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Sholpan [36]
3 years ago
15

What do these mean?

Mathematics
1 answer:
posledela3 years ago
7 0

Answer:

They sound like objectives for a unit of a math or economics class.

Step-by-step explanation:

Data collection would most likely mean analyzing collected data (looking for trends).

Constructing graphs would probably mean making graphs from a set of data (plotting the information).

Interpreting graphs would mean the opposite of the above definition: would look at a graph and then put that information into written form/

Drawing a line of best fit means making a line on a graph that represents the average of all of the data on the graph.

I hope that this helps!

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What is the equation of the line with a slope of -3 and passes through the point (-6,-3)
Taya2010 [7]

Answer:

f(x) = -3x - 21

Step-by-step explanation:

Graphed this equation and it passes through (-6, -3), also known as Point A.

7 0
2 years ago
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
Viktor [21]

When n=0, we have

5^{3^0} + 1 = 5^1 + 1 = 6

3^{0 + 1} = 3^1 = 3

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for n=k, that

3^{k + 1} \mid 5^{3^k} + 1

Now for n=k+1, we have

5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)

so we know the left side is at least divisible by 3^{k+1} by our assumption.

It remains to show that

3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1

which is easily done with Fermat's little theorem. It says

a^p \equiv a \pmod p

where p is prime and a is any integer. Then for any positive integer x,

5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3

Furthermore,

5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3

which goes all the way down to

5^{3^k} \equiv 5 \pmod 3

So, we find that

\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3

QED

5 0
1 year ago
Positive fractions less than 1 with an interval of 1/8 between each pair of fractions
lesya692 [45]

(1/8), (2/8), (3/8), (4/8), (5/8), (6/8), (7/8)

if u want, 2/8=1/4, 4/8=1/2, 6/8=3/4

3 0
3 years ago
Gail practices swimming for 1 and 1 fourth hours swimming every day how much time does she practice in a week
Lorico [155]
If Gail practises swimming for 1 and 1/4 hours a day, then in a week she'll do:

1 1/4 * 7 = 5/4 * 7 = 35/4 = 8 3/4 [hours]

In other words she'll practice 8 hours and 45 minutes a week (assuming that she's still practicing on weekends).
8 0
3 years ago
Please Help need help
velikii [3]

You would round up 58 to 60 and round down for 93 to 90 and round up to 1.5 so the answer is D.


5 0
3 years ago
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