Find the average of the following numbers −30 and 25
1 answer:
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Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric progression is
• = a₁
where a₁ is the first term and r the common ratio
given a₄ = 24, then
a₁ = 24 → (1)
Given a₈ = , then
a₁ =
→ (2)
Divide (2) by (1)
=
=
Hence r = =
Substitute this value into (1)
a₁ × ( )³ = 24
a₁ × = 24, hence
a₁ = 24 × 27 = 648
By graphing the points, The best mode of the data will be the quadratic function
There is 5 steps to find the quadratic function that models the data.
First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
which are the blue circles in the attached figure
Second step ⇒ Draw the parabola you think best fits the data.
Which is the red function in the attached figure.
Third step ⇒ Estimate the coordinates of three points on the
parabola, which are (-1, 0), (2, -3), and (5, 12).
Fourth step ⇒ Substitute the coordinates of the points into the model
y = ax² + bx + c
to obtain a system of three linear equations.
a - b + c = 0 ---------(1)
4a + 2 b + c = -3 ---------(2)
25a + 5 b + c = 12 ---------(3)
Fifth step ⇒ Solve the linear system.
By using the calculator
a = 1 , b = -2 , c = -3
So, the quadratic model for the data is ⇒ y = x² - 2x - 3
There is 5 steps to find the quadratic function that models the data.
First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
which are the blue circles in the attached figure
Second step ⇒ Draw the parabola you think best fits the data.
Which is the red function in the attached figure.
Third step ⇒ Estimate the coordinates of three points on the
parabola, which are (-1, 0), (2, -3), and (5, 12).
Fourth step ⇒ Substitute the coordinates of the points into the model
y = ax² + bx + c
to obtain a system of three linear equations.
a - b + c = 0 ---------(1)
4a + 2 b + c = -3 ---------(2)
25a + 5 b + c = 12 ---------(3)
Fifth step ⇒ Solve the linear system.
By using the calculator
a = 1 , b = -2 , c = -3
So, the quadratic model for the data is ⇒ y = x² - 2x - 3