Answer:
H0: p ≥ 0.03 Ha: p < 0.03
Step-by-step explanation:
1) Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
2) Solution to the problem
On this case we want to test is
, where:
represent the true proportion for the population of broken pieces
What we want to proof need's to be on the alternative hypothesis and the complement on the null hypothesis.
So the correct system of hypothesis for this case would be:
Null hypothesis:
Alternative hypothesis:
H0: p ≥ 0.03 Ha: p < 0.03
Answer:
is the required inequality
Step-by-step explanation:
Let the number of songs = m.
The cost of downloading 1 songs = $1.29
So, the cost of downloading 'm' songs =
dollars
Since, the maximum amount she can spend on downloading songs is $20.
So, we get the inequality, 
Hence, the inequality representing the situation is
.
Answer:
The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using "a. existential" generalization
Step-by-step explanation:
In predicate logic, existential generalization is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier in formal proofs.
Answer: Chuck can paint 65 posts per hour.
Step-by-step explanation:
The data we have here is:
Diana can paint 150 fence posts in a time T
Chuck can pint 130 fence posts in a time T.
In one hour, Diana can paint 10 more fence posts than Chuck.
If D is the hourly rate of Daian, and C is the hourly rate for Chuck, we have:
D = 150/T
C = 130/T
D = C + 10
we can replace the last equation in the first one and geT:
C + 10 =150/T
C = 130/T
Now we can replace the bottom equation in the above one:
130/T + 10 = 150/T
10 = 150/T - 130/T = 20/T
T*10 = 20
T = 20/10 = 2
So T is 2 hours, then whe have:
D = 150post/2hours = 75 posts per hour.
C = 130 posts/2hours = 65 posts per hour.