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IRINA_888
20 days ago
8

Mr. Deets is making an array to display 9 pictures. For each pair of different factors, there are two arrays he can make. How ma

ny different arrays can Mr. Deets make ? Is the number of arrays odd or even Explain.
Mathematics
2 answers:
lawyer [9.2K]20 days ago
6 0

3 distinct arrangements - 1 x 9 (or 9 x 1) and 3 x 3

Thus, the total number of arrangements = 2 x 2 = 4 = an even count

Initially, we identify pairs of different factors of 9.

The pairs of factors for 9 are:

(1, 9) and (3, 3)

For each of these pairs, Mr. Deets can create 2 arrangements.

This means the total arrangements Mr. Deets can construct = 2 x 2 = 4, confirming that the overall number is even.

Svet_ta [9.5K]20 days ago
4 0

Answer:

4 arrangements,

The total number of arrangements is even.

Step-by-step explanation:

∵ The possible pairs of numbers that multiply to yield 9 are,

(3, 3) and (9, 1),

Thus, the possible arrangements would be,

3 × 3, 9 × 1

Note: 9 × 1 can also be expressed as 1 × 9,

According to the provided question,

For every unique factor pair, there are two possible arrangements,

3 × 3 and 9 × 1 represent two unique arrangements without shared factors,

Consequently, the total arrangements = 2 × 2 = 4

This is an even number.

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The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

\boxed{u \ or \ v_i = initial \ velocity}

\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}

\boxed{a = acceleration \ (constant)}

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We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

\boxed{ \ v^2 = u^2 + 2ad \ }

  • a = acceleration (m/s²)
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  • v = takeoff velocity = 1.0 m/s
  • d = displacement = 0.50 mm

First, convert 0.50 mm to meters: \boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}

Solution steps:

Rearrange the formula to isolate acceleration (a).

\boxed{ \ v^2 = u^2 + 2ad \ }

\boxed{ \ v^2 - u^2 = 2ad \ }

\boxed{ \ 2ad = v^2 - u^2 \ }

\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }

Insert the given values into the rearranged equation.

\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }

\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }

\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }

\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }

This yields the flea's acceleration as 1,000 m/s².

Additional resources

  1. Scientific notation: brainly.com/question/7263463
  2. Determining substance mass: brainly.com/question/4053884
  3. Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

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