Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1

an = 2(2)n​

The perimeter of the semicircle is 56.562 cm

Semicircle is when a diameter line is formed by cutting a whole circle into two halves along the diameter line. It is formed when a lining passing through the center touches the two ends on the circle.

How to determine this

To calculate this,

The perimeter of a semicircle = 2π + πr

Where π = 3.142

r = 11 cm

The perimeter of a semicircle = 2(11cm) + 3.142(11cm)

Perimeter = 22cm + 34.562cm

Perimeter = 56.562 cm

Therefore, the perimeter of the semicircle is 56.562cm

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Using Hamilton method for apportioning, the total artists will be 200.

Using Hamilton method for apportioning :

total artists = 94+51+55 = 200

booths = 39

booths for group = (artists in group) / (total artists / no. of booths)

= (artists in group) / (200/39)

booths for painters = (94) / (200/39) = 18.33

= 18 {rounded to nearest integer}

booths for sculptors = (51) / (200/39) = 9.945

= 10 {rounded to nearest integer}

booths for weavers = (55) / (200/39) = 10.725

= 11 {rounded to nearest integer}

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The formula for the volume of a cube whose edge length is E is:

V = E³

We know that for all rectangular prisms, the volume is equal to the product between the 3 dimensions.

The cube is a type of rectangular prism where all the dimensions have the same measure, which is the edge length that we can write as E.

Then the volume V of the cube, which is the product of the 3 dimensions, can be written as:

V = E*E*E

We can simplify that as:

V = E³

That is the formula for the volume.

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Answer: Elevation is going to be greater than 5.71059°

Step-by-step explanation: 60/600 = tan∅ = 0=5.71059°,   so 0> 5.71059°

The volume of a sphere whose diameter is 18 centimeters is 972π cubic centimeters. If its diameter were reduced by half, its volume would be 1/8 of its original volume. So, correct options are D for both blanks.

The diameter of a sphere is 18 cm, so its radius is half of the diameter, which is 9 cm. The formula for the volume of a sphere is (4/3)πr³, where r is the radius of the sphere.

Using this formula, we can calculate the volume of the sphere as follows:

V = (4/3)π(9³)

V = (4/3)π(729)

V = 972π cubic cm

Therefore, the volume of the sphere is 972π cubic cm.

Now, if the diameter of the sphere is reduced by half, the new diameter would be 9 cm, which means the new radius would be half of 9 cm, which is 4.5 cm. Using the same formula for the volume of a sphere, we can calculate the new volume of the sphere as follows:

V' = (4/3)π(4.5³)

V' = (4/3)π(91.125)

V' = 121.5π cubic cm

To find the ratio of the new volume to the original volume, we can divide the new volume by the original volume:

V'/V = (121.5π) / (972π) = 1/8

Therefore, the answer to the first part of the question is option (d) 972π cubic cm, and the answer to the second part of the question is option (d) 1/8.

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The value of z as shown in the pair of similar traingles is 15 in.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

To calculate the value of z, we use the formula of similar triangle below

Note: ΔQWX is similar to triangle QRS

Formula:

From the diagram question below,

Given:

Substitute these values into equation 1 and solve for z

Hence the value of z is 15 in.

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The measure of the angle ∠P is given by the law of sines and ∠P = 46°

Given data ,

Let the triangle be represented as ΔMNP

Now , the measure of side MP = 46

The measure of side MN = 34

And , the measure of ∠MNP = 78°

Now , from the law of sines , we get

So , a / sin A = b / sin B = c / sin C

On simplifying , we get

34 / sin P = 46 / sin 78°

Multiply by sin P on both sides , we get

sin P ( 46 / 0.97814760073 ) = 34

sin P = 0.72297866

Taking inverse on both sides , we get

sin⁻¹ ( 0.72297866 ) = 46.30°

Hence , the measure of angle is P = 46°

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Angle S'Q'R' is same as angle SQR which is equal to

Rigid transformation refers to a type of geometric transformation that preserves the shape and size of an object. In other words, the transformed object is congruent to the original object.

Rigid transformations can be of two types -

Translation refers to moving an object in a straight line, while rotation refers to turning an object around a fixed point.

Rotation, in particular, has the effect of changing the orientation of the object. However, the length of each side and the angles between them will remain the same.

In a rigid transformation, the position of every point in the object is changed, but the distances between points remain unchanged, as well as the angles between lines and the area of the object.

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The height of the cylinder will be 18 inches.

Given that:

Volume, V = 2,769.48 cubic inches

Radius, r = 7 inches

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be given as,

V = π r²h cubic units

The height of the cylinder is calculated as,

2,769.48 = 3.14 x 7² x h

2,769.48 = 153.86h

h = 18 inches

The height of the cylinder will be 18 inches.

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The table that represents a linear function is as shown is option B and it is attached

A  linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

where

y = output variable

m = slope

x = input variable

c = y intercept

The table for a linear function has the variables in the output y increasing at a constant rate.

The only table that represents this movement is the second table having out put values of

-3, -2, -1, 0, 1

The difference here is +1

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The trigonometric relation is solved and the unit circle is plotted

Given data ,

Let the unit circle be represented as A and B

Now , in figure A , we get

The radius of the circle is r = 5 units

And the point on the circle is P ( 5 , 5 )

So , the height of unit circle is h = 5 units

Now , the hypotenuse of the circle is = 2√5 units

From the trigonometric relation , we get

sin θ = opposite / hypotenuse

sin z = √5 / 2√5

sin z = 1/2

Taking inverse on both sides , we get

z = 30°

So , the measure of rotation is 60° counterclockwise

In figure B , we get

The radius of the circle is r = 5 units

And the point on the circle is P ( 5 , -5 )

So , the height of unit circle is h = -5 units

Now , the hypotenuse of the circle is = 2√5 units

From the trigonometric relation , we get

sin θ = opposite / hypotenuse

sin z = √5 / 2√5

sin z = -1/2

Taking inverse on both sides , we get

z = -30°

So , the measure of rotation is 30° clockwise

Hence , the trigonometric relation is solved

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The constant of variation for the case is 2 centimeters per night.

A graph is a non-linear kind of data structure made up of nodes or vertices and edges. The edges connect any two nodes in the graph, and the nodes are also known as vertices. This graph has a set of vertices V= { 1,2,3,4,5} and a set of edges E= { (1,2),(1,3),(2,3),(2,4),(2,5),(3,5),(4,50 }.

The graph shown in the problem has length as the vertical axis and nights as the horizontal axis.

The points through which the straight line passes are (0, 0) and (10, 20).

The equation of the line can be written as follows,

=> [tex]\frac{y-0}{x-0}=\frac{20-0}{10-0}[/tex]

=> [tex]\frac{y}{x}=\frac{20}{10}[/tex]

=> y = 2x

Thus, the above equation implies that y and x are proportional and 2 is constant of variation.

Hence, the constant of variation for the given case is 2 centimeters per night.

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The given question is incomplete, So i take the similar question:

This graph shows how the total length Kimi has knit depends on the number of nights she has spent knitting.

​What is the constant of variation?

____ centimeters per night

The solution of the triangle is shown below;

Angle A - 26.98°

Angle C - 118.6°

Side c -  47.98

If you know the length of one side and the measure of the opposite angle, or the length of two sides and the measure of the angle between them, you can use the Law of Sines to find the other parts of the triangle.

Using the sine rule;

a/Sin A = b/Sin B

aSin B = bsinA

Sin A = bSinB/a

A = Sin-1( bSinB/a)

A = Sin-1(30.9 * Sin 34.42/38.5)

A = 26.98°

Then;

C = (180 - 26.98 + 34.42)

C = 118.6°

Using the sine rule again;

b/sinB = c/Sin C

c = bSin C/Sin B

c = 30.9 * Sin 118.6/Sin 34.42

c = 27.12/0.565

c = 47.98

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An equation to determine p is 12 = 3p/4

The total number of players at the baseball game is 16.

We have the information:

In all the players,  12 choose a bottle of water, which was 3/4 of the total number of players.

We have to find the:

Write and solve an equation to determine p, the total number of players at the baseball game.

Total number of players = p

Out of 12 total player 12 choose a bottle of water which is  of the total number of players and hence the equation will be:

12 = 3/4 of p

12 = 3p/4

By cross multiplication:

48 = 3p

Solve the value of p :

p = 48/3

p = 16

Therefore, the total number of players at the baseball game is 16.

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The measure of angle x is 114.6°

Here, the central angle of sector of circle is represented by x.

We know that the formula for the area of sector.

A = θ/360 × πr²

where  θ is the central angle

and r is the radius of the circle

Here, the area of the sector is equal to the area of the square.

Using the formula for the area of square,

A = side²

A = r²

Since area of sector = area of square,

x/360 × πr² = r²

x = 360/π

x = 114.6°

Thus, the required angle ∠x = 114.6°

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Find the complete question below.

The area of isoceles triangle is  120 square meters

Let us assume that a and c represents the equal sides of isosceles triangle and b represents the base of isosceles triangle such that a = 17 m, b = 16 m and c = 17 m

Let us assume that h represents the height of isosceles triangle.

We know that the formula for the height of isosceles triangle.

h = [tex]\sqrt{a^2-\frac{b^2}{4} }[/tex]

h = [tex]\sqrt{17^2-\frac{16^2}{4} }[/tex]

h = √(225)

h = 15 m

Using the formula for the area of isosceles triangle,

A = 1/2 × base × height

A =  1/2 × b × h

A =  1/2 × 16 × 15

A = 120 sq. m.

Therefore, the required area is  120 sq. m.

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The complete question is:

The sides of isosceles triangle triangle are: 17 m, 17 m and 16 m

Find the area of the isoceles triangle. The area is square meters.

5 × 4 = 20

9 × 5 = 45

6 × 3 = 18

5 × 7 = 35

Mean = 20 + 45 + 18 + 35/4

= 118/4

= 59/2

5 1/8 = 46/8

5 1/2 = 11/2

5 6/25 = 131

5 4/11 = 59/2

Therefore The Answer is A 5 4/11.

The final cost of the couch after adding the 6% sales tax is $728.75.

By dividing the cost of the  lounge by the applicable deals  duty rate, one may calculate the total  quantum of deals  duty.

Since the deals  duty rate is  generally expressed as a chance, you must divide it by 100 to get a numeric.

The decimal  fellow in this situation is0.06 since the deals  duty rate is 6.   settee cost x deals  duty rate equals deals  duty  Deals  duty is equal to687.50 multiplied by0.06.

Deals  duty equals41.25   Accordingly, the  settee is subject to a$41.25 deals  duty.   The final cost of the  lounge after the deals  duty is assessed is calculated by adding the deals  duty  quantum to the  original cost of the  settee.   settee cost plus deals  duty equals total cost

Total price is687.50+41.25

Total cost = 728.75

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Since the diameter of this circle is 7 cm, its area to the nearest whole number include the following: 39 square centimeters.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 7/2 = 3.5 centimeters.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = 3.142 × 3.5²

Area of circle = 38.5 ≈ 39 square centimeters.

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The values of the expressions after multiplication are given below

17 ×82 = 1600

54×671=35000

207×643=260000

First, round each number to one significant digit (the first digit).

Then multiply them.

a) 17   --> rounds to 20

82   --> rounds to 80

20 x 80 = 2 x 8 with two zeros

Value is  1600

b) 54   --> rounds to 50

671   --> rounds to 700

50 x 700 = 5 x 7 with three zeros

= 35000

c) 207   --> rounds to 200

643   --> rounds to 600

200 x 600 = 2 x 6 with four zeros

= 120000

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By rounding to 1 significant figure, estimate the answers to these questions:

a) 17x82

b) 54 x 671

c) 207 x 643​

Therefore, the population is at a maximum approximately 25 hours after the culture was started.

A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.

Here,

To find the time at which the population is at a maximum, we need to find the time when the rate of change of population, or the derivative of p(t), is zero.

p(t) = -1715t² + 85,000t + 10,000

p'(t) = -3430t + 85,000

Setting p'(t) = 0, we get:

-3430t + 85,000 = 0

Solving for t, we get:

t = 24.85

Rounding to the nearest hour, we get:

t ≈ 25

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If a triangle has a right angle (90 degrees), it is called a right triangle. The side opposite the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called the legs.

To find the length of the third side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.

The Pythagorean theorem can be written as:

a^2 + b^2 = c^2

where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

But you already know c, and with that c^2, you want to find a through a^2(you can also look for b, it would be the same)

If you rearrange the equasion you get a^2=c^2-b^

Once we have these lengths

c=15,so c^2 is 15^2=15*15=225

b=10,so b^2 is 10^2=10*10=100

we can plug them into the Pythagorean theorem and solve for the unknown side.

a^2=c^2-b^2

a^2=225-100=1125

If a^2 is 125, then a must be the square route if 125



(a is in you case x)

We

Answer:

The glass cannot fit through the door.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let the height of the door be h.

We know that the diagonal of the glass must be able to fit through the door, so we can set up the following equation:

sqrt(8^2 + h^2) <= 3

Squaring both sides of the inequality, we get:

64 + h^2 <= 9

Subtracting 64 from both sides, we get:

h^2 <= -55

Since a square of a real number cannot be negative, there is no solution to this inequality.

Therefore, the glass cannot fit through the door, regardless of the height of the door.

The door must be at least √55 feet tall, which is approximately 7.42 feet, for the 8-foot wide glass to pass through the 3-foot wide door.

To determine how tall the door must be for the glass to pass through, we first need to calculate the height of the glass. Unfortunately, the height of the glass is not provided in the question. Assuming that the height of the glass is less than or equal to the height of the door, we can proceed as follows:

Let's say the height of the glass is h feet. Then, we know that the glass is a rectangular shape with dimensions of 8 feet by h feet. To pass through the door, the glass needs to be able to fit horizontally and vertically through the opening.

Since the door is 3 feet wide, the glass needs to be able to fit through the opening when turned on its side. Therefore, the height of the glass cannot exceed 3 feet.

So, the door must be at least 3 feet tall for the glass to pass through. However, this assumes that the height of the glass is less than or equal to 3 feet. If the height of the glass is greater than 3 feet, then the door would need to be taller to accommodate the glass.

To determine the minimum height the door must be for the 8-foot wide glass to pass through the 3-foot wide door, you can use the Pythagorean theorem. The glass will need to be tilted diagonally as it passes through the door. Let's label the door's height as 'h' and use the formula:

3² + h² = 8²

9 + h² = 64

h² = 64 - 9
h² = 55
h = √55

The door must be at least √55 feet tall, which is approximately 7.42 feet, for the 8-foot wide glass to pass through the 3-foot wide door.

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Nuclear fusion involves the combination of two light nuclei to form a heavier nucleus with emission of energy.

Since,

A nuclear reaction equation is a representation of the change that takes place as one nucleus is converted to another. A nuclear transformation could be any of the following;

⇒ Nuclear fission

⇒ Nuclear fusion

⇒ Transmutation

We can know that a nuclear fusion is taking place when two nuclei come together to form a larger nucleus and emit energy. I would identify a nuclear fusion when;

⇒ Two light atom combine to give a larger nucleus

⇒ Tremendous energy is produced

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The simplification of the expression −10x - 7x⁴ in the reduced factor form is equal to -1x ( 10 + 7x³ ).

The expression is equal to,

−10x - 7x⁴

From both the terms of the given expression '-1' is the common factor we get,

−10x - 7x⁴

= ( -1 ) ( 10x + 7x⁴ )

Now take variable 'x' common from both the terms of the expressions we get,

= ( -1 × x  ) ( 10 + 7x³ )

= -1x ( 10 + 7x³ )

Now nothing is act as common factor in the given expression we have,

Therefore, the simplified factor of the expression −10x - 7x⁴ is equal to -1x ( 10 + 7x³ ).

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The above question is incomplete, the complete question is:

Factor the expression completely.

−10x - 7x⁴

Answer:

Step-by-step explanation:

Formula for the volume of a cone:

((r^2)(height)(pi)) / 3

Since we are finding the answer in terms of pi, we will use the pi symbol.

The radius is 18.

The height is 30.

18^2 is 324.

324 x 30 is 9720.

9720 / 3 is 3240.

Answer : 3240 pi.

Answer:

2

Step-by-step explanation:

10/ 5 = 2

15 / 5 = 3

2/3

Answer:   2

Step-by-step explanation:

If you do 3+3+3+3+3 it is 15 and then you did it 5 times so you could do 10 divided by 5 to get 2.so2 is your answer.