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3 years ago

Consider a sequence given by the formula f(n)=3n-1 starting with n=1. Generate the first 5 terms of the sequence

Mathematics

1 answer:

Rufina [12.5K]3 years ago

5 0

Answer:

The first 5 terms are 2, 5, 8, 11, 14.

Step-by-step explanation:

You use the formula to find out each term.
f(n)=3n-1 starting with n=1. If n=1 that is the 1st term, if n=2 that is the 2nd term, and so on. n means what number term it is.
Now to find each term:

n=1: f(1)= 3(1)-1= 3-1= 2 The 1st term is 2
n=2: f(2)= 3(2)-1= 6-1= 5 The 2nd term is 5
n=3: f(3)= 3(3)-1= 9-1=8 The 3rd term is 8
n=4: f(4)= 4(3)-1= 12-1= 11 The 4th term is 11
n=5: f(5)= 5(3)-1= 15-1= 14 The 5th term is 14

So the first 5 terms are 2,5,8,11,14

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A university found that of its students withdraw without completing the introductory statistics course. Assume that students reg

polet [3.4K]

Answer:

A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

a. Compute the probability that 2 or fewer will withdraw (to 4 decimals).

= 0.0355

b. Compute the probability that exactly 4 will withdraw (to 4 decimals).

= 0.1304

c. Compute the probability that more than 3 will withdraw (to 4 decimals).

= 0.8929

d. Compute the expected number of withdrawals.

= 6

Step-by-step explanation:

This is a binomial problem and the formula for binomial is:

$P(X = x) = nCx p^{x} q^{n - x}$

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 2) = 20C2(0.3)^2(0.7)^{18}\\P(X = 2) =190 * 0.09 * 0.001628413597\\P(X = 2) = 0.027845872524$

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 1) = 20C1(0.3)^1(0.7)^{19}\\P(X = 1) =20 * 0.3 * 0.001139889518\\P(X = 1) = 0.006839337111$

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 0) = 20C0(0.3)^0(0.7)^{20}\\P(X = 0) =1 * 1 * 0.000797922662\\P(X = 0) = 0.000797922662$

Finally, the probability that 2 or fewer students will withdraw is

$P(X = 2) + P(X = 1) + P(X = 0) \\= 0.027845872524 + 0.006839337111 + 0.000797922662\\= 0.035483132297\\= 0.0355$

b) Compute the probability that exactly 4 will withdraw.

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 4) = 20C4(0.3)^4(0.7)^{16}\\P(X = 4) = 4845 * 0.0081 * 0.003323293056\\P(X = 4) = 0.130420974373\\P(X = 4) = 0.1304$

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 3) = 20C3(0.3)^3(0.7)^{17}\\P(X = 3) = 1140 * 0.027 * 0.002326305139\\P(X = 3) = 0.071603672205\\P(X = 3) = 0.0716$

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1 - 0.1071=0.8929

d) Compute the expected number of withdrawals.

E(X) = 3/10 * 20 = 6

Expected number of withdrawals is the 30% of 20 which is 6.

5 0

3 years ago

15 is 60% of what number?

Mazyrski [523]

15 is 60% of 25. 15/25 is equal to .6 or 60%

8 0

2 years ago

Read 2 more answers

Choose the slope and y-intercept that correspond with the graph. ignore this

krok68 [10]

Answer: The second choice is correct: slope is 3/4, y-intercept is 1

Step-by-step explanation: The y-intercept is where the line crosses the y-axis.

Look for places where the line intersects the grid at "cross-points" like (-4,-2) (0,1) and (4,4)

The slope is rise/run.

The difference in y-values is the rise. 4-1=3 1-(-2) is 3.

The rise is 3.

The difference in x-values is the run. 4-0=4 0-(-4) = 4

The run is 4

Rise/run = 3/4 That is the slope.

8 0

3 years ago

Read 2 more answers

Write an equation in slope-intercept form for the line with slope 1/4 and y intercept -4. Then graph the line

quester [9]

Answer:

Step-by-step explanation:

slope intercept form is y = mx + b

b is the y intercept ( crossing y axis value).... by inspection b = -4

m is the slope of the line, Slope = m = 1/4 note: the slope is positive

the slope equals the 'rise' over 'run'

if the line moves up the slope is positive, if the line moves down the slope is negative

the rise is how many y units does the line go 'up' or 'down'

the run is how many x units does the line go 'left' or 'right'

the rise = 1 Y unit

the run = 4 X units

y = mx + b m =1/4 b = -4

y = (1/4)x + (-4)

y = (1/4)x - 4

graph a line stating at y = -4 and going up (rising) to the right ONE Y Unit for every FOUR X units (the run)

3 0

3 years ago

Which is the slope-intercept form of the equation of a line that passes through (5,-4) and has a slope of 3/4

Andreas93 [3]

Y = mx +b whre m is the slope and b is the y-intercept.

We have the slope 3/4 so put that instead of m

y = 3/4x + b

Now to find the y-intercept (b), plug the ordered pair in and solve for b.

-4 = 3/4 * 5 + b
-4 = 15/4 + b
-31/4 + b

So y = 3/4x - 31/4

4 0

3 years ago