Given the equation y = |x| - 2 and the x values of -2, -1, 0, 1, 2, substitute x and choose the correct set of y values below.

Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

GarryVolchara [31]

Answer:

$a_{n} = 32(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

$a_{n+1} = ra_{n}$

In which r is the common ratio.

This can be expanded for the nth term in the following way:

$a_{n} = a_{1}r^{n-1}$

In which $a_{1}$ is the first term.

This means that for example:

$a_{3} = a_{1}r^{3-1}$

So

$a_{3} = a_{1}r^{2}$

$2 = a_{1}(\frac{1}{4})^{2}$

$2 = \frac{a_{1}}{16}$

$a_{1} = 32$

Then

$a_{n} = 32(\frac{1}{4})^{n-1}$

4 0

3 years ago

A coyote can run at top speed at 44 miles per hour how far can it run in 15 minutes

elena-14-01-66 [18.8K]

15 min is 1/4 of an hour so it can run 44x 1/4 or 44/4 =11miles in 15 min

7 0

3 years ago

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At 9:00 pm bob leaves his home and starts walking to the bus stop at a constant speed of 9.3 feet per second. bob's house is 432

klio [65]

a. define variables for the quantities that are changing (be specific).
We define variables:
t = time in second
d = distance traveled
The variables that are changing are t and d.
As the time increases, the distance decreases.

b. what does it mean to say bob walks at a constant speed of 9.3 feet per second?
It means that for every second that passes, Bob walks 9.3 feet.

c. consider the formula d = 4320 - 9.3t i. what does t represent? ii. what does 9.3t represent? iii. what does d represent?
For this case we have:
t = represents the time in seconds
9.3t = represents the distance traveled by Bob
d = represents the distance Bob must travel to get to the bus stop.

5 0

3 years ago

7x+8(x+1/4)=3(6x-9)-8 need a solution for this problem

valentina_108 [34]

7x+8(x+1/4) = 3(6x-9)-8
7x+8x+2 = 18x - 27 -24
15x + 2 = 18x - 51
+51 + 51
15x + 53 = 18x
-15x = -15x
53 = 3x
17.66 = x

5 0

3 years ago

Which statement is true?

gayaneshka [121]

Answer:

Option: C is the correct answer.

C. Buying a needle and buying thread are dependent events.

Step-by-step explanation:

let A denotes the events of buying a thread.

and B denote the event of buying a needle.

Then A∩B denote the event of buying a needle and a thread.

Also let P denote the probability of an event.

i.e. we are given:

P(A)=0.15

Also P(B|A)=0.25

As we know that:

$P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\i.e.\\\\0.25=\dfrac{P(A\bigcap B)}{0.15}\\\\i.e.\\\\P(A\bigcap B)=0.0375$

As we know that when two events A and B are independent then,

P(A∩B)=∅

otherwise they are dependent events.

Hence, option: C is the correct answer.

6 0

3 years ago

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