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Burka [1]
3 years ago
11

Determine the number of terms n in each geometric series. 13) a1 = 0.75, r = 4, Sn =1023.75

Mathematics
1 answer:
Gnom [1K]3 years ago
5 0

Answer:

Number of terms: n=6

Step-by-step explanation:

We are given:

a₁ = 0.75

r = 4

Sₙ = 1023.75

We need to find number of terms i.e n

The formula used will be:S_n=\frac{a(r^n-1)}{r-1}

Putting values and fining n

S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096

We know that 4^6= 4096

4^n=4^6

Using Exponent rule: a^n=a^b => n=b

n=6

So, Number of terms: n=6

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Which of the following BEST defines an output? please help me, I've been stuck on this one for a while!​
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A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

<h3>What is a function?</h3>

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

<h3>The types of function.</h3>

In Mathematics, there are different types of functions and these include the following;

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In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

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Step-by-step explanation:

first caseworker = 15 active cases

second caseworker = 2 x number of active cases

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7 0
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