Given m||n, find the value of x.

The explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then aₙ = 5 × 2ⁿ⁻¹.

As given in the question,

Given initial terms of the sequence are as follow:

5, 10, 20, 40, 80, 160, 320

a₁ , a₂ , a₃ representing initial terms

a₂ / a₁ = 10 /5

         = 2

a₃ / a₂ = 20 /10

          = 2

a₄ /a₃ = 40 / 20

        = 2

Common ratio 'r ' = 2

First term a₁ = 5

Given sequence is representing the geometric sequence

Explicit formula for nth of the  geometric sequence is given by :

aₙ = a₁ × rⁿ⁻¹

    = 5 × 2ⁿ⁻¹

Therefore, the explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then

aₙ = 5 × 2ⁿ⁻¹.

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To avoid any perfect multicollinearity we need to  exclude any one of the binary class variables for all the entities which are independent of whether an given intercept is present across the given equation or not.

Fixed outcomes is a statistical regression version wherein the intercept of the regression version is authorized to differ freely throughout people or groups. It is frequently implemented to panel information with the intention to manage for any individual-unique attributes that don't range throughout time. Use fixed-outcomes (FE) each time you're most effective inquisitive about reading the effect of variables that fluctuate over time.

FE discover the connection among predictor and final results variables inside an entity (country, person, company, etc.). In many packages which includes econometrics and biostatistics a set outcomes version refers to a regression version wherein the organization method are fixed (non-random) instead of a random outcomes version wherein the organization method are a random pattern from a population.

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The equation to represent the hanger diagram is   5x - 2x = 21 - 12 and weight of 1 triangle in the hanger is 3 gram. .

In the question ,

it is given that ,

the the weight of one square is = 2 gram

the weight of one circle is = 3 gram

and the weight of one triangle is is = x gram

When the hanger is balanced , then weight on Left side =  weight on Right side

we see that left side have 2 triangles , 6 squares and 3 circles ,

and the Right side have 2 circle , 3 square and 5 triangle ,

So , the balanced equation for the hanger can be written as

2*x + 6*2 + 3*3 = 2*3 + 3*2 + 5*x

2x + 12 + 9 = 6 + 6 + 5x

2x + 21 = 12 + 5x

5x - 2x = 21 - 12

3x = 9

x = 3

Therefore , the equation is 5x - 2x = 21 - 12  and the weight of triangle is 3 grams .

The given question is incomplete , the complete question is

There is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram and find the weight of 1 triangle .

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In bayes theorem, you have some starting information, then you collect some new information so that you can UPDATE the original probabilities so you now have better information.

The Bayes' theorem, commonly referred to as the Bayes' rule, is a mathematical formula used in statistics and probability theory to calculate the conditional probability of events. The Bayes theorem essentially describes the likelihood of an event based on prior knowledge of any circumstances that might be relevant to the event.

P(A|B) = [tex]\frac{ P(A) P(B|A)}{P(B)}[/tex]

So it is always the case of conditional probability.

Hence, the original probability is always updated in case of Baye's theorm.

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The sample proportion of the random sample of 50 students is 64% or 0.64.

Given:

the college administrator was only able to survey a random sample of 50 students.

she finds that 32 of these students report having a full- or part-time job.

we are asked to determine the sample proportion = ?

Based on the given conditions, we formulate:

32÷50

simplify:

16/25

= 64% or 0.64

hence we get the required sample proportion.

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Using the Dominant strategy and Nash equilibrium, helps you to choose a number between large sample (0-100) such that the choosing number is 2/3 of average guess of all and become a winner.

Dominant Strategy:

A dominant strategy refers to a player's preference for a particular choice of action, independent of the actions and decisions of other players in a strategy game. A dominant strategy is based on the playoffs the player wins.

The concept of Nash Equilibrium is not too difficult to understand. Imagine any combination of player choices. For example, everyone picks 34 in the hope that it matches her 2/3rds of other people's guesses. Nash proved that every game has at least one such equilibrium if randomized strategies are allowed.

Zeroth order - If everyone was a zero-order thinker, just guess randomly between 0 and 100 and pick a random number. Average = ( 0 + 100 ) / 2 = 50.

1st order thinkers guess 2/3 of 0th order thinkers = (2 / 3) × 50 = 33.

2nd order thinkers guess/3 primary thinkers

= (2 / 3) × 33 = 22.

3rd order - 3rd order thinkers guess 2/3 of 1st order thinkers = (2 / 3) × 22 = 15.

Distribution of k order thinkers and sophisticated thinkers. If the population he is a 0th, 1st, 2nd, 3rd thinker, we can estimate

(2/3) ×(50 + 33 + 22 + 15) / 4 = 20.

Thus, different strategies for different opposing thinkers are discussed here.

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If the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. The area of the rectangle increasing is:  114 cm2/sec.

Using product rule formula

(dA / dt) = L× (dW / dt) + W × (dL / dt)

Where:

dA/dt = Rate that the area of the rectangle is increasing

dL/dt = 3 cm/s

L = 15 cm

dW/dt = 5 cm/s

W = 13 cm

Let plug in the formula

(dA / dt) = (15) × (5) + (13) × (3)

(dA / dt) = 75 + 39

(dA / dt)  = 114 cm2/sec

Therefore 114 cm2/sec is the area of the rectangular.

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The difference between any two successive integer squares is equal to the total of all these two integers, as demonstrated by the completed proof.

Let x represent any integer to prove algebraically.

This means that x+1 should be the following integer.

The claim demands evidence;

(x+1)² - x² = x+(x+1)

Consider the left hand side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Solution)

Similarly, the right side.

= x + (x + 1)

= 2x + 1

Thus, subtracting the difference between two consecutive squared integers equals adding the two integers that since LHS=RHS equality is clear.

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Four special two digit numbers exist: 1, 2, 145, and 40585.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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Integers greater than 0 are positive number.

What is rational number?

A rational number could be a number that may be expressed as the quotient or fraction p/q of 2 integers, a dividend p and a non-zero divisor letter.

Main body:

The definition of positive integers in math states that "Integers that are larger than zero are positive integers". Integers may be classified into 3 types: negative integers, zero, and positive integers. examine the quantity line given below to know the position and worth of positive integers.

1 is that the smallest positive whole number and therefore the greatest positive whole number isn't referred to as the list is endless.

Therefore the definition of positive integer is such as.

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Answer:

find the tan inverse

[tex] { \tan(?) }^{ - 1} [/tex]

of the value to get the angle.

1d.p = 29.2°

Answer: B

Step-by-step explanation: We know that Amy took three hours to get to the hilltop, so A and D are out because they are saying she reached the hilltop in 2 hours, instead of 3. Then we have C and B left. The difference between them is that C is saying that they had a picnic for 4 hours instead of 5.

hope this helps!

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Answer:

B

Step-by-step explanation:

The given graphs are distance-time graphs, where:

As Amy walks from her tent to a hilltop in 3 hours, the first part of the graph should be a straight line with a positive gradient, where the x-values of its endpoints are:

Therefore, we can immediately discount answer options A and D as they suggest that this part of Amy's journey takes only 2 hours.

Amy stops and has a picnic at the top of the hilltop for 5 hours.  Therefore, her distance from the tent during this time does not change as she is not moving.  This will be represented on the graph by a horizontal line that has endpoints at:

Therefore, the graph that displays the given parameters is graph B.

The two column proof for the statemen is as follows

Statement                                         Reason

2(-x + 4) = 3                                      given

-2x + 8 = 3                                         Distributive property of multiplication

-2x = 3 - 8                                          Collection of similar terms

-2x = -5                                              Subtraction property of equality

-2x/-2 = -5/-2                                     Division property of equality

x = 5/2                                               Definition of equality

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

In algebra, we utilize integers with fixed or definite values, such as 2, 13, 0.5, etc. combined with variables like x, y, and z

An instance of algebra is 2( -x + 4) = 3

The distributive property of multiplication is applied when there is multiplication over addition of terms like exemplified here

2(-x + 4)

= -2x + 4

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Answer:

75

Step-by-step explanation:

1) Divide 5 by 1/3.

Use the rule ---> [tex]a\div\frac{b}{c} =a\times\frac{c}{b} .[/tex]

5 * 3

15

Due to this being a proportional equation, you multiply 15 by 5.

5:(1/3)=75

The weight that is left when 18759 grams of bricks are removed is 3.241 kg

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

Pile of bricks = 22 kg

The weight removed from the pile = 18759 grams

The remaining weight can be calculated using the following subtraction equation

Remaining weight = Pile of bricks - The weight removed from the pile

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

Remaining weight = 22 kg - 18759 grams

Convert grams to kg

This gives

Remaining weight = 22 kg - 18.759 kg

Evaluate the difference in the above equation

Remaining weight = 3.241 kg

Hence, the remaining weight is 3.241 kg

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The value of x is 125.

what angle sum property of hexagon?

The formula for the angle sum property is, S = ( n − 2) × 180°, where 'n' represents the number of sides in the polygon.

The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees. The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.

Using angle sum property

120+120+120+100+x+x+10=720

2x+470= 720

2x= 720-470

2x= 250

x=125

hence, the value of x is 125.

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Answer: 6

Step-by-step explanation:

(P.S.: Everything in italics are numbers.)

So the answer will be 6! You're welcome!

2730 sets of officers are possible if there are members and any member can be elected to each position.

Permutations Without Repetition: Permutation repetitions select a set of items from a set of choices that can be distinguished, with each item only being selected once in each set. All collections with unique sets and unique orders of elements in a set are included in the total permutations.

The idea of permutations without replacement must be used because each member can only hold one office and each position holds a specific office.

The formula of permutation is,

p = n! / (n  - r)!

where r denotes the number of elements to be selected and n denotes the number of selections.

From a selection of 15 candidates, there are the following options for electing 3 members to fill a particular position:

p = 15! / (15 - 3)!

= 15! / 12!

= 2730

thus, there are 2730 sets of officers possible.

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Answer:y=-5x-5

Step-by-step explanation:

(0,-5) and (1,-10)

-10-(-5)= -5

1-0=1

-5/1 = -5

Answer:

p = 10

Step-by-step explanation:

4 ^ 10 x 4 ^ 5 = 4 ^ 10+5 = 4 ^ 15

p = 10

An example of rational roots can be given as:

Let the polynomial be: 4x³ + 3x² + 6x + 9;

Then,

coefficient of the variable with the highest degree = 4

coefficient having the variable with degree 0 = 9

Factors of 4 are: 1, 2;

Factors of 9 are: 1, 3;

The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;

Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.

Where all the coefficients are integers.

Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'

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Assuming QF is the full employment equilibrium then in the Figure, if the level of spending is equal to AD1, the AD shortfall would be greater than XZ. The answer is B.

The respective figure as referred in the question is as attached.

Full employment equilibrium refers to the equilibrium where all resources in the economy are fully utilized (employed). Full employment is a situation in which all available labor resources are being used in the most economically efficient way, so there is no cyclical or deficient-demand unemployment.

When the natural rate of unemployment is equal to the unemployment rate, this means the cyclical rate of unemployment is zero. So, when this relationship happens, the economy is considered to be at full employment.

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In order to determine whether this graph shows a proportional relationship, you should determine if the ratios of the two variables plotted on the graph have a constant of proportionality.

In Mathematics, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

In conclusion, the ratio of the two variables plotted on the graph of a proportional relationship is always constant.

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The equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position is [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex] at x = 0, y = -1.

Here, we have been told that the force has a magnitude of = 8 pounds (i)

It stretches a spring to a length of = 1 foot (ii)

The damping force is 0.8 times the instantaneous velocity. (iii)

We use the differential equation of motion of damping force which is =

= mx₂ +λx₁+kx

Using the formula and the values of (i), (ii), and (iii), we get -

= [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex]

This is the required equation of motion.

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Product of first 10 natural numbers is 3628800.

What is natural numbers?

In arithmetic, the natural numbers are those numbers used for enumeration and ordering. Numbers used for enumeration are referred to as cardinal numbers, and numbers used for ordering are referred to as ordinal numbers

Main body:

The first ten natural numbers are 1,2,3,4,5,6,7,8,9,10.

The product is the multiple all numbers.

Product of first 10 natural numbers is given by,

P = 1*2*3*4*5*6*7*8*9*10

P =3628800.

Therefore, Product of first 10 natural numbers is 3628800.

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Answer:

No solution.

Step-by-step explanation:

1. Move terms to the left side

x² - 3x = -8

x² - 3x - (-8) = 0

2. Use the quadratic formula

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

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x² - 3x + 8 = 0

a = 1

b = -3

c = 8

x = [tex]\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}[/tex]

3. Simplify

After simplifying:

x = [tex]\frac{3 + \sqrt{-23} }{2}[/tex]

4. No real solutions because the discriminant is negative.

The square root of a negative number is not a real number.

d = -23.

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Answer: 39 in

Step-by-step explanation: