The Mill Valley Brewery produces 32 ounce bottles of beer. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.8 oz and a sample standard deviation of 0.75 oz. At the 5% level, is there evidence that Mill Valley Brewery is cheating customers by under-filling their bottles?

Answers

Answer 1

Answer:

Answer:

Since the calculated Z= -1.886 lies within the Z∝ = ± 1.96 we fail to reject our null hypothesis that population mean is 31.8 oz. and not 32 ounces. There is evidence that Mill Valley Brewery is cheating customers by under-filling their bottles.

Step-by-step explanation:

Let the null hypothesis be

H0 : u = 31.8 oz against Ha: u ≠ 31.8 oz two tailed test

For a two tailed test and alpha = 0.05 the z∝ = ± 1.96

The rejection region is Z ≥ ± 1.96

Here n = 50

sample mean = x= 31.8 oz

and sample standard deviation= s= 0.75

Population mean= u= 32

Test statistics to be used is

Z= x- u / s/ √n which is approximately normal

Z= 31.8-32/0.75/ √50

z= -1.886

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Find two consecutive whole numbers that 51 lies between.

Answers

Hello,

Let n and n+1 the numbers

n<=51<=n+1
51<=51<=52
50<=51<=51
2 solutions n=50 or n=51.

1/7 times x = 1
5/4 times x=1
3 1/2 times x=1
5/7 times x=1

Answers

( i )

$= > (1)/(7) * x = 1 \n \n \n \n = > (1)/(7) * 7 * x = 1 * 7 \n \n \n \n = > x = 7$

( ii ) :

$= > (5)/(4) * x = 1 \n \n \n \n = > (5)/(4) * (4)/(5) * x = 1 * (4)/(5) \n \n \n \n = > x = (4)/(5)$

( iii ) :

$= > 3(1)/(2) * x = 1 \n \n \n \n = > (7)/(2) * x = 1 \n \n \n \n = > (7)/(2) * (2)/(7) * x = 1 * (2)/(7) \n \n \n \n = > x = (2)/(7)$

( iv ) :

$(5)/(7) * x = 1 \n \n \n \n = > (5)/(7) * (7)/(5) * x = 1 * (7)/(5) \n \n \n \n = > x = (7)/(5)$

How do you solve 2(10-6x)=x-8x
Show work

Answers

2(10)-2(6x)= x-8x
20-12x=x-8x
+12x+12x

20=13x-8x
20=5x
4=x

Hey, Lizzy147!
1st. Distribute 2 to 10 and -6x
20-12x=x-8x
2nd. Move -12x to the other side.
20=13x-8x
Simple math.
20=5x
x=4

If a rectangle measures 54 meters by 72 meters, what is the length, in meters, of the diagonal of the rectangle?Can someone explain this one?

Answers

Use the Pythagoras therom.
let the diagonal be x
⇒54²+72²=x²
⇒8100=x²
x=90meters

let the diagonal be a.
now, as we know that each angle in a rectangle is right angle.
thus we have a right angled triangle.
now, we can apply pythagoras theorum.
a^2 = 54^2 + 72^2
= 2916 + 5184
=8100
thus, a^2 = 8100
thus, a = 90.
Thus the diagonal is 90metres.

What three even numbers add up to 54

Answers

The way I like to do these is like this ... without algebra:

-- If the 54 were split up into three equal pieces,
each piece would be 1/3 of 54 = 18 .

-- Can you take three equal size-18 pieces and change them in
such a way that they're all different but their sum doesn't change,
and they still add up to 54 ?

-- How about like this:
Take 2 away from one piece and glue it onto a different one.
Now they still make the same 54 when you put them all into the same pot.
But now they're all different ... instead of 18, 18, 18, now you have 16, 18, 20.

Look ma ! No algebra !

x = lowest
x+2 = middle
x+4 = largest

x + x+2 + x + 4 = 54

Combine like terms to get 3x + 6 = 54
Subtract 6 (both sides) -6 -6
3x = 48
divide by 3 (both sides) 3 3

x = 16 (smallest even number) x+2 = 18 (middle even number and x+4 = 20 (largest even number) Add them up 16+18+ 20 and sure enough, you get 54

A catering company charges a $300 set up fee and $10 per person for a lunch buffet. Approximately how many people must attend the lunch so that the total cost per person is $14?