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2 years ago

Write a recursive rule and explicit rule for the arithmetic sequence 19,9,-1,-11, ...

1 answer:

6 0

★ Arithmetic Progression [ Explicit and Recursive notation ] ★

Arithmetic Sequence - 19 , 9 , -1 ...

Recursive Notation -

First term = 19
Common difference = -10

In subscript notation - [ a₁ = 19 , aₙ = aₙ-₁ -10 ]
In functional notation - f(n) = f (n -1) -10

Explicit Notation - f ( n ) = f ( 1 ) + d ( n - 1 )

= 19 - 10 ( n -1 )
= 29 - 10n

It's functional and subscript notations resides the same

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For the inverse variation function y = k/x (where x, k > 0), what happens to the value of y as the value of x increases?

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As the value of x increases, y decreases.

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What is the first step to solving this equation (5x-11=42)?

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First, you have to add 11 on both sides, so the answer is A

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The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?

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Answer:

<h2>Therefore the length of a side of a cube is $\sqrt[3]{64}\ or\ 4$ </h2>

Step-by-step explanation:

The volume of a cube is expressed as L³ where L is the length of each side of the cube.

Given volume of a cube = 64in³

On substituting;

64 = L³

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Therefore the length of a side of a cube is $\sqrt[3]{64}\ or\ 4$

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2 years ago

Which r–value represents the strongest negative correlation? –0.7 –0.22 0.38 0.9

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Answer:

Option A is correct.

The value of r = -0.7 represents the strongest negative correlation.

Step-by-step explanation:

A correlation is a value that describes a relationship between two things or variables.

Strongest Negative Correlation says that closer a negative correlation to -1, the stronger the relationship between the two variables.

From the options, we have only two negative values i.e, r= -0.7 and r= -0.22.

We have to find the strongest negative correlation r-value.

By the definition, you can see that -0.7 is very closer to -1 ,

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At 10 percent interest, how long does it take to quadruple your money?

horsena [70]

It takes about 14.55 years for quadruple your money

Solution:

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

Rule of 144 Formula:

$N = \frac{144}{R}$

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

$\rightarrow N = \frac{144}{10} = 14.4$

Thus it takes about 14.4 years for quadruple your money.

Another method:

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

$Amount = Principal(1+\frac{R}{100})^n$

$4 = 1(1+\frac{10}{100})^n$

$4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55$

Thus Option D 14.55 years is correct

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2 years ago