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:
Extra 4 cups to make up 11 cups a day
Step-by-step explanation:
Here we have that Jan obtains 15% of her fluid needs from food, therefore, she gets the remaining 85 % from drinking water
If the recommended daily intake = 2.7 liters or 91.3 oz
And she already consumes 48 oz of water and 16 oz of milk
Note milk is equivalent to 0.87 water therefore total intake = 48 + 16*0.87= 61.92 oz
She needs to take additional (91.3 - 61.92) = 29.4 oz or 3.68 ≈ 4 cups extra to meet her recommended daily dosage.
Answer:
1.) .399
2.) {.369, .429}
Step-by-step explanation:
The proportion of criminals in this sample that were caught was 
=.39944, .399 rounded to three decimal places.
To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.
The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.
The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.
Finally, we need the standard error. The formula for standard error for a proportion with a single population is 
so in this situation it would be 
=.0183.
The confidence interval would be .399±.018×1.645 or .399±.030 {.369, .429}
3 goes into 81, 27 times.
