Answer:
Where 
and 
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for 
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". The letter 
is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for
Answer:
A. Kayla
Step-by-step explanation:
To find the difference between the two numbers we will do:
7°C - (-5°C)
Subtracting a negative number is the same as simply adding, so we can rewrite the equation as:
7°C + 5°C = 12°C
4x - 5y = 24
4(6) - 5(0) = 24
24 - 0 = 24
24 = 24 (correct)....so (6,0) is a solution
4(1) - 5(-4) = 24
4 + 20 = 24
24 = 24 (correct)...and (1,-4) is a solution
A function assigns the values. The force that will be required to move the rock is 48 lbs.
<h3>What is a Function?</h3>
A function assigns the value of each element of one set to the other specific element of another set.
A.) The inverse of the function f(x)=1/x is,
f(x) = 1/x
y = 1/x
x = 1/y
g(x)=1/x
Hence, The inverse of the function f(x)=1/x is g(x)=1/x.
B.) The force that will be required to move the rock using the momentum,
9ft × 80lbs = 15 ft × F
F = 48 lbs
Hence, The force that will be required to move the rock is 48 lbs.
Learn more about Function:
brainly.com/question/5245372
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Step-by-step explanation:
We can write this word problem as two variables. Let us assume that:
x = Natalie's age
y = Fred's age
The first part of the word problem is that "If you add Natalie's age and Fred's age, the result is 39." Therefore:
Natalie's age + Fred's age = 39
x + y = 39
This will be our first equation. The second equation can be derived from the statement that "If you add Fred's age to 4 times Natalie's age, the result is 78." Therefore:
(4 times Natalie's age) + Fred's age = 78
4x + y = 78
We can now form a system of equations and solve for both x and y:
The simplest way to solve would be using the Substitution method, as seen here:
x + y = 39
y = 39 - x
4x + y = 78
4x + (39 - x) = 78
3x + 39 = 78
3x = 39
x = 13
x + y = 39
13 + y = 39
y = 26
Remember that x = Natalie's age and y = Fred's age. Therefore, Natalie's age is 13 years old and Fred's age is 26 years old.
