will mark brainliest also its not 6 and 5

To prove that the explicit formula for the nth term of a geometric sequence is given by an = a₀.rⁿ, we will use mathematical induction. Mathematical induction is a proof technique used to establish a statement or property for all natural numbers or integers greater than or equal to a starting value.

Step 1: Base Case

For n = 0, the formula gives a₀.r⁰ = a₀, which is the first term of the sequence. So, the formula holds true for the initial value.

Step 2: Inductive Hypothesis

Assume that the formula holds for some arbitrary value k, i.e., ak = a₀.rᵏ.

Step 3: Inductive Step

We need to prove that the formula also holds for k+1, i.e., a(k+1) = a₀.r^(k+1).

Using the definition of a geometric sequence, we have:

a(k+1) = r.aₖ

Now substitute the inductive hypothesis into the above equation:

a(k+1) = r.(a₀.rᵏ) = (r.a₀).rᵏ = a₀.r^(k+1)

Therefore, we have shown that if the formula holds for k, then it also holds for k+1.

Step 4: Conclusion

By the principle of mathematical induction, the explicit formula for the nth term of a geometric sequence, given by an = a₀.rⁿ, is true for all non-negative integers n.

Thus, we have proved the claim using mathematical induction.

The question should be:

Recall the following definition of an Geometric Sequence.

A sequence a₀, a₁, a₂, ... is called an geometric sequence if, and only if there is a constant r such that

ak = r.a_k_-1 where k≥ 1.

Also recall that we "claimed" the explicit formula for the nth term of the geometric sequence is given by

an = a₀.rⁿ  where n≥ 0. Use mathematical induction to prove that our claim is true.

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Answer:

-15625

Step-by-step explanation:

Hope this helps!

Answer:

-15,625

Step-by-step explanation:

-5^6 = -(5^6) = -(5 * 5 * 5 * 5 * 5 * 5) = -15,625

SQL (Structured Query Language) is a widely used language for managing relational databases. It is portable among different implementations and based on relational algebra.

SQL is a language designed for managing and manipulating structured data in relational databases. It provides a standardized way to interact with databases and perform various operations such as querying, inserting, updating, and deleting data. One of the advantages of SQL is its portability, meaning that SQL code can be written to work with different database management systems (DBMS) as long as they support the SQL standard. This portability allows for easy migration of databases between different systems.

SQL is based on relational algebra, which is a mathematical framework for working with relational databases. It defines operations and rules for manipulating relations (tables) and performing relational queries. The foundations of SQL are rooted in the principles of relational algebra, providing a solid basis for database management.

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Answer:

x=40, ∠ACB=125, ∠ACD= 55

Step-by-step explanation:

In order to solve this, you have to find the x-value. We know that these angles are supplementary, which means that the angles, ∠ACB and ∠ACD, both add up to 180°.

With this information, we can conclude 3x+5+2x-25=180.

To solve this equation for x,

1. Combine like terms

5x-20=180

2. Add 20 to both sides

5x=200

3. Divide both sides by 5.

x=40

Now we have the x-value. All we have left to do is plug that in to both of the equations for the angles.

1. ∠ACB: 3(40)+5

120+5

∠ACB = 125

2. ∠ACD: 2(40)-25

80-25

∠ACD = 55

Answer:x=40

Step-by-step explanation:

5x-20=180

5x=200

X=40

Answer:

B: no mode

Explanation:

A mode is a number that occurs often in a set of data. Since all of April's temperatures are different, there is no mode.

Answer:

b because mode is the how many times a number pop up it has to be the same

Step-by-step explanation:

73.12 m2

Step-by-step explanation:

determine triangle area.

8x12=96   96/2=48

determine area of half circle

diameter=8

radius=4

4π²/2=25.1327412287

add two areas together.

48+25.1327412287=73.1327412287

round the nearest hundredth

73.1327412287=73.12 m2

Answer:

-2

Step-by-step explanation:

First, you need to find the equation.

f(x) = -3x + b

Now we need to find the y-intercept.

f(x) = -3x + b

f(-9) = -3(1) + b

-9 = -3 + b

-6 = b

f(x) = -3x - 6

The zero of f means that f(x) = 0

f(0) = -3x - 6

f(6) = -3x

x = -2

Answer:

Step-by-step explanation:

Remark

Cos(y) = adjacent Side / hypotenuse

y = 51 degrees

adjacent = 10

Solution

Cos(51) = 10/x              Multiply both sides by x

x cos(51) = 10               Divide by Cos(51)

x = 10 / cos(51)

Cos(51) = .6293

x = 10/0.6293

x = 15.89

The expression for a(t) is 8(1-t)/(1+t)² and A(2) = -8/9.

An expression is a combination of numbers, variables, and operations. Expressions can be used to represent quantities, relationships, and functions. While there are different types of expression such as arithmetic expression, algebraic expression and function, this as an algebraic expression.

To determine the expression that represents a(t); we have to factor the expression 8t/(1+t²).

8t/(1+t²) = 8t/(1+t)(1-t)

Dividing by 1 - t

a(t) = 8t/(1+t)

Simplifying further;

a(t) = 8(1-t)/(1+t)²

To solve for A(2), we need to plug t = 2 into the expression;

A(2) = 8(1-2)/(1+2)²

A(2) = -8/9

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Answer:

0 or 25

Step-by-step explanation:

To solve for x

we first factor

2x^2-50x=0

2x(x-25)=0

To make this equation 0 x has to be 0 or 25

In the absence of the blonde turning down everyone, the pure strategy Nash equilibrium is for all men to choose brunettes. If the blonde turns down everyone, the pure strategy Nash equilibrium remains the same: all men choosing brunettes.

In this case, all four men choose brunettes. Since no man is going for the blonde, their payoff is b if they are the only man going for a brunette. This scenario is a pure strategy Nash equilibrium because no man has an incentive to deviate.

If one man goes for the blonde, his payoff is c. The other three men choose brunettes, resulting in a payoff of b. This situation is not a Nash equilibrium because the man going for the blonde has an incentive to deviate and choose a brunette instead, increasing his payoff to b.

Since the payoffs are the same for any number of men going for the blonde, the pure strategy Nash equilibrium is for all men to choose brunettes. Each man's payoff will be b, regardless of whether they choose the blonde or a brunette.

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Answer:

Part A: 8 meters

Part B: B, D

Step-by-step explanation:

Answer:

212.5 miles

Step-by-step explanation:

The given series Σ (bnₙⁿ cos nπ)/n is conditionally convergent.

To determine the convergence of the series, we need to examine the behavior of the terms and apply the convergence tests. Given that {bₙ} is a sequence of positive numbers that converges to 1/2, we can conclude that bnₙⁿ approaches 1/2 as n approaches infinity.

Considering the term (bnₙⁿ cos nπ)/n, we have the alternating factor cos nπ which oscillates between -1 and 1 as n varies. The absolute values of the terms bnₙⁿ/n decrease monotonically to zero.

By the Alternating Series Test, if a series has alternating signs and the absolute values of its terms decrease monotonically to zero, then the series is conditionally convergent. Therefore, the given series Σ (bnₙⁿ cos nπ)/n is conditionally convergent.

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Complete question - Let {bₙ} be a sequence of positive numbers that converges to 1/2 . determine whether the given series is absolutely convergent, conditionally convergent, or divergent.

[n =1 to infinity]Σ (bnₙⁿ cos nπ)/n =1

a. absolutely convergent

b. conditionally convergent

c. divergent

Answer:

Question 3: 8000

Question 4: 300

Answer:

3. 8,000

4. 300

Step-by-step explanation:

3.

2/5 * 20,000 = 2 * 20,000/5 = 2 * 4,000 = 8,000

Answer: 8,000

4.

Use a proportion.

10/2 = x/60

5/1 = x/60

x = 5 * 60

x = 300

Answer: 300

Answer:

100% of 50 is 50

x = 50

Step-by-step explanation:

Answer:

x = 50

Remember that 100% of anything is the number itself.

Step-by-step explanation:

Since there are 4 people who answered that they had 0 number of scarves we put 4 0's in a set of numbers. Then we see that there are 2 people who have 1 scarf. so there are 2 1's and we keep on going down the line.

{0,0,0,0,1,1,2,3,3,4,5,5} there are 12 numbers here

so we add up all of them

1+1+2+3+3+4+5+5=24

then divide that number by 12 because that's how many numbers there are

24/12=2

The mean of the numbers is 2

Hope that helps :)

Answer:

Step-by-step explanation:

Change:

Percent change:

Answer:

113.04

Step-by-step explanation:

Surface area for a sphere is 4*pi*radius^2

4*3*3*3.14

113.04

The surface area of the sphere with the given radius is 113.04cm².

A sphere is simply a 3-dimensional object with no vertices and edges.

The surface area of a sphere is expressed as;

Area = 4πr²

Given the data in the question;

To determine the surface area of the sphere, we substitute our given values into the expression above.

Area = 4πr²

Area = 4 × 3.14 × (3cm)²

Area = 4 × 3.14 × 9cm²

Area = 113.04cm²

Therefore, the surface area of the sphere with the given radius is 113.04cm².

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Answer:

Step-by-step explanation:

ps. you can use m a t h w a y  and check

it's spaced out cuz it doesn't let me write it well

Answer:

The actual diameter of Venus is 12,100 kilometers.

Step-by-step explanation:

Since William is building a planetary path for people to walk through, and the planetary path will have a model of the sun and model of the planet, and William uses two different scales, he uses 1 cm to 1000 km for the diameter of each planet and 1m to 1000000km for the distance of the sun to each planet, if William makes a model of planet Venus and the model has a diameter of 12.1, to work out the real diameter of Venus the following calculation must be performed:

1 cm = 1000 km

12.1 cm = X km

1 = 1000

12.1 = X

12.1 x 1000/1 = X

12,100 = X

Thus, the actual diameter of Venus is 12,100 kilometers.

The statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is false. The irreducibility of f(x) does not guarantee the irreducibility of f(x²) over R.

The statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is actually false. In other words, just because a polynomial, f(x), is irreducible over the real numbers (R), it does not necessarily mean that its square, f(x²), will also be irreducible over R.

To understand why, let's first clarify the concept of irreducibility.

A polynomial is considered irreducible if it cannot be factored into a product of two or more non-constant polynomials with coefficients in the same field. In this case, we are considering the field of real numbers (R).

Now, when we square a polynomial, such as f(x)² or f(x²), it can lead to changes in its factorization.

The squared polynomial may introduce new factors or change the multiplicity of existing factors.

This means that the irreducibility of the original polynomial, f(x), does not necessarily carry over to the squared polynomial, f(x²).

To illustrate this, let's consider an example. Suppose we have a polynomial f(x) = x² + 1, which is irreducible over R. If we square this polynomial, we get f(x²) = (x² + 1)² = x⁴ + 2x² + 1.

The squared polynomial, in this case, is no longer irreducible over R because it can be factored as (x² + 1)(x² + 1).

This example shows that the irreducibility of f(x) does not imply the irreducibility of f(x²). It's important to carefully analyze the specific factors and properties of each polynomial to determine its irreducibility.

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Answer:

63 degree

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

data from our experiment.....

Answer:

Well, ermm duh

Step-by-step explanation:

The faster you go, the less time it will take

Answer:

x = -51

Step-by-step explanation:

Do I need to explain oorrrrrrrrr.....

Answer:

I cannot see pictures, so I will explain how to find slope, so you can do it on your own.

Step-by-step explanation:

Find 2 coordinates on the line.

Ex: (2,3) and (4,6)

Subtract the y-coords and x-coords from each other and divide.

6-3 = 3

4-2 = 2

3/2

So the example slope is 3/2.

The 3 represents the rise, and 2 represents the run.

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hope it helps

Answer:

4/18

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

A) 1

Step-by-step explanation:

The number 1 was spun the fewest times. We know this because there is only one x above the 1, suggesting it wa spun the fewest times.

Hope it helps!!!