Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Using the formula for calculating the distance between two points as shown;
D = √(x2-x1)²²+(y2-y1)²
Given the coordinates (-2, 4) and (10,2)
x1 = -2, y1 = 4, x2 = 10 and y2 = 2
substitute into the formula;
D = √(10+2)²+(2-4)²
D = √(12²+(-2)²
D = √144+4
D = √148
D = 12.17 units
Hence the distance of Mac,s house from Nate's house is 12.17 units
To find the coordinates of Mac's house, we use the section formula in mathematics. By substitifying the given locations of Nate's house and the park into the formula, we conclude that Mac's house is located at approximately (2, 3.33) which is one third the distance from Nate's house to the park.
In this math problem, we are dealing with points in a 2D cartesian coordinate system. Nate's house is at (-2, 4) and the park is at (10, 2). Mac's house is located one third of the distance between these two points. Following the formula for the coordinates of a point dividing a line segment in a given ratio, we can find Mac's house location.
Let the coordinates of Mac's house be (x, y). We use the formula for section formula which is:
x = [(m*x2 + n*x1) / (m+n)] and y = [(m*y2 + n*y1) / (m+n)]
Here, x1, y1 (-2, 4) are the coordinates of Nate's house, x2, y2 (10, 2) are the coordinates of the park and the ratio m:n is 1:2 since it's one third of the distance from Nate's house to the park.
By substituting these values in the formula, we get x = [(1*10 + 2*-2) / (1+2)] = 2 and y = [(1*2 + 2*4) / (1+2)] = 3.33
So, the coordinates of Mac's house are approximately (2, 3.33).
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In a logical system, axioms and postulates are the mathematical truths that are accepted without proof.
An axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful.
A postulate is an assumption, that is, a proposition or statement that is assumed to be true without any proof. Postulates are the basic structure from which lemmas and theorems are derived.
For the given situation,
Mathematicians assume that axioms are true without being able to prove them.
Postulates are the basic structure from which lemmas and theorems are derived.
From the definition, axioms and postulates are the mathematical truths that are accepted without proof.
Hence we can conclude that in a logical system, axioms and postulates are the mathematical truths that are accepted without proof.
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Answer:A
Step-by-step explanation:it is A
Answer:
The answer to your question is the third option
Step-by-step explanation:
a) This first option is not correct because if a number is less or equal to zero does not affect in if it is a function or not.
b) It option is incorrect because each value of x has two values or y and the defition of function says that x must have only one y value.
c) This is the definition of function, it's correct
d) This option is wrong, is similar to the first option.
The hotel had 289 guests on the day in question. The z-score is a measure of how many standard deviations a data point is away from the mean of the distribution.
In this case, we are given that the number of guests in a hotel per day follows a normal distribution with a mean of 220 and a standard deviation of 30, and that the z-score of the number of guests on a particular day was 2.3.
Using the formula for z-score, we have:
z = (x - mu) / sigma
where x is the number of guests on the given day, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.
Substituting the given values, we have:
2.3 = (x - 220) / 30
Multiplying both sides by 30, we get:
69 = x - 220
Adding 220 to both sides, we get:
x = 289
Therefore, the hotel had 289 guests on the day in question.
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