<span>The definition for discovering the volume of a box is when the person takes the length, the width, and the height of the box. And because we have those values here, there is no math that is necessary to do other than multiplying the numbers together and creating a new unit of inches cubed. The answer is 11040 inches cubed.</span>
Answer:
g = -3
Step-by-step explanation:
Answer:
The conclusion "T" logically follows from the premises given and the argument is valid
Step-by-step explanation:
Let us use notations to represent the steps
P: I take a bus
Q: I take the subway
R: I will be late for my appointment
S: I take a taxi
T: I will be broke
The given statement in symbolic form can be written as,
(P V Q) → R
S → (¬R ∧ T)
(¬Q ∧ ¬P) → S
¬R
___________________
∴ T
PROOF:
1. (¬Q ∧ ¬P) → S Premise
2. S → (¬R ∧ T) Premise
3. (¬Q ∧ ¬P) → (¬R ∧ T) (1), (2), Chain Rule
4. ¬(P ∨ Q) → (¬R ∧ T) (3), DeMorgan's law
5. (P ∨ Q) → R Premise
6. ¬R Premise
7. ¬(P ∨ Q) (5), (6), Modus Tollen's rule
8. ¬R ∧ T (4), (7), Modus Ponen's rule
9. T (8), Rule of Conjunction
Therefore the conclusion "T" logically follows from the given premises and the argument is valid.
Answer:
1) B. The height appear to be reported because there are disproportionately more 0s and 5s.
2) A. They are likely not very accurate because they appear to be reported.
Step-by-step explanation:
The distribution table is shown below:
Last Digit Frequency
0 9
1 1
2 1
3 3
4 1
5 11
6 1
7 0
8 3
9 1
1. Based on the distribution table, we see a very disproportionate distribution. There is a high frequency of 0's and 5's. This lays credence to the heights being reported rather than measured. As such, option B is the correct answer
<u>B. The height appear to be reported because there are disproportionately more 0s and 5s</u>.
2. Since the heights were reported and not measured, they are most certainly not accurate. The conclusion is that the result is not accurate. As such, option A is the correct answer
<u>A. They are likely not very accurate because they appear to be reported</u>.
Part (i)
I'm going to use the notation T(n) instead of 
To find the first term, we plug in n = 1
T(n) = 2 - 3n
T(1) = 2 - 3(1)
T(1) = -1
The first term is -1
Repeat for n = 2 to find the second term
T(n) = 2 - 3n
T(2) = 2 - 3(2)
T(2) = -4
The second term is -4
<h3>Answers: -1, -4</h3>
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Part (ii)
Plug in T(n) = -61 and solve for n
T(n) = 2 - 3n
-61 = 2 - 3n
-61-2 = -3n
-63 = -3n
-3n = -63
n = -63/(-3)
n = 21
Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).
<h3>Answer: 21st term</h3>
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Part (iii)
We're given that T(n) = 2 - 3n
Let's compute T(2n). We do so by replacing every copy of n with 2n like so
T(n) = 2 - 3n
T(2n) = 2 - 3(2n)
T(2n) = 2 - 6n
Now subtract T(2n) from T(n)
T(n) - T(2n) = (2-3n) - (2-6n)
T(n) - T(2n) = 2-3n - 2+6n
T(n) - T(2n) = 3n
Then set this equal to 24 and solve for n
T(n) - T(2n) = 24
3n = 24
n = 24/3
n = 8
This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.
<h3>Answer: 8</h3>
