Twice the difference of a number and is 2equal to8 . Use the variable y for the unknown number.

Answer:

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

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 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 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 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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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.

[tex]\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{c}{\sin(142^o)}=\cfrac{42}{\sin(19^o)}\implies c=\cfrac{42\sin(142^o)}{\sin(19^o)}\implies c\approx 79.4[/tex]

Make sure your calculator is in Degree mode.

The students score for the competitive exam is 110

To find the score of the student, we can use the given information.

For correct answers

Number of correct answers = 70

Marks for correct answers

= Number of correct answers * Marks per correct answer

= 70 * 2

= 140

For wrong answers:

Number of wrong answers = 30

Marks for wrong answers

= Number of wrong answers * Marks per wrong answer

= 30 * -1

= -30

The total score

= Marks for correct answers + Marks for wrong answers

= 140 + (-30)

= 110

Hence the student's score is 110.

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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

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 domain is 0 ≤ b ≤ 6 and the range is c ≥ 30.In this situation, the function that models the total weight of a shipping crate is given as c = 24b + 30, where c represents the total weight of the crate and b represents the number of boxes packed inside.

To determine the domain and range of this function, we need to consider the constraints of the problem. It is mentioned that each crate holds a maximum of 6 boxes.

Domain: The domain refers to the set of input values that the function can accept. In this case, the number of boxes (b) cannot exceed 6 since that is the maximum capacity of each crate. Therefore, the domain of the function is 0 ≤ b ≤ 6, where b is a non-negative integer.

Range: The range represents the set of possible output values of the function. The total weight of the crate (c) is determined by the number of boxes packed inside. Since the weight of the crate increases linearly with the number of boxes, there is no upper limit to the range. The range of the function is c ≥ 30, where c is a non-negative integer representing the weight of the crate.

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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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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

Check the picture below.

Answer:

Step-by-step explanation:

yes

Answer:

Quadrant V

Step-by-step explanation:

A co-ordinate graph only has 4 quadrants!

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 missing side of the triangle given the angle as 71° and hypotenuse as 17 to the nearest tenth is 16.1.

The correct answer choice is option C

Hypotenuse= 17

Opposite = x

Angle = 71°

Sin 71° = opposite / hypotenuse

sin 71° = x / 17

0.95105 = x / 17

cross product

0.95105 × 17 = x

x = 16.1 to the nearest tenth

In conclusion, the missing side of the triangle to the nearest tenth is 16.1

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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: 27

Step-by-step explanation:

V=lwh  

V=(3)(3)(3)

=27

Answer:

27 units

Step-by-step explanation:

If we say the cube is broken up into smaller cubes, volume is the number of tiny cubes total.

An easier way to do this is to remember that the volume equation is V=L*w*h= length*width*height, where the width is 3 cube units, the height is 3 cube units, and the length is 3 cube units. So:

V=3*3*3= 27

If this does not make sense, here is another way to think about volume.

First, lets determine what the area of one surface of the cube is. Area is length times width, so the answer is 9. We can also count the number of cubes, if that is easier.

So we found the area of one face. Now we need to know how many of these square areas makes up the cube. That is, how many 3 by squares will make the cube? From the diagram, we see that there are three cube units across, and if each face area has a width of one cube, then we multiply.

3*9= 27

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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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:  Ans(1)

 In right triangle

     a = 13cos(56°)

   a = 7.3 cm

Ans(2)

   In right triangle

   b = 6/sin(35°)

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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The solution to the given simultaneous equations are:

(-6, -6)

There are different ways to solve simultaneous equations such as:

- Elimination Method

- Substitution Method

- Graphical Method

Now, we are given two simultaneous equations to solve graphically and the equations are:

U = V

8U = 2V - 36

Now, the graph that solves these simultaneous equations is as shown in the attached file.

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The measure of the angle is 35 degrees.

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary.

Let's assume that x is the measure of the angle in question.

The complement of x is the angle that, when added to x, forms a right angle (90 degrees). Therefore, the complement of x can be represented as 90 - x.

According to the problem, the measure of the angle is 130 less than three times its own complement. We can write this information as an equation:

x = 3(90 - x) - 130

Simplifying and solving for x, we get:

x = 270 - 3x - 130

4x = 140

x = 35

Therefore, the measure of the angle is 35 degrees.

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