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3 years ago

If x is a rational number and y=2/3, which statement describess the sum of x and y?

Mathematics

1 answer:

Harman [31]3 years ago

5 0

Answer:

The answer is: The sum of x and y is a rational number.

Step-by-step explanation:

x is a rational number (any).

$\frac{2}{3}$ is a rational number too.

So, the sum of x and y will also be a rational number.

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What is the ratio for the volumes of two similar cylinders, given that the ratio of their heights and radio is 2:3?

gtnhenbr [62]

The answer will be a because they are similar and by law the ratio can be cubed to find ratio of volume

6 0

4 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 sampling distribution of the sampling proportions.

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

If x2 - 6x - 16, what are the x-intercepts?

romanna [79]

If that’s meant to be x^2 - 6x - 16
Then factorise to (x+2)(x-8)
So x intercepts are -2 and 8

8 0

3 years ago

Read 2 more answers

The time between calls made to Amazon's customer service is exponentially distributed with a mean of 10 minutes (taken between e

daser333 [38]

Answer:

The probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

Step-by-step explanation:

Let X = time between calls made to Amazon's customer service.

The average time between calls is, β = 10 minutes.

The random variable X follows an Exponential distribution with parameter $\lambda=\frac{1}{\beta}=\frac{1}{10}=0.10$

The probability distribution function of X is:

$f_{X}(x)=\left \{ {{\lambda e^{-\lambda x};\ x>0}} \atop {0;\ otherwise}} \right.$

Compute the probability that the time between the next two calls is between 3 minutes and 7 minutes as follows:

$P(3$

Thus, the probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

3 0

4 years ago

Read 2 more answers

Carlo borrows 4180 add a rate of 4.1% Per year compounded annually he does not start payments until after 2.8 years which of the

olga_2 [115]

Answer:497.76

Step-by-step explanation:

3 0

3 years ago