Step-by-step explanation:
Molly ran 1/4 of a mile in 1 minute, i.e.
1/4 mile : 1 minute
Multiply both sides by 4 to get time for one mile
1 mile : 4 minutes
Multiply by 4 again to get time for 4 miles
4 miles = 4*4 = 16 minutes.
So it takes Molly 16 minutes to run four miles.
Answer:
The probability that a randomly chosen tree is greater than 140 inches is 0.0228.
Step-by-step explanation:
Given : Cherry trees in a certain orchard have heights that are normally distributed with
inches and
inches.
To find : What is the probability that a randomly chosen tree is greater than 140 inches?
Solution :
Mean -
inches
Standard deviation -
inches
The z-score formula is given by, ![Z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
Now,
![P(X>140)=P(\frac{x-\mu}{\sigma}>\frac{140-\mu}{\sigma})](https://tex.z-dn.net/?f=P%28X%3E140%29%3DP%28%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3E%5Cfrac%7B140-%5Cmu%7D%7B%5Csigma%7D%29)
![P(X>140)=P(Z>\frac{140-112}{14})](https://tex.z-dn.net/?f=P%28X%3E140%29%3DP%28Z%3E%5Cfrac%7B140-112%7D%7B14%7D%29)
![P(X>140)=P(Z>\frac{28}{14})](https://tex.z-dn.net/?f=P%28X%3E140%29%3DP%28Z%3E%5Cfrac%7B28%7D%7B14%7D%29)
![P(X>140)=P(Z>2)](https://tex.z-dn.net/?f=P%28X%3E140%29%3DP%28Z%3E2%29)
![P(X>140)=1-P(Z](https://tex.z-dn.net/?f=P%28X%3E140%29%3D1-P%28Z%3C2%29)
The Z-score value we get is from the Z-table,
![P(X>140)=1-0.9772](https://tex.z-dn.net/?f=P%28X%3E140%29%3D1-0.9772)
![P(X>140)=0.0228](https://tex.z-dn.net/?f=P%28X%3E140%29%3D0.0228)
Therefore, the probability that a randomly chosen tree is greater than 140 inches is 0.0228.
The area of a rectangle is L x W, so 9(5+x) is the formula for the area in factored form. It can be simplified to 45+9x
The required matrix is:
![\left[\begin{array}{ccc}-25&17&0\\8&-1&3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%2617%260%5C%5C8%26-1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We need to apply elementary row operation -2R₂+3R₁ tothe matrix:
![A=\left[\begin{array}{ccc}-3&5&2\\8&-1&3\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%265%262%5C%5C8%26-1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Multiplying Row 2 with -2 and Row1 with 3 and adding,
-9 15 6
-16 2 -6
----------
-25 17 0
After applying this operation, Row 1 will be changed while Row 2 will remain same because we get -2R₂+3R₁ -> R₁
The required matrix is:
![\left[\begin{array}{ccc}-25&17&0\\8&-1&3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%2617%260%5C%5C8%26-1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Keywords: Matrices, elementary row operation
Learn more about matrices at:
#learnwithBrainly
The easiest way to think about this is to give all of the numbers common denominators:
1 can be written as 6/6
0 can be written as 0/6
Now we can see that 5/6 is only 1/6 away from 1, while it is 5/6 away from 0.
So, 5/6 is closer to 1!