You deposit $200 in an account that earns simple interest at an annual rate of
6.5%. How much money is in the account after 3 years?

show work pleaseeee

To rank the steps involved in transforming one couple to another couple in a parallel plane, here is the correct order:

Identify the initial couple and the desired final couple.

Determine the translation vector that will move the initial couple to the desired final couple.

Translate the initial couple using the determined translation vector. This will shift the entire couple in the parallel plane.

Verify that the translation has successfully moved the initial couple to the desired final couple.

If necessary, make any additional adjustments or transformations to align the initial and final couples precisely in the parallel plane.

Confirm that the final couple is now in the desired position and orientation relative to the initial couple, maintaining the parallelism of the plane.

By following these steps in order, you can effectively transform one couple to another in a parallel plane.

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Answer:

Step-by-step explanation:

Set this up as a proportion and solve. The ratios are books:day, so keep in mind that a week is 7 days because your values have to be the same

\(\frac{books}{day}:\frac{68.24}{1}=\frac{x}{7}\) and cross multiply to solve for x, the number of books lent out in a week:

x = 68.24(7) so

x = 477.68 books in a week

Answer:

\(equation \ of \ exponential \ function , y = a (b)^x\\(-1, 20) \\=> 20 = a(b)^{-1}\\=>20 = \frac{a}{b} ---(1)\\\\(1, 5)\\=>5 = a(b)^{1}\\=>5=ab ---(2)\\\\from (1) a = 20b\\substitute \ a \ in \ (2)\\\\\\5 = (20b)b\\5= 20b^2\\\frac{1}{4} = b^2\\\\b = \frac{1}{2}\\substitute \ b \ in \ (2)\\5 = ab\\5 = a (\frac{1}{2})\\\\a = 10\\Therefore , the \ equation : y = 10(\frac{1}{2})^{x}\)

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Answer:

210cm

Step-by-step explanation:

Just do Radius times two, then multiply that answer and 15

Answer: 13.8

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

Answer: Factoring x^2-2x-2=0 x2 − 2x − 2 = 0 x 2 - 2 x - 2 = 0 Use the quadratic formula to find the solutions. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 1 a = 1, b = −2 b = - 2, and c = −2 c = - 2 into the quadratic formula and solve for x x.

Step-by-step explanation:

The project consists of four activities: A, B, C, and D. The normal completion times for these activities are 5, 8, 1, and 5 weeks, respectively.

The project activities are labeled as A, B, C, and D, with their respective normal completion times of 5, 8, 1, and 5 weeks. Activity B has the potential to be crashed, meaning its completion time can be reduced from 8 weeks to 3 weeks. The crash time for activity B is 2 weeks.

Crashing an activity involves allocating additional resources, such as manpower or equipment, to expedite its completion. However, this acceleration comes at an additional cost. In this case, crashing activity B by 2 weeks incurs a cost of $2,000. The crash time for activity B is determined by subtracting the crash time from the normal completion time, resulting in a new completion time of 3 weeks.

Overall, the project has a critical path, which is the longest path of activities that determines the minimum time required for the project's completion. In this scenario, the critical path includes activities A, B, and D, with a total duration of 13 weeks (5 weeks for A, 3 weeks for B, and 5 weeks for D). By crashing activity B, the project's overall duration can be reduced by 5 weeks, resulting in a more expedited completion time.

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The number of calories burned y after x minutes of kayaking is

You should know when we eat and drink more calories than we use up, our bodies store the excess as body fat. If this continues, over time we may put on weight

For kayaking Linear function is y=4.5x

In 45 minute means  x=45

so, y=4.5x

45*45

= 20.25

That means in kayaking will  burnt 20.25 calories in 45

minutes

Therefore, hiking burns more calories.

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The explicit rule for the sequence is f(n) = 6 - 4(n - 1)

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

a1 = 6

a(n) = a(n - 1) - 4

In the above sequence, we can see that -4 is added to the previous term to get the new term

This means that

First term, a = 6

Common difference, d = -4

The nth term is then represented as

f(n) = a + (n - 1) * d

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

f(n) = 6 - 4(n - 1)

Hence, the explicit rule isf(n) = 6 - 4(n - 1)

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Answer:

A.

Step-by-step explanation:

There are 3 ft in a yd. That means if we have 1 ft left over, then we have 1/3 yd left over. Add that to our 1 yd and we get 1 1/3 yds

Answer:

can you change this picture?

By using the concept of depreciation, it can be concluded that-

The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.

What is growth?

Growth is the exponential increase in the value of an asset or article or population at a certain rate over a certain period of time

EPA calculated that the air pollution should decrease by approximately 8% each year

The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.

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Complete Question

One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8% each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?

Given:

QRST is an isosceles trapezoid with RS||QT.

To find:

The value of x, angle R and angle T.

Solution:

If a transversal line intersect two parallel lines then the sum of same sides interior angles is 180 degrees.

\(m\angle Q+m\angle R=180\)

\((6x-22)+(8x+34)=180\)

\(14x+12=180\)

\(14x=180-12\)

\(14x=168\)

Divide both sides by 14.

\(x=\dfrac{168}{14}\)

\(x=12\)

Now,

\(m\angle R=(8x+34)^\circ\)

\(m\angle R=(8(12)+34)^\circ\)

\(m\angle R=(96+34)^\circ\)

\(m\angle R=130^\circ\)

We know that the base angles of an isosceles triangle are equal.

\(m\angle T=m\angle Q=(6x-22)^\circ\)

\(m\angle T=(6(12)-22)^\circ\)

\(m\angle T=(72-22)^\circ\)

\(m\angle T=50^\circ\)

Therefore, \(x=12,\ m\angle R=130^\circ\) and \(m\angle T=50^\circ\).

Answer:

31.5 (rounded)

Step-by-step explanation:

Answer:

5 ∛249

≈ 31.45597 (In decimal form)

Step-by-step explanation:

Answer:

2.5x+50

Step-by-step explanation:

The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

To solve the given initial-value problem, we start by rearranging the equation:
3 11 16 × -(: * *:)* X' = 1 1 3
-(: * *:)* X' = (1/16)  (1/11)  (1/3)
Integrating both sides with respect to t:
-(: * *:)* X = (1/16) t + C1, where C1 is the constant of integration.
Multiplying both sides by the inverse of the matrix -(: * *:) gives:
X = (-1/8) t + C1/8 + C2, where C2 is another constant of integration.
To find the values of C1 and C2, we use the initial condition X(0) = (0) - (5):
X(0) = (-1/8) (0) + C1/8 + C2 = -5
C1/8 + C2 = -5
Since X'(t) = (-3/8), we have X'(0) = (-3/8). Using the equation X'(t) = (-3/8) and the initial condition X(0) = (0) - (5), we can solve for C1:
X'(t) = (-1/8) => (-3/8) = (-1/8) + C1/8 => C1 = -2
Substituting C1 = -2 into C1/8 + C2 = -5 gives:
(-2)/8 + C2 = -5 => C2 = -39/8
Therefore, the solution to the initial-value problem is:
X = (-1/8) t - 1/4 - (39/8)

The solution to the given initial-value problem is X = (-1/8) t - 1/4 - (39/8). The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

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The fifth root of unity is given by  Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

As given in the question,

Using the Euler Identity ,

e^(πi) = -1

Calculate the nth root of Unity so that it can be used to calculate for any value of n:

Zⁿ = 1

⇒Z = (1)^(1/n)

Apply Euler's Formula we get,

Z = cos (2kπ + 0)/n + i sin(2kπ + 0 )/n

⇒Z = cos ( 2kπ / n) + isin( 2kπ / n)

Using Euler' identity  we can write this as :

Z = e^(2kπ/n)

For k = 0 , 1 , 2 , 3..... (n-1)

Now substitute n = 5 to get the value of 5th root of unity we have

Z = e^(2kπ/5)

When k = 0 , 1, 2, 3, 4

k = 0 ⇒ Z = 1

k= 1 ⇒ Z = e^(2πi/5)

k = 2 ⇒ Z = e^(4πi/5)

k= 3 ⇒ Z = e^(-2πi/5)

k = 4 ⇒ Z = e^(-4πi/5)

Therefore, the value of 5th root of unity is equal to Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

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A fully grown adult shark weighs 1.9375 pounds.

Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.

Given that, Scientists have discovered a new glow in the dark shark species that weighs up to 31 ounces when fully grown.

We know that 1 pound =16 ounce

Now, 31 ounces = 31/16 pounds

= 1.9375 pounds

Therefore, a fully grown adult shark weighs 1.9375 pounds.

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Answer:

The height is 7 inches

Step-by-step explanation:

Given

\(Base\ Area = 15in^2\)

\(Volume = 105in^3\)

Required

Determine the height [missing from the question]

The volume of a hexagonal prism is:

\(Volume = Base\ Area * Height\)

Make Height the subject

\(Height = \frac{Volume}{Base\ Area}\)

\(Height = \frac{105in^3}{15in^2}\)

\(Height = \frac{105in}{15}\)

\(Height = 7in\)

Step-by-step explanation:

angles on a straight line = 180

e + 8 + 3e - 4 = 180

4e + 4 = 180

4e = 176

e = 44

Answer:

e=44°

Step-by-step explanation:

(e+8°)+(3e-4)°=180°

e=44°

The 7 inches pen would not fit in the box with dimensions 3 in × 4 in × 5 in

The 7 inches long pen would not fit in a box with dimensions of 3 inches x 4 inches x 5 inches because the dimensions of the box are not long enough to accommodate the length of the pen.

Specifically, the length dimension of the box (3 inches) is less than the length of the pen (7 inches), so the pen would not be able to fit inside the box.

Additionally, even if the length of the box was greater than 7 inches, the width and height dimensions of the box (4 inches and 5 inches, respectively) would likely be too small to accommodate the diameter of the pen.

In conclusion, the pen is too long for the box, and the box is not wide or tall enough to fit the pen.

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To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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If area of "square-field" is 40000 ft square, and Mr. Blackburn is putting a fence diagonally in field, then the length of fence be is 282.84 ft.

The area of the square-field is = 40000 ft²,

We equate this with area formula,

We get,

⇒ (side)² = 40000,

⇒ side = 200,

substituting the side-length as 200 ft, in the diagonal formula,

we get,

⇒ Length of diagonal of field is = (side)√2,

⇒ Length of diagonal of field is = (200)√2,

⇒ Length of diagonal of field is ≈ 282.84 ft.

Therefore, the length of the fence of the field is 282.84 ft.

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Mean age is approximately 15.27 years

Median age is 13 years

Mode age is 14 years

To find the mean, median, and mode of the ages in Mr. Bayham's classroom, let's calculate each of them:

1. Mean:

To find the mean (average), add up all the ages and divide the sum by the total number of ages.

Sum of ages: 14 + 13 + 14 + 15 + 11 + 14 + 14 + 13 + 14 + 11 + 13 + 12 + 12 + 12 + 36 = 218

Total number of ages: 15

Mean = Sum of ages / Total number of ages

= 218 / 15

= 14.5

Therefore, the mean age is approximately 14.5 years.

2. Median:

To find the median, we arrange the ages in ascending order and find the middle value.

Arranging the ages in ascending order: 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 36

Since there are 15 ages, the median will be the 8th value, which is 13.

Therefore, the median age is 13 years.

3. Mode:

The mode is the value that appears most frequently in the data set.

In this case, the mode is 14 since it appears the most number of times (4 times).

Therefore, the mode age is 14 years.

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Given question is incomplete, the complete question is below

The ages of people currently in mr. Bayham classroom are 14,13,14, 15,11,14,14,13,14,11,13,12,12,12,36 find the mean median and mode

Answer:

1. 3) measure of angle 3 and measure of angle 5 are supplementary

2. x=16