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3 years ago

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

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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

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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).

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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.

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3 years ago