Answer:
28 ways
Step-by-step explanation:
After placing 1 ball in each of the seven bins, there are two balls left.
If we place both balls in a single bin, there are 7 different ways to place the balls (place both on bins 1 through 7).
If we place each of the remaining balls in a different bin, the number of ways to place the balls is:
The total number of ways to distribute those balls is 21 + 7 = 28 ways.
Answer:
x = 10
Step-by-step explanation:
By the converse of the side-splitter theorem, if , then KM ∥ JN.
Substitute the expressions into the proportion:
Cross-multiply:
(x – 5)(x+4) = x(x – 3).
Distribute:
Multiply and simplify:
Solve for x: x = 10
Therefore, the value of x that would make KM parallel to JN is 10.
It is given in the question that
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation
To solve for C, we need to get rid of 273.15 and for that we do subtraction, that is
Correct option is the first option .
Answer: There is 20 ounces of liquid in the bowl after adding 8 containers of sparkling water.
Step-by-step explanation:
Since we have given that
Number of ounces of cranberry juice into a punch bowl = 12 ounces
According to question, he uses a container to add sparkling water to the bowl one ounce at a time.
Let the amount of sparkling water added to the bowl be 'x'
Let the total number of ounces of liquid Marcus will have be 'y'.
So, our equation becomes,
Here, we have asked after adding 8 containers of sparkling water .
So, now, our equation becomes,
Hence, there is 20 ounces of liquid in the bowl after adding 8 containers of sparkling water.
Answer:
a) There is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
b) There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
c) There is a 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.3 minutes. This means that .
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
We are working with a sample mean of 37 jets. So we have that:
Total time of 320 minutes for 37 jets, so
This probability is the pvalue of Z when . So
has a pvalue of 0.7422. This means that there is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
Total time of 275 minutes for 37 jets, so
This probability is subtracted by the pvalue of Z when
has a pvalue of 0.0548.
There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
Total time of 320 minutes for 37 jets, so
Total time of 275 minutes for 37 jets, so
This probability is the pvalue of Z when subtracted by the pvalue of Z when
.
So:
From a), we have that for , we have
, that has a pvalue of 0.7422.
From b), we have that for , we have
, that has a pvalue of 0.0548.
So there is a 0.7422 - 0.0548 = 0.6874 = 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.