Miniature dachshunds, a dog breed with very short legs, run at an average speed of 13 mph with a standard deviation of 1.6 mph. Labrador retrievers run at an average speed of 22 mph with a standard deviation of 2.8 mph. Both breeds' running speeds are Normally distributed. A miniature dachshund runs down a street at 14.8 mph. It is chasing a Labrador that is running 25 mph.

Complete Question

Miniature dachshunds, a dog breed with very short legs, run at an average speed of 13 mph with a standard deviation of 1.6 mph. Labrador retrievers run at an average speed of 22 mph with a standard deviation of 2.8 mph. Both breeds' running speeds are Normally distributed. A miniature dachshund runs down a street at 14.8 mph. It is chasing a Labrador that is running 25 mph, use their z-scores to find which dog is running faster relative to its breed

Miniature dachshunds is faster

Step-by-step explanation:

From the question we are told that

   The speed of the Miniature dachshunds is  

    The mean for the Miniature dachshunds is

    The standard deviation for the Miniature dachshunds is  

    The speed of the Labrador is

     The mean for the Labrador is  

    The standard deviation for the Labrador  is  

Generally the z-score for the Miniature dachshunds is

=>  

=>  

Generally the z-score for the Labrador is

=>  

=>  

From the value obtained we see that   , hence miniature dachshund  is  faster

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!