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3 years ago

100 points !!!!!!! PLZ HELP

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

Answer:1. -6 ≤ x < -1 . . . . conjunction

2. x ≤ 6 . . or . . 10 ≤ x . . . . disjunction

3. 7 ≤ x < 12 . . . . conjunction

4. x < -9 . . or . . -3 ≤ x . . . . disjunction

5. 2 ≤ x ≤ 5 . . . . conjunction

6. x ≤ 54 . . or . . 66 ≤ x . . . . disjunction

7. 39 < x ≤ 43 . . . . conjunction

Step-by-step explanation:

I'm assuming its "Pattern". This is because its in a pattern of "Conjunction, Disjunction, Conjunction, Disjunction, etc." and theres 7 letters in the word Pattern.

Usually a problem with this wording will have a list of numbers with letter designators. You find the number that is in the solution set and the corresponding letter is part of the "secret word

Strike441 [17]3 years ago

6 0

Assignment: Combined Inequalities Investigation

− 6 ≤ x < − 1

Answer - F

Conjunction

x ≤ 6 or x > 10

Answer - O

Disjunction

7 ≤ x ≤ 12

Answer - R

Conjunction

x < -9 or x ≥ -3

Answer - M

Disjunction

2 ≤ x ≤ 5

Answer - U

Conjunction

x ≤ 54 or x ≥ 66

Answer - L

Disjunction

39 < x ≤ 43

Answer - A

Conjunction

Place the letters in the box from the problems.

The secret word is Formula.

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Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$