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krok68 [10]
2 years ago
7

In a geometric sequence, the ratio between consecutive terms is...

Mathematics
1 answer:
Leokris [45]2 years ago
6 0
<h3>Answer: The same or equal</h3>

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

  • 6/3 = 2
  • 12/6 = 2
  • 24/12 = 2
  • 48/2 = 2

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

You might be interested in
What is the circumference of a circle with radius pi?​
vfiekz [6]

Answer:

2π² or 19.74

Step-by-step explanation:

  • <em>Circumference of a circle is C = 2πr</em>

Given r = π

<u>Then</u>:

  • C= 2π*π = 2π²

or

  • ≈19.74
6 0
3 years ago
Previous
worty [1.4K]

No change in area

Step-by-step explanation:

The area is 60 square feet for both rectangles.

4 0
2 years ago
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x
natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

       P(a < X < b) =  \int_{a}^{b} \frac{2}{x^{3}} dx = 2\int_{a}^{b} x^{-3} dx

                            = 2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx    { Because \int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a }

                            = 2[ \frac{x^{-2} }{-2}]^{b}_a = \frac{2}{-2} [ x^{-2} ]^{b}_a

                            = -1 [ b^{-2} - a^{-2}  ] = \frac{1}{a^{2} } - \frac{1}{b^{2} }

a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }

     Comparing with general probability we get,

     P(1 < X < 5) = \frac{1}{1^{2} } - \frac{1}{5^{2} } = 1 - \frac{1}{25} = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/8^{2} - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = \frac{1}{6^{2} } - \frac{1}{10^{2} } = \frac{1}{36} - \frac{1}{100 } = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

                                = (\frac{1}{1^{2} } - \frac{1}{6^{2} }) + (1/10^{2} - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

               ⇒  P(1 < X < x) = 0.75

               ⇒  \frac{1}{1^{2} } - \frac{1}{x^{2} } = 0.75

               ⇒  \frac{1} {x^{2} } = 1 - 0.75 = 0.25

               ⇒  x^{2} = \frac{1}{0.25}   ⇒ x^{2} = 4 ⇒ x = 2  

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0
2 years ago
Can I get help with this please?
sammy [17]
First equation:
5(x+1)=20 —— distribute the 5 to the x and 1
5x+5=20 ——- subtract 5 from 20
5x=15 ———— divide by 5 from both sides
X=3 ————— answer

Second equation:
5x+1=20——— subtract 1 from 20
5x=19 ———— divide by 5 from both sides
X=19/5———— answer in fraction form
X=3.8————- answer in decimal form
8 0
3 years ago
PLEASE HELPPP
Lelechka [254]


(x + a)/(ax) = b/x
a= 2
b = 5
(x + 2) /(2x) = 5/x
cross multiply
x * (x+2) = (2x)*5
x^2 + 2x = 10x
x^2 - 8x = 0
x ( x -8) = 0
We get two solutions
x = 0, 8
the solution 0 is extraneous
the solution 8 is valid.

7 0
3 years ago
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