Two different box-filling machines are used to fill cereal boxes on an assembly line. the critical measurement influenced by these machines is the weight of the product in the boxes. engineers are quite certain that the variance of the weight of product is σ 2 = 8 ounces. experiments are conducted using both machines with sample sizes of 81 each. the sample averages for machines a and b are x¯ a = 7.4 ounces and x¯ b = 7.5 ounces. engineers are surprised that the two sample averages for the filling machines are different.(a) use the central limit theorem to determinep(x^b−x^a≥0.2)under the condition that μa=μb.(b) do the aforementioned experiments seem to, in anyway, strongly support a conjecture that the populationmeans for the two machines are different? explain using your answer in (a).

step-by-step explanation: a reaction is first order. if the initial reactant concentration is 0.0200 m, and 25.0 days later the concentration is 6.25 x 10-4 m, then its half-life is:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

ummm seems that u didnt post the attachement !

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.