Which angles are complementary to each other?

The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows

Average number of seats per row = (12 +42)/2= 27

So total seats = average per row x number of rows

= 27 x 16 = 432.

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These are the description of the real numbers.

According to the statement

We have to explain all about the real numbers.

So, For this purpose, we know that the

Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.

From the given information:

Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.

• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.

• Whole numbers include all positive integer values including 0.

• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)

• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)

Using the definitions above :

• 12 = Natural, integer , integer and rational (12/1)

• -15 = Integer, rational (-15/1)

• 1 1/2 = 3/2 = Rational

• 3.18 = rational (terminating decimal)

• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)

• 9.3 = rational (terminating decimal)

• -2 7/9 = -25/9 = rational (a/b)

• root 25 = √25 = ±5 = integer, rational (5/1)

• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .

• negative root 64 = - √64 = - 8 = integer, rational (-8/1)

• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)

• 8/4 = 2 = natural, number, rational, integer

So, These are the description of the real numbers.

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According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}

Therefore, the probability can be written as:

Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]

Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Does the infinite series converge or diverge? The series converges.

If it converges, what is the sum?

a. 1/2 + 3/4 + 9/8 + . . . . .

The sum of the infinite series is -1

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]

Since ,[tex]\vert r\vert < 1[/tex], the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]

The sum of the infinite series is -1

What is an infinite geometric series?

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The diver take her at a distance of 9.2 meters.

A resultant displacement can be used to quantify distance. It involves measuring the coordinate values of the beginning and ending positions. The distance is measured in quantities like meters, centimeters, kilometers, etc.

A diver descends 1.7 meters below the surface of the water while suspended 7.5 meters above it, according to the question.

According to fundamental mathematics, values that are less than zero can be represented as negative values.

She will thus descend (-1.7) meters as she dives below the surface.

The formula may now be expressed as follows: Total Distance = 7.5 - (-1.7) = 9.2 meters.

As a result, the diver descends 9.2 meters below the surface with her.

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The measurement of angle ∠2 is 67.50°.

So,

Therefore, ∠2 is 67.50°.

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The correct question is given below:

Given the regular polygon, find the measure of each numbered angle.

m ∠ 2

The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers

Given data

size of rectangular plate = 5 cm by 3cm.

the length should be within   = 0.25 of 5 cm  

This means the length, L of the rectangular plate can be mathematically represented as

5 - 0.25 ≤ L ≤ 5 + 0.25

4.75 ≤ L ≤ 5.25

Area of rectangle =  Length × Width.

Width = 3

minimum length = 4.75

maximum length = 5.25

minimum length

= 4.75 * 3

= 14.25 cm^2

maximum length

= 5.25 * 3

= 15.75 cm^2

Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

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Answer:9

Step-by-step explanation:

The solution of the simultaneous equation is given by (-7 , 4) .

A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.

For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.

The given pair of simultaneous equation is given as:

x=−2y+1

3x+8y=11

Let us solve the equations by the method of substitution:

From the first equation we take the value of x and put it in the second equation:

3x + 8y = 11

or, 3 ( -2y + 1 ) + 8y = 11

or, -6y +3 +8y = 11

or, 2y + 3 = 11

or, 2y = 8

or, y = 4

Substituting the value of y as 4 in the first equation we get:

x = − 2y + 1

or, x = - 2 × 4 +1

or, x = -8 +1

or, x = -7

Therefore the solution set of the pair of equations is given by (-7 , 4) .

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The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

The formula for calculating the volume of a cone is expressed according to the formula

V = 1/3 pir²h

where

r is the radius of the cone = 10/2 = 5in

h is the height = 2in

Substitute to have;

V = 1/3pi(5)² × 2

V = 50/3pi

Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

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Answer:

-24 < -2 < -7/4 < 1/2 < √5

Step-by-step explanation:

The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.

On this note, it follows from the slope formula that slope;

m = (y2 - y1)/(x2 - x1)

Therefore, the slope of the line segment joining the two points is;

m = (-1.5 - (-3))/(0 - (-6))

m = 1.5/6

m = 1/4.

Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

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Answer:7

Step-by-step explanation:

3-1= 2

5+2=7

Answer:

The 3 integers are 6 8 and 10

Step-by-step explanation:

Comment

Start with the median. That's the middle number of an ordered set of numbers.

a 8 b               is what you have so far.

Now the range between a and b is 4 which means that a and b differ by 4.

a + 4 =  b

The mean will solve this quickly. Put a + 4 for b

[(a + 8  + a + 4)]/3 = 8            Combine like terms

(2a + 12)/3 = 8                       Multiply both sides by 3

3 (2a + 12)/3 = 8 *3              

2a+12 = 24                            Subtract 12 from both sides

2a + 12 - 12 = 24-12               Combine

2a = 12

a = 6

but we know that the range between a (which is 6 ) and b is a + 4 = 10

So b must equal 10

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

The given series is 21+19+17+ . . .

On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.

So the formula will be (-2n +/- something).

Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.

So if n=0, our first term is 21

If n=1, our second term is 19

If n=2, our third term is 17

and so on.

So, we have the expression (21 - 2n).

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

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The number of books published by a small publishing company is 3240.

Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of books be x.

With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.

That is, 44,714+11.50x

With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.

That is, 17,174+20x

Now, the number of books produced will the costs from the two methods be the same.

So, 44,714+11.50x=17,174+20x

⇒ 44,714-17,174=20x-11.50x

⇒ 8.5x = 27540

⇒ x=3,240

Therefore, the number of books published by a small publishing company is 3240.

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The given inequality can be graphed by solving the inequation first.

What is an inequality?

Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.

The given inequality can be solved as

[tex]5y\geq -x-32[/tex]

[tex]for, x=1, 5y\geq -1-32[/tex]

[tex]or, 5y\geq -33[/tex]

[tex]or, y=\frac{33}{5}[/tex]

Solve for two more values of x and then plot the inequality on the graph

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Answer:

8,052

Step-by-step explanation:

(2,014 - 2,012) x (2,014 +2,012)

2 x 4,026

8,052

Answer:

They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.

Step-by-step explanation:

The piecewise function that best models her weekly pay h(t) is given by:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, we have that:

Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:

For up to 40 hours, she receives the standard wage of $12, hence:

h(t) = 12t, 0 ≤  t ≤ 40.

For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:

h(t) = 480 + 18t.

Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:

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The simplification by combining like terms of -(3z -5) + z is -2z + 5.

According to the given question.

We have an expression -(3z -5) + z.

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression -(3z - 5)  +z.

Here -3z and z both are the like terms.

So, we subtract coeffcients of z to simplify the given expression.

Therefore, the simplification of the expression -(3z - 5)  +z is given by

-(3z - 5) + z

= -3z + 5 + z

= -3z + z + 5

= -2z + 5

Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.

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Answer:

6561

Step-by-step explanation:

You multiply by 3 each time.

Answer:16

Step-by-step explanation:

since the increase is 2 units for purple counters

8 ÷ 2 = 4

4×4=16

The simplified expression for (16-12 / 15-11) is 1 .

The given expression is,

( 16-12 / 15-11 )

First we need to solve the numerator which is (16-12) and on simplifying the numerator we can write,

Numerator = ( 16 - 12 ) = 4                         equation 1

Similarly, now we can proceed to solve the denominator which is (15 - 11) and on simplifying the denominator we write,

Denominator  = (15 - 11) = 4                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 16-12 / 15-11 ) as,

(Numerator / Denominator) = (16-12 / 15-11) = (4/4) = 1

The simplified expression for (16-12 / 15-11) is 1 .

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The algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

Given,

The piggy bank contained = $25

The amount added in each day = $1.50

Consider number of days as x

Then the algebraic expression = 25+1.50x

Hence, the algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

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