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3 years ago

What the coordinates of the point (-5,1) after 180° rotation about the origin Is it (-1,5)

1 answer:

3 0

The mapping rule for a 180 degree rotation is:
(x,y) (-x,-y)

1. Multiply the x-coordinate by -1.
2. Multiply the y-coordinate by -1.
3. SImplify

So the coordinate after a 180 degree rotation is: (5,-1)

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galina1969 [7]

Answer:

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Step-by-step explanation:

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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

pleaseeee help please for f(x) = x2 and g(x) = (x − 3)2, in which direction and by how many units should f(x) be shifted to obta

wariber [46]

F(x) should be shifted right 3 units.

4 0

3 years ago

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A storage container for oil is in the shape of a cylinder with a diameter of 10 feet and a height of 17 feet which measurement i

strojnjashka [21]

The answer would be 1335.18

8 0

3 years ago

Which choice is the solution to the inequality below?

Georgia [21]

<h3>hello!</h3>

In order to solve this inequality, we should divide both sides by 9:-

$\sf{9x < 72}$

Why 9? Because x is multiplied by 9, and we need to isolate x in order to find its value.

$\sf{x < 8}$

Hence, that's the solution to the inequality.

<em>It also means that the numbers less than 8 will satisfy the given inequality (make the inequality true)</em>

(Option C is correct :) )

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

8 0

2 years ago

Read 2 more answers