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3 years ago

16, 4,1,... Find the 6th term

Mathematics

1 answer:

Vlada [557]3 years ago

3 0

Let's see what to do...

_________________________________

Step (1)

Look : 16 , 10 , 4 , ...

It is an arithmetic sequence.

So first we have to find the value of the ratio(( d )) .

To do this, we need to subtract each sentence minus the previous sentence.

So we have : 10 - 16 = - 6

_________________________________

Step (2)

To find the nth sentence in an arithmetic sequence, we must use the following equation :

$t(n) = t(1) + (n - 1)d$

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Step (3)

To find the 6th term just need to put the following parameters in the above sequence.

t(1) = 16 ------ n = 6 ------ d = -6

$t(6) = 16 + (6 - 1)( - 6)$

$t(6) = 16 + (5)( - 6)$

$t(6) = 16 + ( - 30)$

$t(6) = 16 - 30$

$t(6) = - 14$

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

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Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. 2x+3y=6

sweet-ann [11.9K]

Answer:

x-intercept: (3, 0)

y-intercept: (0, 2)

Step-by-step explanation:

For a function like:

y = f(x)

The x-intercept is the value of x when y = 0

the y-intercept is the value of y when x = 0

Also remember that an ordered pair is written as (x, y).

In this case we have the equation:

2*x + 3*y = 6

For the x-intercept, we just replace y by zero in the equation, then we get:

2*x + 3*0 = 6

Solving this for x, we get:

2*x = 6

x = 6/2 = 3

Then in this case, the ordered pair for the x-intercept is (3, 0)

For the y-intercept, we just need to replace x by zero in the equation:

2*0 + 3*y = 6

Solving this for y, we get:

3*y = 6

y = 6/3 = 2

Then the ordered pair for the y-intercept is (0, 2)

8 0

3 years ago

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times

cestrela7 [59]

Answer:

5/32

Step-by-step explanation:

If a coin if flipped five times with four heads, then it has exactly one tail. The number of way to arrange four heads and one tail are as follows:

T H H H H

H T H H H

H H T H H

H H H T H

H H H H T

Essentially, there are five way because there are five "positions" where the tail could be.

Then, you need to find the total amount of possibilities for flipping a coin five times. Every time you flip it, there are two possibilities- heads and tails. Therefore, for five flips, the total amount of possibilities is

2x2x2x2x2 = 32

You know that

probability= # of desired outcome

----------------------------------

# of total outcomes

So the probablity is 5/32.

8 0

3 years ago

Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5

lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer: v = 5v + 4u + 1.5sin(3t),

1.5sin(3t)

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1

v represents the "velocity function" i.e v = u'(t)

As v = u'(t)

<em>u' = v</em>

since <em>u' = v </em>

v' = u"

v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )

= 5v + 4u + 1.5sin(3t) ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ = $\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]$ $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ + $\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]$

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

$\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]$ = $\left[\begin{array}{ccc}1\\2.5\\\end{array}\right]$

7 0

3 years ago

Need help with this.

skelet666 [1.2K]

Answer:

-5/2(3x+4)<6-3x (multiply with -5/2)

-15/2x-10<6-3x (multiply with 2)

-15x-20<12-6x (change sides)

-15x+6x<12+20

-9x<12+20

-9x<32

x>-32/9

Hope this will help u :)

3 0

3 years ago

At a benefit concert, fifteen bands have volunteered to perform but there is only enough time for five of the bands to play. Ho

Iteru [2.4K]

Answer:

360,360

Step-by-step explanation:

So we only have 5 spots, but 15 bands to fill those spots.

For the first spot, we can choose from any of the 15 bands, so we have 15 choices.

For the second spot, we can choose from the 14 remaining bands (because we already chose one for the first spot), so we have 14 choices.

For the third spot, by similar reasoning as above, we have 13 choices; for the fourth spot, 12 choices; and for the last spot, we have 11 choices.

We realize that for each of the 15 possible bands in the first spot, we still have 14 possible bands for the second spot, and so on. Thus, we know to multiply instead of add.

Our answer is: 15 * 14 * 13 * 12 * 11 = 360,360

6 0

3 years ago