This is an exponential decay problem.
Using the equation Y = a *(1-rate)^time
where Y is the future value given as 12,000 and a is the starting value given as 13,000.
The rate is also given as 5%.
The equation becomes:
12,000 = 13,000(1-0.05)^x
12,000 = 13,000(0.95)^x
Divide each side by 13000:
12000/13000 = 0.95^x/13000
12/13 = 0.95^x
Use the natural log function:
x = ln(12/13) / ln(0.95)
x = 1.56 years. ( this will equal 12,000
Round to 2 years it will be less than 12000.
Answer:
yes
Step-by-step explanation:
The answer is B. addition or multiplication
Using a calculator, the equation for the line of best fit where x represents the month and y represents the time is given by:
a. y = −1.74x + 46.6
<h3>How to find the equation of linear regression using a calculator?</h3>
To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows, from the given table:
(1, 46), (2, 42), (3,40), (4, 41), (5, 38), (6,36).
Hence, inserting these points in the calculator, the equation for the line of best fit where x represents the month and y represents the time is given by:
a. y = −1.74x + 46.6
More can be learned about a line of best fit at brainly.com/question/22992800
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Answer:
The correct option is;
D. When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent
Step-by-step explanation:
In the proof to show that the sum of the angles in a triangle = 180°, we have;
For a triangle located between two parallel lines, such that the base of the triangle coincides with one of the parallel lines, we have;
The angle formed by one of the base angles and the adjacent side of the extension = 180° by the sum of angles on a straight line
From the attached diagram of a triangle between two parallel lines, we have;
∠e + ∠b = 180° by the sum of angles on a straight line postulate
∠e = ∠a + ∠d by alternate interior angles postulate
∠c = ∠d by alternate interior angles postulate
∴ ∠e = ∠a + ∠c by substitution property
∴ ∠e + ∠b = ∠a + ∠c + ∠b = 180° by substitution property
Therefore, the sum of the interior angles of a triangle, ∠a + ∠c + ∠b = 180°.