For what value of n does StartFraction 216 Superscript n minus 2 Baseline Over (StartFraction 1 Over 36 EndFraction Superscript 3 n?

The volume of cylinder is,

V = 26,940.59 cm³

We have to given that,

The height of a cylinder is 24.8cm

And, the ratio of the diameter of the cylinder to the height of the cylinder is 3:2

Hence, Lenght of height = 2x

And, Diameter of cylinder = 3x

Since, The height of a cylinder is 24.8cm

So,

2x = 24.8

x = 24.8 / 2

x = 12.4 cm

Hence, Diameter of cylinder is,

d = 3x

d = 3 (12.4)

d = 37.2 cm

So, Radius = 37.2 / 2 = 18.6 cm

Thus, Volume of cylinder is,

V = πr²h

V = 3.14 × 18.6² × 24.8

V = 26,940.59 cm³

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The correct pattern and next three terms in the sequence -15, -11, -7, -3, is,

d. Add 4; 1, 5, 9

We have to given that,

The sequence is,

⇒ - 15, - 11, - 7, - 3, ...

Now, We have to see that,

⇒ - 15 + 4 = - 11

⇒ - 11 + 4 = - 7

⇒ - 7 + 4 = - 3

Hence, The rule is add 4 in first term to find next terms.

So, The next three terms are,

⇒ - 3 + 4 = 1

⇒ 1 + 4 = 5

⇒ 5 + 4 = 9

Thus, The correct pattern and next three terms in the sequence -15, -11, -7, -3, is,

d. Add 4; 1, 5, 9

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The descriptions of data sets that could be graphed as dot plots, based on the type of data in dot plots would be:

Dot plots are a type of graph that can be used to represent data that is discrete, or made up of individual points. The data points are represented by dots on the graph, and the horizontal axis represents the different values of the data.

In the case of class size, the data points would represent the number of students in each class. The horizontal axis would represent the different class sizes, and the vertical axis would represent the frequency of each class size.

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Full question is:

Here are descriptions of data sets. Select all descriptions of data sets that could be graphed as dot plots.

A. Class size for the classes at an elementary school

B. Colors of cars in a parking lot

C. Favorite sport of each student in a sixth-grade class

D. Birth weights for the babies born during October at a hospital

E. Number of goals scored in each of 20 games played by a school soccer team

Answer:

x <  4

the 1st number line should be used.

Step-by-step explanation:

3/4(x + 8) > 1/2(2x + 10)

(2)(3)(x + 8) > (4)(1)(2x + 10)

6x + 48 > 8x + 40

6x - 6x + 48 - 40 > 8x - 6x + 40 - 40

8 > 2x

x < 8/2

x < 4

Subtracting 58 cm from 734 cm will give a perfect square.

To find the value that needs to be subtracted from 734 cm to obtain a perfect square, we can start by finding the largest perfect square that is less than or equal to 734.

The largest perfect square less than 734 is 676, which is equal to 26².

To obtain this perfect square, we subtract 676 from 734:

734 - 676

= 58

Therefore, subtracting 58 cm from 734 cm will give a perfect square.

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Step-by-step explanation:

For a right triangle, area = 1/2 base * height

for this triangle  base = 6   height = 14

1/2 * 6 * 14 = 42 cm^2

The distance, d, that the ladder goes up the wall (above the fire truck) is approximately 7.76 meters.

1. Convert the angle from degrees and minutes to decimal form.

  47 degrees 44' = 47 + (44/60) = 47.7333 degrees (rounded to four decimal places)

2. Use trigonometric ratios to find the length of the side opposite the angle.

  sin(47.7333) = Opposite / Hypotenuse

3. Rearrange the formula to solve for the Opposite side.

  Opposite = sin(47.7333) * Hypotenuse

4. Substitute the known values into the equation.

  Opposite = sin(47.7333) * 10.5 meters

5. Calculate the value of sin(47.7333) using a calculator.

  sin(47.7333) ≈ 0.7431

6. Substitute the value of sin(47.7333) and the given value of Hypotenuse into the equation.

  Opposite = 0.7431 * 10.5 meters

7. Calculate the value of Opposite.

  Opposite ≈ 7.76 meters

Therefore, the distance, d, that the ladder goes up the wall (above the fire truck) is approximately 7.76 meters.

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The line which is symmetrical to y=10+3x+x^2 is x = 3/2.

We are given that;

The equation y=10+3x+x^2

Now,

The line of symmetry of a parabola is a vertical line that passes through the vertex of the parabola and divides it into two congruent halves. The equation of the line of symmetry is given by the x-coordinate of the vertex 1.

To find the vertex of a parabola that is given in standard form y = ax^2 + bx + c, you can use the formula 2:

x = -b / 2a

This formula gives you the x-coordinate of the vertex. The y-coordinate can be found by plugging this value into the original equation.

We can rewrite it in standard form by rearranging the terms:

y = -x^2 + 3x + 10

Now you can identify the values of a, b and c:

a = -1 b = 3 c = 10

Using the formula for the x-coordinate of the vertex, you get:

x = -b / 2a x = -(3) / (2 * -1) x = 3/2

Therefore, by symmetry the answer will be  x = 3/2.

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The final value is 13.43, which represents the product of 5.48 and 2.45.

We have,

The concept being demonstrated here is the multiplication of two decimal numbers.

When multiplying decimal numbers, we follow these steps:

- Ignore the decimal points and multiply the numbers as if they were whole numbers.

In this case, we multiply 548 by 245, which gives us 134,260.

- Determine the total number of decimal places in the original numbers.

In this case, the original numbers have a total of four decimal places (two decimal places each).

- Place the decimal point in the product so that it has the same number of decimal places as the total from step 2.

In this case, we need to place the decimal point two places from the right, giving us 1,342.60.

- Round the final result if necessary.

In this case, rounding to two decimal places gives us 1,342.60 rounded to 13.43.

Therefore,

The final value is 13.43, which represents the product of 5.48 and 2.45.

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Answer:

Oliver needs to sell enough fruit to cover the production cost of 50 pineapples in order to turn a profit. If he sells each fruit at a rate of $x, how many fruits does he need to sell to break even on the production cost of all 50 pineapples?

Assuming that producing 50 pineapples cost $200, Oliver must sell fruits worth more than $200 to cover this cost. He must sell at least 50 pineapples at the rate of $x to break even on the production cost of all 50 pineapples.

Therefore, the minimum amount of fruit he needs to sell is calculated as:

$200/$x + 50.

Answer:

If Oliver sells each fruit at $5, then he must sell at least 40 fruits to cover the cost of producing all 50 pineapples ($200 / $5 per fruit = 40 fruits). To make a profit, he must sell more than 40 fruits.

If Oliver sells each fruit at $10, then he must sell at least 20 fruits to cover the cost of producing all 50 pineapples ($200 / $10 per fruit = 20 fruits). To make a profit, he must sell more than 20 fruits.

If Oliver sells each fruit at $15, then he must sell at least 14 fruits to cover the cost of producing all 50 pineapples ($200 / $15 per fruit = 13.33 fruits, rounded up to 14 fruits). To make a profit, he must sell more than 14 fruits.

Step-by-step explanation:

Sorry but I hope that helped you :)

The predicted value of f(x) when x = 6 is 218.

We have the piecewise function as

f(x) = {6x² +2 ,     -6 < x < 9

          12 , 9≤x <13

In this case, x = 6 falls into the interval -6 < x < 9.

Therefore, we will use the corresponding equation for that interval, which is f(x) = 6x² + 2.

Now, substitute x = 6 into the equation to find the value of f(x):

f(6) = 6(6)² + 2

= 6(36) + 2

= 216 + 2

= 218

So, the predicted value of f(x) when x = 6 is 218.

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The area of the actual flower bed is 192 square feet.

We are given that;

Scale = 1 in. : 2 ft.

Actual length: 16 ft

Actual width: 12 ft

Now,

To find the length and width of the actual flower bed, we need to use the scale given in the problem. The scale is 1 in. : 2 ft., which means that 1 inch on the drawing represents 2 feet in real life. The length of the flower bed on the drawing is 8 inches, so the actual length is:

8 inches x 2 feet/inch = 16 feet

Similarly, the width of the flower bed on the drawing is 6 inches, so the actual width is:

6 inches x 2 feet/inch = 12 feet

To find the area of the actual flower bed, we can use the formula for area of a rectangle:

area = length x width

Substituting in the values we found above, we get:

area = 16 feet x 12 feet = 192 square feet

Therefore, by area the answer will be 192 square feet.

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The volume of the given rectangular pyramid is 136 cubic units.

The dimensions of rectangular pyramid are Length = 6 units, Breadth = 8.5 units and Height = 8 units.

The volume of a rectangular pyramid is found using the formula: V = (1/3)× (L×B×H)

Here, volume = 1/3 ×6×8.5×8

= 2×8.5×8

= 17×8

= 136 cubic units

Therefore, the volume of the given rectangular pyramid is 136 cubic units.

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There are 21 different 2-topping pizzas are possible.

We have to given that,

A restaurant has 7 pizza toppings to choose from.

Since, A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Hence, Number of different possible 2-topping pizzas are,

⇒ ⁷ C ₂

⇒ 7! / 2! (7 - 2)!

⇒ 7! / 2! 5!

⇒ 7 × 6 / 2

⇒ 21

Therefore, There are 21 different 2-topping pizzas are possible.

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Answer: d.12

Step-by-step explanation:

The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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Answer:

Step-by-step explanation:

The pressure exerted by the cube on the countertop is 23060 Pa.

We are given that;

Side of cube=30cm

Now,

The force is equal to the weight of the cube, which is the product of its mass and the acceleration due to gravity. To find the mass, you need to multiply the volume and the density of iron. The volume of a cube is the cube of its side, and the density of iron is about 7870 kg/m^3. The acceleration due to gravity is about 9.8 m/s^2. Therefore:

F = mass * gravity F = (volume * density) * gravity F = ((side)^3 * density) * gravity F = ((0.3 m)^3 * 7870 kg/m^3) * 9.8 m/s^2 F = 2075.4 N

The area is equal to the area of one face of the cube, which is the square of its side. Therefore:

A = (side)^2 A = (0.3 m)^2 A = 0.09 m^2

Now that you have the force and the area, you can plug them into the formula for pressure:

P = F / A P = 2075.4 N / 0.09 m^2 P = 23060 Pa

Therefore, by algebra the answer will be 23060 Pa.

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The complete question is;

If an iron cube of 30 cm side is resting on a countertop, what pressure does it exert?

The expression simplified is:

[tex]\frac{y^{-5}}{x^{-3}} = \frac{x^3}{y^5}[/tex]

Remember that a negative power just means that we need to take the inverse, such that:

[tex]n^{-m} = (1/n)^m[/tex]

In this case we want to simplify the expression:

[tex]\frac{y^{-5}}{x^{-3}}[/tex]

Using that rule, we can take the two correspondent inverses, then we will have x to the third power on the numerator and y to the fifth power in the denominator, that is:

[tex]\frac{y^{-5}}{x^{-3}} = \frac{x^3}{y^5}[/tex]

That is the only simplification we can do.

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The inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

Let's denote the distance between Jim and the car as "d" (in feet), and the time elapsed after Jim spots the car as "t" (in seconds).

Given that no car travels faster than 90 feet/second on this road, we can establish the following relationship between distance, time, and speed:

d ≤ 90t

However, Jim has a camera that allows him to see up to 1,080 feet in either direction.

This means that the distance between Jim and the car should be within the range of the camera's visibility, which is 1,080 feet.

Therefore, the inequality representing the possible distances between the car and Jim for any period of time after he spots it is:

-1,080 ≤ d ≤ 1,080

Combining both inequalities, we have:

-1,080 ≤ d ≤ 1,080 and d ≤ 90t

Hence the inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

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Answer: 290 inches squared.

Step-by-step explanation:

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

The surface area for two faces of the rectangular prism is given.

The first one is a square, with a given area of 25 inches squared. The second one is a rectangle with a given area of 60 inches squared.

We know that each rectangle has the same side length and width, meaning that each rectangle has the same area. And since there are 4 rectangles with the same area, we can multiply its area of 60 inches squared by 4, getting the number 240.

The same rule applies to the squares, as there are two squares, we can multiply 25 by 2, and get 50.

Lastly we need to add up the total areas to get the whole surface area, which is 50 + 240 = 290 inches squared.

Answer: 126units³

You can find the volume by using LxWxH and dividing the object into two boxes

Step-by-step explanation:

For example

(4x3x7)+(6x7x1)=the volume

(84)+(42)=126

Volume=126units³

The answer is written as

Your given expression is "n^3 + 4". However, to solve an equation, you need to have an equals sign, that is, there needs to be something on the other side of the equation.

For example, if you had "n^3 + 4 = 0", then you could solve for n:

n^3 + 4 = 0,

n^3 = -4,

n = ∛(-4).

But with only "n^3 + 4", there isn't anything to solve for because it's not set equal to anything. This is an expression, not an equation.

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The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .

Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.

This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .

The rough sketch of the curve having the bell shape is shown attached to the question.

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Answer:

66-26 = 40

Step-by-step explanation:

u = 40 degrees

Answer:

Its D 1/221

Step-by-step explanation:

The calculated slope of the line is 1/2

From the question, we have the following parameters that can be used in our computation:

The linear graph

The slope of the line can be calculated using

Slope = change in y/change in x

Using the above as a guide, we have the following:

Slope = (0 + 2.5)/(5 - 0)

Evaluate

Slope = 1/2

Hence, the slope of the line is 1/2

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We can solve the inequality |x + 3| < 1 by considering two cases:

Case 1: x + 3 ≥ 0

If x + 3 ≥ 0, then the inequality simplifies to:

x + 3 < 1

Subtracting 3 from both sides gives:

x < -2

So the solution set for this case is -3 < x < -2.

Case 2: x + 3 < 0

If x + 3 < 0, then we have:

-(x + 3) < 1

Multiplying both sides by -1 (which reverses the direction of the inequality) gives:

x + 3 > -1

Subtracting 3 from both sides gives:

x > -4

So the solution set for this case is -4 < x < -3.

Combining the solution sets from both cases, we get:

-4 < x < -2

Therefore, the solution to the inequality |x + 3| < 1 is the open interval (-4, -2).