The sides of the box are 12in by 12in by 30in.
The interior diagonal =[12^2+12^2+30^2]0.5
=[144+144+900]^0.5
=1188^0.5
The final answer is 34.47in.
My deepest apology if this is not what you meant.
= 34.47in.
Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
Answer:
Step-by-step explanation:
42/14 = 57/x
42x = 57*14
42x = 798
x = 19 months
Starting off, we can multiply the third equation by 2 and add it to the third to get rid of both the x and y variables. Next, we get z=1. Plugging that into 3y-5z=-23, we get 3y-5=-23. Adding 5 to both sides, we get 3y=-18. After that, we can divide both sides by 3 to get y=-6. Plugging that into -2x-y-z=-3, we get -2x+6-1=-3=-2x+5. Subtracting 5x from both sides, we get -2x=-8. After that, we can divide both sides by -2 to get x=4.
The statement which best describes the association between the variables X and Y is the <em>moderate positive association</em>. It is observable that the values of X and Y are increasing, however, not in a perfect manner as there are some minor deviations. But nonetheless, the direction is clear and the values are close to each other so they have a moderate positive association.
