In which number does the 9 represent 1/10 of the value that it represents in 92300

New York City is the most expensive city in the United States for lodging. The room rate is $204 per night (USA Today, April 30,

Sever21 [200]

Answer:

a. 0.35197 or 35.20%; b. 0.1230 or 12.30%; c. 0.48784 or 48.78%; d. $250.20 or more.

Step-by-step explanation:

In general, we can solve this question using the <em>standard normal distribution</em>, whose values are valid for any <em>normally distributed data</em>, provided that they are previously transformed to <em>z-scores</em>. After having these z-scores, we can consult the table to finally obtain the probability associated with that value. Likewise, for a given probability, we can find, using the same table, the z-score associated to solve the value <em>x</em> of the equation for the formula of z-scores.

We know that the room rates are <em>normally distributed</em> with a <em>population mean</em> and a <em>population standard deviation</em> of (according to the cited source in the question):

$\\ \mu = \$204$ <em>(population mean)</em>

$\\ \sigma = \$55$ <em>(population standard deviation)</em>

A <em>z-score</em> is the needed value to consult the <em>standard normal table. </em>It is a transformation of the data so that we can consult this standard normal table to obtain the probabilities associated. The standard normal table has a mean of 0 and a standard deviation of 1.

$\\ z_{score}=\frac{x-\mu}{\sigma}$

After having all this information, we can proceed as follows:

<h3>What is the probability that a hotel room costs $225 or more per night? </h3>

1. We need to calculate the z-score associated with x = $225.

$\\ z_{score}=\frac{225-204}{55}$

$\\ z_{score}=0.381818$

$\\ z_{score}=0.38$

We rounded the value to two decimals since the <em>cumulative standard normal table </em>(values for cumulative probabilities from negative infinity to the value x) to consult only have until two decimals for z values.

Then

2. For a z = 0.38, the corresponding probability is P(z<0.38) = 0.64803. But the question is asking for values greater than this value, then:

$\\ P(z>038) = 1 - P(z$ (that is, the complement of the area)

$\\ P(z>038) = 1 - 0.64803$

$\\ P(z>038) = 0.35197$

So, the probability that a hotel room costs $225 or more per night is P(x>$225) = 0.35197 or 35.20%, approximately.

<h3>What is the probability that a hotel room costs less than $140 per night?</h3>

We follow a similar procedure as before, so:

$\\ z_{score}=\frac{x-\mu}{\sigma}$

$\\ z_{score}=\frac{140-204}{55}$

$\\ z_{score}= -1.163636 \approx -1.16$

This value is below the mean (it has a negative sign). The standard normal tables does not have these values. However, we can find them subtracting the value of the probability obtained for z = 1.16 from 1, since the symmetry for normal distribution permits it. Then, the probability associated with z = -1.16 is:

$\\ P(z$

Then, the probability that a hotel room costs less than $140 per night is P(x<$140) = 0.1230 or 12.30%.

<h3>What is the probability that a hotel room costs between $200 and $300 per night?</h3>

$\\ z_{score}=\frac{x-\mu}{\sigma}$

<em>The z-score and probability for x = $200:</em>

$\\ z_{score}=\frac{200-204}{55}$

$\\ z_{score}= -0.072727 \approx -0.07$

$\\ P(z$

<em>The z-score and probability for x = $300:</em>

$\\ z_{score}=\frac{300-204}{55}$

$\\ z_{score}=1.745454$

$\\ P(z$

Then, the probability that a hotel room costs between $200 and $300 per night is 0.48784 or 48.78%.

<h3>What is the cost of the most expensive 20% of hotel rooms in New York City?</h3>

A way to solve this is as follows: we need to consult, using the cumulative standard normal table, the value for z such as the probability is 80%. This value is, approximately, z = 0.84. Then, solving the next equation for <em>x:</em>

$\\ z_{score}=\frac{x-\mu}{\sigma}$

$\\ 0.84=\frac{x-204}{55}$

$\\ 0.84*55=x-204$

$\\ 0.84*55 + 204 =x$

$\\ x = 250.2$

That is, the cost of the most expensive 20% of hotel rooms in New York City are of $250.20 or more.

6 0

4 years ago

Help will give Brainly points

masya89 [10]

Answer:

x=√14

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the right angle), with acute angles measuring 45° and 45°, the hypotenuse (the side opposite from the right angle) labeled as x, and one of the legs (one of the sides that makes up the right angle) labeled as √7

As these two angles are the same measure, the triangle is isosceles.

So that means that the measure of the other leg (the unmarked side) is also √7.

This triangle is a special type of triangle; a 45°-45°-90° triangle. For this triangle, if the length of the legs are a, then the hypotenuse has the length a√2

In this case, √7 is a, and as x is the measure of the hypotenuse, it must be equal to a√2, which substituting the values of a would get √7 * √2, which is √14.

The radical cannot be simplified further, so √14 is the answer.

Hope this helps!

4 0

3 years ago

Infections seldom start with a single bacterium. Suppose that you cut yourself on a rusty nail that puts 25

Soloha48 [4]

Answer: There would be 12,000 bacteria 8 hours after the initial infection.

Step-by-step explanation: You start with 25 cells and if they divide every 15 minutes, 25 multiplied by 15 gets you 375 cells every quarter of an hour. Then if you multiply that by the 32 quarter hours, you get 12,000 cells. To check that you can also multiply 25 by 15, still 375, then 375 by 4 for each quarter of the hour, then that gets you 1,500 cells every hour. If you multiply that by 8 for the 8 hours they have time to divide, you still get 12,000 cells.

I hope this helps!

3 0

3 years ago

What is the area of a hexagon with a side length of 10? it also has a rectangle in it with other measurements but the question i

Anastaziya [24]

Answer:

there is a formula for a hexagon .. it's

Area = 3 $\sqrt{3\\}$ /2 * $length^{2}$

where length is the length of one side, assuming all sides are equal

Step-by-step explanation:

3* $\sqrt{3}$ /2= 7.348469228.........

since the length is 10... the length squared is 100

then the total area of the hexagon is 734.8469228...... $units^{2}$ .. what ever they are

if you want to work with some concepts.. you could also say that a hexagon is just a box with the corners cut off and the triangles that are missing are the equilateral right triangles with a hypotenuse of 10 . and since 2 pieces of those triangles make a square.. you can subtract two squares of that size from the bigger box that the hexagon fits into. this is a long way to figure this out but might be good for trigonometry practice :)

it will also be 734.8463288..... see if you can work that out :)

6 0

3 years ago

Find area of shaded triangle

vova2212 [387]

Answer:

2 units

Step-by-step explanation:

3 0

3 years ago