Derek has the opportunity to buy a money machine today. The
money machine will pay Derek $22,614.00 exactly 6.00 years from
today. Assuming that Derek believes the appropriate discount rate
is 10.00%,

Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

The explicit formula for the sequence [tex]\(a_n\)[/tex] is:

[tex]\(a_n = \begin{cases} 4n + 3 & \text{if } n \text{ is even} \\ 4n - 2 & \text{if } n \text{ is odd} \end{cases}\)[/tex]

To find an explicit formula for the sequence [tex]\(a_n\)[/tex] that satisfies the recurrence relation [tex]\(a_n = 2n-1 + 2a_{n-2}\)[/tex] with initial conditions [tex]\(a_1 = 2\)[/tex] and [tex]\(a_2 = 7\)[/tex], we can proceed as follows:

First, let's examine the first few terms of the sequence:

[tex]\(a_1 = 2\)\\\(a_2 = 7\)\\\(a_3 = 2(3) - 1 + 2a_1 = 5 + 2(2) = 9\)\\\(a_4 = 2(4) - 1 + 2a_2 = 8 + 2(7) = 22\)\\\(a_5 = 2(5) - 1 + 2a_3 = 9 + 2(9) = 27\)\\[/tex]

We can observe that the even-indexed terms [tex]\(a_2, a_4, a_6, \ldots\)[/tex] are increasing by a factor of 2, while the odd-indexed terms [tex]\(a_1, a_3, a_5, \ldots\)[/tex] are increasing by a factor of 3. This pattern suggests that we can split the sequence into two separate sequences:

For even-indexed terms:

[tex]\(b_n = a_{2n}\)[/tex]

For odd-indexed terms:

[tex]\(c_n = a_{2n-1}\)[/tex]

Let's find explicit formulas for both [tex](\(b_n\))[/tex] and [tex](\(c_n\))[/tex]:

1. Even-indexed terms [tex](\(b_n\))[/tex]:

The recurrence relation becomes:

[tex]\(b_n = 2(2n) - 1 + 2b_{n-1}\)[/tex]

To simplify the formula, let's rewrite [tex]\(b_n\)[/tex] as [tex]\(b_{n+1}\)[/tex] (i.e., shifting the index by 1):

[tex]\(b_{n+1} = 2(2n + 2) - 1 + 2b_{n}\)[/tex]

Subtracting the two equations, we get:

[tex]\(b_{n+1} - b_n = 4\)[/tex]

This is a simple arithmetic progression with a common difference of 4. To find an explicit formula for [tex]\(b_n\)[/tex], we can use the formula for the nth term of an arithmetic progression:

[tex]\(b_n = b_1 + (n - 1) \cdot \text{{common difference}}\)[/tex]

Substituting [tex]\(b_1 = a_2 = 7\)[/tex] and the common difference of 4, we have:

[tex]\(b_n = 7 + (n - 1) \cdot 4 = 4n + 3\)[/tex]

2. Odd-indexed terms [tex](\(c_n\))[/tex]:

The recurrence relation becomes:

[tex]\(c_n = 2(2n-1) - 1 + 2c_{n-1}\)[/tex]

Similar to before, let's rewrite [tex]\(c_n\)[/tex] as [tex]\(c_{n+1}\)[/tex]:

[tex]\(c_{n+1} = 2(2n + 1) - 1 + 2c_{n}\)[/tex]

Subtracting the two equations, we get:

[tex]\(c_{n+1} - c_n = 4\)[/tex]

Again, this is an arithmetic progression with a common difference of 4. Applying the formula for the nth term of an arithmetic progression:

[tex]\(c_n = c_1 + (n - 1) \cdot \text{{common difference}}\)[/tex]

Substituting [tex]\(c_1 = a_1 = 2\)[/tex] and the common difference of 4, we have:

[tex]\(c_n = 2 + (n - 1) \cdot 4 = 4n-2[/tex]

1) [tex]\cdot 4 = 4n - 2\)[/tex]

Now that we have explicit formulas for both [tex]\(b_n\)[/tex] and [tex]\(c_n\)[/tex], we can combine them to obtain the explicit formula for the original sequence [tex]\(a_n\)[/tex]:

For even-indexed terms, [tex]\(a_{2n} = b_n = 4n + 3\)[/tex]

For odd-indexed terms, [tex]\(a_{2n-1} = c_n = 4n - 2\)[/tex]

Therefore, the explicit formula for the sequence [tex]\(a_n\)[/tex] is:

[tex]\(a_n = \begin{cases} 4n + 3 & \text{if } n \text{ is even} \\ 4n - 2 & \text{if } n \text{ is odd} \end{cases}\)[/tex]

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Answer:

DB = 10

m∡C = 106°

Step-by-step explanation:

DE = EB

20x - 8 = 16x + 12

4x = 20

x = 5

DB = 5 doubled, or 10

m∡A + m∡D = 180

3y + 7 + 2y + 8 = 180

5y + 15 = 180

5y = 165

y = 33

m∡A = m∡C

m∡A = 3(33)+7 = 106°

m∡C = 106° also

Answer:

X = 1/2, 2

Step-by-step explanation:

= (2x-1)(x-2)

Answer:

OK I DON'T KNOW IF THIS IS IT BUT THE ANSWER IS POSSIBLY 0??? AND IF I DOESN'T WORK I'M SORRY

Step-by-step explanation:

Answer:

(6,8)

Step-by-step explanation:

midpoint=(x1+x2)÷2,(y1+y2)÷2

a(4,15) b(8,1)

x=4+8=12÷2=6

y=15+1=16÷2=8

Answer=(6,8)

Answer:

B

Step-by-step explanation:

Sarah's house is not shown in graph

Answer:

-42

Step-by-step explanation:

Answer:

(D) 3/10

Step-by-step explanation:

So its split into 10 different rates each and its on the third split So 3/10.

Answer:  16° F

Step-by-step explanation:

30-15=16

Answer:

119

Step-by-step explanation:

Answer:

x= 61

Step-by-step explanation:

i think

Answer: One of the ways you can do all this is by zearn or by listening by your teacher.

Answer:

1 e

2 a

3 b

4 c

5 d

Step-by-step explanation:

i did the answers to the first question i dont know the rest sorry

The comparison of systolic blood pressure in the sitting and standing positions is an example of testing the difference between matched pairs from two dependent populations.

The scenario described involves measuring the systolic blood pressure of the same set of patients in two different positions (sitting and standing). This creates a dependency between the measurements because each patient serves as their own control. In this case, the appropriate statistical test would be a paired t-test or a related test for dependent samples.

Two means from independent populations: This option would be suitable if the measurements were taken from two different groups of patients who were independent of each other, but in this case, the same individuals were measured in both positions. Two population proportions: This option would be applicable if the data involved proportions or categorical variables, rather than continuous measurements like blood pressure.

Matched pairs from two dependent populations: This option accurately represents the scenario described, as the measurements were taken from the same individuals in both positions, making them dependent on each other.

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Answer:

The angle at B is the same as the angle at E so equate them to each other to find x

2x+4=40°

2x=40-4

2x=36

x=36/2=18

Step-by-step explanation:

Hope this is helpful! stay safe and God Bless:)))

The proportion of packs that contain less than 340g is approximately 0.0918 or 9.18%. The likelihood of a pack containing exactly 330g cannot be determined without additional information.

To find the proportion of packs that contain less than 340g, we need to calculate the z-score and use the standard normal distribution table. The Calculating z-score:

z = (x - µ) / σ

Where x is the value we want to find the proportion for (in this case, 340g), µ is the mean (350g), and σ is the standard deviation (4.18g).

Substituting the values, we have:

z = (340 - 350) / 4.18 ≈ -2.39

Next, we look up the corresponding z-score in the standard normal distribution table. The area to the left of -2.39 represents the proportion of packs that contain less than 340g. Consulting the table, we find that the area is approximately 0.0091 or 0.91%.

Therefore, the proportion of packs that contain less than 340g is approximately 0.0918 or 9.18%.

To determine the likelihood of a pack containing exactly 330g, we need more information. Specifically, we would need the probability density function (PDF) of the distribution to calculate the exact likelihood. Without the PDF, we cannot determine the likelihood of a specific weight like 330g.

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The theoretical mean for a draw from a Poisson distribution with parameter λ is equal to λ itself. In this case, λ = 37, so the theoretical mean is also 37.

Explanation:

The Poisson distribution is commonly used to model the number of events occurring within a fixed interval of time or space, when these events occur with a known average rate λ. The probability mass function of the Poisson distribution is given by P(X=k) = (e^(-λ) * λ^k) / k!, where X represents the random variable representing the number of events and k is the observed value.

The Central Limit Theorem states that when independent random variables are added, their sum tends toward a normal distribution, regardless of the shape of the original distribution. For a Poisson distribution, as the parameter λ increases, the distribution becomes more symmetric and bell-shaped, resembling a normal distribution.

Since the mean of a Poisson distribution is equal to its parameter λ, the theoretical mean for a draw from a Poisson distribution with parameter 1 = 37 is 37. This means that, on average, 37 events are expected to occur within the given interval.

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Answer:

The second one

Step-by-step explanation:

She started with x dollars and then used 8 dollars to buy a football game ticket, so x-8. Then, she is left with 56 dollars, so x-8=56. Therefore, the second story represents the equation.

Answer:

-5

Step-by-step explanation:

Rewrite x - 2 as -3 - 2, which comes out to -5.

Answer:

B

Step-by-step explanation:

6.5 * 24 = 156

Therefore B

Answer:

Blanks top to bottom: 6^2, 36, 9, 108, 101

Step-by-step explanation:

Use PEMDAS which stands for parentheses, exponents, multiplication, division, addition, and subtraction. Listed in this specific order, you must look and solve for each one first, starting with parentheses.

4.

12 × ((4+2)^2/4) - 7

Solve for inside of parentheses first:

12 × ((6)^2/4) - 7

12 × (36/4) - 7

12 × 9 - 7

108 - 7

101

Answer:

[tex]6x^{3} -25x^{2} +6x+5[/tex]

Step-by-step explanation:

Transformation of function f with a feature of the transformed function.

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique

Given function is : f(x)= log x

g(x)=-f(x-3) is vertical asymptote of x=3

j(x)= f(x+3) is x-intercept of (-2,0)

h(x)=3f(x)-3 is domain of (0, ∞)

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Answer:

Step-by-step explanation:

Answer:

I don't know the answer I am sorry I really need points to ask a important question sorry you can report me if you want but I want you to know that I really points

Answer:

The answer is 25 degree because there is ( 8x-1)

Answer:

80??

Step-by-step explanation: