How to solve this problem

A sequence is a list of numbers that follow a specific pattern. Each number in the sequence is called a term. Sequences can be finite (meaning they have a specific number of terms) or infinite (meaning they continue without end).

Arithmetic sequences are a type of sequence where each term is found by adding a constant value to the previous term. This constant value is called the common difference, denoted as d. The formula for the nth term (or any term) of an arithmetic sequence is:

an = a1 + (n-1)d

In other words, we can find any term of an arithmetic sequence by adding the common difference to the previous term.

(i) The next term in the sequence is 27.

(ii) To get this answer, we can see that each term is 6 greater than the previous term

b) To find the tenth term we can write the formula for the nth term of the sequence using the common difference d = 6 and the first term a1 = 3:

an = a1 + (n - 1)d

Substituting n = 10, a1 = 3, and d = 6, we get:

a10 = 3 + (10 - 1)6

a10 = 3 + 54

a10 = 57

Therefore, the 10th term of the sequence is 57

The vocabulary term for segment a is an apothem.

The area of this polygon is 41.6 yd².

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

Area of regular polygon = (n × s × a)/2

Where:

By substituting the given parameters into the formula for the area of a regular polygon, we have the following:

Area of regular polygon = (6 × 4 × 2√3)/2

Area of regular polygon = (24 × 2√3)/2

Area of regular polygon = 83.1/2

Area of regular polygon = 41.6 yd².

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The value of stock after 8 days is $20.

Since the unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that Price of the stock =  $8

The number of days price fall = 8 days

a) the price of the stock changes by = $7x 8

                                                           = $56

  Price of stock decreased by $56

b) Price of stock after 8 days

                    = $36 - $56

                    = $20

Hence,  the value of stock after 8 days is equal to $20

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Using implicit differentiation the second derivative is d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

Since we have the function x⁴ + y⁴ = 16, we desire to find the second derivative by implicit differentiation. We proceed as follows.

Since  

x⁴ + y⁴ = 16

Taking the first derivative of the function, we have that

d(x⁴ + y⁴)/dx = d16/dx

dx⁴/dx + dy⁴/dx = d16/dx

4x³ + 4y³ × dy/dx = 0

4y³ × dy/dx = -4x³

dy/dx =  -4x³/4y³

dy/dx = -x³/y³

We now differentiate again to take the second derivative of the function. So, we have that

dy/dx = -x³/y³

Using the quotient rule, we have dy/dx = (udv/dx - vdu/dx)/v² where u = -x³ and v = y³.

So, substituting this into the equation, we have that

d(dy/dx)/dx = (-x³dy³/dx - y³d-x³/dx)/(y³)²

= [-x³dy³/dy × dy/dx  - y³d(-x³/dx)]/(y³)²

= [-x³2y² × dy/dx  + y³2x²]/(y³)²

d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

The second derivative is d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

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The calculated value of the function f(3) in the mapping of ordered pairs is -3

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

The mapping

Where

Mapping implies that we pair x values to y values

On the mapping, we have the following representation

3 ---- -1

This means that the value of  f(3) = -1

This is true because the x values 3 in the domain points to the y value -1 in the range

Hence, the value of  f(3) is -1

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The point (3, b) lies on the circle with radius 6 and center (-1, -1), the possible values of b are 3.47 or -5.47.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

Substituting the given points into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - (-1))² = 6²

(x + 1)² + (y + 1)² = 36.

Since the point (3, b) lies on the circle, we have;

(3 + 1)² + (b + 1)² = 36.

16 + b² + 2b + 1 = 36

b² + 2b - 19 = 0

By solving the quadratic function, the possible values of b is given by;

x = 3.47 or x = -5.47.

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Answer:

[tex] \frac{ - .8 + .6}{2} = \frac{ - .2}{2} = -.1[/tex]

The solutions to the quadratic equation 3x² + x - 12 = 1 are given as follows:

[tex]x = \frac{-1 \pm \sqrt{157}}{12}[/tex]

The quadratic function in the context of this problem is defined as follows:

3x² + x - 12 = 1

Placing it into standard format ax² + bx + c = 0, we have that the equation is given as follows:

3x² + x - 13 = 0.

The coefficients are given as follows:

a = 3, b = 1, c = -13.

The discriminant is:

D = b² - 4ac

D = 1² - 4 x 3 x -13

D = 157.

Then the solutions are given as follows:

[tex]x = \frac{-1 \pm \sqrt{157}}{12}[/tex]

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The relative frequency table can be completed as follows:

January - June (Men) = 60%

January - June (Women) = 40%

July - December (Men) = 40%

July -December (Women) = 60%

The estimation showed a high degree of nearness to the original values.

To complete the frequency table, we will begin by making the estimate as the question instructs. Finally, we will compare the values of the new estimated table with the original table.

The January - June record for men shows a frequency rate of 60% if we do the estimation. With the original figures, the value is 57.1% and this figure is very close to 60%. So, estimates give us a good insight into the correct values of numbers.

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Equation (2x + 10)⁴*(x + 5)³ simplifies to 16(x + 5)⁷.

We can simplify this expression by factoring out the common factor of (2x + 10) from the first term and (x + 5) from the second term:

(2x + 10)⁴ × (x + 5)³ = (2(x + 5))⁴ × (x + 5)³

We can simplify the first term by expanding the fourth power:

(2(x + 5))⁴ = 16(x + 5)⁴

Now we have:

(2x + 10)⁴*(x + 5)³ = 16(x + 5)⁴ * (x + 5)^3

We can simplify this expression further by adding the exponents of the common factor (x + 5):

16(x + 5)⁴ * (x + 5)³ = 16(x + 5)⁴⁺³ = 16(x + 5)⁷

Therefore, (2x + 10)⁴*(x + 5)³ simplifies to 16(x + 5)⁷.

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Given question is incomplete, the complete question is below

Assuming that x ≠ -5, simplify (2x + 10)⁴×(x + 5)³.

Answer:

B) -1

Step-by-step explanation:

To answer this question you need to use Pedmas*.

Pembas states:

P - Parenthasess

E - Exponents

D - Divison

M - Multiplication

A - Addition

S - Subtraction

So in this problem, you need to solve the parentheses. In the parentheses there is nothing to solve so we move on to exponents. There are no exponents so we move on to division/multiplication. There is a division symbol so we divide left to right.

After dividing 10 / -2 we get an answer of -5. We can now add 4 + -5 to get our final answer of -1

Answer:  Ans(1)

 In right triangle

     a = 13cos(56°)

   a = 7.3 cm

Ans(2)

   In right triangle

   b = 6/sin(35°)

Answer:

Step-by-step explanation:

28

V=b*w*h

b=2

w=2

h=7

V=2*2*7=28

Answer:

B.28

Step-by-step explanation:

Volumn=Base*Height

=2*2*7

=28

The volume of the given triangular prism is 144 cm³.

option A.

The volume of a triangular prism can be calculated by multiplying the area of the base triangle by the height of the prism.

The formula for calculating the volume of a triangular prism is:

Volume = Base Area × Height

Given the base of the triangular prism is a triangle with a base of 8 cm and a height of 3 cm, the area of the base triangle can be calculated as:

Base Area = 0.5 × base × height

Base Area = 0.5 × 8 cm × 3 cm

Base Area = 12 cm²

The volume of a triangular prism is calculated as;

Volume = Base Area × Height

Volume = 12 cm² × 12 cm

Volume = 144 cm³

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Answer:

Step-by-step explanation:

yes

After considering the given data we conclude that the the real numbers  are a = (-3/4) × (1/∛7), (3/4) ×(1/∛7),

In order to evaluate equations with fraction, we have to follow these steps
1. First Identify the operations that are being applied to the unknown variable.
2. Then Apply the inverse operations, one at a time, to both sides of the equation.
3. Finally write  the last answer,
For the given  case, we have 1/{64a³ + 7} - 7 = 0. We can evaluate this  by first adding 7 to both sides of the equation to get 1/{64a³ + 7} = 7.
Therefore we can take the reciprocal of both sides to get {64a³ + 7} = 1/7. Finally, we can subtract 7 from both sides to get {64a³} = -48/7.

Hence , the real number(s) that satisfy the equation are a = (-3/4) × (1/∛7) , (3/4) ×(1/∛7).
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Answer:

A. To form an even number, the last digit must be either 8 or 5, since they are the only even digits in the set. Since a digit can be used at most once, there are two choices for the last digit.

For the first digit, there are four choices (1, 3, 5, or 7), since we cannot use 0 or the last digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

Therefore, the total number of four-digit even numbers that can be formed is: 2 x 4 x 4 x 3 = 96.

B. To form a number less than 3000, the first digit must be 1, 3, or 5. There are three choices for the first digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

For the fourth digit, there are two choices remaining (since we cannot use the first digit).

Therefore, the total number of four-digit numbers less than 3000 that can be formed is: 3 x 4 x 3 x 2 = 72.

Check the picture below.

Answer: 270 ft²

Step-by-step explanation:

The dimensions of 1 room is 10 ft x 12 ft

The other room is 10 ft x 15 ft

For area multiply the length and width and add the 2 areas

so A1 =  10x12=120 ft²

A2 = 10x15 =150 ft²

Total area is 150+120 =270 ft²

The Empty seats according to the equation will be:

United Continental = 90

American airlines = 30

Southwest airlines = 40

Let the seats in American airlines = x

so according to give condition The United continental airlines have 3x seats. and  the seats in Southwest airlines  = y  and Combined empty seat in American, United continental and  Southwest airlines = 160

4x + y = 160

59.3x + 12.4y = 2275

After solving, x = 30 and y = 40

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The actual weight of rice in a bag labeled as a 20 pound bag is expected not to have a normal distribution.

What is normal distribution ?

A normal distribution is a common probability distribution that is bell-shaped and symmetrical around its mean value. In a normal distribution, the mean, median, and mode are all equal, and the distribution is defined by two parameters: its mean and standard deviation.

The actual weight of rice in a bag labeled as a 20 pound bag is expected not to have a normal distribution. This is because the weight of rice in a bag labeled as 20 pounds may vary due to differences in packing and other factors, and is not necessarily a normally distributed variable. The delay of flights, weights of children, and test scores are all examples of variables that may have a normal distribution under certain conditions.

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There are 17,297,280 ways to choose 7 letters, without replacement, from 12 distinct letters when the order matters.

What is permutation?

A permutation of 2 lines is a reordering of two distinct elements. In other words, given two elements, a permutation of 2 lines is a way of arranging them in a different order. For example, if the two elements are A and B, the possible permutations of 2 lines are AB and BA.

If the order of the choices matters, we need to use the concept of permutations. The number of ways to choose 7 letters from 12 distinct letters without replacement and with order mattering is given by:

12P7 = 12! / (12-7)!

= 12! / 5!

= 12 x 11 x 10 x 9 x 8 x 7 x 6

= 17,297,280

Therefore, there are 17,297,280 ways to choose 7 letters, without replacement, from 12 distinct letters when the order matters.

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The value of x, y and z in the triangle is 6.0, 8.8 and 12.4 respectively.

A triangle is a plane shape with three sides.

To calculate the value of x in the triangle above, we use the formula below

Formula:

Where:

Substitute these values into equation 1 and solve for x

Similarly, to calculate the value of y, we use the formula below

Where:

Substitute these values into equation 2 and solve for y

Also to find the value of z we use the formula below

Where:

Substitute into equation 3 and solve for z

Hence, the values of z is 12.4.

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The total surface area of the figure is 315π square feet, or approximately 988.8 square feet if we use a value of 3.14 for π.

Given information:

The cylinder is sitting on the base of the cone.

The diameter of the base is 14 feet.

The slant height of the cone is 9 feet and the height of the cylinder is 11 feet.

To find the total surface area of the figure, we need to find the surface area of the cone and the surface area of the cylinder and add them together.

The surface area of the cone:

The radius of the cone is half of the diameter, which is 7 feet.

The lateral surface area of the cone can be found using the formula:

L = πrs, where r is the radius and s is the slant height.

L = π(7)(9) = 63π square feet

The base of the cone is a circle with a radius of 7 feet, so its area is:

A = πr² = π(7²) = 49π square feet

The surface area of a cylinder:

The radius of the cylinder is also 7 feet since it shares the same base as the cone.

The lateral surface area of the cylinder is:

L = 2πrh, where r is the radius and h is the height.

L = 2π(7)(11) = 154π square feet

The base of the cylinder is another circle with a radius of 7 feet, so its area is:

A = πr² = π(7²) = 49π square feet

Total surface area:

Adding the lateral surface area and the base area of the cone and cylinder, we get:

63π + 49π + 154π + 49π = 315π square feet

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The algebraic description of this transformation is (x, y) = 2/3(x, y)

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

The scale factor is calculated as

Scale factor  = P'/P

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-6, 8)'/(-9, 12)

Evaluate

Scale factor  = 2/3

So, the scale factor  is 2/3

This means that the algebraic description is (x, y) = 2/3(x, y)

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Applying the Pythagorean theorem, the value of c is 6.0.

A Pythagorean theorem is a principle that can be used to determine the unknown side of a given right triangle when the values of its other two sides are given. Pythagorean theorem states:

[tex]Hyp^{2}[/tex] = [tex]Adj^{2} + Opp^{2}[/tex]

So that from the given question, applying the Pythagorean theorem;

[tex]c^{2}[/tex] = [tex]a^{2} + b^{2}[/tex] - 2abCos θ

But, a = 2.15  and b = 5.61

So that;

[tex]c^{2}[/tex] = [tex]2.15^{2}[/tex] + [tex]5.16^{2}[/tex]

      = 4.6225 + 31.472

[tex]c^{2}[/tex] = 36.0946
c = [tex]\sqrt{36.0946}[/tex]

 = 6.0079

c = 6.0

The value of c is 6.0.

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The end of the stencil is located at, (x_2,y_2)=(9,3) is the required answer.

The given line is divided in the ratio 1:3 and the coordinate of the point P at which the line is divided is (3,0).

The best approach is to use the section formula which relates to the internal division of a line.

Given a line from (x_1,y_1) \: to\: (x_2,y_2) which is divided in the ratio m:n, the coordinates of the point P of division is derived using the formula:

[tex]P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)[/tex]

In our given case,

P(x,y)=(3,0)

m:n=1:3

(x_1,y_1) =(1,-1)

Our goal is to determine the end of the stencil (x_2,y_2)

Thus:

[tex](3,0)=left(\dfrac{1x_2+3(1)}{3+1} ,\dfrac{1y_2+3(-1)}{3+1}\right)\\Matching \: coordinates\\dfrac{1x_2+3(1)}{3+1}=3\\x_2+3=3*4\\x_2=12-3=9\dfrac{1y_2+3(-1)}{3+1}=0\y_2-3=0*4\y_2=3+0=3[/tex]

Therefore, the end of the stencil is located at, (x_2,y_2)=(9,3) is the required answer.

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