Which of the following are perfect squares? Check all that apply.

Many states run lotteries to raise money. A website advertises that it knows "how to increase YOUR chances of Winning the Lott

Crank

Complete question is;

Many states run lotteries to raise money. A website advertises that it knows "how to increase YOUR chances of Winning the Lottery." They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a "lucky" number to play, but maybe some numbers are luckier than others. Let's use a simulation to see how well this system works. To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number. Any value can be picked, but for this exercise, pick 1 as the lucky number. What proportion of the time do you win?

Answer:

10%

Step-by-step explanation:

We are told that To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number.

This means the total number of single digits that could possibly be a winning one is 10.

Since we are told that only 1 can be picked, thus;

Probability of winning is; 1/10 = 0.1 or 10%

5 0

3 years ago

It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de

scoray [572]

Answer:

a) $P(X$

$P(z$

b) $P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

$P(z>-0.583)=1-P(Z$

c) $P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) $z=1.28$

And if we solve for a we got

$a=72000 +1.28*12000=87360$

So the value of height that separates the bottom 90% of data from the top 10% is 87360.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

$X \sim N(72000,12000)$

Where $\mu=72000$ and $\sigma=12000$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using excel or the normal standard table and we got:

$P(z$

Part b

$P(X>65000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>-0.583)=1-P(Z$

Part c

$P(X>100000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

And if we solve for a we got

$a=72000 +1.28*12000=87360$

So the value of height that separates the bottom 90% of data from the top 10% is 87360.

5 0

3 years ago

Liam buys three identical plastic

liq [111]

The number of rectangular prism container that would be set on the shelf is: 4.

<h3>What is the Volume of a Rectangular Prism?</h3>

Volume of rectangular prism = length × width ×height

Given the following:

Volume of three containers = 135 in.³
Volume of each rectangular prism container = 135/3 = 45 in.³
One face = width × height = 4.5 × 2 = 9 in.

Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³

45 = length × 9

length = 5 in.

Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.

The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.

Learn more about rectangular prism on:

brainly.com/question/1015291

7 0

2 years ago

A circular pond has a radius of 35 feet. What is the diameter of the pond?

SVEN [57.7K]

Answer:

I believe the radius is half the circle which makes the diameter 2x the radius which is 35+35= 70

4 0

2 years ago

Can someone help with this I didn’t pay attention in math and I have homework ‍♀️

Lady bird [3.3K]

Answer:

C.

Step-by-step explanation:

Even though it is absolute value, 17 is still the greatest answer. If a number is in absolute value it will never be negative, only positive values can come out of an absolute value.

An example for absolute value would be if you had to measure the amount of distance away from something, even if its behind you, it would still be a positive number of length away from you.

If you had the absolute value of -25, it would automatically be equal to 25.

So circling back to the original problem, the absolute value of 17 would be greater than 3, -4 and -8. If (hypothetically) it was the absolute value of -17 it would still be greater because it would equal 17.

I hope that made sense, im sorry that it's a bit lengthy. Have a good day :)

7 0

2 years ago