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2 years ago

What is the common ratio between successive terms in the sequence 1.5, 1.2, 0.96, 0.768

Mathematics

1 answer:

Pani-rosa [81]2 years ago

6 0

Answer:

To determine the common ratio of a geometric sequence. You just need to divide any two consecutive terms on it. You can see below that all of them have the same quotient.

1.2 / 1.5 = 0.8

0.96 / 1.2 = 0.8

0.768 / 0.96 = 0.8

Decimal form = 0.8

Fraction form = 4/5

Check:

1.5 x 0.8 = 1.2

1.5 x 4/5 = 6/5 = 1 1/5 = 1.2

Therefore, the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768 is 0.8 or 4/5.

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A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how

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Answer:

4.9 years

Step-by-step explanation:

Future value is the sum of amount invested and its compounded interest for a specific period of time and on a specific interest rate.

Investment = Present value = $9,500

Future value = $12,600

To find the numbers of years we will use following formula

Future value = Present value x ( 1 + r )^n

r = interest rate = 5.75%

n = number of periods = ?

Placing values in the formula

$12,600 = $9,500 x ( 1 + 5.75%/4 )^n

$12,600 / $9,500 = 1.014375^n

1.3263 = 1.014375^n

Log 1.3263 = n log 1.014375

n = Log 1.3263 / log 1.014375

n = 19.7856 Quarters

n = 4.9 years

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2 years ago

The equation y 4.9t 2 3.5t 2.4 relates the height y in meters to the elapsed time t in seconds for a ball thrown downward at 3.5

tamaranim1 [39]

Answer:

$t \approx 0.43\,s$

Step-by-step explanation:

The vertical displacement function is $y(t) = -4.9\cdot t^{2}-3.5\cdot t + 2.4$ , where $y(t)$ is measured in meters and $t$ in seconds. Ball hits the ground when $y(t) = 0$ . That is:

$-4.9\cdot t^{2}-3.5\cdot t + 2.4 = 0$

Whose roots can be found by using the General Formula for Second-Order Polynomials:

$t_{1,2} = \frac{3.5\pm \sqrt{(-3.5)^{2}-4\cdot (-4.9)\cdot (2.4)} }{2\cdot (-4.9)}$

Solutions of this polynomial are:

$t_{1} \approx 0.43\,s,t_{2} \approx -1.14\,s$

Only the first root is physically consistent.

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2 years ago

Help!!

Xelga [282]

Answer:

D. 63%

Step-by-step explanation:

the white marble was picked out 41 of the 65 times, so 41/65

divide 41 by 65 in your calculator and you get .6307

then multiply it by 100 because it asked for a percentage and you get 63%

Ta-Da!

6 0

1 year ago

Read 2 more answers

In a study of the progeny of rabbits, Fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. The sequence

expeople1 [14]

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

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1 year ago

Alison wants to distribute the carnations and roses equally among the 6 flower shops. Factor the expression from Part A using 6

mixer [17]

Answer:

Step-by-step explanation:

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1 year ago