G how many distinct ordered arrangements of the letters of the word boogaboo can be made?

1 answer:

3 0

In the word "boogaboo", there are eight (8) letters while there are only four distinct letters. The number of distinct ordered arrangements can be calculated through the equation,

n = 8!/(2!)(4!)

where there are 2 letter b's and 4 letter o's. The answer to this item is 840.

Answer: 840

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Rich makes $12.50 an hour. If Rich works 56 hours in one week, how much would he earn for the week?

Roman55 [17]

The answer should be $700

Because $12.50 · 56 = $700

7 0

3 years ago

What is the simplified expression for,

Nostrana [21]

Here are a few rules you need to know for this equation:

Multiplying exponents of the same base: $x^m\times x^n=x^{m+n}$
Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
Turning a negative exponent to a positive one: $x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m$

So this is our algebraic expression: $\frac{3^{-4}\times 2^3\times 3^2}{2^4\times 3^{-3}}$

Firstly, multiply 3^-4 and 3^2: $\frac{3^{-4+2}\times 2^3}{2^4\times 3^{-3}}=\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}$

Next, divide:

$\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}=3^{-2-(-3)}2^{3-4}=3^12^{-1}$

Next, turn the negative exponent into a positive one: $3^12^{-1}= \frac{3}{2}$

<u>Your final answer is 3/2, or 1.5.</u>

6 0

2 years ago

Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.

jek_recluse [69]

Answer:

Choice B: $y = 2\, (x - 6)^{2} + 5$ .

Step-by-step explanation:

For a parabola with vertex $(h,\, k)$ , the vertex form equation of that parabola in would be:

$\text{$y = a\, (x - h)^{2} + k$ for some constant $a$}$ .

In this question, the vertex is $(6,\, 5)$ , such that $h = 6$ and $k = 5$ . There would exist a constant $a$ such that the equation of this parabola would be:

$y = a\, (x - 6)^{2} + 5$ .

The next step is to find the value of the constant $a$ .

Given that this parabola includes the point $(7,\, 7)$ , $x = 7$ and $y = 7$ would need to satisfy the equation of this parabola, $y = a\, (x - 6)^{2} + 5$ .