Solve for x (x5 − 2 = 3.7)

Using the Ratio Test the series ∑(n³ / \(4^n\)) converges. Option A is the correct answer.

To determine the convergence or divergence of the series ∑(n³ / \(4^n\)), we can apply the Ratio Test.

The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.

Let's apply the Ratio Test to the given series:

lim n → ∞ |(\(a_n\) + 1) / \(a_n\)| = lim n → ∞ |((n + 1)³ / \(4^{(n + 1)\)) / (n³ / \(4^n\))|

We simplify the expression by multiplying by the reciprocal:

lim n → ∞ |((n + 1)³ / \(4^{(n + 1)\)) × (\(4^n\) / n³)|

Next, we simplify the expression inside the absolute value:

lim n → ∞ |((n + 1)³ × \(4^n\)) / (\(4^{(n + 1)\) × n³)|

Now, we can cancel out the common factors:

lim n → ∞ |(n + 1)³ / (4 × n³)|

Simplifying further:

lim n → ∞ |(n + 1) / (4n)|³

Taking the limit as n approaches infinity:

lim n → ∞ |(1 + 1/n) / 4|³

Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.

Therefore, the answer is:

A. Converges

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The question is -

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.

∑ n = 1 to ∞ (n³ / 4^n)

lim n → ∞ |(a_n + 1) / a_n| = _______

A. Converges

B. Diverges

The probability that any two children will both like lima beans is 0.0016 or 0.16%.

Assuming that every child's choice for lima beans is independent of the other, we will use the binomial distribution to calculate the probability that two kids out of a group of will both like lima beans.

Let p be the chance that a child likes lima beans, which we realize is 0.04 primarily based on the survey. The probability that anyone infant does no longer like lima beans is then 1 - p = 0.96.

The possibility that each children will like lima beans is given through the binomial chance mass feature:

P(X = 2) = (2 choose 2) * \(p^2 * (1 - p)^{(2-2)} = p^2 = (0.04)^{2 }= 0.0016\)

So the chance that any two children will both like lima beans is 0.0016, or 0.16%. that is a very low probability, this means that that it is not likely that any two children selected at random will both like lima beans.

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Main answer:Long multiplication is a method of multiplying two difficult-to-multiply numbers.

supporting answer:

what is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

body of the answer:

let us understand long multiplication by taking an example

     6.Add the two partial products

final answer: by following above steps we can perform long multiplication

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Long multiplication is a method of multiplying two difficult-to-multiply numbers.

What is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

Let us understand long multiplication by taking an example

1. Write the two numbers one beneath the other in the order of their digits. On top, write the larger number, and on the left, a multiplication sign.

2. Multiply the top number's one digit by the bottom number's one digit.

3. Put a 0 below the one's digit,

4. Multiply the top number's ones digit by the bottom number's tens digit.

5. Multiply the top number's tens digit by the bottom number's tens digit.

6. Add the two partial products

By following the above steps we can perform long multiplication

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A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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For the above set of similar triangles, the value of x is 23 units.

Similar triangles have the same proportionate side lengths and related angle measurements. Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion). Similar triangles will have the same form but may or may not have the same size. Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Here,

Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion).

x-10/39=12/36

x-10=13

x=23

The value of x for given set of similar triangles is 23 units.

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Answer:

x= 107.3-51

56.3

Step-by-step explanation:

Equation: First define your variables. We'll say x= the second number.

So we can make our equation x= 107.3-51

107.3-51 is 56.3.

So the solution is 56.3

Answer:

56.3 i the second angle

Step-by-step explanation:

107.3=x+51

subtract 51

56.3 is the second angle

Answer:

rational

Step-by-step explanation:

I'm smart uhujjjjjhbbjjhh

Answer: rational number

Step-by-step explanation: branilest please

Answer:

\(y=2x+3\)

Step-by-step explanation:

The slope-intercept form is \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept.

\(y=mx+b\)

Using the slope-intercept form, the slope is 2.

\(m=2\)

So in order for us to find an equation that is parallel, the slopes must be equal. We need to find the parallel line using the point-slope formula.

We use the slope 2 and a given point \((2,7)\) to substitute for x1 and y1 in the point-slope form \(y-y^1 = m (x-x^1)\), which is derived from the slope equation: \(m=\frac{y2-y1}{x2-x1}\)

Now we simplify the equation and keep it in point-slope form.

\(y-7=2\)  × \((x-2)\)

Simplify \(2\) × \((x-2)\)

\(y-7=2x-4\)

\(Rewrite.~y-7=0+0+2~x~(x-2)\)

\(Simplify~ by~adding~zeros.~y-7=2 ~x~(x-2)\)

\(Apply~the~distributive~property.~y-7=2x+2~X~-2\)

\(Multiply~2~by~-2.~y-7=2x-4\)

Last, We move all terms not containing y to the right side of the equation.

Add 7 to both sides of the equation.

\(y=2x-4+7\)

Add −4 and 7 and your answer will be: \(y=2x+3\)

Happy Pride Month!

Answer:

320m

Step-by-step explanation:

let the two runners be A and B

with Va and Vb as their velocities

velocity=distance/time

Va=720/4*60

=3m/s

Vb=720/5*60

=2.4m/s

Let the 2 runners start from a common position X and meet at Y

so the 2 consecutive meetings happen at X and Y

so we have to find time of meeting at Y as we know that of X (which is t=0)

720=Va*t+Vb*t

t(5.4)=720

t=133.33 or t=720/5.4

therefore distance travelled by B =Vb*t

=2.4*720/5.4

=319.99m

=320m

Answer:

If you know how to do the vertices, just plot them on the grid and after ploting the vertices then draw lines to connect them together and make the shape it says on the question. Hope this helps:)

Any more questions, ask me.

Answer:

a sense of cohesion

Step-by-step explanation:

Team cohesion is a concept of how a team stays committed and values the interest of its members. A group can remain in a stable state when cohesion is strong, but the lack of cohesion made it prone to fall apart. The research of group cohesion is an important subject for study o how people stay interested in making large institutions work efficiently. It is referred to as a group of individuals with the same values and skills. And such a group and members of their group are dependable on each other.

In other to command respect and the acceptance of other people's view during a group discussion, it is imperative than contributing members can prove their inputs or view with evidence.

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Answer:

t = (q - r) / rs

Step-by-step explanation:

Right now you have q=rst+r so if you want to find t you must move the variables around. Like this:

q=rst+r (or r+rst)

so so get rid of the r first

like this: (q-r)=rst

divide by rs to find t

so t=(q-r)/rs

Answer:

C

Step-by-step explanation:

trust

The average speed of Lee is 70 km/hr.

To clear up this trouble we want to understand the concept of average speed.

average speed is given while we divide the overall distance blanketed with the aid of the total time taken.

right here, it's miles given that Lee and Johnson each drove a hundred and forty Km. additionally, it's miles given that lee drove for two hours.

So, average speed of Lee = \(\frac{140}{2}\)

                                         = 70 km/hr

Here, the average speed at which Lee drove the car and went to business meeting is 70 km/hr.

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Answer:

The cost for the snow skis for 4.5 hours is $ 77.5.

Step-by-step explanation:

Since renting snow skis costs $ 15 per hour plus a $ 10 usage fee, to create a step function that models the cost of snow skis in terms of the number of hours the snow skis were rented and determine the cost for the snow skis if you were skiing for 4.5 hours the following calculation must be performed:

10 + (15X) = Cost per hour

10 + 15 x 4.5 = X

10 + 67.5 = X

77.5 = X

Therefore, the cost for the snow skis for 4.5 hours is $ 77.5.

Using Lagrange multipliers, the largest possible volume of a rectangular box can be found with a given diagonal length l.

Let's denote the dimensions of the rectangular box as length (L), width (W), and height (H). The volume (V) of the box is given by V = LWH. The constraint equation is the Pythagorean theorem: L² + W² + H² = l², where l is the given diagonal length.

To find the largest possible volume, we can set up the following optimization problem: maximize the volume function V = LWH subject to the constraint equation L² + W² + H² = l².

Using Lagrange multipliers, we introduce a new variable λ (lambda) and set up the Lagrangian function:

L = V + λ(L² + W² + H² - l²).

Next, we take partial derivatives of L with respect to L, W, H, and λ, and set them equal to zero to find critical points. Solving these equations simultaneously, we obtain the values of L, W, H, and λ.

By analyzing these critical points, we can determine whether they correspond to a maximum or minimum volume. The critical point that maximizes the volume will give us the largest possible volume of the rectangular box with a diagonal length l.

By utilizing Lagrange multipliers, we can optimize the volume function while satisfying the constraint equation, enabling us to determine the dimensions of the rectangular box that yield the maximum volume for a given diagonal length.

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With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

Answer:

It will be $40.00

Step-by-step explanation:

hope this helps

Answer: it is B

Step-by-step explanation: uhhh do 40 X .25 and uhh there you go yeah that’s right

The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.

The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:

lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009

So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.

So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.

Therefore, lim x→49 x^2 - 7x - 49 = 343.

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Answer:

- 2.2 × 10 to the 2nd

Step-by-step explanation:

if its scientific notation that should be correct

Answer:

what's your question

Step-by-step explanation:

ello

Answer:

23)  m∠T = 20°

24)  m∠ABC = 75°

Step-by-step explanation:

Circle Theorem vocabulary

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

From inspection of the given circle, the inscribed angle is ∠T and the intercepted arc is RS.  Therefore, applying the inscribed angle theorem:

\(\implies m \angle T=\dfrac{1}{2}\overset{\frown}{RS}\)

\(\implies m \angle T=\dfrac{1}{2} \cdot 40^{\circ}\)

\(\implies m \angle T=20^{\circ}\)

Therefore, the measure of ∠T is 20°.

Quadrilateral ABCD is a cyclic quadrilateral since every vertex of the quadrilateral touches the circumference of the circle.

The opposite angles in a cyclic quadrilateral sum to 180°.

Therefore:

\(\implies \angle A + \angle C = 180^{\circ}\)

\(\implies 10x^{\circ} + (4x+12)^{\circ} = 180^{\circ}\)

\(\implies 10x + 4x+12 = 180\)

\(\implies 14x+12 = 180\)

\(\implies 14x = 168\)

\(\implies x=12\)

To calculate the measure of angle ABC, substitute the found value of x into the expression for ∠ABC:

\(\implies \angle ABC=(6x+3)^{\circ}\)

\(\implies \angle ABC=(6(12)+3)^{\circ}\)

\(\implies \angle ABC=(72+3)^{\circ}\)

\(\implies \angle ABC=75^{\circ}\)

Therefore, the measure of ∠ABC is 75°.

(x-4)(x+9) is equivalent to x^2+5x-36

all you need to do is factor the equation

Answer:

Solution of the system will be (-3, 6).

Step-by-step explanation:

If a system of linear equations have been given in the question then we can find the solution of the linear equations by solving these equation algebraically.

But when a graph of the system of equation have been given solution of the system is the point of intersections Or common points lying on both the lines.

From the given graph,

Coordinates of the common point of both the lines is (-3, 6).

Therefore, solution of the system will be (-3, 6).

Answer:  (-3, 6)

Step-by-step explanation:

you can see where the lines met

Answer:

The 4th graph.

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

f(2)=4 means when x=2. F(x) or you may call it y, equals 4, so find the one that when x=2, y=4, then its your answer.