we are given
6 × 8 = 48
we know that
commutative property of multiplication:
now, we will verify each options
option-A:
we have
6 × 8 = 48
now, we can find it's commutative
so, we get
8 × 6 = 48
so, this is TRUE
option-B:
we have
6 × 8 = 48
now, we can find it's commutative
so, we get
8 × 6 = 48
so, this is FALSE
option-C:
we have
6 × 8 = 48
now, we can find it's commutative
so, we get
8 × 6 = 48
so, this is FALSE
Answer:
Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.
Step-by-step explanation:
Let us assume the time taken by Dwight to split a cord of firewood = K hrs
So, the per hour rate of Dwight =
As, Joe uses 3 LESS hours then Dwight.
So, the time taken by Joe to split a cord of firewood = (K- 3) hrs
So, the per hour rate of Joe =
Now, when both of them wok together, it takes them 2 hours.
So, the per hour rate of BOTH of them =
⇒ Per hour rate of ( Dwight + Joe) =
Now, solving for the value of K , we get:
Implies either K = 6 Or K = 1
But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.
⇒ K = 6 hours
Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.
Answer:
The 95% confidence interval would be given by (122;138)
And the correct interpretation for this case is:
c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % where by a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that
Now we have everything in order to replace into formula (1), for this case we got:
The 95% confidence interval would be given by (122;138)
And the correct interpretation for this case is:
c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.