find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (assume that n begins with 1.) − 1 64 , 2 81 , − 3 100 , 4 121 ,

Answer:

see image

Step-by-step explanation:

Hope this is clear enough, if not feel free to ask me any questions.

Mixture is kept undisturbed for some time. After some time, sand being heavier and insoluble in water, settles down at the bottom of container.

Sand and water are separated in this situation using filtering. The filter funnel, which is lined with filter paper, is filled with the sand and water mixture.

The paper allows the water to escape and accumulate in the beaker. Sand particles build up in the filter funnel because they can't pass through the filter paper. One of humankind's first methods of water treatment, distillation desalination is still a widely used treatment method today.

Many ancient civilizations employed this method to turn seawater into drinkable water aboard their ships. The differing densities of salt and sand are the basis for another physical separation technique. Sand has a density of 2.65 g/cm3, but salt has a density of 2.16 g/cm3. 

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(a) \([17] + [21] \cdot [98] - [5] = [12]\) in \(\mathbb{Z}_{13}\).

(b) If we are working in the ring \(\mathbb{Z}_{157}\), the value of \(n\) is 157.

(a) To explicitly check the expression \([17] + [21] \cdot [98] - [5]\) in \(\mathbb{Z}_{13}\), we need to perform the operations using modular arithmetic.

First, let's compute \([21] \cdot [98]\):

\[ [21] \cdot [98] = [21 \cdot 98] \mod 13 = [2058] \mod 13 = [0] \mod 13 = [0]\]

Next, we can substitute the results into the original expression:

\[ [17] + [0] - [5] = [17] - [5] = [12]\]

(b) We are given the expression \([5] \cdot [7] \cdot [8] \cdot [9]\) in \(\mathbb{Z}_n\) and we need to find the value of \(n\) if the expression makes sense.

To find the value of \(n\), we can evaluate the expression:

\[ [5] \cdot [7] \cdot [8] \cdot [9] = [5 \cdot 7 \cdot 8 \cdot 9] \mod n\]

We are given that the result is equal to 157:

\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]

To find \(n\), we can solve the congruence equation:

\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]

Since 157 is a prime number, there are no factors other than 1 and itself. Therefore, we can conclude that the value of \(n\) is 157.

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The number 16.8 in the equation means the points with which his score will increase in every game.

The stated equation has the constant 16.8 associated with the number of years. The number indicates that the person earns 16.8 additional points after each game. This number adds on to the total score. In other words, it indicates the points by which his score increase per game. Considering the equation, it p = 16.8t + 80.5. Here, p refers to y-axis, 16.8 is the slope and t is the x-axis. The 80.5 is the y-intercept and indicates the starting average per game.

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The meaning of the graph is that the value of x is no less than -1

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

x ≥ − 1

The above expression is an inequality that implies that

The value of x is no less than -1

Next, we plot the graph

See attachment for the graph of the inequality

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Question

What does the graph of x ≥ −1 mean?

42 kg = 92.59684 lbs.

Kilograms (kg) and pounds (lbs) are both units of measurement for weight, but they are not directly interchangeable. To convert a measurement of weight from kilograms to pounds, you will need to use a conversion factor.

1 kilogram is equal to 2.20462 pounds. 42 kilograms is equal to 92.59684 pounds. The conversion factor between kilograms and pounds is 1 kg = 2.20462 lbs.

To convert a measurement of weight from kilograms to pounds, you will multiply the number of kilograms by the conversion factor of 2.20462.

For example,

if you have a measurement of 42 kilograms, you would multiply 42 x 2.20462 to get 92.59684 pounds.

It's important to note that when measuring weight, it's important to use the same system of measurement as the requirement, as using the wrong measurements can greatly affect the outcome of the calculation. It's always good to know the conversion factors to make your calculations easier.

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Answer:

The bottom left one

Step-by-step explanation:

They are the only graph that has one output for each x value

For the function that is locate any absolute extreme points over the given interval  h (x) - x 3 - 5x2 - 6x, 10 a we get absolute maximum for x and y  (-0.380, 0.488) (10, 350) and  absolute minimum for x and y (-2, -22) and (4.38, -52.924)

Both critical point lies in domain -2 \(\leq\) n \(\leq\) 10. We know that h (n) is not define at both side of interval end point so n = -2 and n = 10 are critical point,

The critical point are point where f(n) is defined and its derivative is zero or undefined.

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

6

Step-by-step explanation:

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer:

\(\frac{1}{9}\)

Step-by-step explanation:

each term is \(\frac{1}{3}\) of the previous term, that is

\(\frac{3}{9}\) = \(\frac{1}{3}\) = \(\frac{\frac{1}{3} }{1}\) = \(\frac{1}{3}\)

the next term in the sequence is then

\(\frac{1}{3}\) × \(\frac{1}{3}\) = \(\frac{1}{9}\)

The area of the sector is 16π square inches.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360) x \(\pi r^2\)

where r is the radius of the circle.

In this case, the radius is given as 8 inches.

We are also given that the central angle measures from 60 to 150 degrees. To calculate the area of the sector, we need to find the size of the central angle first.

To do this, we subtract the smaller angle from the larger angle:

150 - 60 = 90 degrees

So, the central angle is 90 degrees.

Now, we can substitute the values into the formula:

Area of sector = (90/360) x \(\pi 8^2\)

Area of sector = (1/4) x π(64)

Area of sector = 16π square inches

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Answer:

16/7sin(2x)

Step-by-step explanation:

-8×1/cos(x)×⅐×1/sin(x)

-8/7cos(x)sin(x)

-8/⁷/²×sin(2x)

-8/7sin(2x)/2

16/7sin(2x)

Answer:

- \(\frac{8}{7}\) tanx

Step-by-step explanation:

Using the identities

secx = \(\frac{1}{cosx}\) , cscx = \(\frac{1}{sinx}\) , tanx = \(\frac{sinx}{cosx}\)

Given

\(\frac{8secx}{-7cscx}\)

= \(\frac{\frac{8}{cosx} }{\frac{-7}{sinx} }\) ← multiply numerator/ denominator by sinx

= \(\frac{8\frac{sinx}{cosx} }{-7}\)

= - \(\frac{8}{7}\) tanx

Answer:

7 hours

Step-by-step explanation:

20.00 + 10x = 90

10x = 70

x = 7

Answer:

20 + 10x = 90  (where x is the number of hours spent raking leaves)

7 hours

Step-by-step explanation:

let x = number of hours spent raking leaves

Given:

20 + 10x = 90

To solve:  20 + 10x = 90

Subtract 20 from both sides:

⇒ 10x = 70

Divide both sides by 10:

⇒ x = 7

Therefore he spent 7 hours raking the leaves.

Answer:

3/11

Step-by-step explanation:

You add up all of the candies so 20+19+28 which is 66

18 is the number of strawberry candies so it becomes 18 over 66, 18/66

Symplify 18/66 and it becomes 3/11

Answer:

3) x = −11

4) x = 40/11 or 3.636363... (it keeps going)

5)

Step-by-step explanation:

3) 5x/6 − ( 2x − 1/2 ) + 4 − 2x/3 = 11

Step 1: Simplify both sides of the equation.

5x/6 − ( 2x−1/2 ) + 4 − 2x/3 = 11

5x/6 + − x + 1/2 + − 2/3x + 4/3 = 11  ( Distribute )

5/6x + − x + 1/2 + − 2/3x + 4/3 = 11

( 5/6x + − x + − 2/3x ) + ( 1/2 + 4/3 ) = 11  ( Combine Like Terms )

−5/6x + 11/6 = 11

Step 2: Subtract 11/6 from both sides.

−5/6x + 11/6 − 11/6 = 11 − 11/6

−5/6x = 55/6

Step 3: Multiply both sides by 6/(-5).

( 6/−5 ) * ( −5/6x ) = ( 6/−5 ) * ( 55/6 )

x = −11

4) 10 - 2x = 3/4x

x = 40/11

(going to also be long I so wont put my work here)

5) -3( x - 3 ) - 9x - 9 = 4( x + 2 ) - 12

x = 1/4

(again, is long so wont put work)

Answer:

solutions at -1 and 11

Step-by-step explanation:

(-b ± √b²-4ac) / 2a

in this problem, a = 1, b = -10, c = -11

(10±√100-4(-1)(-11)) / 2(1) =

(10 + √144) / 2 = 22/2 = 11

(10 - √144) / 2 = -2 / 2 = -1

Answer:

7

Step-by-step explanation:

2+5=7

Answer:7

Step-by-step explanation: 2+5=7

Answer:

3

Step-by-step explanation:2-5

What are you talking about the Song rolling down the river ?

or a poem by that name or maybe some thing else ?

The length of a side of the hexagon or square is - 16 units

The length of a side of the hexagon or square = x

The perimeter of the square = 4 × lengths of its side

                                               = 4x

The perimeter of the hexagon = 6 × lengths of its side

                                                   = 6x

According to the question,

                            4x + 32 = 6x

                       ⇒ 6x - 4x = 32

                       ⇒  2x = 32

                       ⇒  x = 16

So, the length of a side of the hexagon or square is - 16 units.

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Answer:

153

Step-by-step explanation:

x+27+63+117=360

x+207=360

x=153

Answer:3 $,9$,36$

Step-by-step explanation:

Since he bought a cup of plain coffee which costs 1$ and he is carrying 4$ with him he has saved 3$ he would have used to buy a latte.If he does it continously for 3 times a week his saving per day i.e 3$ ×3,a month which is 3$×3(for a week)×4week which makes a month which is 32$.So the answers are 3$,9$ and 36$

Answer: y = x + 8

Step-by-step explanation:

Step-by-step explanation:

100+14.75%

100+14=114

=114.75%

The first five terms of the Fourier series of the function f(z) = e on the interval [-T,T] are: a₀ = 2T, a₁ = (2iT/π), a₂ = 0, b₁ = (-2iT/π), b₂ = 0.



These coefficients represent the amplitudes of the sine and cosine functions at different frequencies in the Fourier series representation of the given function.



To find the Fourier series coefficients, we integrate the function f(z) = e multiplied by the corresponding exponential functions over the interval [-T,T]. Starting with a₀, which represents the average value of f(z), we find that a₀ = 2T since e is a constant function. Moving on to a₁, we evaluate the integral of e^(iπz/T) over the interval [-T,T], resulting in a₁ = (2iT/π). Next, a₂ and b₂ are found to be 0, as the integrals of e^(2iπz/T) and e^(-2iπz/T) over the interval [-T,T] are both equal to 0. Finally, we calculate b₁ by integrating e^(-iπz/T), yielding b₁ = (-2iT/π). These coefficients determine the amplitudes of the sine and cosine functions at different frequencies in the Fourier series representation of f(z) = e on the interval [-T,T].

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The equations smaller number is -2 and the larger number is 3.

The smaller number as "x" and the larger number as "y". Based on the given information the following equations:

Six times the smaller number minus the larger number is -15:

6x - y = -15

Thirteen more than twice the smaller number is three times the larger number:

2x + 13 = 3y

A system of two equations use various methods, such as substitution or elimination.

use the substitution method to solve the system:

From equation 2),

2x - 3y = -13

express 6x from equation 1) in terms of y:

6x = -15 + y

x = (-15 + y) / 6

Substituting this value of x into equation 2)

2((-15 + y) / 6) - 3y = -13

Simplifying and solving this equation

(-30 + 2y) - 18y = -78

-16y = -48

y = 3

Substituting the value of y back into equation 1),  find the value of x:

6x - 3 = -15

6x = -12

x = -2

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Answer:

43°

Step-by-step explanation:

the blue angle is congruent with the 80° because they are vertical angles

the red angle is 57° because 123° and 57° angles are supplementary angles

the green angle is 43° because the sum or angles in a triangle is 180°