1. a. Write out the first five terms of the sequence, determine whether the sequence converges, and if so find its limit. (5 pts) { (-1)"+11 n2 n=1 b. Use an-1/2, to show that the given sequence {2,} is strictly increasing or strictly decreasing. (5 pts) {ne *}n=1

Answer:

39%

Step-by-step explanation:

0.39 x 100%=39%

Answer:

(Look at comments)

Answer:

jnkj

Step-by-step explanation:

Using the concept of inclusion-exclusion, there are total of 5 students who play both cricket and football.

To find the number of students who play both cricket and football, we can use the inclusion-exclusion principle.

Let A be the set of students who play cricket, B be the set of students who play football, and C be the set of students who do not play either sport.

We know that

\(|A| = 13, |B| = 16\), and \(|C| = 6\).

We want to find \(|A\) ∩ \(B|\).

Using the inclusion-exclusion principle, we have:

\(|A\) ∪ \(B| = |A| + |B| - |A\) ∩ \(B|\)

This formula counts the number of students who play cricket or football or both. We can use this formula to find \(|A\) ∩ \(B|:\)

\(|A\) ∪ \(B| = |A| + |B| - |A\) ∩ \(B|\)

\(30 - |C| = 13 + 16 - |A\) ∩ \(B|\)

where,

30 = total number of students

\(|C|\) = students who don't play any sport

\(24 = 29 - |A\) ∩ \(B|\) (substituting \(|C| = 6\))

\(|A\) ∩ \(B| = 5\)

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Answer:

-459 is rational, and an integer

Answer:

see explanation

Step-by-step explanation:

In a rectangle

• All angles are right angles

• the diagonals are congruent

In Δ WXV the sum of the 3 angles = 180°

∠ WXZ = ∠ XWY = \(\frac{180-64}{2}\) = \(\frac{116}{2}\) = 58°

∠ YXZ = 90° - 58° = 32°

∠ WVZ = 180° - 64° = 116° ( adjacent angles are supplementary )

∠ XWZ = 90° ( by definition of rectangle )

∠ XZY = ∠ WXZ = 58° ( corresponding angles )

Answer:

30%

Step-by-step explanation:

Original price (100%) = $130

Discounted price = $91

Discount = 130-91 = $39

$130 = 100%

$1 = 100/130

$39 = 100/130 × 39 = 30 %

% discount = 30%

Answer:

\(y=\frac{3}{4}+2x\)

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Because for example you have a square and that square has little multiple squares which are one meter square

Answer:

A”(-3, -18) B” (0, -27) C” (-12, -30)

Step-by-step explanation:

Two transformations have been listed beneath the graph. Complete them in order to get the solution.

The first transformation is a translation. A translation involves moving the shape across the graph without altering its form. To receive the coordinates for this. Add the <-3, -8> given to coordinates A, B, and C. Which should result in the following: A (-1, -6) B (0, -9) C (-4, -10)

Now complete the second transformation, which is a dilation. Dilations happen when a shape is either made smaller or larger by a set number. To complete the second transformation: take the number given: “3” and multiply each number in the coordinate sets you got after the first transformation by this number.

Which should result in: A”(-3, -18) B” (0, -27) C” (-12, -30)

If Zach can walk \(7\frac{1}{2}\) blocks in 15 minutes, then Zach can walk 30 blocks in one hour at this rate.

We can start by figuring out how many blocks Zach can cover in a minute if he can cover \(7\frac{1}{2}\) in 15 minutes. We may accomplish this by dividing \(7\frac{1}{2}\) by 15:

7.5 blocks ÷ 15 minutes = 0.5 blocks per minute

So, Zach can walk 0.5 blocks in one minute. We must change the time units from minutes to hours in order to determine the number of blocks he can cover in an hour. The number of blocks per hour can be calculated by multiplying the 0.5 blocks per minute by the number of minutes in an hour:

0.5 blocks per minute × 60 minutes per hour = 30 blocks per hour.

Hence, Zach can cover 30 blocks in an hour by walking at this pace.

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The mass of the fifth man is 153 kg.

The mean mass of five men is 76 kg.

The masses of four of the men are 72 kg, 74 kg, and 81 kg.

To solve this problem, we need to apply the concept of the mean of a set of data.

The mean is the average of all the values in a set of data.

It is calculated by adding up all the values and dividing by the total number of values in the set.

To find the mass of the fifth man, we need to use the mean of the entire set and the masses of the four men that are already given.

The formula to find the mean of a set of data is:

\(Mean = \frac{(sum of all the values)}{(total number of values)}\)

Let x be the mass of the fifth man.

Then we can write an equation using the given information:

\(Mean = \frac{(72 + 74 + 81 + x)}{5}\)

Substitute the given mean of 76 kg into the equation and solve for x:

\(76 = \frac{(72 + 74 + 81 + x)}{576 × 5} = 227 + x\)

Multiply both sides by 5:

\(380 = 227 + x\)

Subtract 227 from both sides:

\(153 = x\)

Therefore, the mass of the fifth man is 153 kg.

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Answer:

-5.8

Step-by-step explanation:

Answer:

The answer will be 10

Step-by-step explanation:

\(2\frac{1}{2} = \frac{5}{2}\)

\(\frac{5}{2}\) ÷ \(\frac{1}{4} = \frac{5}{2} x \frac{1}{4}\) = \(\frac{20}{2}\)

\(\frac{20}{2} =\) 10 (in its simplest form)

The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

We have to given that,

To Divide 2 1/2 divided by 1/5 in simplest form.

We can simplify,

⇒ 2 1/2 ÷ 1/4

Change into improper fraction,

⇒ 5/4 ÷ 1/4

⇒ 5/4 × 4/1

⇒ 20/4

⇒ 5

Therefore, The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

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The isospin ⊗ spin wavefunctions for the four different spin states of a Δ0 particle, in terms of the wavefunctions of the quarks it is composed of, are:

|3/2, 3/2⟩ = |u↑d↑⟩

|3/2, 1/2⟩ = (√3/2)|u↓d↑⟩ + (√1/2)|u↑d↓⟩

|3/2, -1/2⟩ = (√1/2)|u↓d↑⟩ - (√3/2)|u↑d↓⟩

|3/2, -3/2⟩ = |u↓d↓⟩

The Δ baryons are composed of three quarks: two down (d) quarks and one up (u) quark. The isospin of a particle represents its behavior under rotations in the isospin space, which is related to the behavior of the particle under the strong force. The spin of a particle represents its intrinsic angular momentum.

For the Δ0 particle, which has isospin 3/2, there are four different spin states. Each spin state corresponds to a different combination of up and down quark spin projections along the z axis. The isospin ⊗ spin wavefunctions represent the composite wavefunctions of the quarks that make up the Δ0 particle for each spin state.

In the first spin state, |3/2, 3/2⟩, both the up and down quarks have their spins aligned in the upward direction. In the second spin state, |3/2, 1/2⟩, the up quark has its spin aligned upward while the down quark has its spin aligned downward. The third spin state, |3/2, -1/2⟩, has the up quark with its spin aligned downward and the down quark with its spin aligned upward. Finally, in the fourth spin state, |3/2, -3/2⟩, both the up and down quarks have their spins aligned in the downward direction.

These wavefunctions provide a mathematical description of the different spin states of the Δ0 particle, taking into account the wavefunctions of the constituent quarks. They help us understand the quantum mechanical properties and behavior of the Δ0 baryon in terms of its quark composition.

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The maximum number of  14 hours that the crane is Used.

Step: 1 According to the question    

         1500 + (250)h ≤ 5000

          1500 + 250h ≤ 5000

Step: 2

1500 + 250h - 1500 ≤ 5000 - 1500                      

250h ≤ 3500                      

Divide by 250 into both sides

250h/250h ≤ 3500/250                          

h ≤ 14

What is Divide?

Split, in its simplest form, is to divide into two or more equivalent portions, spaces, groups, or divisions. Split, in plain English, is to provide the entire item to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

Divide or division is denoted by the letters, slash (/), or a horizontal line. When dealing with a variety of problems and calculations, these symbols are useful. Also, "x by y" or "x over y" might be interpreted as "x/y" or "x y."

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Answer:

394.13 to 2 D.P.s

Step-by-step explanation:

Area = pi r^2

= 3.142 * 11.2^2

= 394.132.

The area of this circle up to 2 decimal places will be 394.13 square units.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius of the circle is 11.2 units and takes π to be 3.142. Then the area is given as,

A = π x (11.2)²

A = 3.142 x 125.44

A = 394.13 square units

The area of this circle up to 2 decimal places will be 394.13 square units.

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The number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula \(n^{p}\) = n × n × n × ... × n, where n is the base number and p is the exponent. For example,\(4^{2}\) = 16 and \(4^{3}\)= 64.

The number of times a number is multiplied by itself is known as the power or exponent. For example, let's say we have the number 4. If we want to calculate 4 to the power of 2 (\(4^{2}\)), we are essentially multiplying the number 4 by itself twice. This is written as 4 multiplied by 4, which is equal to 16. In mathematical notation, the calculation is written as \(4^{2}\)  = 16.To calculate the power of a number, we can use the exponent formula: \(n^{p}\) = n × n × n × ... × n

where n is the base number and p is the exponent. For example, if we want to calculate\(4^{3}\) (4 to the power of 3), we would write the formula as 4 × 4 × 4 = 64. The corresponding mathematical notation is \(4^{3}\) = 64.

In summary, the number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula \(n^{p}\) = n × n × n × ... × n, where n is the base number and p is the exponent. For example,\(4^{2}\) = 16 and \(4^{3}\)= 64.

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Answer:

OMH OKOK WAIT IMMA TRY TO FIND IT

The amount of fencing he needs for this project is 247 feet.

Data;

To find the length of the fence required, we need to find the perimeter of the figure and note that this is excluding the perimeter of the house.

The perimeter of the figure is

\(P = 2(14+6) + 17 = 57in\)

The perimeter of the figure is 57in.

But we were told that every 3 in represents 13 feet.

\(3in = 13ft\\57in = x\\x = \frac{57 * 13}{3} \\x = 247ft\)

The amount of fencing he needs for this project is 247 feet.

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The minimum angle that each leaf of the bridge should open is 47 degrees.

We can use the cosine function to solve this problem. The cosine function gives the ratio of the adjacent side to the hypotenuse of a right triangle. In this case, the adjacent side is the distance between the pivot point and the ship, which is 90 feet. The hypotenuse is the length of each leaf of the bridge, which is 130 feet.

The cosine function is defined as:

cos(theta) = adjacent / hypotenuse

cos(theta) = 90 / 130

theta = cos^-1(90 / 130)

theta = 46.2 degrees

The nearest degree to 46.2 degrees is 47 degrees.

Therefore, the minimum angle that each leaf of the bridge should open is 47 degrees.

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Answer:

mean = 5+9+9+6+6+11+8+4/7 = 8.29

median = 6

mode = 6

range = 11 - 4 = 7

Answer:

Step-by-step explanation:

5 , 9 , 6 , 6 , 11 , 8 , 4

Mean = sum of all data ÷ number of data

         \(= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7\)

Median: To find median, arrange in ascending order and medianis the middle term

4 , 5 , 6 , 6 , 8 , 9 , 11

Middle term = 4th term

Median = 6

Mode: a number that appears most often is mode

6 appears 2 times

Mode = 6

Range:

Range = maximum value - minimum value

          = 11 - 4

          = 7

the value of f(5) is 10, which is option (b) ,  the value of f(-2) is -12, which is option (d).  To find the value of f(5) using synthetic substitution, we first set up the synthetic division table as follows:

5 | 3  -9  -20

   |||___

   |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below the second coefficient (-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).

6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:

-2 | 1   0   8   24

  |_|||

  |    |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, -2) outside the division symbol. We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).

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Answer:

m = 3/2

Step-by-step explanation:

You want to find the slope, or the change in y coordinates over change in x-coordinates.

The first given point is E(-2, -4)

The second point is F(2, 2)

Coordinates are given in (x, y), so following the equation and computing the  x and y coordinates of E - F for both the numerator and denominator:

\(\frac{y_2 - y_1}{x_2-x_1} = \frac{-4 -2}{-2 -2} = \frac{-6}{-4} = \frac{3}{2}\)

You could also have went the other way and calculated F - E for the numerator and denominator and get the same answer.

Finally, to check you can also look at the graph through the rise over run (rise/run) method and see that from E, you go up 3 (rise) and to the right 2 (run) to get to the next point on the line.

The solutions to the original equation in the interval [0, 2π) are:

θ = 0, π/2, π, 3π/2, π/8, 3π/8.

We have,

Double-angle formula for sine: sin(2θ) = 2 sin(θ) cos(θ)

Double-angle formula for cosine: cos(2θ) = 2cos²(θ) - 1

Let's substitute these double-angle formulas into the equation:

−sin(2θ) − cos(4θ) = 0

−(2 sin(θ)cos(θ)) − (2cos²(2θ) - 1) = 0

2 sin(θ)cos(θ) + 2cos²(2θ) - 1 = 0

And,

cos(4θ) = 2 cos² (2θ) - 1

Now the equation becomes:

2 sin(θ) cos(θ) + cos(4θ) = 0

Now, factor out a common term:

cos(4θ) + 2 sin(θ) cos(θ) = 0

To solve for θ, each term to zero:

cos(4θ) = 0

2 sin(θ) cos(θ) = 0

Solving for θ:

cos(4θ) = 0

4θ = π/2, 3π/2 (adding 2π to get solutions in the interval [0, 2π))

θ = π/8, 3π/8

And,

2 sin(θ) cos(θ) = 0

This equation has two possibilities:

sin(θ) = 0

cos(θ) = 0

For sin(θ) = 0, the solutions are θ = 0, π (within the interval [0, 2π)).

For cos(θ) = 0, the solutions are θ = π/2, 3π/2 (within the interval [0, 2π)).

Thus,

The solutions to the original equation in the interval [0, 2π) are:

θ = 0, π/2, π, 3π/2, π/8, 3π/8.

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

Answer:

Option C

Step-by-step explanation:

we have

x+2y=2 ------> equation A

-4x+4y=-8 ------> equation B

Multiply equation B by -1 both sides

-1(-4x+4y)=-8*(-1)

4x-4y=8 -----> equation C

Adds equation A and equation C

x+2y=2

4x-4y=8

--------------

5x-2y=10 ----> equation D

An equivalent system of equations is equation A and equation D

so

x+2y=2 ------> equation A

5x-2y=10 ----> equation D

Answer:

C

Step-by-step explanation:

i took the test

The speed of the airplane in still air is 21.5 mph.

An airplane flying with the wind takes 2 hours with a 25-mph tailwind to reach its destination. the return trip takes 4 hours flying against the wind.

We must calculate the wind speed from the ground speed and airspeed as we cannot measure the wind speed directly from the aeroplane.

Flying at 35 mph requires four hours. Consequently, the distance is

25 * 2 = 50 miles.

For the same route, a return trip takes 5 hours.

Hence V-Vs= 50/4 = 12.5.

Therefore, V+Vs= 25 (1).

V-Vs = 12.5-----(2).

We obtain V=21.5 mph Vs=2.5 mph by solving for (1) and (2).

Thus, V = 21.5 mph is the airplane's windless speed.

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Answer:

No inverse function:  (a), (b), (c)

Inverse function exists:  (d)

Step-by-step explanation:

The graph of h(x) = (x - 2)^2 + 3 is a parabola that opens upward and has vertex at (2, 3).  If the entire graph is drawn, and the horizontal line test then applied, h(x) would not have an inverse, because the horizontal line would intersect the  parabolic graph twice.

Note that if we restricted the domain to x ≥ 2, the resulting graph would pass the horizontal line test.  This would also be true for x ≥ 3, x ≥ 4, and so on.  Not so for (a) x < 1.  False for x > -5.  True for x < 3.  True for x > 4.

No inverse function:  (a), (b), (c)

Inverse function exists:  (d)