after 4 years what is a total amount of a compound interest investment of $30,000 at 2% interest compounded monthly?round to the nearest cent

Answer:

35/37

Step-by-step explanation:

In this question, we are to calculate the ratio that represents the cosine of angle O

Firstly, please check the attachment for the diagram of the triangle.

Mathematically, the trigonometric term Cos means the ratio of the length of the adjacent to that of the hypotenuse

The hypotenuse is the longest length which is 37 which represents the length ON

The side adjacent to angle O is the side OP which is 35

Thus, the ratio representing the cosine of angle O is 35/37

For a distribution that is symmetric, the left whisker is equal in length to the right whisker.

In a symmetric distribution, the left and right whiskers are of the same length. Symmetry implies that the distribution is balanced around its central point, which is usually the mean or median.

Consequently, the left side of the distribution mirrors the right side resulting in whiskers that have equal lengths. This balance ensures that the distribution is equally spread on both sides allowing for a clear representation of the spread and variability of the data.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Sammy originally took out approximately $5357.14 to fund his education.

The rate of interest, also known as the interest rate, is the percentage amount charged by a lender or financial institution for the use of borrowed money or for the extension of credit. It is the cost of borrowing money, typically expressed as an annual percentage of the amount borrowed or owed.

Let X be the amount Sammy took out originally to fund his education.

After 5 years, the amount he has to pay back is X + (0.08X5) = X + 0.4X = 1.4X.

We know that 1.4X = $7500, so we can solve for X:

1.4X = $7500

X = $7500 / 1.4

X ≈ $5357.14

Therefore, Sammy originally took out approximately $5357.14 to fund his education.

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Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y)  → (x - 8, y + 10).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:

(x, y)                               →                  (x - 8, y + 10)

J (8, -2)                        →                  (8 - 8, -2 + 10) = J' (0, 8).

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Answer:

The answer is 17150.

Step-by-step explanation:

First, I did 175/5 to get 35 than did 490*35.

There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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The appropriate frame size for the given task set is 140.

The frame size is the length of a time interval in which all the tasks in the system are scheduled to be executed. The frame size must be a multiple of the period of each task in the system.

In this case, the periods of the tasks are 5, 7, 12, and 45. The smallest common multiple of these periods is 140. Therefore, the appropriate frame size for the given task set is 140.

Here is a more detailed explanation of the calculation of the frame size:

The first step is to find the least common multiple of the periods of the tasks. The least common multiple of 5, 7, 12, and 45 is 140.

The second step is to check if the least common multiple is also a multiple of the execution time of each task. The execution time of each task is equal to its period in this case. Therefore, the least common multiple is also a multiple of the execution time of each task.

Therefore, the appropriate frame size for the given task set is 140.

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The correct ordering of the graphs from least value of n to greatest value of n is A, B, C.

The three graphs, A, B, and C, represent the results of three simulations of a sampling distribution of a sample mean. Graph A has a value of n of 200, Graph B has a value of n of 200 and Graph C has a value of n of 0. Thus, the correct ordering of the graphs from least value of n to greatest value of n is A, B, C. To understand this, it is important to note that as the value of n increases, the sample means will be more representative of the population. Therefore, Graph A with the lowest value of n would have the least representative sample means, followed by Graph B and Graph C with the highest value of n having the most representative sample means.

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The value of cos C is 3/5

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

In a right angle triangle, the longest side is called the hypotenuse and the other two sides are called opposite and adjacent. The line facing the acute angle( tetha) is the opposite. The ratio of the sides with the acute angle are called trigonometric ratio.

sin(tetha) = opp/ hyp

cos( tetha) = adj/ hyp

tan(tetha) = opp/adj

In the triangle, using angle C,

opposite = 4

adjascent = 3 and hypotenuse = 5

cos (C) = 3/5

therefore the value of cos (C) = 3/5

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Answer:

2.88

Step-by-step explanation:

Answer:

k=3 is your answer

Step-by-step explanation:

given equation :

9x²+12xy+(k+1)y²=0

comparing above equation with

ax²+2hxy+by²

we get

a=9

h=12/2=6

b=k+1

since lines are coincident

ø=0

Tan0=±[2√(h²-ab)]/(a+b)

we get

h²=ab

6²=9(k+1)

36/9=k+1

4=k+1

k=4-1=3

The value of k will be;

⇒ k = 3

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The pair of equation is,

⇒ 9x² + 12xy + (k + 1)y² = 0

Now,

We know that;

The condition of coincide of pair of line ax² + 2hxy + by² = 0 is,

⇒ h² = ab

So, For the equation of the pair of line 9x² + 12xy + (k + 1)y² = 0, we have;

⇒ 2h = 12

⇒ h = 6

⇒ a = 9

⇒ b = (k + 1)

Substitute all the values in given condition for coincide , we get;

⇒ h² = ab

⇒ 6² = 9 (k + 1)

⇒ 36/9 = k + 1

⇒ 4 = k + 1

⇒ k = 4 - 1

⇒ k = 3

Thus, The value of k = 3

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The probability

a) All three cards are aces is: P(all three cards are aces) = 4/22,100 ≈ 0.000181

b)  All three cards are black is: P(all three cards are black) = 2,600/22,100 ≈ 0.117647

c) all three cards are spades is:  P(all three cards are spades) = 286/22,100 ≈ 0.012959

(a) To find the probability that all three cards are aces, we need to divide the number of ways in which we can select three aces by the total number of ways to select any three cards from the deck. There are 4 aces in the deck, so the number of ways to select three aces is given by:

C(4,3) = 4

where C(n,r) denotes the number of combinations of r objects chosen from a set of n distinct objects.

The total number of ways to select any three cards is given by:

C(52,3) = (52 * 51 * 50) / (3 * 2 * 1) = 22,100

Therefore, the probability that all three cards are aces is:

P(all three cards are aces) = 4/22,100 ≈ 0.000181

(b) To find the probability that all three cards are black, we need to divide the number of ways in which we can select three black cards by the total number of ways to select any three cards from the deck. There are 26 black cards in the deck (13 clubs and 13 spades), so the number of ways to select three black cards is given by:

C(26,3) = (26 * 25 * 24) / (3 * 2 * 1) = 2,600

Therefore, the probability that all three cards are black is:

P(all three cards are black) = 2,600/22,100 ≈ 0.117647

(c) To find the probability that all three cards are spades, we need to divide the number of ways in which we can select three spades by the total number of ways to select any three cards from the deck. There are 13 spades in the deck, so the number of ways to select three spades is given by:

C(13,3) = (13 * 12 * 11) / (3 * 2 * 1) = 286

Therefore, the probability that all three cards are spades is:

P(all three cards are spades) = 286/22,100 ≈ 0.012959

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90° counterclockwise rotation

Answer:

c

Step-by-step explanation:

The option that is a vertex of the second triangle is; J (2, 13)

We are told that the rug is to have a triangle with vertices at (8, 13), (2, -13), and (14, -13).

Now, She wants the rug to have a second triangle that is the reflection of the first triangle. across the x-axis.

Now the transformation rule to reflect a coordinate across the x-axis is expressed as; (x, y) → (x, -y)

Thus, the new coordinates would be;

(8, -13), (2, 13), and (14, 13).

Looking at the options, the only one that follows the reflection transformation is J(2, 13)

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An algorithm to find the substring from the given string that is the same when read forwards and backwards in python language.

Here's a basic algorithm in Python to find the longest palindromic substring:

def longest_palindromic_substring(input_str):

   n = len(input_str)

   if n == 0:

       return ""

   dp = [[False for _ in range(n)] for _ in range(n)]

   longest_len = 1

   longest_start = 0

   for i in range(n):

       dp[i][i] = True

   for start_idx in range(n - 1, -1, -1):

       for end_idx in range(start_idx + 1, n):

           if input_str[start_idx] == input_str[end_idx]:

               if end_idx - start_idx == 1 or dp[start_idx + 1][end_idx - 1]:

                   dp[start_idx][end_idx] = True

                   if end_idx - start_idx + 1 > longest_len:

                       longest_len = end_idx - start_idx + 1

                       longest_start = start_idx

   return input_str[longest_start : longest_start + longest_len]

The above algorithm uses dynamic programming to solve the problem in O(n^2) time complexity, where n is the length of the input string.

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Answer:

$72

Step-by-step explanation:

im guessing

The volume of the given cylinder is 400π cubic millimeter.

Given that, a cylinder has a radius of 5 mm and a height of 8 mm.

We know that, the volume of a cylinder is πr²h.

Here, volume = π×5²×8

= π×25×8

= 400π

Therefore, the volume of the given cylinder is 400π cubic millimeter.

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Answer:

24

Step-by-step explanation:

You do the opposite of whats states -54 divided by -6 because it says the number was multiplied which gives us 9 then since 15 was subtracted we instead add 15 which equals 24.

Answer:

the number is -5.7

Step-by-step explanation:

do everything in reverse operations,

-54 divided by -6= 9.3

9.3-15= -5.7

For proof you can do it yourself on a calculator.

Age and you can also use weight too

you can easily group people by their age and weight but not by eye color

example

age people

5 - 10 14

10 - 15 5

the table above shows that we have 14 people within the range of 5 to 10 years

and likewise the weight of the people can serve the same purpose

The client's feelings of being judged and criticized by the social worker are an example of transference.

Transference occurs when an individual unconsciously transfers feelings, emotions, and expectations from past significant relationships onto a current person or situation. In this case, the client's fear of disapproval and rejection from others in his life, which he mentioned during the initial assessment, is being projected onto the social worker.

Transference can manifest in various ways, including feeling misunderstood, judged, or criticized by the therapist or other individuals in positions of authority. It often stems from unresolved conflicts or unresolved emotions associated with past relationships, particularly those with primary caregivers or significant figures from the individual's early life.

It is important for the social worker to recognize and address the transference in a sensitive and therapeutic manner. By acknowledging the client's feelings and exploring their origins, the social worker can help the client gain insight into their past experiences and develop a healthier perspective on the therapeutic relationship. This process can contribute to the client's overall growth and well-being.

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Answer:

D

Step-by-step explanation:

Answer:

4/25=0.16=16%

3/11=0.27=27%

Step-by-step explanation:

Answer:

\({ \rm{ \frac{d \{f(x) \}}{dx} = 3 {x}^{(3 - 1)} }} \\ \\ { \boxed{ \rm{ \frac{d \{f(x) \}}{dx} = 3 {x}^{2} }}}\)

Answer:                                                                                                                    f^1(x) = 3x^2

Step-by-step explanation:                                                                 Firstly you can show first workings as                                             f^1(x) = lim - > 0  (fx+h - f(x))   / h                                                             f(x) = x^3                                                                                                    f(x+h) = (x+h)^3  then see the simplification in bold  (to separate x   with x powers)                                                                                            f^1(x) lim - > 0 = (x+h)^3 - x^2 + 2xh + h^2 - x^3 / h                                Then re-arrange                                                                                  f^1(x) lim - > 0 = (x^3 + 2x^2h+xh^2+x^2h+2xh^2+h^3-x^3/  h              Then reduce h^ powers                                                                    f^1(x) lim - > 0 = 2x^2h +xh^2 +x^2h + 2h^2 +h^3 / h                             Then cancel out h through bringing to front to multiply f^1(x) lim - > 0 = h * (2x^2 + xh^2 + x^2h + 2h^2 +h^2 ) /h                                                                                                 Then raise by 1st power f^1(x) lim - > 0 =(2x^2 + xh^2 + x^2h +  2h^2 +h^2 )                                                                                               Then plug in for (h) = 0                                                                            f^1 = (3x^2 + x(0)+ 2x(0) +(0)^2 )                                                             To find that  f^1(x) = 3x^2  

f^1(x) = 3x^2

The ordered pair are (-5/3, 0) and (0, 5)

Given the equation y = 3x + 5

To get the ordered pair of the equation, we will find the x and y-intercept

The x-intercept of the equation occur at y = 0

0 = 3x + 5

-3x = 5

x = -5/3

Hence the ordered pair of the solution is (-5/3, 0)

The y-intercept of the equation occur at x = 0

y = 3(0) + 5

y = 0 + 5

y = 5

Hence the ordered pair of the solution is (0, 5)

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The correct research method for the study mentioned in the question is a Field survey.

Field survey can be defined as a research method used to collect data from a target population. In this study, researchers used a survey questionnaire to gather data from participants. The research aimed to test the theory that the exposure to multiple versions of fake news on various social media platforms made people believe the news.

The researchers surveyed 1,455 participants with an average age of 27, and 42% were male. The participants were exposed to 24 false news stories, and one group was exposed to multiple versions of fake news, while the other group was only exposed to each news story once.

The findings suggested that the more familiar the news was, the more accurate and believable it was. This familiarity effect lasted for up to a month. Hence, the research method used in this study was a field survey.

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Answer:

\(area = \frac{45}{360} \times \pi {(15)}^{2} \\ = 88.35729338221 \\ = 88.6 \: (3sf)\)