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2 years ago

What is the recursive formula of the geometric sequence? 1, 5, 25, 125, 625, ...

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

4 0

The recursive formula of the geometric sequence is given by option D; an = (1) × (5)^(n - 1) for n ≥ 1

<h3>How to determine recursive formula of a geometric sequence?</h3>

Given: 1, 5, 25, 125, 625, ...

first term, a = 1

Common ratio, r = 25/5

= 5

n = number of terms

an = a × r^(n - 1)

= 1 × 5^(n - 1)

an = (1) × (5)^(n - 1) for n ≥ 1

Learn more about recursive formula of geometric sequence:

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A new restaurant with 134 seats is being planned. Studies show that 62% of the customers demand a smoke-free area. How many se

zzz [600]

Answer: 100

Step-by-step explanation:

Given : The total number of seats planned in new restaurant =134

The percentage of customers demand a smoke-free area = 62%

It can also be written as $62\%=\dfrac{62}{100}=0.62$

The mean of this binomial distribution will be :-

$\mu=np\\\\\mu=(134)(0.62)=83.08$

Standard deviation:-

$\sigma=\sqrt{np(1-p)}\\\\\Rightarrow\sigma=\sqrt{134(0.62)(0.38)}\approx5.6$

Now, the number of seats should be in the non-smoking area in order to be very sure of having enough seating there :-

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3 years ago

Find the slope of each line and then determine if the lines are parallel, perpendicular or neither. If a value is not an integer

Aleonysh [2.5K]

As given by the question

There are given that the point of two-line

$\begin{gathered} (1,\text{ 7) and (5, 5)} \\ (-1,\text{ -3) and (1, 1)} \end{gathered}$

Now,

From the condition of a parallel and perpendicular line

If the slopes are equal then the lines are parallel

If the slopes are negative reciprocal then the lines are perpendicular

If the slopes are neither of the above are true then lines are neither

Then,

First, find the slope of both of line

So,

For first-line, from the formula of slope

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{5_{}-7_{}}{5_{}-1_{}} \\ m_1=-\frac{2}{4} \\ m_1=-\frac{1}{2} \end{gathered}$

Now,

For second-line,

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{1_{}-(-3)_{}}{1-(-1)_{}} \\ m_1=\frac{4}{2} \\ m_1=2 \end{gathered}$

The given result of the slope is negative reciprocal because

$\begin{gathered} -\frac{1}{2}=-(-\frac{2}{1}) \\ -\frac{1}{2}=2 \end{gathered}$

Hence, the slope of line1 is -1/2, and slope of line2 is 2 and the lines are perpendicular.

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1 year ago

angle 0 is in quadrant 1 with sin0 = 2/5. Use the Pythagorean identity, sin^2 0 + cos^2 0 = 1, to calculate the value of cos0 as

Gwar [14]

We know that
sin²x+cos²x=1
so
clear cos x
cos x=(+/-)√[1-sin²x]

in this problem
<span>Angle 0 is in quadrant 1 -----> cos o and sin o are positive
</span>sin o=2/5
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the answer is
cos o=√21/5

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3 years ago

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3 years ago

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7.<br> 2. What is the product of 50 and 100?<br> 2<br> 50<br> O 150<br> O 5,000<br> .

Helga [31]

Answer:

it's 5000

Step-by-step explanation:

50*100=5000

hope it helps:p

6 0

3 years ago