5. The average of the first 5 numbers was 200. The average of the wo
numbers was 400. What was the overall average?
6. Find the volume and the surface area of the right prism whose base is
and whose sides are 10 centimeters high. Dimensions are in meters.
20
12
7
40
30.9
Use substitution to solve for x and y:

Answer:

11 words

Step-by-step explanation:

Thera are 56 words shared equally among 7 lines

Therefore there are 56/7 = 8 words per line

On the last line by adding 3 words, there will be 8 + 3 = 11 words

Answer: The value of sin(2x) can be found using the identity:

sin(2x) = 2sin(x)cos(x)

Since sin(x) = -1/2, we can use the Pythagorean identity to find the value of cos(x):

cos^2(x) + sin^2(x) = 1

So

cos^2(x) = 1 - sin^2(x) = 1 - (-1/2)^2 = 1 - 1/4 = 3/4

Taking the square root of both sides:

cos(x) = ± sqrt(3)/2

Since sin(x) is negative and cos(x) must be positive, we get:

cos(x) = sqrt(3)/2

Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:

sin(2x) = 2sin(x)cos(x) = 2 * (-1/2) * sqrt(3)/2 = -sqrt(3)

So the exact value of sin(2x) is -√(3).

Step-by-step explanation:

Z18 with modulo addition satisfies all four group axioms and is a group.

Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.

what is the binary operation?

In mathematics, a binary operation is a function that takes two elements from a set and returns another element from the same set.

For a set to form a group with a binary operation, the set must satisfy the four group axioms: closure, associativity, identity, and inverse.

1. Z18 with modulo addition:

Hence, Z18 with modulo addition satisfies all four group axioms and is a group.

2. Z18 with modulo multiplication:

Hence, Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.

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Answer:

y = - x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = [tex]\frac{-4=1}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - x - 2 ← equation of line

The volume of the given prism in question is 276.7 cubic yd

The formula for calculating the volume of a square based prism is expressed as:

V = BH/3

where

B is the base area

H is the height of the prism

Determine the height using Pythagoras theorem

b^2 = 13^2 - 10^2

b^2 = 169 - 100

b^2 = 69

b = √69
b = 8.3yd

Determine the required volume

V = (10*10)(8.3)/3

V = 830/3

V = 276.7 cubic yd

Hence the volume of the prism is given as 276.7 cubic yd

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d. Data is inadequate as it is not possible to determine the direction of D's house relative to A's house.

Directions refer to the relative positions of objects or locations in space. It describes the orientation and location of an object in relation to another object or a reference point.

Based on the information given, . Further information is needed to determine the direction.

Hence, d. Data is inadequate

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Answer:

Уравнение 1 + tan(a) * tan(b) = (cos(a + b))/(cos(a) + cos(b)) может быть упрощено, используя тождество tan(a) * tan(b) = (sin(a) * sin(b))/(cos(a) * cos(b)) и тождество sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b). Однако дальнейшее упрощение может быть невозможным, поскольку уравнение уже в довольно простой форме.

The computed mean is 18.8 and it is more than 32.1 than the actual mean.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

The mean of the data is given as:

x' = ∑x / n

∑x = 29 + 13 + 6 + 45 + 1 = 94

x' = 94 / 5 = 18.8

The difference between the actual mean and the calculated mean is:

D = 50.9 - 18.8

D = 32.1

Hence, the computed mean is 18.8 and it is more than 32.1 than the actual mean.

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The area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.

Given that, a trapezoid has base lengths of 16 centimeters and 13 centimeters, the height of the trapezoid is 10 centimeters, we are asked to find the area of the trapezoid,

Area of the trapezoid = (sum of the bases) × height / 2

Length of bases = 16 cm and 13 cm

Height = 10 cm

Area of the trapezoid = 16+13 × 10/2

= 145

Hence, the area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²

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Answer:28%

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

46 = 10b - 34

Move 34 to the other side by adding 34 to each side

80 = 10b

Divide 10 on each side to get b on one side

8 = b

The value of the missing side assuming that all the intersecting sides meet at right angles would be = 6ft.

From the diagram above, the length and the width of one side of the figure is given as;

Length = 13 ft

width = 16 ft

This is supposed to be the same for the other missing side length and width ;

That is ;

width = 11 + 5 = 16 ft

Length = 13 = 7 + ?

Make ? that subject of formula;

? = 13-7 = 6 ft

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-p + 2p^2 is a quadratic function, which is a polynomial function of degree 2.

Quadratic function is a polynomial function of degree 2, written in the standard form as ax^2 + bx + c, where a, b, and c are constants, and x is a variable.

The graph of a quadratic function is a parabola which opens up or down depending on the value of a. The most common application of quadratic functions is in solving problems related to parabolic motion, such as finding the maximum height, time of flight, or range of a projectile.

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It cost $17.82 to buy the papers needed for this reports

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. Therefore:

Amount of paper printed = 141 pages long * 18 copies = 2538 pages

Paper is sold in reams (500 pages) for $3.51 each. Hence:

Amount spent on papers = 2538 pages * ($3.51 / 500 pages) = $17.82

About $17.82 was spent on papers

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Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.

An angle, according to Euclidean geometry, is a shape comprised of two rays, referred as the angle's extremity, which meet at a vertex in the center. When two rays are combined, the surfaces on which they are focused may take on an angle. A plane collision also produces an angle. Dihedral angles are the name given to them. Angles are the shapes that two rays or lines with similar terminations can take in plane geometry.

Here,

a) he closest value to 0.32 is the cosine of 71.8º, which is approximately equal to 0.32.

Therefore, the angle α that satisfies

=>cos α = 0.32 is between 70º and 75º.

b) To find the value of the angle α that satisfies sin α = 0.20, it is necessary to look in the table of sine values ​​for angles of 0º, 30º, 45º, 60º and 90º, and find the closest value to 0.20.

The closest value to 0.20 is sine 11.5º, which is approximately equal to 0.20.

Therefore, the angle α that meets

=> sin α = 0.20 is between 10º and 1

Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.

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The cube root can be estimated in the range:

3 < ∛29 < 4

And the value is ∛29 = 3.1

First we need to find two perfect cubes that bound our number.

We know that:

3*3*3 = 3^3 = 27

4*4*4 = 64

Then:

27 < 29 < 64

∛27 < ∛29 < ∛64

3 < ∛29 < 4

So we have an estimation of the cube root, and it will be closer to 3 than to 4, so we can estimate this as:

∛29 = 3.1

3.1 = 29.7

So it is a good estimation.

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The area and perimeter of the shape is 4.65cm² and 9.5cm

Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle. Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

Perimeter of the triangle = 3.2+ 2.0+4.3

= 9.5cm

The area of the triangle = ½bh

= 1/2 ×3.1 × 3

= 4.65 cm²

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416 ÷ 100 = 4.16

4.16 ÷ 10 = 0.416

41600 ÷ 1000 = 4.1600 = 4.16

4.16 ÷ 100 = 0.0416

41.6 ÷ 100 = 0.416

When you divide by a power of 10, you move the decimal to the left the number of 0's in the number.

    ÷ 10 and you move the decimal point 1 place to the left

    ÷ 100 and you move the decimal point 2 places to the left

    ÷ 1000 and you move the decimal point 3 places to the left

Answer:

416 / 100 = 4.16

4.16 / 10 = 0.416

41600 / 1000 = 41.6

4.16 / 100 = 0.0416

41.6 / 100 = 0.416

Step-by-step explanation:

When you divide a number by another number, you find out how many times the second number fits into the first one. For example, in the expression 416 / 100, you are finding out how many times 100 fits into 416. The answer is 4.16, meaning 100 fits into 416 4 times with a remainder of 16.

Similarly, in the expression 4.16 / 10, you are finding out how many times 10 fits into 4.16. The answer is 0.416, meaning 10 fits into 4.16 0 times with a remainder of 4.16.

In the expression 41600 / 1000, you are finding out how many times 1000 fits into 41600. The answer is 41.6, meaning 1000 fits into 41600 41 times with a remainder of 600.

In the expression 4.16 / 100, you are finding out how many times 100 fits into 4.16. The answer is 0.0416, meaning 100 fits into 4.16 0 times with a remainder of 4.16.

In the expression 41.6 / 100, you are finding out how many times 100 fits into 41.6. The answer is 0.416, meaning 100 fits into 41.6 0 times with a remainder of 41.6.

On solving the provided question, we can say that the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.

Mathematicians study numbers and their variations, equations and related structures, shapes and their places, and potential placements for these things. The term "function" refers to the relationship between a set of inputs, of which each has an associated output. An relationship of inputs and outputs known as a function is one in which each input leads to a single, distinct output. Each function is given a domain or a codomain, or scope. The letter f is frequently used to indicate functions (x). Entry is an x. The four major kinds of accessible functions are on functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions.

Function K is given as y = 1/2x + 2, so the slope of K is 1/2 and the y-intercept of K is 2.

To find the slope and y-intercept of function H, we can use the given points (x,y):

When x = -2, y = 0, so we have the point (-2,0)

When x = 1, y = 4.5, so we have the point (1,4.5)

When x = 5, y = 10.5, so we have the point (5,10.5)

When x = 8, y = 15, so we have the point (8,15)

We can use two of these points to find the slope of H:

slope = (change in y) / (change in x) = (10.5 - 4.5) / (5 - 1) = 6/4 = 3/2

To find the y-intercept of H, we can use the point (0,b) where x = 0:

b = y - mx = 4.5 - (3/2)(1) = 3

So the equation for function H is y = (3/2)x + 3, which has a slope of 3/2 and a y-intercept of 3.

Now we can compare the two functions:

A) The slope of function K is greater than the slope of function H. False, since 1/2 < 3/2.

B) The y-intercept of function K is greater than the y-intercept of function H. False, since 2 < 3.

C) The slope of function K is equal to the slope of function H. False, since 1/2 ≠ 3/2.

D) The y-intercept of function K is less than the y-intercept of function H. True, since 2 < 3.

Therefore, the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.

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Answer:

(x + 1)^2 + (y + 5)^2 = 169

Step-by-step explanation:

The equation of a circle centered at (h,k) with radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

To find the equation of the circle, we first need to find the center and the radius.

Given that the circle is centered at (-1,-5), h = -1 and k = -5.

Next, we need to find the radius. To do this, we use the point (0,-18) that lies on the circle and use the distance formula:

r = sqrt[ (0-(-1))^2 + (-18-(-5))^2 ] = sqrt[ 1^2 + (13)^2 ] = sqrt[1 + 169] = sqrt[170] = 13

So, the equation of the circle is:

(x + 1)^2 + (y + 5)^2 = 13^2

Therefore, the equation of the circle centered at (-1,-5) that passes through (0,-18) is:

(x + 1)^2 + (y + 5)^2 = 169

The velocity of the two trains are 79m/s and 66m/s

Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per second.

Using addition of vectors:

The total displacement = d2-d1

displacement = velocity × time

Represent the velocity of faster train by v

therefore the velocity of the slower train = v -13

855 = 5v +5(v-13)

855 = 5v+5v+65

855 = 10v +65

10v = 855-65

10v = 790

v = 790/10

v = 79 m/s

the rate of the second train = 79-13 = 66m/s

therefore the rate of the two trains are 79m/s and 66m/s

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Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

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Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.

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The composition of functions f and g is:

(f o g) =6x^2 + 15x + 2

Here we have two known functions:

f(x) = 3x + 2

g(x) = 2x^2 + 5x

We want to find the composition:

(f o g)

That just means that we need to evaluate function f(x) in x = g(x), we wikk get:

(f o g) = 3*g(x) + 2

Now we can replace g(x) there to get:

(f o g) = 3*(2x^2 + 5x) + 2

          = 6x^2 + 15x + 2

That is the composition.

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Answer: To use synthetic division to find f(3), we will divide the polynomial 9v² - 28v + 19 by v - 3.

Here's the process:

| 9 -28 19|

v-3|____________|

9(3)² - 28(3) + 19

| 9 -84 57|

0 -96 38

So, f(3) = 9(3)² - 28(3) + 19 = 9(9) - 28(3) + 19 = 81 - 84 + 19 = -4 + 19 = 15.

So f(3) = 15.

Step-by-step explanation:

Answer:

 x = 1/2. 

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

The two adjacent vertices of the triangle are A(5; 3) and B(7; 7), and one point on the opposite side is P(-2; 9). To find the coordinates of the third vertex, we need to find the midpoint of AB and extend it to P.

The midpoint of AB can be calculated by finding the average of their x-coordinates and y-coordinates:

C = ((A_x + B_x)/2, (A_y + B_y)/2) = ((5 + 7)/2, (3 + 7)/2) = (6, 5)

Next, we can use the midpoint C and point P to find the slope of the line connecting them:

m = (P_y - C_y) / (P_x - C_x) = (9 - 5) / (-2 - 6) = 4 / -8 = -0.5

Since the slope of a line perpendicular to this one is -2, we can use the midpoint C and the slope to find the equation of the line connecting C and the third vertex D:

y - C_y = -2 (x - C_x)

y - 5 = -2 (x - 6)

Expanding and solving for x, we get:

y = -2x + 17

Substituting the y-coordinate of P (-2) into this equation:

-2 = -2x + 17

Solving for x:

x = 7.5

Finally, we can use the x-coordinate to find the y-coordinate:

y = -2x + 17 = -2 * 7.5 + 17 = 5.5

So the third vertex is D (7.5, 5.5).

The vertices of the triangle are A (5, 3), B (7, 7), and D (7.5, 5.5).

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{3 }{ 4 }[/tex]

Answer: 3

Step-by-step explanation:

      The line y = 3x + 7 has a slope of 3. Slope-intercept form equations have a slope of m when written as y = mx + b. See the attached picture for more information.

y = mx + b ➜ y = 3x + 7 ➜ y = 3x + 7 ➜ 3

Answer:

Step-by-step explanation:

The ratio at which the y-value varies when the x-value changes is shown by a line's slope. The coefficient of x in the equation y = 3x + 7 is 3, therefore y rises by 3 units for every unit increase in x. The slope is thus 3. This indicates that the line will climb 3 units along the y-axis for every unit you move to the right along the x-axis.