Answer:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
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".
Solution to the problem
Let X the random variable that represent the area of a population, and for this case we know the distribution for X is given by:
Where and
We select a a sample of n =4 and since the distribution for X is normal then we know that the distribution for the sample mean is given by:
And we want to find this probability:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
Answer:
Step-by-step explanation:
To shift a function F(x) a units to the left, we do:
In this problem, we have that:
So, shifting 2 units left:
Then
To shift a units down, we do:
Shifting 6 units down
Answer:
Step-by-step explanation:
Hint: (a + b)(a -b)= a² - b²
(√2+√7)(√2-√7)=(√2)²-(√7²) = 2 - 7 = -5
Answer:
Step-by-step explanation:
Given that there is a triangle XYZ with vertices (0, 0), Y(0, –2), and Z(–2, –2)
This triangle is rotated to form image triangle X'(0, 0), Y'(2, 0), and Z'(2, –2).
We find that origin remains the same.
Hence point of rotation is about the origin
Now (0,-2) is transformed to (2,0)
This is possible if point is rotated about origin anticlockwise a degree of 90
Let us check new coordinate of Z by anticlockwise rotation of 90
We get Z'(2,-2)
Hence the transformation is rotation about origin anticlockwise by degree 90
Answer:
2 benches
Step-by-step explanation:
1.) 150 + 100x = 175x
2.) 150 = 75x
Final answer: 2 = x