What is the reason for the fourth and eighth steps in the proof?

What is the common ratio of the geometric sequence below 625,125,25,5,1,...

shepuryov [24]

Answer: $\frac{1}{5}$

Step-by-step explanation:

In the geometric sequence we can see each time we are dividing by 5. That is the same as multiplying by $\frac{1}{5}$ so that is the common ratio.

5 0

3 years ago

There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In

Nina [5.8K]

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the <em>sampling distribution of the sampling proportions</em>.

The mean and standard deviation of this sampling distribution is:

$\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}$

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

$P(0.45$

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

$z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)$

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

$P(p>0.8)=P(z>z^*)$

The z value is calculated as before:

$z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0$

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

8 0

3 years ago

Find the complement of 73°<br><br>

Nimfa-mama [501]

Answer:

18°

Step-by-step explanation:

90-72= 18

The complement of 73 is the angle that when added to 73 forms a right angle which is 90° xd

5 0

3 years ago

A department store sells logo shirts at an original price of $20. Every month that a shirt doesn’t sell, the store reduces the s

Tasya [4]

Given:
Original price = 20
reduces selling price by 25% every month it's not sold.

First markdown month:
20 * (100%-25%) = 20 * 75% = 15

Second markdown month
15 * 75% = 11.25

Macy, employee gets a 50% discount off the current price.
11.25 * 50% = 5.625
11.25 - 5.625 = 5.625 or 5.63

The pre-tax price of the shirt for Macy will be $5.63

3 0

3 years ago

Read 2 more answers

A line has a slope of 3/5. a line parallel to that line would have a slope of

nekit [7.7K]

-3/5 they have opposite slopes so they would never touch but are parallel.

4 0

3 years ago