(3^-2 × 4^-2)^-3 = 12^x
In the given expression find the value of x.​

The total of five terms of the series we need to add in order to find the sum to the indicated accuracy.

A series called convergent  if the sequence of it's own partial sums tends to the a limit; that is, when addition one after the other with in order specified by the indices, partial sums become increasingly closer to a certain number.

Step1: The given series is a alternating series;

\(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{6}}\)

where \(a_{n}=\frac{1}{n^{6}}\) is decreasing monotonically with n>1.

Thus, the given alternating series is convergent series.

As a result, we determine the smallest n such that; \(a_{n}\) < 0.00005.

Thus, it is concluded that the total of the series' first n-1 terms approximates the sum within in the allowed error.

Step 2: We must discover the smallest n such that,

\(\begin{aligned}\frac{1}{n^{6}} & < 0.00005 \\\frac{1}{n^{6}} & < \frac{5}{100000}\end{aligned}\)

Taking reciprocal both side,

Because both side is positive, the inequality is reversed.

\(\begin{aligned}n^{6} & > \frac{100000}{5} \\n^{6} & > 20000\end{aligned}\)

Use hit and trial to get the result.

         \(\begin{gathered}a_{2}=2^{6}=64 \\a_{3}=3^{6}=729 \\a_{4}=4^{6}=4096\end{gathered}\)

\(\begin{gathered}a_{5}=5^{6}=15625 \\a_{6}=6^{6}=46656 \quad( > 20000)\end{gathered}\)

The smallest integer that fulfils this inequality gets satisfied is n=6.

As a result, n=6 is the lowest amount with an inaccuracy of less than 0.00005.

Therefore, to calculate the sum inside that allowed error, we simply have to add the very first five terms in the series.

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The complete question is-

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? \(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{6}}\)

Answer: If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal

Step-by-step explanation:

Answer:John

Step-by-step explanation: John got 3 shirts each for 25.25

Jayda got 4 shirts each for 27

Step-by-step explanation:

please see my work as attached

Answer:

comparing the means of three or more groups

Step-by-step explanation:

Answer:

5⁻² = 1 / 5² = 1/25 and 2³ = 2 * 2 * 2 = 8 so the answer is 1/25 / 8 = 1/200.

\(10 \sqrt{1 } \sqrt{2} \)

Answer:43.5

Step-by-step explanation:You have to Add to get your answer.I'll show you how I got 43.5:

1.8+32=33.8

33.8+5=38.8

38.8=4.7=43.5

Your answer is: 43.5

hope this was helpful:)

Therefore, there are 4 vertices in this graph.

Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.

We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.

If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:

3v + 2 * 4 = 20

3v = 12

v = 4

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To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

the answer is 2.66

Step-by-step explanation:

use the calculater

9514 1404 393

Answer:

  110°

Step-by-step explanation:

The sum of angles in a triangle is 180°. The measure of the third angle is ...

  180° -20° -50° = 110° . . . third angle

Answer:

The measurement of third angles of triangle is 110°.

Step-by-step explanation:

Given :-

Two angles in a triangle have measurements of 20° and 50 °.

To Find :-

Measurement of third angles of triangle

Solution :-

We know that the sum of all angles of triangle is 180°.

20° + 50° + x = 180°

combine like terms

70° + x = 180°

subtract both side from 70°.

70° - 70° + x = 180° - 70°

x = 110 °

Hence, measurement of third angie of triangle is 110°.

The volume of a cube is increased by 27 times its actual volume if the surface area of the new cube is triple that of the original cube.

cube is a 3-dimensional surface having all sides equal.

hence, the volume of a cube=v =\((x)^3\)

where x represent the side of a cube

know if we triple the length of a cube I,e x=3x

        v\(=(3x)^3\\\\=3x*3x*3x\\\\=27x^3\)

hence, if a cube is increased to form a new cube such that the surface area of the new cube is triple that of the original cube.  its volume is increased by a factor of 27.

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When two biased dice are rolled, the probability of obtaining a sum of 6 is 5/18 or approximately 0.2778. There are five possible ways to roll a sum of 6.

When two dice are thrown and each of them is biased, a four is obtained four times as often as any of the other numbers. In this problem, we have to find out the probability of getting a sum of 6 when the dice are rolled. The probability of rolling a sum of 6 is obtained by summing the probabilities of all the ways of rolling a sum of 6.

There are five ways to roll a sum of 6, and we have to compute the probability of each one. The first way is to roll a 2 on one die and a 4 on the other die. The probability of rolling a 2 on one die is 1/6, and the probability of rolling a 4 on the other die is 4/6.

So the probability of getting a sum of 6 is 1/6 × 4/6 = 4/36 = 1/9. The second way is to roll a 4 on one die and a 2 on the other die. The probability of rolling a 4 on one die is 4/6, and the probability of rolling a 2 on the other die is 1/6.

So the probability of getting a sum of 6 is 4/6 × 1/6 = 4/36 = 1/9. The third way is to roll a 3 on one die and a 3 on the other die. The probability of rolling a 3 on one die is 1/6, and the probability of rolling a 3 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fourth way is to roll a 5 on one die and a 1 on the other die. The probability of rolling a 5 on one die is 1/6, and the probability of rolling a 1 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fifth way is to roll a 1 on-one die and a 5 on the other die. The probability of rolling a 1 on one die is 1/6, and the probability of rolling a 5 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. Therefore, the total probability of rolling a sum of 6 is 1/9 + 1/9 + 1/36 + 1/36 + 1/36 = 5/18, which is approximately 0.2778.

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Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.

It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.

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Answer:

I believe the answer would be 4 :) hope this helps

the answer is definitely 4

Answer:

volume of cube=441cm³

l³=441cm³

l=

\( \sqrt[3]{441} \)

length=7.6cm

Answer:

1) Solution (2,-3)

2) Solution (-1, \(-\frac{3}{2}\))

3) Solution (\(\mathbf{-\frac{1}{2},-\frac{5}{2}}\))

Step-by-step explanation:

We need to solve equations using elimination

1) \(2x+2y=-2\\3x-2y=12\)

Let:

\(2x+2y=-2--eq(1)\\3x-2y=12--eq(2)\)

Adding both equations:

\(2x+2y=-2\\3x-2y=12\\--------\\5x=10\\x=\frac{10}{5}\\x=2\)

We get value of x = 2

Now, put value of x into equation 1 to find value of y

\(2x+2y=-2\\Put\:x=2\\2(2)+2y=-2\\4+2y=-2\\2y=-2-4\\2y=-6\\y=-6/2\\y=-3\)

So, we get y = -3

Solution (2,-3)

2) \(4x-2y=-1\\-4x+4y=-2\)

Let:

\(4x-2y=-1--eq(1)\\-4x+4y=-2--eq(2)\)

Adding both equations

\(4x-2y=-1\\-4x+4y=-2\\------\\2y=-3\\y=\frac{-3}{2}\)

We get: y= -3/2

Now find value of x by putting value of y in eq(1)

\(4x-2y=-1\\Put\:y=\frac{-3}{2}\\4x-2( \frac{-3}{2})=-1\\4x+3=-1\\4x=-1-3\\4x=-4\\x=\frac{-4}{4}\\x=-1\)

We get x = -1

Solution (-1, \(-\frac{3}{2}\))

3) \(x-y=2\\x+y=-3\)

let:

\(x-y=2--eq(1)\\x+y=-3--eq(2)\)

Add both equations:

\(x-y=2\\x+y=-3\\-----\\2x=-1\\x=-\frac{1}{2}\)

We get x = -1/2

Now, put value of x in equation 2

\(x+y=-3\\-\frac{1}{2}+y=-3\\y=-3+ \frac{1}{2}\\y=\frac{-6+1}{2}\\y=\frac{-5}{2}\)

We get y = -5/2

Solution (\(\mathbf{-\frac{1}{2},-\frac{5}{2}}\))

The statement "The equation ax=0 gives an explicit description of its solution set" is true.

When the equation ax=0 is given, the solution set is explicitly described as x = 0.

In other words, the only solution to the equation is x being equal to zero. This can be verified by dividing both sides of the equation by a (assuming a is non-zero), which yields x = 0/a = 0.

Therefore, the solution set is explicitly described as x = 0.

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The given statement is false because In programming, the break and continue statements serve different purposes and can be used independently or together within nested loops.

The break statement is used to exit the current loop prematurely. When encountered, it terminates the loop and continues with the next statement after the loop. This can be useful when a specific condition is met, and you want to stop the execution of the loop immediately.

The continue statement, on the other hand, is used to skip the current iteration of a loop and move on to the next iteration. It allows you to skip certain iterations based on a specific condition without terminating the entire loop.

Both break and continue statements can be used within nested loops. In such cases, the break statement will exit only the innermost loop it is placed in, while the continue statement will skip to the next iteration of the innermost loop.

By using break and continue strategically within nested loops, you can control the flow of execution based on specific conditions. This flexibility allows you to fine-tune the behavior of your program and optimize its efficiency.

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Note : This is a computer science question

Answer:

True

Step-by-step explanation:

True. A z-score, also known as a standard score, is a statistical measure that helps to determine how far a particular value is from the mean relative to the data set's standard deviation.

A z-score is a dimensionless quantity that expresses the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean. A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean.

To calculate the z-score for a given value, the formula is: z = (x - μ) / σ where z is the z-score, x is the value being considered, μ is the mean of the data set, and σ is the standard deviation of the data set.

For example, if the mean of a data set is 50 and the standard deviation is 10, and we are interested in finding the z-score for a value of 65, the calculation would be: z = (65 - 50) / 10 = 1.5. This indicates that the value of 65 is 1.5 standard deviations above the mean of the data set.

Z-scores are useful for comparing values across different data sets or for identifying extreme values in a data set. Values with high positive or negative z-scores are typically considered to be outliers, indicating that they are further from the mean than most other values in the data set.

In summary, the statement "z-score helps to determine how far a particular value is from the mean relative to the data set's standard deviation" is true. Z-scores are a statistical measure that help to express the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean.

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Answer: B, 37 cm

Step-by-step explanation: To find the perimeter of a shape, you have to add all sides. So, 3.5 + 3.5 = 7. 13 + 7 = 20. 20 + 4 =24. And, 24 + 13 = 37. So, that eliminates C & D. So, now we need to focus on the measurement. So, since that is in cm, we now know It's B.

Answer:

Step-by-step explanation:

(5,2)

Explanation

Step 1

if you have 2 points P1 and P2 , the midpoint is given by:

where

Let

T=(9,8)

Midpoint(7,5)

U=unknown

Step 2

replace

Step 3

solve for x and y

and

I hope this helps you

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer:

5

Step-by-step explanation:

The easiest way to do this is to add the new members to the old and then divide by 11. Ignore the remainder.

13 + 52 = 65

65 / 11 = 5 with 10 left over. Ignore the 10. That's not a complete team.

The answer is 5

Answer:

x = 3

Step-by-step explanation:

• the diagonals of an isosceles trapezoid are congruent , then

11x - 6 = 3x + 18 ( subtract 3x from both sides )

8x - 6 = 18 ( add 6 to both sides )

8x = 24 ( divide both sides by 8 )

x = 3

Answer:

Step-by-step explanation:

where is the swan?