A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The missing value in the table below is 343. The correct option is A.
<h3>What is geometrical series?</h3>
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given table if closely observed forms a geometric progression, this is because the value of the dependent variable, y is increasing by a common ratio. The common ratio in the table is,
Common ratio = y₂/y₁ = 1/(1/7) = 7
Now, for any geometric progression, the value of the nth term is given as,
Tₙ = a₁ (r)⁽ⁿ⁻¹⁾
where a₁ is the first term of the geometric progression and r is the common ratio. Therefore, the nth term of the series is,
T = a₁ (r)⁽ⁿ⁻¹⁾
Tₙ = (1/7) (7)⁽ⁿ⁻¹⁾
y = (1/7)(7)⁽ˣ⁻¹⁾
Now, the value of the y when the value of x is 5 is,
y = (1/7)(7)⁽ˣ⁻¹⁾
y = (1/7)(7)⁽⁵⁻¹⁾
y = (1/7)(7)⁴
y = (1/7) × 2401
y = 343
Hence, the missing value in the table below is 343.
Learn more about Geometrical Series here:
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Answer:
1.5 nautical miles
Step-by-step explanation:
See the attached diagram.
The submarine starts to dive at point A and diving along AB.
If the distance traveled underwater i.e. AB = 1.7 Nautical miles and C is the point directly above its current position at B.
Then Δ ABC is a right triangle having ∠ BAC = 28° {Given}
So, using trigonometry we can write
⇒ 
nautical miles.
Therefore, the surface distance that the submarine travels is 1.5 nautical miles. (Answer)
Answer:
6 times
Step-by-step explanation:
Let the number of times you visit the pool = x
At a local swim club you can purchase an annual membership for 24 dollars which will allow you 1 dollar admission to the pool all summer.
= $24 + $1× x
= 24 + x
If you do not purchase the membership the pool admission is 5 dollars.
= 5 × x
= 5x
Hence:
24 + x = 5x
Collect like terms
24 = 5x - x
4x = 24
x = 24/4
x = 6 times
The number of times you must visit the pool with a membership that would equal the cost of paying full price is 6 times.
Some examples of multiples of 2/5 are 4/10, 6/15, 8/20, 10/25, 12/30, and 14/35.
