Need some help on this

yan [13]

Answer:

S = 8

Step-by-step explanation:

An infinite geometric series is defined as limit of partial sum of geometric sequences. Therefore, to find the infinite sum, we have to find the partial sum first then input limit approaches infinity.

However, fortunately, the infinite geometric series has already set up for you. It’s got the formula for itself which is:

$\displaystyle \large{\lim_{n\to \infty} S_n = \dfrac{a_1}{1-r}}$

We can also write in summation notation rather S-term as:

$\displaystyle \large{\sum_{n=1}^\infty a_1r^{n-1} = \dfrac{a_1}{1-r}}$

Keep in mind that these only work for when |r| < 1 or else it will diverge.

Also, how fortunately, the given summation fits the formula pattern so we do not have to do anything but simply apply the formula in.

$\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{1-0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = 8}$

Therefore, the sum will converge to 8.

Please let me know if you have any questions!

6 0

2 years ago

Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

Mekhanik [1.2K]

Answer:

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

$np \geq 10$ and $n(1-p) \geq 10$

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Out of 124 software users

This means that $n = 124$

Assume the probability that a given software user will call technical support is 97%.

This means that $p = 0.97$

Conditions:

$np = 124*0.97 = 120.28 \geq 10$

$n(1-p) = 124*0.03 = 3.72 < 10$

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0$

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

3 0

3 years ago

the measurement of one angle of a right angle is 42 degrees what is the measurement of the third angle

kogti [31]

The angles of a triangle all add up to 180°. In fact, it can be generalized that the sum of the interior angles of an n-sided polygon is equal to 180°(n–2).

A right triangle must have a right angle, which is equal to 90°. If the other angle is 42°, that means that we can find the third angle by subtracting 90° + 42° from 180°.

x = 180° – (90° + 42°) = 48°

8 0

3 years ago

Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books

Oksi-84 [34.3K]

Answer: The correct option is (A) $120-3w=24;~32.$

Step-by-step explanation: Given that Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read.

We are to find the equation that can be used to determine the number of weeks it will take Raymond to have only 24 books left.

Also, we are to find the number of weeks.

The number of weeks it will take Raymond to have only 24 books left is represented by 'w'.

We have

number of books read by Raymond is 1 week = 3.

So, number of books read by Raymond is w weeks = 3w.

Since, there are total 120 books on his bookshelf, so the number of books left to read after w weeks will be

$120-3w.$

According to the given information, we get

$120-3w=24\\\\\Rightarrow 3w=120-24\\\\\Rightarrow 3w=96\\\\\Rightarrow w=32.$

thus, the required equation is $120-3w=24$ and number of weeks is 32.

Option (A) is correct.

8 0

3 years ago

State which of the following sets of ordered pairs represents a function. Please pick the best option

IRINA_888 [86]

Answer:

set A and set B...it is the best and right option bro...option c is wrong because 2 elements of domain has relation with 1 range

3 0

3 years ago