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3 years ago

Rewrite using factors and exponents, then simplify 1. 1000/100 2. 9/81 3. 4/64

1 answer:

4 0

1) 1000 / 100 ⇒ 10 / 1 = 10
1000 ÷ 100 = 10
100 ÷ 100 =   1

2) 9/81 ⇒ 1/9
  9 ÷ 9 = 1
81 ÷ 9 = 9

3) 4/64 ⇒ 1/16
  4 ÷ 4 =   1
64 ÷ 4 = 16

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Suppose that a box contains 7 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random without repl

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Answer:

E(x) = 1.43 (Approx)

Step-by-step explanation:

Given:

Total number of camera = 7

Defective camera = 5

Sample selected = 2

Computation:

when x = 0

P(x=0) = 2/7 × 1/6 = 2/42

P(x=1) = [2/7 × 5/6] + [5/7 × 2/6] = 20/42

P(x=2) = 5/7 × 4/6 = 20/42

So,

E(x) = [0×2/42] + [1×20/42] + [2×20/42]

E(x) = 1.43 (Approx)

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Answer:

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Step-by-step explanation:

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2 years ago

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AleksandrR [38]

It will be 5 cm and use 3.14 to multiply

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1 year ago

The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

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3 years ago

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Fittoniya [83]

Answer:

They give evidence of cultural, religious, or social characteristics of the people

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