What is 65 ÷ 10^2 ?

64, –48, 36, –27, ... Which formula can be used to describe the sequence?

nordsb [41]

Answer:

$\boxed{a_n \: = \: 64 \: \times \: ( - \frac{3}{4} ) ^{n \: - \: 1} }$

Step-by-step explanation:

We first compute the ratio of this geometric sequence.

$r \: = \: \frac{ - 48}{64} \\ \\ r \: = \: \frac{36}{ - 48} \\ \\ r \: = \: \frac{ - 27}{36}$

We simplify the fractions:

$r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4}$

We deduce that it is the common ratio because it is the same between each pair.

$r \: = \: - \frac{3 }{4}$

We use the first term and the common ratio to describe the equation:

$a_1 \: = \: 64; \: r \: = \: - \frac{3 }{4}$

<h3>We apply the data in this formula:</h3>

$\boxed{a_n \: = \: a_1 \: \times \: {r}^{ n \: - \: 1} }$

_______________________

<h3>We apply:</h3>

$\boxed {\bold{a_n \: = \: 64 \: \times \: {( - \frac{3}{4} )}^{ n \: - \: 1} }}$

Data: The unknown "n" is the term you want

<h3>MissSpanish</h3>

4 0

2 years ago

Write a one-sentence story problem about a ratio.

Serga [27]

There are 2 flutes and 1 drum. What is the ratio?

4 0

3 years ago

Read 2 more answers

An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted t

Romashka-Z-Leto [24]

Answer:

Test statistic = 1.664

Step-by-step explanation:

The hypothesis :

H0 : μ = 47.2

H1 : μ ≠ 47.2

Given that :

Sample mean, xbar = 47

Sample size, n = 250

Standard deviation, σ = 1.9

The test statistic :

(xbar - μ) ÷ (σ/√(n))

T = (47 - 47.2) ÷ (1.9/√(250))

T = (0.2 / 0.1201665)

Test statistic = 1.664

7 0

3 years ago

Please help! It would be very much appreciated :)

Trava [24]

Answer:

Cos 45=6/x

x=6/cos 45=6√2

x=6√2

tan 45=y/6

y=tan45 ×6

y=6

2.

sin 60=y/10

y=sin60×10

y=5√3

again

Cos 60=x/10

x=½×10

x=5

3.

Sin 45=x/5

x=1/√2×5 or

x=5√2/2

again

y=5√2/2 or 5/√2[base angle of right angled isosceles triangle]

4.

Sin 30=8/x

½×x=8

x=8*2

x=16

again

cos 30= y/x

√3/2×16=y

y=8√3

5.

sin 60=7/x

x=7/[√3/2]

x=14/√3 or 14√3/3

again

cos 60=y/x

½×14√3/3=y

7√3/2=y

y=7√3/2

Note:

Sin angle =perpendicular/hypotenuse

Cos angle =base/hypotenuse

Tan angle =perpendicular /base

7 0

3 years ago

(2y-5)(5y+7) answer this quickly lol

Stolb23 [73]

Well this is a little tricky.. But my guess would be: y = (-1.4, 2.5)

8 0

3 years ago

Read 2 more answers