How to do this? And the answer

Part A

Nat2105 [25]

Answer:

A. $f(n) =0.2n+4.8$

B. The y intercept is 4.8

Step-by-step explanation:

Given

$a_n= 5 + 0.2(n-1)$

Solving (a): Write as a function.

To do this, we simply substitute f(n) for $a_n$

$a_n= 5 + 0.2(n-1)$ becomes

$f(n)= 5 + 0.2(n-1)$

Open Bracket

$f(n) = 5 + 0.2n-0.2$

Collect Like Terms

$f(n) =0.2n-0.2 + 5$

$f(n) =0.2n+4.8$

B. The y intercept.

To get the y intercept, we set n to 0

i.e

$f(0) =0.2 * 0+4.8$

$f(0) =0+4.8$

$f(0) =4.8$

Hence, the y intercept is 4.8

4 0

2 years ago

"What is the probability of drawing a jack or queen from a standard deck of cards?"

Natasha2012 [34]

Well, there are 52 cards in a deck, with 4 suits. there is a Jack and queen per suit, so that is a total of 8 jacks and queens in the deck. that probability looks like 8:52 as a ratio, or 2:13 simplified. so, you are likely to draw a Jack or queen 8 out of 52 times, or 2 out of 13 times

5 0

3 years ago

If georgia has 8 watermelons and ate 2, how many does she have now

Sedaia [141]

Step-by-step explanation:

Now she has 6 watermelons.

4 0

3 years ago

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Solve the equations by factoring:<br><br>x^2−3x−40=0<br><br>4x^2−81=0

Alja [10]

Answer:

see explanation

Step-by-step explanation:

Given

x² - 3x - 40 = 0

Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)

The factors are - 8 and + 5, since

- 8 × 5 = - 40 and - 8 + 5 = - 3, thus

(x - 8)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 5 = 0 ⇒ x = 5

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

Given

4x² - 81 = 0 ← this is a difference of squares and factors in general as

a² - b² = (a + b)(a - b), thus

4x² - 81

=(2x)² - 9²

= (2x + 9)(2x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = - $\frac{9}{2}$

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = $\frac{9}{2}$

8 0

3 years ago

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Spam e-mail containing a virus is sent to 1000 e-mail addresses. After 1 second, a recipient machine broadcasts 10 new spam e-ma

pickupchik [31]

Answer:

Answer explained below

Step-by-step explanation:

Spam e-mail containing a virus is sent to 1000 e-mail addresses. After 1 second, a recipient machine broadcasts 10 new spam e-mails containing the same virus, after which the virus disables itself on that machine. (1) Write a recursive definition (i.e. recurrence relation) to show how many spam emails will be sent out after n seconds. (2) Solve the recurrence relation. (3) How many e-mails are sent at the end of 20 seconds

1.START T=0.....

1000 EMAILS SENT AND RECEIVED BY 1000 M/CS.

T=1.....

EACH OF THE M/C SENDS 10 NEW MAILS ....

.................................

LET M[N] BE THE NUMBER OF MAILS SENT OUT AFTER N SECONDS.

SO , EACH OF THESE M/CS WILL SEND 10 MAILS IN NEXT 1 SECOND.

HENCE NUMBER OF MAILS SENT IN N+1 SECONDS=M[N+1]=

M[N+1]=10*M[N].......................1

THIS IS THE RECURRENCE RELATION.....

2.SOLUTION .....

M[N+1]=10M[N]=10*10M[N-1]=10*10*10M[N-2]=........

M(N+1)=[10^1][M(N)]=[10^2][M(N-1)]=[10^3][M(N-2)]=..........=[10^N][M(1)]=[10^(N+1)][M(0)]

M[N+1]=[10^(N+1)][1000]=[10^(N+1)][10^3]=[10^(N+4)]......................................2

THIS IS THE NUMBER OF MAILS SENT AFTER N+1 SECONDS .....OR ....

M[N]=[10^(N+3)].............................................3

..................IS THE SOLUTION FOR NUMBER OF MAILS SENT AFTER N SECONDS.....

3.AFTER N=20 SECONDS , THE ANSWER IS ....

M[20]=10^(20+3)=10^23

8 0

3 years ago

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