The mean and standard deviation for number of battery crimes in the U.S. from 1985 to 2000 are X = 326,845 and sx = 27,569. The mean and standard deviation for number of property crimes in the U.S. for the same time period are y = 634,235 and Sy = 42,268. The correlation coefficient is r = 0.92. Find the equation for the least- squares regression line for number of property crimes compared with number of battery crimes.
A: y = 1.41 + 173,214.37x
B: y = 173,214.37 + 1.41x
C: y = 421,052.69 + 0.65x
D: y = 0.65 + 421,052.69x
E: Unable to determine the equation​

Answers

Answer 1

Answer:

The correct answer is: A

Step-by-step explanation:

The value of the slope and intercept is:

=0.92(42268/27569)

=1.410518

a=y-bx

=634235-1.410518×326845

=173214.3716

The eququation for the least-square regression line is:

y=173214.3716 + 1.4105518x

Round to the 2 decimal place:

=173,214.37 +1.41x

Answer 2

The equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37

How to determine the least square regression equation?

The given parameters are:

Mean x, μ = 326,845 Standard deviation of x, σ = 27,569Mean y, μ = 634,235 Standard deviation of y, σ = 42,268Correlation coefficient, r = 0.92

Calculate the slope (m) using:

m = r * Sy/Sx

This gives

m = 0.92 * 42268/27569

Evaluate

m =1.41051761036

Approximate

m = 1.41

The y-intercept (c) is calculated using:

c = μy -m * μx

So, we have:

c = 634235 - 1.41051761036 * 326845

Evaluate

c = 173214.371642

Approximate

c =173214.37

The least-square regression line equation is represented as:

y = mx + c

So, we have:

y = 141x + 173214.37

Hence, the equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37

Read more about least squares regression at:

https://brainly.com/question/14563186

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation: 

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This deals with linear equations with one unknown.

Overview

Steps

Terms and topics

1 result(s) found

a=9

See steps

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (3*a+1)/7-(4)=0  

Step by step solution :

STEP

1

:

           3a + 1

Simplify   ——————

             7    

Equation at the end of step

1

:

 (3a + 1)    

 ———————— -  4  = 0  

    7        

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  7  as the denominator :

        4     4 • 7

   4 =  —  =  —————

        1       7  

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Add the two equivalent fractions which now have a common denominator

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————————————————  =  ———————

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STEP

3

:

Pulling out like terms

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Equation at the end of step

3

:

 3 • (a - 9)

 ———————————  = 0  

      7      

STEP

4

:

When a fraction equals zero

4.1    When a fraction equals zero ...

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 ——————— • 7 = 0 • 7

    7    

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Equations which are never true:

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Solving a Single Variable Equation:

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Answers

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Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of -36.14 degrees Celsius and a boiling point of 324.84 degrees Celsius . What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid​ state?

Answers

Answer:

i. When the temperature is above [tex]616.712^{o}[/tex]F, it changes to gas.

ii. When the temperature is below [tex]-33.052^{o}[/tex]F, it changes to solid.

Step-by-step explanation:

Matter generally exists in either a solid, liquid or gaseous form. With each phase having a certain range of temperature.

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Given that: melting point of the substance = [tex]-36.14^{o}[/tex]C

⇒ F =  [tex]\frac{9}{5}[/tex] x [tex]-36.14^{o}[/tex] + 32

      = [tex]-33.052^{o}[/tex]F

The boiling point = [tex]324.84^{o}[/tex]C

F =  [tex]\frac{9}{5}[/tex] x  [tex]324.84^{o}[/tex] + 32

  = [tex]616.712^{o}[/tex]F

The melting point of the substance is [tex]-33.052^{o}[/tex]F, and boiling point is [tex]616.712^{o}[/tex]F.

Therefore, the range of temperatures for which the substance is not in a liquid state are:

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ii. When the temperature is below [tex]-33.052^{o}[/tex]F, it changes to solid.

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Answers

Answer: A) True because the leading coefficient is negative

Explanation:

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The leading coefficient is -1 as it's the coefficient of the leading term.

It might help to write -x^2 as -1x^2

The negative leading coefficient makes the parabola open downward, so each endpoint goes off to negative infinity. The graph looks like a frowny face. You can think of a negative emotion going with a frowny face, so that negative emotion matches with the negative leading coefficient. There are probably other ways to remember but that's the trick I use.

715,000___7.15 x 10^5
>
<
=

Answers

7.15 x 10^5 is 715,000 so they are equal

John took all his money from his savings account. He spent 198 on a radio and 4/12 of what was left on presents for his friends. Of the money remaining, John put 2/9 into a checking account and the last remaining 980 was left to charity. How much money did John originally have in his savings account?

Answers

Answer:

John had $2088 originally in his savings accounts.

Step-by-step explanation:

Let John had $x originally in his saving account

He spent $198 on a radio. The remaining money = x - $198

4/12 of what was left, he spent on presents for his friends. Remainig money = x - 198 - 4/12*(x-198)

= (1 - 4/12) of (x-198)

= 2/3 of (x-198)

John then put 2/9 if his remaining money into a checking account.

Now, the remaining money = 2/3*(x-198) - 2/9 of (x-198)

= (1 - 2/9) * 2/3*(x-198)

= 7/9 * 2/3*(x-198)

= 14/27(x-198)

Money left with him = $980

14/27(x-198) = $980

x - 198 = $980 * 27 / 14

x - 198 = 1890

x = 1890 + 198

x = 2088

Hence, John had $2088 originally in his savings accounts.

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