What is x in 81=x-3(-5+4x)?

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv

sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints. If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

4 0

3 years ago

Coin flips. if you flip a fair coin 10 times, what is the probability of (a) getting all tails? (b) getting all heads? (c) getti

Tju [1.3M]

C i hope this helps getting all heads there is about a 0.1 chance and a 0.1 chance of getting all tails

7 0

4 years ago

The National Assessment of Educational Progress (NAEP) gives a math assessment every year to 12th graders in the U.S. On the mat

amid [387]

Answer:

The correct answer is option 2.

Step-by-step explanation:

In this case we need to test whether young men nationwide have a mean score below 275 in the National Assessment of Educational Progress math assessment.

The hypothesis is defined as follows:

H₀: μ = 275 vs. Hₐ: μ < 275

The significance level of the test is α = 0.05.

The p-value of the test is computed as, p-value = 0.20.

Decision rule:

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard the null hypothesis.

A large p-value (> 0.05) specifies fragile proof against the null hypothesis, so you fail to discard the null hypothesis.

p-value = 0.20 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.

Thus, it can be concluded that there is not enough evidence to conclude that the mean score is less than 275 for young men nationwide.

Thus, the correct answer is option 2.

5 0

3 years ago

The relationship shown is linear. Write the equation of the line in slope intercept form (y=mx+b).

slega [8]

Answer:

y=mx+b Example:

Graph the equation

y−2x=1

rewrite in slope-intercept form

y=2x+1

Identify the slope and the y-intercept

m = 2 and b = 1

Plot the point corresponding to the y-intercept, (0,1)

picture23

The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2)

picture24

And once you have your second point you can just draw a line through the two points and extend it in both directions.

picture25

You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct.

Our second point = (1, 3)

y−2x=1

3−2⋅1=3−2=1

Our second point is a solution to the equation i.e. the line we drew is correct.

A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation.

y=mx

In a direct variation the nonzero number m is called the constant of variation.

You can name a function, f by using the function notion

f(x)=mx+b

f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions.

A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions.

The most basic function in a family of functions is called the parent function. The parent function of all linear functions is

f(x)=x

Step-by-step explanation:

5 0

3 years ago

Which numbers are the means of the proportion shown

Over [174]

$\bold{{Answer}}$

B.2.And30

What is the means of a proportion?

1 : harmonious relation of parts to each other or to the whole : balance, symmetry. 2a : proper or equal share each did her proportion of the work. b : quota, percentage. 3 : the relation of one part to another or to the whole with respect to magnitude, quantity, or degree : ratio.

A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

please correct me if im wrong

6 0

3 years ago

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