Answer:
84.13% of bottles will have volume greater than 994 mL
Step-by-step explanation:
Mean volume = u = 1000
Standard deviation = 
= 6
We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.
x = 994
Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:
Substituting the values, we get:
This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.
i.e. P(z > -1)
From the z-table this value comes out to be:
P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:
P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%
Answer:
He use 97 pound of type A coffee
Step-by-step explanation:
Let's call A the pounds of type A coffee that Austin used this month and B the pounds of type B coffee that Austin used this month.
From the sentence: Type A coffee costs bill $5.70 per pound and type B coffee costs $4.65 per pound and the total cost is $943.50, we can formulated the equation 1 as:
5.70*A + 4.65*B=943.50
Because the total cost is the sum of the cost of every type of coffee.
Additionally, from the sentence: This month bill made 181 pounds of the blend, we can formulate the equation 2 as:
A + B = 181
Solving for B, we get:
B = 181 - A
Now, for find the value of A we need to replacing this last equation on equation 1, and solving for A as:
5.70*A + 4.65*B=943.50
5.70*A + 4.65*(181-A)=943.50
5.70*A + 841.65 - 4.65*A = 943.50
5.70*A - 4.65*A = 943.50 - 841.65
1.05*A = 101.85
A = 101.85/1.05
A = 97
So, this month, he use 97 pound of type A coffee.
Your answer is 45 meters.
We can find this because we know that the total length of the track is 100 meters. Since Juliet starts at the 10 meter mark, she only has 90 meters left to run.
Then, she runs for 45 meters, which brings her to a total of 55 meters on the track. This means that to find how much she has left we just do 100 - 55 = 45 meters.
I hope this helps!
Answer:
The factored form of the equation is (x+4)(x-6)=0.
Step-by-step explanation:
Because (x-4)(x+2)=x^2-4x+2x-8=16,
so that means x^2-2x-8=16,
move 16 to the other side,
you get x^2-2x-8-16=0,
simplify,
you get x^2-2x-24=0,
which satisfies (x+4)(x-6)=0 when factored out.
Because (x+4)(x-6)=x^2+4x-6x-24=x^2-2x-24=0.
