Are the series absolutely, conditionally convergent, or divergent?

Answers

Answer 1

Answer:

Step-by-step explanation:

∑ sin(nπ/4) / (n³ + 3n)

This is less than 1 / n⁴ for all n > 1. 1/n⁴ is a convergent p-series, so the lesser series also converges. │aₙ│converges for the same reason, so this is absolutely convergent.

∑ (-1)ⁿ⁺¹ ln(n + 1) / (n + 1)

This is an alternating series. bₙ is positive and decreasing, and lim(n→∞) bₙ = 0, so the series converges. Now we need to check if│aₙ│converges. Using comparison test, │aₙ│is greater than 1/n for all n ≥ 6. 1/n is a divergent p-series, so the greater series│aₙ│also diverges. So this is conditionally convergent.

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What is the value of x in the figure?

Answers

Answer:

x=65

Step-by-step explanation:

Both sides have to equal the same, which is 145. 145-15=130, 130/2=65. So basically you have to do inverse operation to solve this.

In January 2010, Diana invested $4,500 in an account that paid interest compounded annually. the table showstopper balance of the account at different times. what was Diana's balance, in dollars and cents, in January 2014. the numbers on the table are, For the month Jan. 2011-$4,635.00Jan. 2012-$4,774.05
Jan. 2013-$4,917.27

Answers

Final answer:

The question is related to compound interest. Diana's account balance in 2014 cannot be precisely calculated with the provided information, but based on the increasing balance trend, it would be larger than the 2013 balance of $4,917.27.

Explanation:

The subject of this question is compound interest, which is used in Mathematics. When Diana invested $4,500 in an account in 2010, the balance in the account increased each year due to the interest being compounded, or added to the principal amount. For example, by January 2011, the balance had grown to $4,635.00. The balance continued to grow each subsequent year.

To find Diana's balance in 2014, we would typically need to apply the formula for compound interest. However, in this case, the question only provides the balances for the years up to 2013. If a similar growth pattern continued, we could expect that the balance in 2014 would be larger than the $4,917.27 balance of 2013. Without a specific interest rate or an exact balance for 2014, we cannot precisely calculate the 2014 balance.

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Answer:

500,000

Step-by-step explanation:

80-1

What is the probability that the average of four babies' weights will be within .6 pounds of the mean; will be between 8.4 and 9.6 pounds

Answers

The probability will be "0.7497".

Given:

Mean,

Standard deviation,

Number of babies,

The standard error of sample will be:

→ $S.E. = (sd)/(√(n) )$

$= (0.6)/(√(4) )$

$= (0.6)/(2)$

$= 0.3$

hence,

→ P(4 babies will be between 8.4 - 9.6 pounds)

$P(8.4 \leq X \leq 9.6) = (((8.4-9))/(0.3) \leq X \leq ((9.6-9))/(0.3) )$

$= P(-2 \leq X \leq 2)$

$= P(Z \leq 2) - P(Z \leq -2)$

$= 0.9772-0.2275$

$= 0.7497$

Thus the above response is right.

Learn more:

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Complete question:

Some sources report that the weights of full-term newborn babies in a certain town have a mean of 9 pounds and a standard deviation of 0.6 pounds and are normally distributed.

Answer: 0.7497

Step-by-step explanation:

Mean = 9

sd = 0.6

n = 4

P(4 babies will be between 8.4 and 9.6 pounds)

P(8.4 ≤ X ≤ 9.6)

Standard error of the sample (S. E) :

S. E = sd/√n

= 0.6 /√4

= 0.6/2

= 0.3

P(8.4 ≤ X ≤ 9.6)= ((P(8.4 - 9) / 0.3) ≤ X ≤ (9.6 - 9)/0.3)

P(8.4 ≤ X ≤ 9.6) = P(-2 ≤ X ≤ 2)

P(Z ≤ 2) - P(Z < - 2)

0.9772 - 0.2275 = 0.7497

Solve for x x/8−9=1

x=

Answers

Answer:

x = 80

Step-by-step explanation:

9+1=10 so x/8 must equal 10.

80/8 = 10 and subract by 9 = 1

1. X/-1 (divid X to 1)
2. -1• X/-1 = 1• -1
( multiple -1 by both sides)
3. X= -1

I hope this helps

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna. If the wire makes an angle of 58deg 20min with the group find the length of the wire.