All categories

4 years ago

Find the pattern and use it to list the nth term in the sequence. 1, 1/32,1/243,1/1024,1/3125

1 answer:

5 0

$1;\ \frac{1}{32};\ \frac{1}{243};\ \frac{1}{1024};\ \frac{1}{3125}\\\\1=\frac{1}{1^5}\\\\\frac{1}{32}=\frac{1}{2^5}\\\\\frac{1}{243}=\frac{1}{3^5}\\\\\frac{1}{1024}=\frac{1}{4^5}\\\\\frac{1}{3125}=\frac{1}{5^5}\\\vdots\\\\a_n=\frac{1}{n^5}\ where\ n\in\mathbb{N^+}$

You might be interested in

Find the smallest 3-digit number which gives the remainder 1 when divided by 3 and by 4.

trasher [3.6K]

Multiples of 3 plus 1 remainder are:

3n+1

Multiples of 4 plus 1 remainder are:

4n+1

Since these multiples must be the same number must be a multiple of 12 plus a remainder of one, which is:

12n+1

And the smallest such three digit number is:

12n+1>99 subtract 1 from both sides

12n>98 divide both sides by 12

n>8.17

Since n must be an integer, n=9

So then number is 12n+1

12(9)+1=109

4 0

3 years ago

Which expression is equivalent to 2cos^2(x/2)- cos(x)? Edge 2020

olchik [2.2K]

Given:

The expression is

$2\cos^2(\dfrac{x}{2})-\cos (x)$

To find:

The expression which is equivalent to the given expression.

Solution:

We have,

$2\cos^2(\dfrac{x}{2})-\cos (x)$

We know that,

$\cos x=2\cos^2 (\dfrac{x}{2})-1$

Using this formula, the given expression can be written as

$2\cos^2(\dfrac{x}{2})-\left(2\cos^2(\dfrac{x}{2})-1\right)$

$=2\cos^2(\dfrac{x}{2})-2\cos^2(\dfrac{x}{2})+1$

$=1$

Therefore, the given expression is equivalent to 1.

4 0

3 years ago

In de pas monch. Goran rencad 6 video games and 3 DVDS. The rental price for each video game was $290. The rental price for each

Nimfa-mama [501]

Answer:

$27.30

Step-by-step explanation:

just do 290x6+330x3=2730

but just do this $27.30

so x is $27.30

7 0

3 years ago

You have just used the network planning model and found the critical path length is 30 days and the variance of the critical pat

joja [24]

Answer:

0.726 is the probability that the project will be completed in 33 days or less.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 days

Variance = 25 days

Standard Deviation,

$\sigma = \sqrt{\text{Variance}} = \sqrt{25} = 5$

We assume that the distribution of path length is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(completed in 33 days or less)

$P( x \leq 33) = P( z \leq \displaystyle\frac{33 - 30}{5}) = P(z \leq 0.6)$

Calculation the value from standard normal z table, we have,

$P(x \leq 33) = 0.726 = 72.6\%$

0.726 is the probability that the project will be completed in 33 days or less.

8 0

3 years ago

The quotient of a number t and 4.2 is at most 15.

frosja888 [35]

Answer:

$t \leq 63$

Step-by-step explanation:

Quotient of two numbers also means the result of the two numbers after division.

If the quotient of a number t and 4.2 is at most 15., this can be expressed using the inequality;

$\dfrac{t}{4.2}\leq 15$ (note that at most 15 means that the highest value we can have is 15 after taking the quotient of the number hence the reason of the inequality sign.)

On solving the inequality for the variable t

$\dfrac{t}{4.2}\leq 15\\\\multiply \ both \ sides \ by \ 4.2\\\\\dfrac{t}{4.2}* 4.2\leq 15 * 4.2\\\\t \leq 63$

Hence t is at most 63

6 0

3 years ago