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3 years ago

Each term in the sequence below is 20 less than 5 times the previous term. What is the value of x+y?

Mathematics

1 answer:

ziro4ka [17]3 years ago

5 0

Answer:

The value of x + y is -16.

Step-by-step explanation:

If each term is calculated by multiplying the previous one times 5 and then subtracting 20 from that result, then we can use that information to relate the first term (x) and the second one (0).

Following the info above, the following equation applies:

0 = 5 x - 20

then we solve for x:

5x = 20

x = 20/5

x = 4

Now we do the same study relating the second term (0) and the third one (y):

y = 5 (0) - 20

y = -20

Now that we have the value for both unknowns, we can estimate what they ask you: The value of x + y:

x + y = 4 + (-20) = 4 - 20 = -16

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HW7. In a weighted voting system with four players the winning coalitions are the following: {P1, P2, P3, P4}, {P1, P2, P3}, {P1

ehidna [41]

Answer:

Step-by-step explanation:

a). Underline the critical player(s) in each winning coalition?

{P1, P2, P3, P4}, {P1, P2, P3}, {P1, P2, P4}, {P1, P3, P4}, {P2, P3, P4}, {P1, P2}, {P1, P3}, {P1, P4}

b). Find the Banzhaf power distribution of the weighted voting system?

12 instances of criticality P1: 6/12 = .5P2: 2/12 = 16.66%P3: 2/12 = 16.66%P4: 2/12 = 16.66%

c). Determine which players, if any, are dictators, and explain briefly how you can tell?

There are no dictators in this weighted voting system, since no one player is alone in a winning coalition; equivalently, no one player has 100% of the power.

d). Determine which players, if any, have veto power, and explain briefly how you can tell?

There are no veto power players, since no player is critical in the grand coalition.

e). Determine which players, if any, are dummies, and explain briefly how you can tell?

There are no dummies, since each player is critical in at least one winning coalition.

6 0

4 years ago

Read 2 more answers

What is the sequence rule for : 1.8, 2.58, 3.90, 4.95, 6

slamgirl [31]

I believe there is a typo in the problem. It should be:<span>1.8, 2.85, 3.90, 4.95, 6
If that was the case, the answer will be easy.

In this sequence, the rule is start at 1.80 then keep add 1.05. You can try to put them all into the equation

</span>1.80 + 1.05= 2.85
2.85+ 1.05= 3.90
3.90+ 1.05= 4.95
4.95+ 1.05= 6.00

7 0

4 years ago

Please help me.....................

Alenkasestr [34]

Answer:

87.92 in

Step-by-step explanation:

The formula for the circumference of a circle is C=2πr.

C = 2(3.14)(14) = 87.92

4 0

3 years ago

Let an = –3an-1 + 10an-2 with initial conditions a1 = 29 and a2 = –47. a) Write the first 5 terms of the recurrence relation. b)

zlopas [31]

We can express the recurrence,

$\begin{cases}a_1=29\\a_2=-47\\a_n=-3a_{n-1}+10a_{n-2}7\text{for }n\ge3\end{cases}$

in matrix form as

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}\begin{bmatrix}a_{n-1}\\a_{n-2}\end{bmatrix}$

By substitution,

$\begin{bmatrix}a_{n-1}\\a_{n-2}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}\begin{bmatrix}a_{n-2}\\a_{n-3}\end{bmatrix}\implies\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}^2\begin{bmatrix}a_{n-2}\\a_{n-3}\end{bmatrix}$

and continuing in this way we would find that

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}\begin{bmatrix}a_2\\a_1\end{bmatrix}$

Diagonalizing the coefficient matrix gives us

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}-5&0\\0&2\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

which makes taking the $(n-2)$ -th power trivial:

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}-5&0\\0&2\end{bmatrix}^{n-2}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}(-5)^{n-2}&0\\0&2^{n-2}\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

So we have

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}(-5)^{n-2}&0\\0&2^{n-2}\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}\begin{bmatrix}a_2\\a_1\end{bmatrix}$

and in particular,

$a_n=\dfrac{29\left(2(-5)^{n-1}+5\cdot2^{n-1}\right)-47\left(-(-5)^{n-1}+2^{n-1}\right)}7$

$a_n=\dfrac{105(-5)^{n-1}+98\cdot2^{n-1}}7$

$a_n=15(-5)^{n-1}+14\cdot2^{n-1}$

$\boxed{a_n=-3(-5)^n+7\cdot2^n}$

6 0

3 years ago

I need help with 28,29,30 <br> Also can you explain how you got it? Please help me

koban [17]

Answer:area of big square is 9x6 = 54 sq ft. Area of smaller square is 6x4 = 24 square feet. So if you throw a dart, you have a 24/54 or 4/9 chance of hitting the shaded spot.

Step-by-step explanation:

4 0

4 years ago