boy can row a boat at a constant rate of 5 mi/hr in still water, as indicated in the figure. He rows upstream for 15 minutes and then rows downstream, returning to his starting point in another 10 minutes.
(a) Find the rate of the current. mi/hr
(b) Find the total distance traveled. mi

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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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.

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 graph of the function is attached below.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function,  f(x) = 3√x -2

To graph the function f(x) = 3√x -2, we can follow these steps:

f(0) = 3√0 - 2 = -2

f(1) = 3√1 - 2 = 1

f(8) = 3√8 - 2 ≈ 4.9

f(27) = 3√27 - 2 ≈ 7.2

Here, the graph of f(x) = 3√x -2 is attached below.

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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)

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

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%

The probability that the last person to board sits in the assigned seat is always 1/2, regardless of the number of people n in the line.

The issue can be tackled utilizing numerical enlistment.

Base Case:

At the point when n = 2, there are two travelers and two seats. The principal traveler takes an irregular seat, and the subsequent traveler will sit in his doled out seat with likelihood 1/2 or take the other seat with likelihood 1/2. Consequently, p2 = 1/2.

Inductive Speculation:

Accept that for some certain number k, pk = 1/2.

Inductive Step:

Think about n = k+1 travelers. The principal traveler takes an irregular seat. There are two cases to consider:

Case 1: The primary traveler sits down relegated to the k+1-th traveler. For this situation, the last traveler will be ensured to sit in his doled out seat, and the leftover k travelers can be considered as a subproblem with similar circumstances. By the inductive speculation, the likelihood that the last traveler in the subproblem sits in his alloted seat is 1/2. Thusly, the likelihood that the last traveler in the first issue sits in his doled out seat for this situation is 1/(k+1) + (k/(k+1)) * 1/2 = (k+2)/(2(k+1)).

Case 2: The primary traveler sits down other than the one doled out to the k+1-th traveler. For this situation, the issue lessens to the case with k travelers, and the likelihood that the last traveler in the decreased issue sits in his doled out seat is pk = 1/2 (by the inductive speculation). Thusly, the likelihood that the last traveler in the first issue sits in his doled out seat for this situation is (k/(k+1)) * 1/2 = k/(2(k+1)).

Joining the two cases, we have:

pk+1 = (k+2)/(2(k+1)) + k/(2(k+1)) = (k+1)/(2(k+1)) = 1/2.

Consequently, by numerical acceptance, the likelihood that the last individual to board sits in the appointed seat is dependably 1/2, no matter what the quantity of individuals n in the line.

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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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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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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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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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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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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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If the length of a rectangle is four times its width. if the area of the rectangle is 256 cm2, the perimeter of the rectangle is 80 cm.

Let's first use the given information to write two equations relating the length and width of the rectangle:

The length L is four times the width W: L = 4W

The area A is 256 cm²: A = LW = 256

Substituting equation 1 into equation 2, we get

4W^2 = 256

Solving for W, we get:

W^2 = 64

W = 8 (since we're looking for a positive value)

Substituting this value back into equation 1, we get:

L = 4W = 32

Therefore, the length and width of the rectangle are 32 cm and 8 cm, respectively.

The perimeter of the rectangle is twice the sum of its length and width:

P = 2(L + W) = 2(32 + 8) = 80 cm

So the perimeter of the rectangle is 80 cm.

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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.

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 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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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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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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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 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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Answer: 8/9

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

48 / 54 = 8/9

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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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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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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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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Answer:

1. 40

2. 351

3. 49

Step-by-step explanation:

just multiply the 2 numbers!

5 times 8 is 40

13 times 27 is 351

7 times 7 is 49

(square is the same on every side so every side is 7)