since the triangle is isosceles and right-angled, the base and height are equal. Let's denote the base and height as 'x'.

8 = (1/2) * x * x

16 = x^2

x = √16

x = 4

Therefore, the length of the hypotenuse of the triangle is 4√2 (using the Pythagorean theorem).

Now, the diameter of the circle is equal to the hypotenuse of the triangle. So, the diameter of the circle is 4√2.

The radius of the circle is half the diameter, so the radius is (4√2)/2 = 2√2.

The area of a circle is calculated using the formula:

Area = π * radius^2

Plugging in the value of the radius, we get:

Area = π * (2√2)^2

Area = π * 4 * 2

Area = 8π

Therefore, the area of the circle circumscribed about the isosceles right triangle with area 8 is 8π.

Answer:

input 1 : output 3

Step-by-step explanation:

For the graph y = x+2/x where x = 1, y = 3. So find which equation when input 1, outputs 3.

The vertex of the parabola of the given quadratic equation is (-5, 1).

The given quadratic equation is y²+4x-2y+21=0.

Rewrite in vertex form and use this form to find the vertex (h,k).

Here, y²-2y=-4x-21

Add 1 to both the sides of an equation, we get

y²-2y+1=-4x-21+1

(y-1)²=-4x-20

(y-1)²= -4(x+5)

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

So, the vertex (-5,1)

Therefore, vertex of the parabola of the given quadratic equation is (-5, 1).

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"Your question is incomplete, probably the complete question/missing part is:"

Complete the square to find the vertex of this parabola.

y²+4x-2y+21=0.

Answer:

Math mode activated

Step-by-step explanation:

The number of machines that become inoperative during a given day follows a binomial distribution with parameters n = 100 (the number of machines) and p = 0.002 (the probability that a machine will become inoperative).

The probability that fewer than two machines will be inoperative during a particular day is the sum of the probabilities that zero or one machine will be inoperative. This can be calculated using the binomial probability mass function as follows:

P(X < 2) = P(X = 0) + P(X = 1)

= (100 choose 0) * (0.002)^0 * (1 - 0.002)^100 + (100 choose 1) * (0.002)^1 * (1 - 0.002)^99

= 1 * 1 * 0.817 + 100 * 0.002 * 0.818

= 0.817 + 0.164

= 0.981

Therefore, the probability that fewer than two machines will be inoperative during a particular day is approximately 0.981.

The perimeter of figure is,

P = 24.50 feet

And, the area of the figure is,

A = 45.68 feet²

Since, we know that;

The perimeter of a circle is equal to the circumference

C = 2πr

where,

C is the circumference of the circle

r is the radius of the circle

we have, r = 4 feet

substitute in above equation,

C = 2 × 3.14 × 4

C = 25.12 feet

In the figure

the triangle ABC is a right triangle,

Applying the Pythagoras Theorem find the length side CB

CB² = AB² + AC²

we have, AB = AC = 4 feet

CB² = 4² + 4²

CB² = √32

CB = 5.67 feet

The perimeter of the figure is equal to 3/4 of the circumference plus the length side CB

so we get;

P = 3/4 (25.12) + 5.66

P = 24.50 feet

Now, we know that,

the area of a circle is equal to

A = πr²

where, r is the radius of the circle

we have, r = 4 feet

substitute

A= 3.14 × 4²

A = 50.24 feet²

the area of the triangle ABC is equal to,

A = 1/2 bh

Here, b = √32 ft

h = √32/2 ft

Hence, WE get;

A = 1/2 x √32 x √32/2

A = 8 feet²

Since, the area of the figure is equal to 3/4 of the area of the circle plus the area of the triangle ABC,

A = 3/4 (50.24) + 8

A = 45.68 feet²

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Plotting the polar coordinates: (-5, 5pi/4) matched with the image at

C (image plotted is attached)

Polar coordinates are a coordinate system used to describe the position of a point in a two-dimensional plane.

Unlike rectangular coordinates (x, y), which use Cartesian coordinates to represent a point's position as distances along the x and y axes, polar coordinates represent a point's position using a distance from the origin (r) and an angle from the positive x-axis (θ).

The graph calculator showed the graph matching with the option C

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The resulting matrix is shown below:

3 0   1   1

4 20 2 20

3 -2  0   6

A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

We can write  resulting matrix after replacing R2 with R2 + 3R3 as:

3 0 1 1

4 2 2 2

3 -2 0 6

We Perform the row operation:

R2 = R2 + 3R3

3 0 1 1

4 2 2 2 + 3(6) = 20

3 -2 0 6

In conclusion, the resulting matrix is:

3 0   1    1

4 20 2 20

3 -2  0   6

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Mr. Casey's class raised $448 during the fundraiser.

Percentage is simply number or ratio expressed as a fraction of 100.

Given that, Ms. Dawson’s class raised $560, which is 25% more than Mr. Casey’s class raised.

To determine ​how much Mr. Casey’s class raised,

We represent the amount raised by Mr. Casey's class as "x".

Since Ms. Dawson's class raised 25% more than Mr. Casey's class.

To calculate 25% more than x, we can multiply x by 1.25

(since 25% is equivalent to 0.25 in decimal form and 100% is 1) and set it equal to $560.

Hence:

1.25x = 560

To solve for x, we divide both sides of the equation by 1.25:

x = 560 / 1.25

x = 448

Therefore, Mr. Casey's class raised $448.

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The function has a maximum value of 1

Option D is the correct answer.

We have,

The y-coordinate on the graph is the function value.

Now,

From the graph of the function,

The maximum is at the point = (-2, 1)

This means,

1 is the maximum value.

And,

From the graph of the function,

The minimum value can be calculated because the graph is infinitely down the graph.

Thus,

The function has a maximum value of 1

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The area measured is 129 .

Given function,

y=2x²+4x+3

Now,

The area under the curve is given by integration over the specified region.

Thus,

[tex]\int\limits^5_2 {2x^2 + 4x + 3} \, dx[/tex]

Now integrating the above function,

[tex]\int\limits^5_2 {2x^2} \, dx + \int\limits^5_2 {4x} \, dx + \int\limits^5_2 {3} \, dx[/tex]

Solving the integration and put the limits.

Thus,

Area under the curve is 129 .

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The break even number is 500 units

The parameters given in the question are

Fixed expenses is $7,000

Contribution margin is $14/unit

The formular for break even number is

= fixed expenses/contribution margin

= 7000/14

= 500

The break even number is 500 units

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Answer: It is around 3000 dolallars for you

Step-by-step explanation:

I am a Tax Preitor

The cost to manufacture a unit of energy drink, the selling price and the fixed monthly cost, indicates;

a. C(x) = 1.20·x + 8,000

b. R(x) = 2·x

c. Please find attached the graph of the Revenue and Cost functions showing the break-even point, created with MS Excel.

d. 10,000 units

e. $20,000

The cost function is an function that describes the cost of producing a specified number if units of a services or goods.

a. The cost of production = The variable cost + The fixed cost

The variable cost = The cost per unit × The number of units produced

The cost per unit = $1.20

The fixed cost per month = $8,000

Let x represent the number of units produced per month, we get;

Cost of production, C(x) = 1.20·x + 8,000

b. The revenue function, R(x) = The selling price per item sold × The number of items sold

The selling price per energy drink = $2

Let x represent the number of units sold, we get;

Therefore, the revenue function is; R(x) = 2·x

c. Please find attached the graph for the Revenue and Cost functions, showing the break-even point, created with MS Excel

d. The coordinates of the break-even point on the graph is; (10,000, 20,000), therefore, the number of energy drinks the manufacturer has to sell to break even is; x = 2,000 units of the energy drinks.

e. The revenue the manufacturer has to take to break-even is equivalent to the cost at the same number of units sold, which is $20,000

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The equivalent expression of  -4(5x-9)+6(2x+5) is 28x + 30.

The given expression is,

-4(5x-9)+6(2x+5)

We know that,

Equivalent expressions are expressions that perform the same function notwithstanding their appearance. If two algebraic expressions are equivalent, they have the same value when the same value for the variable are used.

And Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

Now to find the equivalent of it simplifying this,

Open the brackets,

⇒ -20x + 36x + 12x + 30

⇒  28x + 30

Thus,

Equivalent expression is 28x + 30.

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The scale factor of triangle J'K'L is determined as 2.

Dilation is a technique for creating similar figures. It is also a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors.

In the given diagrams of triangle, we can conclude the following;

consider triangle JKL, the height of the triangle = (6 - 3.5) = 2.5

consider triangle J'K'L', the height of the triangle = (12 - 7) = 5.0

The scale factor of triangle J'K'L is calculated as follows;

S . F = New height / old height

S. F = 5.0 / 2.5

S. F = 2

Thus, the scale factor of triangle J'K'L is calculated from the ratio of the new height to the old height.

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Answer:

The answer would be 2

Step-by-step explanation:

The coordinates of JKL

J (8,12)

K (4,8)

L (12,6)

and Prime J'K'L'

J' (4,6)

K' (2,4)

L' (6,3)

have a similar factor 2

for example, if we were able to multiply J' aka (4,6) by 2 then we would get the pre image coordinates aka J (8,12). And vice versa, if we divided the coordinates of J (8,12) by the scale factor 2 we would end up geting the prime numbers, J' (4,6).

Thanks for letting me answer <3

Jordan needs 18.72 yards of blue ribbon.

This will require 12.48 spools of blue ribbon.

The total cost of the blue ribbon will be $18.44.

24 yards of ribbon * 0.78 = 18.72 yards of blue ribbon

18.72 yards of blue ribbon / 150 inches/spool = 12.48 spools of blue ribbon

12.48 spools of blue ribbon * $1.48/spool = $18.44

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Answer:

Step-by-step explanation:

Not sure how to solve this problem as the margin of error is based on the average that the man found, but the average is not given. Please update this question. A margin of error of 2% means that there is only a 2% difference. And here it would be at 6.732 or 6.48 as the new mean

The sets A and B are not equal, but they are equivalent.

We have,

The concept used is set notation and comparison.

a)

The sets A and B are equivalent because they contain the same elements, which are real numbers (x) that satisfy the given conditions.

b)

Sets A and B are not equal because the condition in Set A includes endpoints 97 and 102, while the condition in Set B excludes endpoints 96 and 103.

Therefore, the sets have different boundaries and elements.

Thus,

The sets A and B are not equal, but they are equivalent.

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The boiling point of water is approximately 100 degrees Celsius or 212 degrees Fahrenheit at standard atmospheric pressure.

This temperature represents the point at which water transitions from a liquid state to a gaseous state, forming water vapor. It is a well-known and crucial property of water, widely used as a reference point in various scientific, industrial, and everyday applications.

The boiling point of water is influenced by atmospheric pressure, with lower pressures resulting in a lower boiling point and higher pressures leading to a higher boiling point. For instance, at higher altitudes where atmospheric pressure is lower, water boils at temperatures below 100 degrees Celsius.

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If they maintain a constant speed the entire way, Michelle and Temba would have covered 140 km in 1 hour and 24 minutes.

The following equation can be used to determine the average speed of Michelle and Temba:

Distance x time speed

They covered 30 kilometers in 18 minutes, so their average speed is:

speed = 30 / (18 / 60) = 30 / 0.3, or 100 km/hr.

They would have traveled the following distance in 1 hour and 24 minutes, or in 1 hour + (24 / 60) hours, or 1.4 hours:

The distance= speed × time, or 100 × 1.4 = 140 km.

Therefore, it is important to remember that their speed and the actual distance they travel can be impacted by real-world variables like traffic, road conditions, and vehicle maintenance.

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complete question :-

Michelle and Themba are travelling from cape town to Johannesburg by car. they travel 30km in 18 minutes and continue at a constant speed. how far will they have travelled in 1 hour 24 minutes?​

Answer: Hope this helps :)

Step-by-step explanation:

The slope of the given line y = 5x - 3 is 5. The slope of a line perpendicular to it would be the negative reciprocal of 5, which is -1/5. Using the point-slope form of a line, we can find the equation of the line perpendicular to y = 5x - 3 that passes through the point (-3,4) as follows: y - y1 = m(x - x1), where (x1,y1) is the point (-3,4) and m is the slope -1/5. Substituting these values into the equation gives us: y - 4 = (-1/5)(x + 3). Simplifying this equation gives us: y = (-1/5)x - 3/5 + 4, or y = (-1/5)x + 17/5.

Answer:

To find the equation of a line perpendicular to y=5x-3 and which passes through (-3,4), we first need to find the slope of the line y=5x-3. The slope of this line is 5.

Since we want to find the equation of a line that is perpendicular to y=5x-3, we know that the slope of this new line will be the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Now that we know the slope of the new line, we can use the point-slope form of a line to find its equation. The point-slope form of a line is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.

Using the point (-3,4) and the slope -1/5, we get:

y-4=-1/5(x-(-3)

y-4=-1/5(x+3)

y-4=-1/5x-3/5

y=-1/5x+23/5

Therefore, the equation of a line perpendicular to y=5x-3 and which passes through (-3,4) is y=-1/5x+23/5.

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

thank you so much

Step-by-step explanation:

for the information

Sure. Will do. .........................................................................

The number of sheets of plastic that Katie would need is 2 sheets of plastic.

In Mathematics, the surface area of a square pyramid can be calculated by using this mathematical equation:

Surface area of square pyramid = [tex]a^2+2a\sqrt{(\frac{a}{4})^2 +h^2}[/tex]

where:

For the height, we have:

8.8² = h² + (13.2/2)²

77.44 = h² + 43.56

h² = 77.44 - 43.56

h = √33.88

Height, h = 5.8 m.

By substituting the given side lengths into the formula for the surface area of a square pyramid, we have the following;

Surface area of square pyramid = [tex]13.2^2+2(13.2)\sqrt{(\frac{13.2}{4})^2 +5.8^2}[/tex]

Surface area of square pyramid = 406.2 ft².

Now, we can determine the number of sheets of plastic:

Number of sheets of plastic = 406.2/14²

Number of sheets of plastic = 406.2/196

Number of sheets of plastic = 2.07 ≈ 2 sheets of plastic.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The sum of all of your customer Accounts Receivable is listed as part of Current Assets on your balance sheet.

A current asset is described as  any asset which can reasonably be expected to be sold, consumed, or exhausted through the normal operations of a business within the current fiscal year or operating cycle or financial year.

The Current assets generally fall under one of six sub-accounts in the Current Assets account and they include:

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