Answer:
The value of the test statistic is 
Step-by-step explanation:
The formula for the test statistic is:

In which X is the statistic,
is the mean,
is the standard deviation and n is the number of observations.
In this problem, we have that:

So



The value of the test statistic is 
Dont cheat do it your self
Answer:
Step-by-step explanation:
Our equations are

Let us understand the term Discriminant of a quadratic equation and its properties
Discriminant is denoted by D and its formula is

Where
a= the coefficient of the 
b= the coefficient of 
c = constant term
Properties of D: If D
i) D=0 , One real root
ii) D>0 , Two real roots
iii) D<0 , no real root
Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .
Let us start with

Hence we have two real roots for this equation.


Hence we do not have any real root for this quadratic

Hence D>0 and thus we have two real roots for this equation.

Hence we have one real root to this quadratic equation.
Answer:
32 pavers
Step-by-step explanation:
step 1
Find out the area of one square paver
The area of a square is

where
s is the length side of the square
we have

substitute

step 2
Find out the area of the rectangular patio
we know that
The area of a rectangle is

we have

substitute

step 3
Find out the number of pavers needed to build the patio
Divide the area of the rectangular patio by the area of one paver

The equation of a circle:

(h,k) - the coordinates of the centre
r - the radius
The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:

(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

The centre of the circle is (2,5).
The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:


The radius is 5.