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Wewaii [24]
3 years ago
13

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfill

ing or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct alternative hypotheses is
a. The average is greater than or equal to 12 ounces.
b. The average is not equal to 12 ounces.
c. The average is less than 12 ounces.
d. The average is equal to 12 ounces.
Mathematics
1 answer:
gavmur [86]3 years ago
5 0

Answer:

b. the average is not equal to 12 ounces.

Step-by-step explanation:

a and is incorrect because being equal to 12 ounces is what we want.

c  - we want to look for greater than 12 as well as less than.

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1. Which of the following systems is consistent and dependent?
Kamila [148]

Answer:

Choice d.

Step-by-step explanation:

Consistent means the linear functions will have at least one solution.

Independent means the it will just that one solution.

Dependent means the system will have infinitely many solutions.

So we are looking for a pair of equations that consist of the same line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

If m and b are the same amongst the pair, then that pair is the same line and the system is consistent and dependent.

If m is the same and b is different amongst the pair, then they are parallel and the system will be inconsistent (have no solution).

If m is different, then the pair will have one solution and will be consistent and independent.

---------------------------

Choice A:

First line has m=1 and b=4.

Second line has m=1 and b=-4.

These lines are parallel.

This system is inconsistent.

Choice B:

First line is x+y=4 and it isn't in y=mx+b form.

Second line is 2x+2y=6 and it isn't in y=mx+b form.

These lines do have the same form though. This is actually standard form.

If you divide second equation by 2 on both sides you get:  x+y=3

The lines are not the same.

We are looking for the same line.

Now we could go ahead and determine to call this system.

If x+y has value 4 then how could x+y have value 3.  It is not possible. There is no solution. These lines are parallel.

Need more convincing. Let's put them into slope-intercept form.

x+y=4

Subtract x on both sides:

y=-x+4

m=-1 and b=4

x+y=3

Subtract x on both sides:

y=-x+3

m=-1 and b=3.

The system is inconsistent because they are parallel.

Choice c:

I'm going to go ahead in put them both in slope-intercept form:

3x+y=3

Subtract 3x on both sides:

y=-3x+3

So m=-3 and b=3

2y=6x+6

Divide both sides by 2:

y=3x+3

So m=3 and b=3

The m's are different so this system will by consistent and independent.

Choice d:

The goal is the same. Put them in slope-intercept form.

4x-2y=6

Divide both sides by -2:

-2x+y=-3

Add 2x on both sides:

y=2x-3

m=2 and b=-3

6x-3y=9

Divide both sides by -3:

-2x+y=-3

Add 2x on btoh sides:

y=2x-3

m=2 and b=-3

These are the same line because they have the same m and the same b.

This system is consistent and dependent.

8 0
3 years ago
If ³√a=am , what is m​
Zina [86]

\sqrt[3]{a}  =  {a}^{m}  \\  =  >  { a}^{ \frac{1}{3} }  =  {a}^{m}  \\  =  > m =  \frac{1}{3}

<u>Answer</u><u>:</u>

<u>m =  \frac{1}{3}</u>

Hope you could understand.

If you have any query, feel free to ask.

8 0
2 years ago
Please help and thank you
Scorpion4ik [409]

Answer:

a

Step-by-step explanation:

6 0
2 years ago
Alicia bought a frozen lemonade for $3.71. She gave the clerk a $5 bill. How much change should she receive?
Grace [21]
5 - 3.71 = $1.29
hope this helps! :)
8 0
2 years ago
Read 2 more answers
In a particular class, exams are worth 50% of the overall grade, quizzes are worth 30% of the overall grade, homework is worth 1
Paha777 [63]

Answer:

The student's overall grade is 85.79%

Step-by-step explanation:

Given in the question that:

Exam = 50%; Quiz = 30%, Home work = 15% and Class participation = 5%

The total giving us 100%.

A particular student scored the following;

87.9% on exams, 77.8% quiz, 90% Home work and 100%  on class participation

Calculating the percentages the student had for each;

Exam total = 50*0.879 = 43.95% earned

Quiz = 30*0.778 = 23.34% earned

Home work = 15*0.9 = 13.5% earned

Class participation = 5*1 = 5% earned

Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%

3 0
3 years ago
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