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3 years ago

Calculate a5 for the geometric sequence in which a1=1600 and the common ratio is 3/4.

Mathematics

2 answers:

Cloud [144]3 years ago

8 0

Answer:

a₅ = 506.25 option a

Step-by-step explanation:

Given that,

first term a₁ = 1600

common ratio (r) = $\frac{3}{4}$

We need to find the fifth term of the geometric progression

We know that the nth term formula

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

So, n = 5

a₅ = 1600 $(\frac{3}{4})^{5-1}$

a₅ = 1600* $(\frac{3}{4}) ^{4}$

a₅ = 1600*81/256

a₅ = $\frac{2025}{4}$

a₅ = 506.25 option a

That's the final answer

zysi [14]3 years ago

8 0

Answer:

A. 506.25

Step-by-step explanation:

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The following data represent the flight time (in minutes) of a random sample of seven flights from one city to another city. 28

anzhelika [568]

Answer:

$Range = 281-256= 25$

In order to calculate the sample deviation we need to calculate the mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X= 265$

And the standard deviation can be calculated with this formula:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s = 8.426$

Step-by-step explanation:

For this case we have the following data given:

281, 269, 259, 265, 256, 259, 266

The range is defined as:

$Range = Max -Min$

And if we replace we got:

$Range = 281-256= 25$

In order to calculate the sample deviation we need to calculate the mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X= 265$

And the standard deviation can be calculated with this formula"

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s = 8.426$

4 0

3 years ago

Harold is twice as old as Jack, who is three years older than Dan. If Harold's age is five times Dan's age, how old in years is

never [62]

Dan's age is x.
Jack is three years older than Dan, so his age is x+3.
Harold is twice as old as Jack, so his age is 2(x+3).

Harold's age is five times Dan's age.
$2(x+3)=5x \\
2x+6=5x \\
6=5x-2x \\
6=3x \\
\frac{6}{3}=x \\
x=2 \\ \\
x+3=2+3=5$

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