Simplify the expression 3 to the third power times 32+12 divided by 4

The following estimated regression equation was developed for a model involving two independent variables.

Alik [6]

Answer:

(a): y increases on average by 8.63/unit of x1 in the first equation and increases on average by 9.01/unit of x1 in the second

(b): Yes

Step-by-step explanation:

Given

$\wedge y = 40.7 + 8.63x_1 +2.71x_1$

$\wedge y = 42.0 + 9.01x_1$

Solving (a): An interpretation of x1 coefficient

We have the coefficients of x1 to be 8.63 and 9.01

Literally, the coefficient represents the average change of y-variable per unit increase of the dependent variable

Since the coefficients of x1 in both equations are positive, then that represents an increment on the y variable.

So, the interpretation is:

y increases on average by 8.63/unit of x1 in the first equation and increases on average by 9.01/unit of x1 in the second

Solving (b): Multicollinearity

This could be the cause because x1 and x2 are related and as a result, x2 could take a part of the coefficient of x2

7 0

3 years ago

Evaluate the determinant for the following matrix: -4 -4 -3

expeople1 [14]

A suitable calculator finds the determinant to be ...

... B. -203

_____

This can be calculated by hand by copying the first two columns to the right of the given matrix, then forming the sum of products of the downward diagonals and subtracting the sum of products of the upward diagonals.

... (-4)(3)(-5) +(-4)(-5)(-5) +(-3)(3)(2) -(-5)(3)(-3) -(2)(-5)(-4) -(-5)(3)(-4)

... = 60 -100 -18 -45 -40 -60

... = -203

3 0

4 years ago

L1 and L2 are two straight lines. The origin of the coordinate axes is O. L1 has equation 5x + 10y = 8 L2 is perpendicular to L1

Ivenika [448]

Answer:

40 sq units

Step-by-step explanation:

$5x + 10y = 8\\\Rightarrow y=\dfrac{8-5x}{10}\\\Rightarrow y=-\dfrac{1}{2}x+\dfrac{2}{5}$

Slope of $L_2$ is $m_2$

$m_1m_2=-1\\\Rightarrow m_2=-\dfrac{1}{m_1}\\\Rightarrow m_2=-\dfrac{1}{-\dfrac{1}{2}}\\\Rightarrow m_2=2$

$L_2$ passes through point $(8,6)$

$y-6=2(x-8)\\\Rightarrow y=2x-16+6\\\Rightarrow y=2x-10$

Point at x axis where $L_2$ intersects is

$0=2x-10\\\Rightarrow x=\dfrac{10}{2}\\\Rightarrow x=5$

Point $A$ of the triangle will be $(5,0)$

$L_2$ intersects line $x=-3$ . The point is

$y=2\times(-3)-10\\\Rightarrow y=-6-10\\\Rightarrow y=-16$

The points of the triangle are $A(5,0), O(0,0), B(-3,-16)$

Area of triangle is given by

$A=\dfrac{|A_x(B_y-O_y)+B_x(A_y-O_y)+O_x(A_y-B_y)|}{2}\\\Rightarrow A=\dfrac{|5(-16-0)+-3(0-0)+0(0-(-16))|}{2}\\\Rightarrow A=40\ \text{sq units}$

The area of the triangle is 40 sq units.

6 0

3 years ago

A spinner has 5 evenly spaced sections numbered 1 to 5. Rasheed will perform an experiment to model the theoretical probability

bogdanovich [222]

Answer:

1/5 ¡!!!!!!!!!!!!!!!!!!!!!!

4 0

3 years ago

Read 2 more answers

An object was launched from the ground. The graph below shows the path that the object took. Use the graph to answer questions 9

denis-greek [22]

Using the concepts of domain and range, it is found that for the function given in the graph:

The domain is [0, 4].

The range is [0,64].

<h3>What are the domain and the range of a function?</h3>

The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains the values of the horizontal axis.

The range of a function is the set that contains all the values of the output. In a graph, it is the set that contains the values of the vertical axis.

The graph in this problem gives the <u>height of a projectile after t seconds</u>, hence:

The domain is [0, 4].

The range is [0,64].

More can be learned about the domain and range of a function at brainly.com/question/10891721

3 0

2 years ago