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densk [106]
3 years ago
7

Help me and you get 100 points and Brainliest

Mathematics
2 answers:
OlgaM077 [116]3 years ago
8 0

hey someone else has already answered this!

a. To find the least squares regression equation for a group of (x,y) points:

Step 1: For each point(x,y), we need to calculate x² and xy first.

Step 2: Sum all x, y, x² and xy, which gives us Σx, Σy, Σx² and Σxy

Step 3: Calculate Slope m: m = (NΣxy − Σx Σy)/ N(Σx²) − (Σx)² , here N is the number of data.

Step 4: Calculate Intercept b: b = Σy − m(Σx)/ N

Step 5: Assemble the equation as y= mx+b

Here, we have ∑x = 120, ∑y= 1379, ∑x²= 919.5, ∑xy= 10466 and N= 16

So, m= (NΣxy − Σx Σy)/ N(Σx²) − (Σx)²

=

=

=  

= 6.33

and b = Σy − m(Σx)/ N

=

=

=

= 38.71

So, the least squares regression equation is : y= mx+b ⇒ y= 6.33x +38.71

b. When x= 8, then y= (6.33×8)+38.71 = 50.64 + 38.71 =89.35

The approximate test score of a student who sleeps an average of 8 h a night is 89.35%

EVERYTHING IS FROM sicista on brainly!

GrogVix [38]3 years ago
8 0

Answer

Yep, that guy answered it

Step-by-step explanation:

give me or him brainliest, but mostly the other guy

and go ahead and thank sicista

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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.
PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put  (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² +  (2/√3)cx + c² = 1

⁴/₃x² +  (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

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