$\text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. }$

question 47

Multiple Choice

$\text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. }$

• A) \(\sum _ { n = 0 } ^ { \infty } 75 \left( \frac { 1 } { 100 } \right) ^ { n }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \left( \frac { 75 } { 10 } \right) ^ { n }\)
• C)\(\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } \left( \frac { 1 } { 100 } \right) ^ { n }\)
• D)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } - \left( \frac { 1 } { 100 } \right) ^ { n }\)
• E)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } + \left( \frac { 1 } { 100 } \right) ^ { n }\)

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Definitions:

Altered States

Conditions of consciousness that differ significantly from one's normal waking state, induced by factors like meditation, drug use, or sleep.

Consciousness

The state of being aware of and able to think about one's own existence, sensations, thoughts, surroundings, etc.

Circadian Cycle

A natural, internal process that regulates the sleep-wake cycle and repeats roughly every 24 hours.

Hypothalamus

A small region of the brain located below the thalamus that plays a crucial role in many essential functions, including hormone regulation, temperature control, and hunger.