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2 years ago

The length of a field in yards is a function f( n ) of the the length in n feet. Write a function rule for this situation.

Mathematics

1 answer:

Phantasy [73]2 years ago

4 0

Answer:

$f(n)=\frac{1}{3}n$

Step-by-step explanation:

To convert from feet to yards, divide by the value 3.

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What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

olga nikolaevna [1]

5(x-2)(x+4)>0 For this to be true, both parenthetical terms must be both positive or both negative.

x<-4 and x>2

x=(-oo,-4),(2,+oo)

6 0

2 years ago

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The numbers of teams remaining in each round of a single-elimination tennis tournament represent a geometric sequence where an i

Anit [1.1K]

Answer:

$a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}$

Step-by-step explanation:

We are given the following in the question:

The numbers of teams remaining in each round follows a geometric sequence.

Let a be the first the of the geometric sequence and r be the common ration.

The $n^{th}$ term of geometric sequence is given by:

$a_n = ar^{n-1}$

$a_4 = 16 = ar^3\\a_6 = 4 = ar^5$

Dividing the two equations, we get,

$\dfrac{16}{4} = \dfrac{ar^3}{ar^5}\\\\4}=\dfrac{1}{r^2}\\\\\Rightarrow r^2 = \dfrac{1}{4}\\\Rightarrow r = \dfrac{1}{2}$

the first term can be calculated as:

$16=a(\dfrac{1}{2})^3\\\\a = 16\times 6\\a = 128$

Thus, the required geometric sequence is

$a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}$

4 0

3 years ago

A typical middle-income household in 1980 earned $34,757. A similar household in 2009 earned $38,550. What was the relative incr

S_A_V [24]

Given conditions are :

In 1980's, a typical middle-income household earned= $34,757

In 2009, a similar middle-income household earned= $38,550

And we have to find relative increase in income for these households from 1980 to 2009.

So first we will find the total increase in amounts.

$38550-34757=3793$

Relative increase = $\frac{3793}{34757}*100$

= 10.91% or rounding it off we get approx 11%.

Hence, the answer is 11%.

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3 years ago

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Find all the real fourth roots of 4096

goldfiish [28.3K]

Answer:

The square root of 4096 is 64. The cube root of 4096 is 16. The fourth root of 4096 is 8 and the fifth root is 5.2780316430916.

Step-by-step explanation:

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2 years ago

If you continue adding fractions according to this pattern when will you reach a sum of 2?

mr Goodwill [35]

Answer:

You will never be able to reach the sum of 2

Step-by-step explanation:

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2 years ago