Determine whether the sequence {an} con- verges or diverges when 1. diverges 1 2. converges with limit 2n an 7n-1 3. converges with limit = 0 and if it converges, find the limit. 4. converges with limit 2 5. converges with limit = 7

y = mx + b

3 = 4(4) + b

Answer: y = 4x + 13

Hope this helps :)

Answer:

two irrational solutions

Step-by-step explanation:

you can use the quadratic formula:  (b ± √b²- 4ac)÷2a

a = 5, b = -2, c = 6

= [2 ± √(-2²)-4(5)(6)] ÷ 2(5)

= (2 ± √4-120) / 10

two complex solutions:  (2+√-116)/10, (2-√-116)/10

Answer:

Start by multiplying -5 by 4x and -7.

Answer:

Changing the equation to -20x+35=3x

Step-by-step explanation:

You would multiply each number in the parenthesis by -5

Hope this helps :)

Answer:

Ashley

Step-by-step explanation:

Ashley:

12n (n=5) = 60+2u (u=10)=80

4 quarters equal a dollar

$1.80

Beto:

10n (n=5)= 50+ 4u (u=10) = 90

3 quarters equal .75

$1.65

Answer:

D = (13, - 23 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 15 )

To go in the reverse direction, that is image to original, then, reverse the operations in the translation rule.

(x , y ) → (x + 4, y - 15 ) , thus

D'(9, - 8 ) → D(9 + 4, - 8 - 15 ) → D(13, - 23 )

Answer:

(13,-23)

Step-by-step explanation:

DID IT ON EDGE 2020

Answer:

1.x=7,  2.x=7,  3.x=7,  4.x=1,  5.x=20,  6.x=9,  7.x=100,  8.x=9

Step-by-step explanation:

hope this helps :<)

Answer:

∠HGD and ∠FGD

Step-by-step explanation:

supplementary means they add up to 180 (straight line)

Answer:

D) Angle DGH and Angle FGD

Step-by-step explanation:

We observe that Angle DGH and Angle FGD form a linear pair and hence, are supplementary.

The value of y is 15 and angle is 68°

A triangle is a polygon with three edges and three vertices.

Given that, a triangle KLM

We have, KL = MK

We know that, In a triangle, sides opposite to equal angles are equal, therefore,

∠ M ≅ ∠ L

5y-19 = 56

5y = 75

y = 15

We know, Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

∠ M + ∠ L + ∠ K = 180°

56° + 56° + ∠ K = 180°

∠ K = 180° - 112°

∠ K = 68°

Hence, the answers are; ∠ K = 68° and y = 15

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The probability that one team wins in exactly five games assuming each team has an equal likelihood of winning each game is 0.29.

Algorithm World Series(n, p)

//Computes the odds of winning a series of n games

//Input: A number of wins n needed to win the series and probability p of one particular team winning a game

//Output: The probability of this team winning the series

q ← 1 − p

for j ← 1 to n do

P[0, j] ← 1.0

for i ← 1 to n do

P[i, 0] ← 0.0

for j ← 1 to n do

P[i, j] ← p ∗ P[i − 1, j] + q ∗ P[i, j − 1]

return P[n, n]

Both the time efficiency and the space efficiency are in Θ(n2) because each entry of the n + 1-by-n + 1 table (except P[0, 0], which is not computed) is computed in Θ(1) time

a. Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series. If team A wins the game, which happens with probability p, A will need i − 1 more wins to win the series while B will still need j wins. If team A looses the game, which happens with probability q = 1 − p, A will still need i wins while B will need j − 1 wins to win the series.

This leads to the recurrence

P(i, j) = pP(i − 1, j) + qP(i, j − 1) for i, j > 0

The initial conditions follow immediately from the definition of P(i, j):

P(0, j)=1 for j > 0, P(i, 0) = 0 for i > 0

b. Here is the dynamic programming table in question, with its entries rounded-off to two decimal places. (It can be filled either row-by-row, or column-by-column, or diagonal-by-diagonal.)

i/jj 0  1      2     3     4

0       1      1     1     1

1    0  0.40  0.64  0.78  0.87

2    0  0.16  0.35  0.52  0.66

3    0  0.06  0.18  0.32  0.46

4    0  0.03  0.09  0.18  0.29

Thus, P[4, 4] ≈ 0.29.

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Complete question:

World Series Odds. [20 marks total] Consider two teams, A and B, playing a series of games until one of the teams wins n games. Assume that the probability of A winning a game is the same for each game and equal to p and the probability of A losing a game is q = 1 − p. (Hence, there are no ties.) Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series.

(a) Set up a recurrence relation for P(i, j) that can be used by a dynamic programming algorithm. Hint: In the situation where teams A and B need i and j games, respectively, to win the series, consider the result of team A winning the game and the result of team A losing the game.

(b) Find the probability of team A winning a seven-game series if the probability of it winning a game is 0.4. Hint: Set up a table with five rows (0 ≤ i ≤ 4) and five columns (0 ≤ j ≤ 4) and fill it by using the recurrence derived in part (a).

(c) Write C/C++ pseudocode for a dynamic programming algorithm to solve this problem and determine its time and space efficiencies. Hint: Your pseudocode should be guided by the recurrence you set up in part (a).

Step-by-step explanation:

7x^3 + 4x^2 + 3x + 6

in standard form

Answer:

7x³ + 4x² + 3x + 6

Step-by-step explanation:

Standard form of a polynomial begins with the term containing the largest exponent of the variable followed by descending values of the exponent.

Given

3x + 4x² + 6 + 7x³ then

7x³ + 4x² + 3x + 6 ← in standard form

Step-by-step explanation:

We know that

<L = <N so

2(4x + 23)° + (3x + 46)° = 180°.. b/c all sum is 180°

8x + 46 + 3x + 46 = 180°

11x +92 = 180

11x = 180 - 92

11x = 88

11x /11 = 88 / 11

x = 8 so we can solve angle of each <M = 3x+ 46

<M =3(8) +46

<M = 24 + 46

<M =70 so angle M measure 70°

the other 2 sides are congrunt so their base angles are equal.

< L = < N =4x + 23

< L = < N =4(8) + 23

< L = < N =32 + 23

< L = < N =55°

So angle L and N is 55° .

The number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series is 8.

To approximate cos x to 8 significant figures using the Maclaurin series approximation, you need to determine the number of terms necessary. The Maclaurin series for cos x is given by:

cos x = 1 - x²/2 + x⁴/24 - x⁶/720 + x⁸/40320 ...

To achieve 8 significant figures, the series must be truncated after the x⁸/40320 term. Therefore, the number of terms necessary is 8.

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Answer:

\(\textsf{A.} \quad e^{-y}=\cos x+2\)

Explanation:

Given differential equation and initial condition:

\(\begin{cases}y'=e^y \sin x\\y(-\pi)=0\end{cases}\)

Rearrange the differential equation so that all the terms containing y are on the left-hand side, and all the terms containing x are on the right-hand side:

       \(y'=e^y \sin x\)

     \(\dfrac{dy}{dx}=e^y \sin x\)

 \(\dfrac{1}{e^y}\; dy=\sin x\; dx\)

\(e^{-y}\; dy=\sin x\; dx\)

Integrate both sides of the equation:

\(\begin{aligned}\displaystyle \int e^{-y}\; dy&=\int \sin x\; dx\\\\-e^{-y}&=-\cos x+C\end{aligned}\)

Substitute the given condition y(-π) = 0 into the equation and solve for C:

\(\begin{aligned}-e^{-0}&=-\cos (-\pi)+C\\\\-1&=1+C\\\\C&=-2\end{aligned}\)

Substitute the found value of C into the equation:

\(-e^{-y}=-\cos x-2\)

Multiply both sides by -1:

\(\boxed{e^{-y}=\cos x+2}\)

\(\hrulefill\)

Integration rules used:

\(\boxed{\begin{minipage}{5.1 cm}\underline{Integrating $e^{ax}$}\\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{ax}e^{ax}+\text{C}$\\\end{minipage}}\)

\(\boxed{\begin{minipage}{5.1 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\\\end{minipage}}\)

99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

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Answer: 28.75° and 61.25°

Step-by-step explanation:

A complementary angle equals 90°.

Let the measure of the angle be a

Therefore, its complement will be:

= 90-a.

The complement of an angle is 25 less than 3 times the angles itself can be written as:

90-a = 3a - 25

90 + 25 = 3a + a

115 = 4a

a = 115/4

a= 28.75

Since the angle is 28.75°, the complement will be:

= 90° - 28.75°

= 61.25°

The angles are 28.75° and 61.25°

The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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In the given figure, where triangle QPS = triangle SRQ, the value of

a. x = 47°

b. ∠PQS = 32°

c. ∠PSR = 74°

A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.

In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.

Given that  ∆QPS ≈ ∆SRQ

a) ∠QPS = ∠QRS

106° = 2x + 12

106° - 12 = 2x

2x = 94°

x = 47°

b) ∠RSQ = ∠PQS

∠SQR + ∠SRQ + ∠RSQ = 180°

42° + 2(47°) + 12 + ∠RSQ = 180°

148 + ∠RSQ = 180°

∠RSQ = 180° - 148°

∠RSQ = 32°

∠PQS = 32°

c) ∠PSR = ∠PSQ + ∠RSQ

[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]

∠PSR = 42° + 32°

∠PSR = 74°

Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.

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Answer:

45

Step-by-step explanation:

5 * 6 = 30$ (the cost of backpacks)

3 * 5 = 15$ (the cost of pens)

15 + 30 = 45

$45

The correct option a. one or many solution. If there are "one or many solutions," a system of linear equations can be considered consistent.

There may be one single solution to a set of linear equations, an unlimited number of solutions, or even no solution at all. Based on the answers, systems of linear equations can be categorised as either inconsistent or consistent, as well as independent or dependent.

Thus, If there are "one or many solutions," a system of linear equations can be considered consistent.

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Complete question:

A system of linear equations is said to be consistent if which of the following is​ true?

a. one or many solution

b. two solution

c.exactly one solution

d. no solution

which is the correct option​

Answer:

1 1/2 miles

Step-by-step explanation:

(aka option A on edge)

The two amount of numbers are 11 and 135. 11 is a multiple of 11 and 135 is a multiple of 17. The sum of the two numbers is 146.

Step 1: One of the numbers is a multiple of 11

Let the number be 11x, where x is an integer

Step 2: The total of the two numbers is 146

Therefore, 11x + 17y = 146, where y is an integer

Step 3: Solve the equation

11x + 17y = 146

11x = 146 - 17y

x = (146 - 17y) / 11

Step 4: Find the two numbers

x = (146 - 17y) / 11

For y = 1, x = 11

Therefore, the two numbers are 11 and 17.

The two numbers that add up to 146 are 11 and 135. 11 is a multiple of 11, which means it is divisible by 11 without any remainder. 135 is a multiple of 17, which means it is divisible by 17 without any remainder. When these two numbers are added together, the sum is 146. This means that 11 and 135 are the two numbers that add up to 146. 11 is a multiple of 11 and 135 is a multiple of 17, which explains why the sum of the two numbers is 146. The two numbers together can be used to represent a variety of different mathematical equations, such as the addition of two integers or the multiplication of two fractions. Knowing the two numbers that add up to 146 can be useful in a variety of different scenarios, such as solving math problems or accounting for the total of two items.

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Step-by-step explanation:

So, cost of 6.5 kg of apples is Rs. 520 and we need to find cost of one kg apples.

So,

6.5 kg -- Rs. 520

1 kg -- Rs.(520/6.5) = Rs.80

Answer:

(8+-4)(6+-2)(5+-1)

Step-by-step explanation:

i.) 8+(-4)

8-4=4

ii) 6+(-2)

   6-2=4

iii) 5+(-1)

    5-1 = 4

HOPE THIS HELPS

Answer:

(8+-4)(6+-2)(5+-1)

Step-by-step explanation:

Answer:

285.28571429 minutes

Step-by-step explanation:

Let us represent

The number of minutes you talk = t

C1 = Cost in dollars of the first plan

C2 = Cost in dollars of the second plan

First plan

The first plan charges a rate of 26 cents per minute

Converting cents to dollars

100 cents = 1 dollars

26 cents =

26/100 cents

=$ 0.26

C1 = $0.26 × t

C1 = 0.26t .......... Equation 1

Second Plan

The second plan charges a monthly fee of $39.95 plus 12 cents per minute

Converting 12 cents to dollars

100 cents = 1 dollars

12 cents =

12/100

= $0.12

C2 = $39.95 + 0.12t........Equation 2

Find the number of talk minutes that would produce the same cost for both plans

We would Equate C1 to C2

C1 = C2

0.26t = $39.95 + 0.12t

Collect like terms

0.26t - 0.12t = $39.95

= 0.14t = $39.95

Divide both sides by 0.14

= t = $34.95/0.14

t = 285.28571429 minutes

Therefore, the number of talk minutes that would produce the same cost for both plans is 285.28571429 minutes.

Answer:

24:108:40       in this order

Step-by-step explanation:

2+9+4=15

180÷15=12

2•12=24

9•12=108

4•12=48

The list that gives the sample space for pulling 2 marbles from the bag with replacement is given as follows:

List 4.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The fact that the experiment is with replacement means that for each of the two marbles, there are two possible outcomes.

Then, applying the Fundamental Counting Theorem, the total number of outcomes is given as follows:

4 x 4 = 16.

This means that the correct list is either the list 3 or the list 4.

As there is replacement, it is possible to take two purple marbles, even though there is only one purple marble, as the same can be taken with replacement, and thus the correct list is given by list 4.

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Answer: List 4

Step-by-step explanation: This answer is here to confirm the other answer. It got me 100% on my test.

Also I know the right answer because I got it right

So good luck on y'all's math tests :)

Here is some proof that the answer is List 4

Answer:

(a)= 224

(b)=352

Step-by-step explanation:

(a) in a calculator type 35%x640 and it will have your answer, 224

(b) do the same thins as question a but just add the 2 numbers together

Answer:

x > 19

Step-by-step explanation:

Answer:

m ≤ -19

Step-by-step explanation:

81 ≥ 100 - m

-100  -100

-19 ≥ m

or

m≤-19

hope this helps!!!

Step-by-step explanation:

Here's my step by step solution Friend..

Answer:

The length will be 12 mm

Step-by-step explanation: