Find the mean 12, 13, 15, 16, 24, 15, 22, 10, 9, 13, 13, 18, 16, 25, 23, 24

Round to two decimals

The value of the matrix E is such that EA = D (E is the product of the two elementary matrices corresponding to the two-row operations) will be:

Matrix E = | 0 1 0 |

                | 1 0 0 |

We can find the elementary matrices corresponding to the two-row operations and multiply them together to obtain the matrix E.

First-row operation: Add -4 times the first row to the second row.

This is equivalent to multiplying A on the left by the elementary matrix:

| 1 0 0 |

|-4 1 0 |

| 0 0 1 |

Call this matrix E1.

E1A =

|  1 2 4    |     | 1 0 0  |     | 1 2 4    |

|-4 -6 -12| *   | -4 1 0 | = |-5 -6 -2 |

| 3 4 3    |     | 0 0 1  |    | 3 4 3    |

Next row operation: Swap the first and third rows.

This is equivalent to multiplying E1A on the left by the elementary matrix:

| 0 0 1 |

| 0 1 0 |

| 1 0 0 |

Call this matrix E2.

E2E1A =

| 3  4    3 | | 0 0 1 |   | -5 -6 -2 |

|-4 -6 -12| *| 0 1 0 | = | -4 -2 4 |

| 1   2   4  | | 1 0 0 |     | 1 2 4 |

Therefore, the matrix E that satisfies EA = D is given by:

E = E2E1 = | 0 0 1 | | 1 0 0 |

E = | 0 0 1 |

EA = D

| 0 1 0 | * |-4 1 0 | = | 0 1 0 |

| 1 0 0 |   | 0 0 1 |    | 1 0 0 |

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The notation for this sample is denoted by [tex]\overline{x}[/tex].

The entire group about whom you want to make conclusions is referred to as a population.

The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

Given, In a survey of 1917 cell phone users, the mean was 13.10 phone calls a day.

This a sample so the notation for the mean is [tex]\overline{x}[/tex].

If it is for population then the notation of mean would have been [tex]\mu[/tex].

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The probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%. The probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%. The expected number of e-mails received during 15 minutes is 1.25. The probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%

We know that the average number of e-mails received per hour is 5. Therefore, the parameter λ of the Poisson distribution is also 5, since the Poisson distribution's mean and variance are both equal to λ.

The probability of receiving no e-mails during an hour (or during any other fixed time interval of length t) can be calculated using the Poisson distribution as follows:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-5) * 5^0 / 0! ≈ 0.0067

Therefore, the probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%.

The probability of receiving at least three e-mails during an hour can be calculated as follows:

P(X ≥ 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We already know the value of P(X = 0) from part (a), so we just need to calculate P(X = 1) and P(X = 2) using the Poisson distribution:

P(X = 1) = e^(-5) * 5^1 / 1! ≈ 0.0337

P(X = 2) = e^(-5) * 5^2 / 2! ≈ 0.0842

Substituting these values into the equation above, we get:

P(X ≥ 3) = 1 - (0.0067 + 0.0337 + 0.0842) ≈ 0.8754

Therefore, the probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%.

Since the expected number of e-mails received per hour is 5, the expected number of e-mails received during 15 minutes (i.e., a quarter of an hour) is:

E(X) = λ * t = 5 * (1/4) = 1.25

Therefore, the expected number of e-mails received during 15 minutes is 1.25.

The probability of receiving no e-mails during 15 minutes can be calculated using the Poisson distribution with λ = 1.25 and t = 1/4:

P(X = 0) = e^(-λt) * (λt)^0 / 0! = e^(-1.25/4) * (1.25/4)^0 / 0! ≈ 0.7788

Therefore, the probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%.

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Answer: We can start by expanding the square on the left-hand side of the equation:

(s + t)^2 = s^2 + 2st + t^2

We know that s^2 + t^2 = 6, so we can substitute that into the equation:

(s + t)^2 = 6 + 2st

We also know that st = c + 5, so we can substitute that into the equation:

(s + t)^2 = 6 + 2(c + 5)

Simplifying the right-hand side:

(s + t)^2 = 6 + 2c + 10

So, in terms of c, (s + t)^2 = 6 + 2c + 10.

Step-by-step explanation:

Answer:

$2.79

Step-by-step explanation:

We know

Peter bought a sandwich for $4.25, a drink for $2.17, and a cookie for $0.79.

4.25 + 2.17 + 0.79 = $7.21

If he paid with a $10 bill, how much change did Peter get?

10 - 7.21 = $2.79

So, Peter get $2.79 in change.

The speed of the fire is 3.214 miles per hour (rounded to three decimal places)

It is defined as the distance traveled by an object per unit of time, typically in meters per second (m/s) or kilometers per hour (km/h).

Speed can be calculated by dividing the distance traveled by the time taken to cover that distance. It is a scalar quantity, meaning it only has magnitude and no direction.

Let's call the horizontal distance the fire advanced during the 6 minutes "d." We can use the tangent function to find d:

tan(12.3°) = (3334 - h) / d

tan(10.5°) = (3334 - h) / d

Solving for d in each equation, we get:

d = (3334 - h) / tan(12.3°)

d = (3334 - h) / tan(10.5°)

Since the time interval is the same for both observations, the fire advanced a distance equal to the difference between the two distances:

d = [(3334 - h) / tan(12.3°)] - [(3334 - h) / tan(10.5°)]

Plugging in the values and simplifying:

d = 1698.5 feet (rounded to the nearest tenth)

To find the speed at which the fire is spreading towards the ranger, we need to convert the distance from feet to miles, and the time from minutes to hours:

d = 1698.5 feet / 5280 feet per mile = 0.3214 miles

t = 6 minutes / 60 minutes per hour = 0.1 hours

The speed of the fire is then:

s = d / t = 0.3214 miles / 0.1 hours = 3.214 miles per hour (rounded to three decimal places)

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Answer:

Step-by-step explanation:

h = 100 *  400000 - 20000 / 20000   =  38000000/ 20000  = 1900/1  = 1900%

Please find attached the graph of the function of the length with respect to the width of the rectangle, created with MS Excel, where, 1 ≤ W ≤ 11, and the perimeter of the rectangle is 24 cm.

A graph of a function, is a representation of the ordered pairs of the points of the function, (x, f(x)), on the coordinate plane.

Whereby the figure is a rectangle, we get;

Perimeter = 2 × Length of the rectangle + 2 × Width of the rectangle

Let P represent the perimeter of the rectangle and let L represent the length of the rectangle and let W represent the width of the rectangle, we get;

P = 2·L + 2·W

The perimeter of the rectangle. P = 24

Therefore;

24 = 2·L + 2·W

2·L = 24 - 2·W

L = (24 - 2·W)/2 = 12 - W

L = 12 - W

The graph of the above linear equation representing the length of the rectangle, L, where the width, W is; 1 ≤ W ≤ 11.

Please find attached the required graph of length, L to the width W of the rectangle created with MS Excel

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Answer: 8/9

Step-by-step explanation: 3 x 16 = 48 ounces

48 / 54 = 8/9

The number of cells in the Petri dish after 10 hours is 2¹⁰ = 1024 cells in the dish.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The number of cells in the Petri dish after each hour can be represented by the expression 2ⁿ, where n is the number of hours that have passed.

So, after 1 hour, there are 2¹ = 2 cells in the dish.

After 2 hours, there are 2² = 4 cells in the dish.

After 3 hours, there are 2³ = 8 cells in the dish.

And so on.

Therefore, after 10 hours, there are 2¹⁰ = 1024 cells in the dish.

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a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16

b) Probability that not all ticketed passengers who show up can be accommodated is 0.67

c) The probability that you will be able to take the flight is 96%

Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights

In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.

(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.

(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is

=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.

(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.

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Answer:

1 /2

Step-by-step explanation:

3×1 = 3

So it is 3 /6 = 1/2

3/6 ÷2 = 1/2

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

A pentagon has a 41.5 cm circumference, and its sides are each 8.3 cm long.

When you already know the value of one side, calculating the perimeter of a pentagon is made much simpler. The five sides of each pentagon are equal. If the length of one side is given to you.

Since a pentagon has five sides, we will abbreviate each side's length as "s". The lengths of all five sides add up to the perimeter of the pentagon, allowing us to formulate the following equation:

5s = 41.5

We must put "s" on one side of the equation alone in order to solve for it. Divide both sides by 5 to do this: s = 8.3

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The equation of the plane passing through P1(12,3), P2(3,2,1), and perpendicular to the plane 4−y+2z=7 is -3x + 51y - 8z = -39.

To find a plane that passes through the points P1(12,3) and P2(3,2,1) and is perpendicular to the plane 4−y+2z=7, we can follow these steps:

Find the normal vector of the given plane by taking the coefficients of x, y, and z in the equation 4−y+2z=7. The normal vector is (1, -1, 2), because the coefficients of x, y, and z are 1, -1, and 2 respectively.

Find the direction vector of the line passing through P1 and P2 by subtracting the coordinates of P1 from P2. The direction vector is (-9, -1, -2), because P2 - P1 = (3-12, 2-3, 1-0) = (-9, -1, -2).

Find the cross product of the normal vector of the given plane and the direction vector of the line passing through P1 and P2 to get the normal vector of the plane we are looking for. The cross product is:

(1, -1, 2) x (-9, -1, -2) = (-3, -17, -8)

Plug one of the given points, say P1(12,3), and the normal vector we found in step 3 into the point-normal form of the equation of a plane:

-3(x - 12) - 17(y - 3) - 8(z - 0) = 0

Simplifying, we get:

-3x + 51y - 8z = -39

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Answer:

a. (-0.93,-0.37)

Step-by-step explanation:

The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of a coordinate plane. To find the coordinates of a point on the unit circle corresponding to a given central angle, we can use the relationship between the angle and the coordinates of the point.

For a central angle of 202 degrees, the point on the unit circle would be found by using the formula:

x = cos(202°)

y = sin(202°)

Rounding the results to the nearest hundredth, we have:

x = -0.927

y = -0.3746

So the coordinates of the point on the unit circle corresponding to the central angle of 202 degrees are (-0.93, -0.37).

Answer:

a. (-0.93, -0.37)

Step-by-step explanation:

A unit circle has its center at (0, 0) and a radius of 1.

The coordinates on the unit circle (x, y) are equivalent to (cos θ, sin θ), where θ is the angle (measured anticlockwise from the positive x-axis).

Therefore, given θ = 202°, the coordinates of the corresponding point on the unit circle are:

Therefore, the point on the unit circle is (-0.93, -0.37).

The required interval of domain for the composite function is  [-2, 3].

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The domain of fog(x) is the set of all values of x for which the composition function fog(x) is defined.

fog(x) means that we plug g(x) into f(x), so we have:

fog(x) = f(g(x)) = f(x^2 - x) = √(6 - (x^2 - x))

= √(6 - x^2 + x)6

For the expression under the square root to be defined, we must have 6 - x^2 + x ≥ 0. This is a quadratic inequality that can be factored as:

-(x - 3)(x + 2) ≤ 0

The solutions of this inequality are -2 ≤ x ≤ 3.

However, we also need to check that the expression under the square root is non-negative, so we need to exclude the values of x that make 6 - x^2 + x < 0. This inequality holds for x < -2 or x > 3.

Therefore, the domain of fog(x) is [-2, 3].

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Answer:

Infinitely many solutions

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{-16+n+14n=-16+15n}[/tex]

Which can be simplified (for left side) to:

[tex]\displaystyle{-16+15n=-16+15n}[/tex]

Both sides are same, meaning that there are infinitely many solutions since no matter which n-values you substitute in, you'll end up getting true equation.

On the SAT her z-score was 1.4 and on the ACT her z-score was 1.5 Thus, due to the higher z-score, she performed better on the ACT.

The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the ACT scores utilizing the Z- score -

Z = X - u/a

Calculating the SAT score -

Where X = 1850, u = 1500 and a = 250

Z = 1850 - 1500/250

= 350/250

= 1.4

Similarly,

Calculating the ACT score -

Where X = 28, u = 20.8 and a = 4.8

Z = 28 - 20.8/4.8

= 7.2/4.8

= 1.5

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The probability that X is between 90 and 110 = 0.2 if a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.40.

The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.

The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare. Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.

A normally distributed random variable x has a mean of 100

P(x < 90) = 0.4

The probability that X is between 90 and 110

Mean is 100

Hence P (< 100) = 0.5  as Mean is centered

Hence

P  (90 < X < 100) = 0.5 - 0.4 = 0.1

The difference between 100 and 90 is 10

The difference between 100 and 110 is 10

and 100 is Mean

Hence P  (100 < X < 110) = P  (90 < X < 100) = 0.1

Adding Both

P ( 90 < X < 110) = 0.1 + 0.1 = 0.2

The probability that X is between 90 and 110 = 0.2

Using z score table.

Z  = ( Value - Mean) /SD

Z score for 0.4 = -0.254

-0.253 = (90 - 100)/SD

SD ≈ 39.53

Z = ( 110 - 100)/39.53

Z = 0.253

For z score  < 0.253, the probability is 0.6

Hence Probability in Between is 0.6 - 0.4 = 0.2

The probability that X is between 90 and 110 = 0.2

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The height of the triangle is 3/5.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

A right-angled triangle.

Let the values of the hypotenuse in parts be m and n.

So,

(1)² = (5/4)m

m = 4/5

And n = 9/16 x 4/5

n = 9/20

So, the height of the triangle is,

h² = 9/20 x 4/5

h² = 9/25

h = 3/5

Therefore, h = 3/5.

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The numbers that are solutions to the inequality k > -5 are given as follows:

A. -4.

F. -4.99.

G. -0.5.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is given as follows:

k > -5.

Meaning that the solutions are all the numbers that are greater than -5.

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The vectorial equation of the line that passes through (4, 0, - 3) and is parallel to the vector <2, - 4, 6> is equal to (x, y, z) = (4, 0, - 3) + t · (2, - 4, 6).

According to linear algebra, three-dimension lines can be derived from the knowledge of a point and a vector slope, whose formula is introduced below:

(x, y, z) = P(x, y, z) + t · M(x, y, z)

Where:

Two lines are parallel when they have the same vector slope. If we know that P(x, y, z) = (4, 0, - 3) and M(x, y, z) = (2, - 4, 6), then the vectorial equation of the line is:

(x, y, z) = (4, 0, - 3) + t · (2, - 4, 6)

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Answer:

1/2 (half)

Step-by-step explanation:

4f over 2g then 1f over x

2/4 to get 1/2

each friend gets half (1/2)

Answer:

Communist countries use authoritarian governments because it requires the absolute obedience to authority figures. Communism is an extreme form of socialism because there is no private ownership or political freedom.

Step-by-step explanation:

The four points on the graph of this function f(x) = √(x + 1) + 4 has been plotted on the graph shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given absolute value function f(x) = √(x + 1) + 4 as shown in the graph attached below.

By observing critically the graph (see attachment), the four ordered pairs (points) that fit on its axes include the following:

Ordered pair = (-1, 4), which is the leftmost.

Ordered pair = (0, 5).

Ordered pair = (3, 6).

Ordered pair = (8, 7).

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Answer:

ur mom jk its

c

Step-by-step explanation:

The ordered pair that doesn't represent a function is: D.. {(-1,7), (7, 1), (5,-7), (7,-8)}.

A function is a mathematical concept that associates an input (or argument) to a unique output (or value). In mathematical notation, a function is represented as f(x), where x is the input, and f(x) is the output. The association between the input and output is defined by a set of rules, or a formula, that assigns a unique output value to each input value

In a function, for each unique x-value, there must be exactly one corresponding y-value.

D. {(-1,7), (7, 1), (5,-7), (7,-8)} does not represent a function because the same x-value (7) corresponds to two different y-values (1 and -8).

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Based on the information, we can infer that the range is an adequate indicator to affirm that the price difference of the Big Mac in different countries is minimal.

To find the range of the given data we must perform the following procedure:

We must find the highest and lowest data, in this case the highest and lowest data are 6.8 and 1.98 respectively. So, to find the range we must find the difference between these two data:

6.8 - 1.89 = 4.91

To find the variance we must apply the following formula:

S² = 1 / 11 - 1 ( 205.59 - (44.67)²/11)

S² = 2.42

To find the standard deviation we must apply the following formula:

S = [tex]\sqrt[n]{variance}[/tex]

S = [tex]\sqrt{2.42}[/tex]

S = 1.56

Based on the above data, we can infer that the range is an indicator that the difference in the Big Mac price in different countries is minimal.

Note: This question is incomplete. Here is the complete information:

Attached image

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