Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then sele
ct none.
When m1 = mB
ab//dc
ad//bc
or
none
When m1 = mB
ab//dc
ad//bc
or
none
2 answers:
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Answer:
The probability that the quality control manager will shut down the machine is 0.0002.
Step-by-step explanation:
We are given that a machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The target mean fill volume is µ = 2.0 liters.
A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.
<u><em>Let </em></u><u><em> = sample mean fill volume</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean fill volume = 2 liters
= standard deviation = 0.05 liters
n = sample of bottles = 50
Now, it is provided that he will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.
- So, Probability that the sample of these 50 bottles is less than 1.95 is given by = P(
< 1.95)
P( < 1.95) = P(
<
) = P(Z < -7.07) = 1 - P(Z
7.07)
= 1 - 0.9999 = 0.0001
- Probability that the sample of these 50 bottles is greater than 2.1 is given by = P(
P( > 2.1) = P(
>
) = P(Z > 14.14) = 1 - P(Z < 14.14)
= 1 - 0.9999 = 0.0001
Because the highest critical value in the z table is given as x = 4.40 for area of 0.99999.
Therefore, probability that the quality control manager will shut down the machine = 2 0.0001 = 0.0002.
The picture in the attached figure
we know that
If line GJ bisects the angle FGH, that means we also know that the angle FGH is divided into two equal sizes.
Now, we have
Angle FGJ = Angle HGJ
Angle GJF = Angle GJH
This information means that angle GHJ = angle GFJ
We have two congruent right-angled triangle
We can then further deduce that
Side GF = Side GH
Since triangle FGJ and triangle GJH are congruent,
then
side FJ equals to side JH
3x-8=16
3x=16+8
3x=24
x=8 units
Hence,
the length of FH = 2×8=16 units
the answer is
FH=16 units
we know that
If line GJ bisects the angle FGH, that means we also know that the angle FGH is divided into two equal sizes.
Now, we have
Angle FGJ = Angle HGJ
Angle GJF = Angle GJH
This information means that angle GHJ = angle GFJ
We have two congruent right-angled triangle
We can then further deduce that
Side GF = Side GH
Since triangle FGJ and triangle GJH are congruent,
then
side FJ equals to side JH
3x-8=16
3x=16+8
3x=24
x=8 units
Hence,
the length of FH = 2×8=16 units
the answer is
FH=16 units