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S_A_V [24]
3 years ago
12

Finding β0 and β1 . The equation for a straight line (deterministic) is y = β0 + β1x. If the line passes through the point (0,1)

, then x = 0, y = 1 must satisfy the equation. That is, 1 = β0 + β1(0). Similarly, if the line passes through the point (2,3), then x = 2, y = 3 must satisfy the equation: 3 = β0 + β1(2). Use these two equations to solve for β0 and β1, and find the equation of the line that passes through the points (0,1) and (2,3).
Mathematics
1 answer:
Anton [14]3 years ago
8 0

Answer:

y = x + 1  

Step-by-step explanation:

We are given the following in the question:

y = \beta_0 + \beta_1x

The line passes through (0,1).

1= \beta_0 + \beta_1(0)\\\Rightarrow 1= \beta_0

The line passes through (2,3)

3= \beta_0 + \beta_1(2)\\\Rightarrow 3= 1 + \beta_1(2)\\\Rightarrow 2 = 2\beta_1\\\Rightarrow \beta_1 = 1

Thus, the equation of the line that passes through the points (0,1) and (2,3) is given by:

Slope:

m = \beta_1 = 1

Intercept:

c = \beta_0 = 1

Equation:

y = x + 1

is the required equation.

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Select the correct answer.
iris [78.8K]

The future value of $1,000 invested at 8% compounded semiannually for five years is \bold{\$ 1,480}

<u>Solution:</u>

\bold{A = P (1 + i )^{n}} ----------- equation 1

A = future value  

P= principal amount  

i = interest rate

n = number of times money is compounded  

P = 1000

i = 8 %

\mathrm{n} = \text { compounding period } \times \text {number of years}

(Compounding period for semi annually = 2)

\mathrm{n} = \text { compounding period } \times \text {number of years}

Dividing “i” by compounding period

i = \frac{8 \%}{2} = 0.04

Solving for future value using equation 1

\begin{array}{l}{A = 1000(1 + 0.04)^{10}} \\\\ {=1000 (1.04)^{10}}\end{array}

= 1480.2

\approx 1,480 \$

3 0
3 years ago
How do you do this question
ella [17]

Answer:


Step-by-step explanation:


5 0
4 years ago
Solve by graphing if possible: 12n² + 11 = 0
ioda

Answer:

No real solutions

Step-by-step explanation:

5 0
3 years ago
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For each diagram, describe a translation, rotation, or reflection that takes line ℓ to line ℓ′. Then plot and label A′ and B′, t
inn [45]

Answer:

  1. translate down 3
  2. reflect across the horizontal line through A

Step-by-step explanation:

1. There are many transformations that will map a line to a parallel line. Translation either horizontally or vertically will do it. Reflection across a line halfway between them will do it, as will rotation 180° about any point on that midline.

In the first attachment, we have elected to translate the line down 3 units.

__

2. Again, there are many transformations that could be used. Easiest is one that has point A as an invariant point, such as rotation CW or CCW about A, or reflection horizontally or vertically across a line through A.

Any center of rotation on a horizontal or vertical line through A can also be used for a rotation that maps one line to the other.

In the second attachment, we have elected to reflect the line across a horizontal line through A.

6 0
3 years ago
I need to know what is the square root of 7
antiseptic1488 [7]
Square Root of 7
= 2.64575131106
5 0
3 years ago
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