MATHEMATICS COLLEGE

Which is the better buy?17-ounce jar of pickles for $8.84
2-pound jar of pickles for $25,28

Answers

Answer 1
Answer:

Answer:

The 17 ounce. Less money per pickle.

Step-by-step explanation:
Answer 2
Answer: 1 pound = 16 ounce
2 pound = 32 ounce
8.84/17 = $0.52 per ounce
25.28/32 = $0.79 per ounce

Based on those, the 17 ounce jar has a better deal

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Find the values of x and y.X=?Y=?
The sum of two numbers is -14, if one number is subtracted from the other, their difference is 2, find the numbers.
My elderly relatives liked to tease me at weddings saying “ you’ll be next!” They soon stopped, once I started doing the same at funerals

Find the slope of the line that passes through the point (0,-3) and (4,5)

Slope=?

Answers

It depends which pair goes first but the formula is Y2-y1 over x2-x1

Answer: m=2

(0,-3) = (x1,y1)

(4,5) = (x2,y2)

Slope = (y2-y1)/(x2-x1)

          = (5-(-3))/(4-0)

          = (5+3)/(4)

          = (8)/(4)

          = 2

35 points plz helpEvaluate −4(14)6x for x=13.

Enter your answer as a fraction in simplest form in the box.

Answers

Answer:

-15228

Step-by-step explanation:

Given the expression :

-4(14)6x for X = 13

To evaluate ; simply substitute 13 for X in the equation :

-14(14)6(13)

-14 * 14 * 6 * 13 = - 15228

Suppose an individual makes an initial investment of $3,000 in an account that earns 6.6%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.)(a) How much is in the account after the last deposit is made?
(b) How much was deposited?
(c) What is the amount of each withdrawal?
(d) What is the total amount withdrawn?
I get A and C. If you could explain B and D I'd appreciate it.

Answers

Answer:

  b) $17,400

  d) $33,517.20

Step-by-step explanation:

a) $28,482.19 . . . . future value of all deposits

__

b) The initial deposit was $3000, and there were 144 deposits of $100 each, for a total of ...

  $3000 +144×100 = $17,400 . . . . total deposited

__

c) $558.62

__

d) 60 monthly withdrawals were made in the amount $558.62, for a total of ...

  60×$558.62 = $33,517.20 . . . . total withdrawn

_____

Additional information about (a) and (c)

(a) The future value of the initial deposit is the deposit multiplied by the interest multiplier over the period.

  A = P(1 +r/n)^(nt) = 3000(1 +.066/12)^(12·12) = 3000·1.0055^144 ≈ 6609.065

The future value of $100 deposits each month is the sum of the series of 144 terms with common ratio 1.0055 and initial value 100.

  A = 100(1.055^144 -1)/0.0055 ≈ 21,873.123

So, the total future value is ...

  $6609.065 +21873.123 ≈ $28482.188 ≈ $28,482.19

__

(c) The withdrawal amount can be found using the same formula used for loan payments:

  A = P(r/n)/(1 -(1 +r/n)^(-nt)) = $28482.19(.0055)/(1 -1.0055^-60) ≈ $558.62

Final answer:

The total amount deposited in the account was $17,400 including an initial investment of $3,000 and subsequent monthly payments of $100 for 12 years. The total amount withdrawn was equal to the final balance after the last deposit.

Explanation:

Let's tackle each question one by one:

  1. You've mentioned that you have already figured out part (a) and (c), so let's move on to part (b).
  2. (b) How much was deposited?The individual started with an initial deposit of $3,000. After that, they deposited $100 at the end of each month for 12 years. That's 12 years * 12 months/year * $100/month, for a total of $14,400. So, if you add the initial deposit, the total amount deposited over the whole period is $3,000 + $14,400 = $17,400.
  3. (d) What is the total amount withdrawn?The total amount withdrawn is the same as the final balance of the account after the last deposit, as the question states the account balance will be zero after the withdrawals. Since you have already figured out part (a) which is the account balance after the last deposit, the total amount withdrawn corresponds to that sum.

Learn more about Compound Interest here:

brainly.com/question/34614903

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Mike won 7 of his wrestling matches, lost 6 matches, and tied 2 matches. What percent of all of Mike's matches did he win?

Answers

Mike won 46.67% of all of his matches.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

The total number of matches that Mike wrestled is:

Total matches = number of matches won + number of matches lost + number of matches tied

Total matches = 7 + 6 + 2

Total matches = 15

To find the percentage of matches that Mike won, we can use the formula:

Percentage = (Number of matches won / Total number of matches) x 100%

Plugging in the values we know, we get:

Percentage = (7 / 15) x 100%

Percentage = 0.4667 x 100%

Percentage = 46.67%

Therefore, the Percentage = 46.67%.

To learn more about the percentage;

brainly.com/question/24159063

#SPJ5

Answer:

Mike won 46.67% of his matches

Step-by-step explanation:

Mike participated in a total of 7 + 6 + 2 = 15 matches.

The percentage of matches that Mike won can be found by diving the matches he won by the total number of matches and multiplying it by 100 to convert the decimal to a percentage.

(7/15) x 100% ≈ 46.67%

Therefore, Mike won approximately 46.67% of his matches.

2. Anne needs to know how much of her back yard will be used by her newcircular pool. *
1 point
11 feet
What is the area of the pool? Use 3.14 for T.

Answers

Answer:

see below

Step-by-step explanation:   6  13  8  09

area = π r²    is the equation to calculate the area of the pool   r = radius

I don't no if the 1.11 ft is the diameter of the radius, so I will use the 1.11 ft as the diameter

diameter = 2×radius

diameter / 2 = radius

area = π (d/2)²   = T (d/2)²              d = diameter      π  = T      

        = 3.14(1.11 / 2)²              

        = 3.14 × (0.555)²

        = 0.9677 ft²    which seems like a small pool!

Three friends — let’s call them X, Y , and Z — like to play pool (pocket billiards). There are some pool games that involve three players, but these people instead like to play 9-ball, which is a game between two players with the property that a tie cannot occur (there’s always a winner and a loser in any given round). Since it’s not possible for all three of these friends to play at the same time, they use a simple rule to decide who plays in the next round: loser sits down. For example, suppose that, in round 1, X and Y play; then if X wins, Y sits down and the next game is between X and Z. Question: in the long run, which two players square off against each other most often? Least often? So far what I’ve described is completely realistic, but now we need to make a (strong) simplifying assumption. In practice people get tired and/or discouraged, so the probability that (say) X beats Y in any single round is probably not constant in time, but let’s pretend it is, to get a kind of baseline analysis: let 0 < pXY < 1 be the probability that X beats Y in any given game, and define 0 < pXZ < 1 and 0 < pY Z < 1 correspondingly. Consider the stochastic process P that keeps track of

Answers

Answer:

Step-by-step explanation:

(a) If the state space is taken as S = \{(XY),(XZ),(YZ)\} , the probability of transitioning from one state, say (XY) to another state, say (XZ) will be the same as the probability of Y losing out to X, because if X and Y were playing and Y loses to X, then X and Z will play in the next match. This probability is constant with time, as mentioned in the question. Hence, the probabilities of moving from one state to another are constant over time. Hence, the Markov chain is time-homogeneous.

(b) The state transition matrix will be:

P=\begin{vmatrix} 0 & p_(XY) & (1-p_(XY))\n p_(XZ)& 0& (1-p_(XZ))\n p_(YZ)&(1-p_(YZ)) & 0\end{vmatrix},

where as stated in part (b) above, the rows of the matrix state the probability of transitioning from one of the states S = \{(XY),(XZ),(YZ)\} (in that order) at time n and the columns of the matrix state the probability of transitioning to one of the states S = \{(XY),(XZ),(YZ)\} (in the same order) at time n+1.

Consider the entries in the matrix. For example, if players X and Y are playing at time n (row 1), then X beats Y with probability p_(XY), then since Y is the loser, he sits out and X plays with Z (column 2) at the next time step. Hence, P(1, 2) = p_(XY). P(1, 1) = 0 because if X and Y are playing, one of them will be a loser and thus X and Y both together will not play at the next time step. P(1, 3) = 1 - p_(XY), because if X and Y are playing, and Y beats X, the probability of which is1 - p_(XY), then Y and Z play each other at the next time step. Similarly,P(2, 1) = p_(XZ), because if X and Z are playing and X beats Z with probabilityp_(XZ), then X plays Y at the next time step.

(c) At equilibrium,

vP = v,

i.e., the steady state distribution v of the Markov Chain is such that after applying the transition probabilities (i.e., multiplying by the matrix P), we get back the same steady state distribution v. The Eigenvalues of the matrix P are found below:

:det(P-\lambda I)=0\Rightarrow \begin{vmatrix} 0-\lambda & 0.6 & 0.4\n 0.975& 0-\lambda& 0.025\n 0.95& 0.05& 0-\lambda\end{vmatrix}=0

\Rightarrow -\lambda ^3+0.9663\lambda +0.0337=0\n\Rightarrow (\lambda -1)(\lambda ^2+\lambda +0.0337)=0

The solutions are

\lambda =1,-0.0349,-0.9651. These are the eigenvalues of P.

The sum of all the rows of the matrixP-\lambda I is equal to 0 when \lambda =1.Hence, one of the eigenvectors is :

\overline{x} = \begin{bmatrix} 1\n 1\n 1 \end{bmatrix}.

The other eigenvectors can be found using Gaussian elimination:

\overline{x} = \begin{bmatrix} 1\n -0.9862\n -0.9333 \end{bmatrix}, \overline{x} = \begin{bmatrix} -0.0017\n -0.6666\n 1 \end{bmatrix}

Hence, we can write:

P = V * D * V^(-1), where

V = \begin{bmatrix} 1 & 1 & -0.0017\n 1 & -0.9862 & -0.6666 \n 1 & -0.9333 & 1 \end{bmatrix}

and

D = \begin{bmatrix} 1 & 0 & 0\n 0 & -0.9651 & 0 \n 0 & 0 & -0.0349 \end{bmatrix}

After n time steps, the distribution of states is:

v = v_0P^n\Rightarrow v = v_0(VDV^(-1))^n=v_0(VDV^(-1)VDV^(-1)...VDV^(-1))=v_0(VD^nV^(-1)).

Let n be very large, say n = 1000 (steady state) and let v0 = [0.333 0.333 0.333] be the initial state. then,

D^n \approx \begin{bmatrix} 1 & 0 & 0\n 0& 0 &0 \n 0 & 0 & 0 \end{bmatrix}.

Hence,

v=v_0(VD^nV^(-1))=v_0(V\begin{bmatrix} 1 & 0 & 0\n 0 &0 &0 \n 0& 0 & 0 \end{bmatrix}V^(-1))=[0.491, 0.305, 0.204].

Now, it can be verified that

vP = [0.491, 0.305,0.204]P=[0.491, 0.305,0.204].
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