Answer:
x=20
Step-by-step explanation:
Answer:
e
Step-by-step explanation:
Answer:
![P(X](https://tex.z-dn.net/?f=P%28X%3C225%29%3D0.351)
Step-by-step explanation:
Assuming a mean of $204 per night and a deviation of $55.
a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?
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".
Let X the random variable that represent the cost per night at the hotel, and for this case we know the distribution for X is given by:
Where
and ![\sigma=55](https://tex.z-dn.net/?f=%5Csigma%3D55)
And let
represent the sample mean, the distribution for the sample mean is given by:
![\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%28%5Cmu%2C%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
We are interested on this probability
![P(X>225)](https://tex.z-dn.net/?f=P%28X%3E225%29)
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}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
If we apply this formula to our probability we got this:
![P(X>225)=P(\frac{X-\mu}{\sigma}>\frac{225-\mu}{\sigma})](https://tex.z-dn.net/?f=P%28X%3E225%29%3DP%28%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%3E%5Cfrac%7B225-%5Cmu%7D%7B%5Csigma%7D%29)
![=P(Z>\frac{225-204}{55})=P(Z>0.382)](https://tex.z-dn.net/?f=%3DP%28Z%3E%5Cfrac%7B225-204%7D%7B55%7D%29%3DP%28Z%3E0.382%29)
And we can find this probability on this way:
![P(Z>0.382)=1-P(Z](https://tex.z-dn.net/?f=P%28Z%3E0.382%29%3D1-P%28Z%3C0.382%29%3D0.351)
Answer:
There are 24 nickels
Step-by-step explanation:
Let x represent the number of nickels
Let y represent the number of quarters
—————————————————————
Value Value
Type Number of of
of of each all
Coin Coin Coin Coin
—————————————————————
Nickels | x | $0.05 | $0.05x
Quarters | y | $0.25 | $0.25y
—————————————————————
Totals 28 ——— $2.20
•••••••••••••••••••••••••••••••••••••••••••••••••
The first equation comes from the “Number of coins” column.
(Number of nickels) + (Number of quarters) = (total number of coins)
Equation: x + y = 28
—————————————————————
The second equation comes from the “value of all coins” column.
(Value of all nickels) + (Value of all quarters) = (Total value of all coins)
0.05x + 0.25y = 2.20
Remove the decimals by multiplying each term by 100:
5x + 25y = 220
—————————————————————
So we have the system of equations:
{x + y = 28
{5x + 25y = 202
Solve by substitution. Solve the first equation for y:
x + y = 28
y = 28 - x
Substitute (28 - x) for y in 5x + 25y = 220
5x + 25 (28 - x) = 220
5x + 700 - 25x = 220
-20x + 700 = 220
-20x = -480
x = 24
The number of nickels is 24.
————————————————————
Substitute in y = 28 - x
y = 28 - (24)
y = 4
The number of quarters is 4.
————————————————————
Checking:
24 nickels is $1.20 and 4 quarters is $1.00
That’s 28 coins.
Indeed $1.20 + $1.00 = $2.20
————————————————————
Answer:
C
Step-by-step explanation:
To solve it will be easier to turn 7 into a rational number with the same denominator as 5/7
To do this make ratios
![\frac{7}{1}=\frac{x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B1%7D%3D%5Cfrac%7Bx%7D%7B7%7D)
Now solve for x
x = 49
This means that the fraction will be 49/7
This can also be written as ![6\frac{2}{7}](https://tex.z-dn.net/?f=6%5Cfrac%7B2%7D%7B7%7D)