give the slope of the line with equation 17x = -34; then graph the line

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:

Step-by-step explanation:

x = 9

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:

Topic : CIRCLE

1. Capture/ cut outs pictures that represents a Circle then paste it in a long band paper.

2. Make a reflection in CERA form

C-Content (min. 5sentence)

E- experience(min. 5 sen.)

R-reflection (min.5 sent.)

A- Application (min.5

The correct answer is option B. 232.6 mg/mL which is the concentration of the vial after reconstitution.

To determine that 232.6 mg/mL is the concentration of the antibiotic vial after reconstitution, we need to calculate the amount of antibiotic in grams divided by the final volume in milliliters.

The vial states that it needs to be reconstituted with 8.6 mL of sterile water for a final volume of 10 mL. This means that the antibiotic will be dissolved in 8.6 mL of sterile water.

Since the vial contains 2 grams of antibiotic, the concentration can be calculated as follows:

Concentration = Amount of antibiotic (g) / Final volume (mL)

Concentration = 2 g / 8.6 mL

Simplifying the expression, we get:

Concentration ≈ 0.2326 g/mL

Therefore, the correct option is B) 232.6 mg/mL, the concentration of the vial after reconstitution.

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Answer:

the probability that a test correctly classifies as positive individuals who have preclinical disease

Step-by-step explanation:

Sensitivity represents the true positive percentage

Lets take an example if there is 90% sensitivity that means there are 90% people who have the target disease considered the test positive

So according to the given options, it is the probability in which if the test is done in a correct manner so this means that the positive individuals have the preclinical disease

Therefore the first option is correct

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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The present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly is $131,488

To calculate the present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly, we can use the formula for compound interest:

Present Value = Future Value / (1 + r/n)^(n*t)

Where:

Future Value = $150,000

Interest Rate (r) = 2% = 0.02 (converted to decimal)

Number of Compounding Periods per Year (n) = 4 (quarterly compounding)

Number of Years (t) = 6

Substituting these values into the formula, we have:

Present Value = $150,000 / (1 + 0.02/4)^(4*6)

Calculating inside the parentheses first:

Present Value = $150,000 / (1 + 0.005)^(24)

Next, calculate the exponent:

Present Value = $150,000 / (1.005)^(24)

Using a calculator or spreadsheet, we can evaluate the expression inside the parentheses and then divide $150,000 by that result to find the present value. Rounding to the nearest dollar, the present value needed is $131,488.

Therefore, the amount to be invested now or the present value needed is $131,488.

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Answer:

1. y=2x^2-8X-1

2. y=-6x^2+36x-63

3. y=-3x^2+18x-34

4. y=9x^2+54x+76

5. y=-x^2+8x-22

6. y=6x^2-48x+90

7. y=8x^2+16x+5

8. y=2x^2-8x+1

Have a great day :)

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

Hence, option D is the correct answer to the given question.

The correct answer to the given question is the option D. i.e r=0.818 represents a stronger correlation because 0.818 > -0.926. Explanation: The strength of the correlation can be determined by the magnitude of the correlation coefficient. The correlation coefficient values vary between -1 to 1. If the value of correlation coefficient is close to -1 or 1, it indicates strong correlation. On the other hand, if the value of correlation coefficient is close to 0, it indicates a weak correlation.A correlation coefficient value of -0.926 indicates a strong negative correlation. A correlation coefficient value of 0.818 indicates a strong positive correlation. Hence, option D is the correct answer to the given question.

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Answer:

when a = 6, substitute 6 in the equation for a:

7(a + 2) = 7(6)+ 14

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

When a = 6

7(a+2)

7(6+2)

7(8)

56

Answer:

Part A: 8 meters

Part B: B, D

Step-by-step explanation:

Answer: I believe your answer is correct .

Answer:

yes i belive  u got it right

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

Yes, it is possible to fill all twenty mugs.

Answer:

y=2x+3

Step-by-step explanation:

Lets verify

[tex]\\ \sf\longmapsto -1=2(-2)+3=-4+3=-1[/tex]

[tex]\\ \sf\longmapsto 1=2(-1)+3=-2+4=1[/tex]

Hence verified

Answer:

C): y = 2x + 3

Step-by-step explanation:

• when x is -2:

[tex]{ \tt{y = 2(- 2) + 3}} \\ { \tt{y = - 1}}[/tex]

• when x is -1:

[tex]{ \tt{y = 2( - 1) + 3}} \\ { \tt{y = 1}}[/tex]

• since y holds for -2 and -1, it'll hold for other positive integers.

Answer:

[tex]5\sqrt[3]{5}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{625}[/tex] factor [tex]625^{1/3}[/tex]=[tex]5(5^{1/3} )[/tex]=5\sqrt[3]{5}

Hope that helps :)

Answer:

-43 yards is the answer...

Answer: 32, 27, 20

Step-by-step explanation: This is a quadratic table.

Answer:

12 feet or 4 feet.......

Answer: it's  1 1/2

please give me brainlest

Answer:

1.8

Step-by-step explanation:

- hope this helps!!

Answer:

the answer is  10

Step-by-step explanation:

Answer: 10

Why? Because 10x5=50 and then 10x2=20 ten can be used for both of them! Hope this helps^^ please give me brainlist if you could but you don’t have too!^^

Answer:

Answer is (a)

Step-by-step explanation:

Well I didn’t really do any work but you can tell right away theres a ton of slope options so you can’t eliminate from there, BUT when you look at the y-intercept, 3 is the only y-intercept option here and the only choice with the y-intercept of 3 is (a).

Answer:

Part A

750, 2250, 6750, 20250, 60750

Part B

1640250

Answer:

The slope is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{Y_{2} -Y_{1} }{X_{2}-X_{1} }[/tex]

-7-(-3)= -7+3= 4

4/?

7-(-9)= 7+9 = 16

4/16=1/4

I hope this helps :-)

After taking the given data into consideration we conclude that
a) the half-life of the unknown radioactive element is approximately 1921.7 days.
b) approximately 1011.4 days, or about 2.77 years, for a sample of 100 mg to decay to 55 mg.

(a) The half-life of a radioactive element is the time needed for half of the material to decay. To find the half-life of the unknown radioactive element, we can use the fact that in 560 days, the radioactivity of a sample decreases by 36 percent. Let T be the half-life of the element. Then, we have:
[tex]0.5 = (1 - 0.36)^{(560/T)}[/tex]
Simplifying this equation, we get:
[tex]0.5 = 0.64^{(560/T)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.5) = ln(0.64)^{(560/T)}[/tex]
[tex]ln(0.5) = (560/T) * ln(0.64)[/tex]
Solving for T, we get:
[tex]T = -560 / (ln(0.64) * ln(0.5))[/tex]
[tex]T \approx 1921.7 days[/tex]

(b) To find how long it will take for a sample of 100 mg to decay to 55 mg, we can use the half-life formula:
[tex]N = N_0 * (1/2)^{(t/T)}[/tex]
where:
N is the final amount, which is 55 mg in this case
[tex]N_0[/tex] is the initial amount, which is 100 mg in this case
t is the time it takes for the sample to decay from [tex]N_0[/tex] to N
T is the half-life of the element, which we found to be approximately 1921.7 days
Substituting the values, we get:
[tex]55 = 100 * (1/2)^{(t/1921.7)}[/tex]
Simplifying this equation, we get:
[tex]0.55 = (1/2)^{(t/1921.7)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.55) = (t/1921.7) * ln(1/2)[/tex]
Solving for t, we get:
[tex]t = -1921.7 * ln(0.55) / ln(1/2)[/tex]
[tex]t \approx 1011.4 days[/tex]
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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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A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.16. The probability of success on trial 9 is 0.16.

In a binomial experiment, there are two outcomes that are possible in each trial: a success and a failure.

A binomial experiment consists of a fixed number of trials.

The term "probability" refers to the measure of how likely an event is to happen.

The probability of success on trial 5 is 0.16.

We are required to calculate the probability of success on trial 9.

Since the experiment consists of a fixed number of trials, we can say that probability of success in each trial is the same.

Let us assume the probability of success is p.

Therefore, the probability of failure in each trial is (1-p).

The probability of success on trial 5 is 0.16.

Therefore, p = 0.16.

The probability of failure on trial 5 is

1-p = 1-0.16

1-p = 0.84

The probability of success on trial 9 is given by:

P(success on trial 9) = p

P(success on trial 9) = 0.16.

Therefore, the probability of success on trial 9 is 0.16, which is option E.

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