LORE
38.42
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table.
Running Play Outcomes
Play 1
-3 yards
Play 2
2 yards
Play 3
-1 yard
Play 4
-2 yards
Play 5
-3 yards
Play 6
1 yard
What is the average change in field position per running play?
-6 yards per play
-1 yard per play
Oyards per play
1 yard per play

Answer:

1, commutative property of addition

2. associative property of addition

Step-by-step explanation:

The expected number of minutes until the frogs stop jumping is 4, regardless of their initial positions.

Let's consider the probability that all three frogs are at different vertices at a given time. The first frog can land on any of the 12 vertices, the second frog can land on either of the two adjacent vertices to the first frog, and the third frog can land on either of the two adjacent vertices to the second frog that are not adjacent to the first frog. Therefore, the probability that all three frogs are at different vertices is:

\(P(all $ different) = 12 * 2/11 * 2/10 = 24/55\)

If all three frogs are at different vertices, then none of them can jump to the other two vertices adjacent to their current position, otherwise they will meet. Therefore, the next time they can meet is after the first jump of the frog that is alone, and this will happen with probability 1/3.

If two frogs meet, the expected number of minutes until the third frog joins them is just the expected number of minutes until two frogs meet, which is the same as the expected number of minutes until the frogs stop jumping. Therefore, it suffices to compute the expected number of minutes until the frogs jump to the same vertex for the first time, given that all three frogs are at different vertices.

Let T be the expected number of minutes until the frogs jump to the same vertex for the first time. Conditioning on the first jump, we have:

\(T = 1/3 * 1 + 2/3 * (T + 1)\)

The first term corresponds to the case where the frog that is alone jumps to one of the two vertices adjacent to one of the other frogs and they meet. The second term corresponds to the case where the frog that is alone jumps to the vertex adjacent to the other frog and the third frog jumps to the same vertex with probability 1/2, or they jump to different vertices with probability 1/2 and we are back to the starting position, but with one less frog being alone.

Solving for T, we get:

T = 4

Therefore, the expected number of minutes until the frogs stop jumping is 4, regardless of their initial positions.

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Answer:

this is the answer but it must be 20 character long

8x+3

Answer:

$15 more

Step-by-step explanation:

first divide 20 by 4 and that is 5

then subtract 5 from 20 and the difference is 15

therefore the difference is $15 more :)

(a) The runtime of the code is O(\(n^3\)), representing a cubic time complexity. (b) The runtime of the code is O(n), representing a linear time complexity. (c) The runtime of the code is O(log n), representing a logarithmic time complexity.

(a) Deriving the runtime of the nested loops:

Let's analyze the code:

```cpp

for (i = 1; i <= n; i++) {

   for (j = n; j >= 1; j--) {

       for (k = 1; k <= i + j; k++) {

           // Some constant number of atomic/elementary operations

       }

   }

}

```

The outer loop runs `n` times, the middle loop also runs `n` times, and the inner loop runs `i + j` times.

For each iteration of the innermost loop, a constant number of atomic/elementary operations are performed. Let's denote this constant as `c`.

The number of iterations of the innermost loop can be approximated as `2n` because in the worst case, `i` and `j` can both reach their maximum values of `n`.

Now, let's calculate the total runtime:

T(n) = c * (2n) * n * n

     = 2c * \(n^3\)

Therefore, the runtime of the code is O(\(n^3\)), representing a cubic time complexity.

(b) Deriving the runtime of the nested loops:

```cpp

for (i = 1; i <= n - 8; i++) {

   for (j = i; j <= i + 8; j++) {

       // No operations within the inner loop

   }

}

```

In this case, the outer loop runs `(n - 8)` times, and the inner loop runs `(i + 8 - i + 1) = 9` times, which is a constant number.

Thus, the runtime of the code is proportional to `(n - 8) * 9`, which simplifies to `9n - 72`.

Therefore, the runtime of the code is O(n), representing a linear time complexity.

(c) Deriving the runtime of the loop:

```cpp

i = n;

while (i >= 2) {

   for (j = 1; j <= i; j++) {

       // No operations within the loop

   }

   i = i / 2;

}

```

In this case, the outer loop runs logarithmically with base 2. The value of `i` is halved in each iteration until it becomes less than 2.

Let `k` represent the number of iterations of the outer loop. Then, we have:

\(2^k\) <= n

k <= log2(n)

Hence, the runtime of the code is O(log n), representing a logarithmic time complexity.

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Mary used 66 pounds of type A coffee and 82 pounds of type B coffee to make a total of 148 pounds of the blend, with a total cost of $694.20.

Let's assume Mary used x pounds of type A coffee and (148 - x) pounds of type B coffee.

The cost of type A coffee is $5.30 per pound, so the cost of the type A coffee used is 5.30x.

The cost of type B coffee is $4.20 per pound, so the cost of the type B coffee used is 4.20(148 - x).

According to the given information, the total cost of the blend is $694.20. Therefore, we can set up the equation:

5.30x + 4.20(148 - x) = 694.20

Simplifying and solving for x

5.30x + 621.60 - 4.20x = 694.20

1.10x = 72.60

x = 66

Mary used 66 pounds of type A coffee. Therefore, she used (148 - 66) = 82 pounds of type B coffee.

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To create a sign chart for the polynomial function F(x) = -(x+5)(x-2)(2x-4)(x-4)², we will examine the intervals defined by the critical points and the zeros of the function.

1. Determine the critical points  -

  - The critical points occur where the factors of the polynomial change sign.

  - The critical points are x = -5, x = 2, x = 4, and x = 4 (repeated).

2. Select test points within each interval  -

  - To evaluate the sign of the polynomial at each interval, we choose test points.

  - Common choices for test points include values less than the smallest critical point, between critical points, and greater than the largest critical point.

  - Let's choose test points  -  x = -6, x = 0, x = 3, and x = 5.

3. Evaluate the sign of the polynomial at each test point

  - Plug in the test points into the polynomial and determine the sign of the expression.

The sign chart for F(x) = -(x+5)(x-2)(2x-4)(x-4)² would look like this

Intervals              Test Point         Sign

-∞ to -5                  -6                    -

-5 to 2                   0                       +

2 to 4                    3                      -

4 to ∞                    5                      +

Note  - The signs in the "Sign" column indicate whether the polynomial is positive (+) or negative (-) in each interval. See the attached sign chart.

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The solution to the equation is (a) -2.

To solve the equation log(3x) = log(2) + log(x - 1), we can use the properties of logarithms.

According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:

log(3x) = log(2(x - 1))

Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:

3x = 2(x - 1)

Expanding the equation:

3x = 2x - 2

Bringing all terms to one side:

3x - 2x = -2

x = -2

Therefore, the solution to the equation is x = -2.

The correct answer is (a) -2.

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Answer:

is it 1?

Step-by-step explanation:

To solve for m, divide both sides by 5/6

M = 85/ 5/6

When dividing by a fraction flip the fraction over and multiply

M = 85 x 6/5 = (85 x 6)/5 = 510/5 = 102

He drove 102 miles on Monday

Answer: hello your question is incomplete attached below is the complete question

answer : AEIJKGFCH

Step-by-step explanation:

The first Image is the first part of the question, to write the correct order of letter to the finish line, we will use the details on the first image.

Hence the Correct order of letter to the Finish line: AEIJKGFCH

Problem

Evaluate. 7(n + 5) = (7 x 4) + (7 x 5)

Solution

For this case we can distribute the terms in the left

7n +35 = 28 +35

And we can subtract 35 in both sides and we got:

7n = 28+35-25= 28

7n =28

And dividing both sides by 7 we got:

n = 28/7 = 4

And then the solution for this case would be:

n=4

Answer:

just be like im really trying to work on getting my grades up i fell off a little bit bc of some stuff at home and im busy sometimes but im serious about my work and it would mean the world to me if you could let me redo some assignents that i failed or that are locked i want my parents to be proud of me for once, thanks (they name)

Step-by-step explanation:

The probability (>6)?" is 0.

The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event is rolling a number greater than 6 on a standard six-sided die.

Since there are no numbers greater than 6 on a six-sided die, the number of favorable outcomes is 0. The total number of possible outcomes is 6 (the numbers 1 through 6 on the die).

Therefore, the probability of rolling a number greater than 6 is 0/6, or 0. In other words,

it is impossible to roll a number greater than 6 on a standard six-sided die. So, the answer to the question "what is the probability (>6)?" is 0.

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Answer:

  8 is Your answer.

Answer:

that's the answer

Step-by-step explanation:

hope it help

Answer:

x+6/x-9

Step-by-step explanation:

Hope this helps

Answer:

B = 119! The answer is 119!

Step-by-step explanation:  

The augmented matrix is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

We have given system of linear equation is,

\(x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.\)

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

\(1\ -1\ -4\ 5\)

the second row is

\(2\ 0\ 2\ 0\)

and the third row is

\(4\ 1\ 1\ 3\)

Therefore the augmented matrix for this linear system is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

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The augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.

The given equation has three variables so the matrix form will be of \(3\times3\)

The given linear equations are

\(x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3\)

From the above equations, we will make an augmented matrix.

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The first equation will be followed by the first row of the matrix and the rest will be followed the same.

Thus the augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

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Answer:

p < -2 that's is the solution

Answer:

60 mph

Step-by-step explanation:

Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:

\(D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45\)

The distance between both cars is given by:

\(D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\\)

Solving the quadratic equation for the velocity of the eastbound car:

\(18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph\)

The velocity of the southbound car is:

\(S=E+15=45+15\\S=60\ mph\)

The southbound car is driving at 60 mph.

The value of the sample statistic is used to estimate the value of the population parameter.

The sample statistic is the value that is calculated from the sample data, which is used to make inferences about the population parameter. Sample statistics are used to estimate population parameters. A sample statistic is an estimate of a population parameter that is obtained from a sample, whereas a population statistic is a value that is computed from a population.

Therefore, the correct answer is a. sample statistic.

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Answer:

√113

10.6301458127

10.63 (2 d.p)

Step-by-step explanation:

The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²]

x₂ = (-1)

x₁ = 6

y₂ = 8

y₁ = 16

Substitute those values into the equation:

√[(-1 - 6)² + (8 - 16)²]

Perform the arithmetic (the subtractions inside the brackets:

√[(-7)² + (-8)²]

Square the values:

√[49 + 64]

Add them

√[113]

Calculate the square root of the value:

√[113] = 10.6301458127

Whether you want the answer in one of these forms, it's up to you/your teacher:

√113

10.6301458127

10.63 (2 d.p)

Answer:

135.55

Step-by-step explanation:

Answer:

53degree

82+45=127

We know

There is 180 degree in the angle

For the missing value

180-127= 53

Answer:

Answer is in the attached screenshot! :)

Step-by-step explanation:

Please let me know if you have any questions! :)

A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

\(n = (Z^2 × p × (1-p)) / E^2\)
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

\(n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2\)
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

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Applying the leg rule, the length of UX in the right triangle is: 4.92 units.

The leg rule relates the length of the hypotenuse of a right triangle and its legs. It is given as:

Hypotenuse/leg = leg/part.

Given the following:

Plug in the values

13/8 = 8/UX

Cross multiply:

13(UX) = 64

UX = 64/13

UX = 4.92 units

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According to the information we can infer that participants are likely to make more accurate decisions about which cards to flip over in the new version, likely because the new content makes the problem more concrete and relatable to everyday life (option B).

In the new version of the Wason four-card task, the content involves a familiar scenario of reading a textbook and receiving an exam grade. This scenario is more relatable to everyday life compared to the original version with abstract numbers and letters.

When a problem is relatable and has real-life context, participants tend to have a better understanding of the situation and are more likely to make accurate decisions. The content of the new version provides participants with a clearer mental model, allowing them to relate the "if-then" conditional statement to their own experiences.

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