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3 years ago

Consider the following data points.

Mathematics

2 answers:

Hoochie [10]3 years ago

8 0

Answer:

the equation of the least-squares line for the data is: $\hat Y=9.3+1.3x$

Step-by-step explanation:

In a simple linear regression model, such as, $\hat Y=b_0+b_1x$ , the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:

$b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}$

For the data provided you have to:

$S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4$ , thus:

$b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3$

the equation of the least-squares line for the data is:

$Y=9.3+1.3x$

Naddika [18.5K]3 years ago

3 0

Answer:

y= 9.3 1.3

Step-by-step explanation:

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18(5−3w) =<br> can someone help me pls

nika2105 [10]

Answer:

90-54w

Step-by-step explanation:

use the distributive property

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2 years ago

Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more t

Burka [1]

The system of linear inequalities x + 10y ≤ 80, x ≥ 30 and y ≤ 4 is represented in a graph below

<h3>Graph of Linear Inequality</h3>

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

To solve this problem, we would require the use of graph which can easily be done with a graphing calculator.

x + 10y ≤ 80

x ≥ 30

y ≤ 4

The graph of the inequalities is attached below

Learn more on graph of linear inequality here;

brainly.com/question/19443475

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4 0

1 year ago

Scientist are studying a bacteria sample. The function f(x)=360(1.07)^x gives the number of bacteria in the sample at the end of

Lapatulllka [165]

Options :

A. The initial number of bacteria is 7.

B. The initial of bacteria decreases at a rate of 93% each day.

C. The number of bacteria increases at a rate of 7% each day.

D. The number of bacteria at the end of one day is 360.

Answer:

C. The number of bacteria increases at a rate of 7% each day.

Step-by-step explanation:

Given the function :

f(x)=360(1.07)^x ; Number of bacteria in sample at the end of x days :

The function above represents an exponential growth function :

With the general form ; Ab^x

Where A = initial amount ;

b = growth rate

x = time

For the function :

A = initial amount of bacteria = 360

b = growth rate = (1 + r) = 1.07

If ; (1 + r) = 1.07 ; we can solve for r to obtain the daily growth rate ;

1 + r = 1.07

r = 1.07 - 1

r = 0.07

r as a percentage ;

0.07 * 100% = 7%

7 0

2 years ago

Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (2, 3)

lozanna [386]

Standard equation of a circle: <em>(x-h)² + (y-k)² = r²</em> where <em>(h, k)</em> is the center and <em>r </em>is the radius. In the case of our equation here, <em>(x-5)² + (y+3)² = 25</em>, we can conclude that our circle has a center at (5, -3) and a radius of 5 units.

We can use the distance formula with the center (5, -3) and our point (2, 3) to see how far away they are...if the distance between them is less than the radius of the circle, it is on the interior. If it's equal, it's on the circle. If it's greater, it's on the exterior.

Distance = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Distance = $\sqrt{(-3-3)^2+(5-2)^2}$

Distance = $\sqrt{(-6)^2+3^2}$

Distance = $\sqrt{36+9}$

Distance = $\sqrt{45}\approx6.7082$

$6.7082>5,\ so\ (2,3)\ is\ on\ the\ \boxed{exterior}$

8 0

3 years ago

Help!!! ASAP!!!!!!!!

Svet_ta [14]

Answer:

-18y = 1

y = -1/18

5x - 9(-1/18)= -2

5x + 1/2 = -4/2

5x = -5/2

x = - 25/2

6 0

3 years ago