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Inga [223]
3 years ago
8

Simplify the expression 8^5/3

Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

Answer:

10992 2/3

Step-by-step explanation:

Hello!

8^{5} = 32768. \\$32768 \div$ 3: \\\\10922\quad{\text{Remainder}\quad \:2.

{\text{We can also represent this as\:} 10922 \: \frac{2}{3}.

Thus, the simplified version is \boxed{10922 \frac{2}{3}}.

Hope this helps!

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What is the vertex of the graph y = x^2 + 6x - 5 ?
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Given:  <span>y = x^2 + 6x - 5.  Then a = 1, b = 6 and c = -5.

The x-coord. of the vertex is given by x = -b / (2a), which here is x = -6 / (2*1) = -3.

Use the given formula </span><span>y = x^2 + 6x - 5 to find the value of y when x = -3:

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3 years ago
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the popu
tia_tia [17]

Answer:

The minimum head breadth that will fit the clientele is 4.4 inches.

The maximum head breadth that will fit the clientele is 7.8 inches.

Step-by-step explanation:

Let <em>X</em> = head breadths of men that is considered for the helmets.

The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 6.1 and standard deviation, <em>σ</em> = 1.

To compute the probability of a normal distribution we first need to convert the raw scores to <em>z</em>-scores using the formula:

z=\frac{x-\mu}{\sigma}

It is provided that the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.

Compute the minimum head breadth that will fit the clientele as follows:

P (X < x) = 0.043

⇒ P (Z < z) = 0.043

The value of <em>z</em> for this probability is:

<em>z</em> = -1.717

*Use a <em>z</em>-table.

Compute the value of <em>x</em> as follows:

z=\frac{x-\mu}{\sigma}\\-1.717=\frac{x-6.1}{1}\\x=6.1-(1.717\times 1)\\x=4.383\\x\approx4.4

Thus, the minimum head breadth that will fit the clientele is 4.4 inches.

Compute the maximum head breadth that will fit the clientele as follows:

P (X > x) = 0.043

⇒ P (Z > z) = 0.043

⇒ P (Z < z) = 1 - 0.043

⇒ P (Z < z) = 0.957

The value of <em>z</em> for this probability is:

<em>z</em> = 1.717

*Use a <em>z</em>-table.

Compute the value of <em>x</em> as follows:

z=\frac{x-\mu}{\sigma}\\1.717=\frac{x-6.1}{1}\\x=6.1+(1.717\times 1)\\x=7.817\\x\approx7.8

Thus, the maximum head breadth that will fit the clientele is 7.8 inches.

5 0
3 years ago
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Answer:

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