A fisherman can row upstream at mph and downstream at mph. he started rowing upstream until he got tired and then rowed downstream to his starting point. how far did the fisherman row if the entire trip took ​hours?

The expanded form of a number is helpful because it allows us to understand the value and place of each digit within the number. By writing a number in expanded form, we can break it down into its constituent parts, making it easier to comprehend and manipulate.

Here are a few ways in which the expanded form is helpful:

1. Place value understanding: The expanded form helps us understand the place value of each digit within the number. It shows how each digit contributes to the overall value of the number based on its position. For example, in the number 325, the digit 5 is in the ones place, the digit 2 is in the tens place, and the digit 3 is in the hundreds place. The expanded form makes it clear that the number is composed of 3 hundreds, 2 tens, and 5 ones.

2. Addition and subtraction: When performing addition or subtraction with multi-digit numbers, the expanded form allows us to align the digits correctly based on their place value. This makes it easier to carry or borrow when necessary. For example, when adding 325 and 187, we can break down the numbers into their expanded forms (300 + 20 + 5) and (100 + 80 + 7) and then perform the addition digit by digit.

3. Number sense and estimation: The expanded form helps develop number sense and estimation skills. By breaking down a number into its expanded form, we can quickly assess the magnitude of each digit and understand the overall value of the number. This can be useful for estimating or approximating calculations.

4. Place value manipulations: The expanded form allows us to manipulate the digits of a number based on their place value. This is particularly helpful when dealing with operations like multiplication and division, where we need to consider the place value of each digit to obtain the correct result.

In summary, the expanded form of a number provides valuable information about the value and place of each digit, aiding in understanding, calculation, estimation, and manipulation of numbers.

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Answer:

a = 8

Step-by-step explanation:

The question has given us the following equation of a line:

[tex]y-2= \frac{2}{7}(x-1)[/tex],

and told us that it contains the point (a, 4). It then asks us to find the value of a.

To do this, we have to understand the following: since point (a, 4) is on the given line, these coordinates satisfy the equation of the line. In other words, if we substitute the given values into the equation, the equality will still be valid.

Therefore, we can simply substitute (a, 4) into the equation and then solve for a:

[tex]y-2= \frac{2}{7}(x-1)[/tex]

⇒ [tex]4 - 2 = \frac{2}{7}(a-1)[/tex]

⇒ [tex]2 = \frac{2}{7}(a - 1)[/tex]

⇒ [tex]2 \div \frac{2}{7} = a - 1[/tex]      [Dividing both sides of the equation by [tex]\frac{2}{7}[/tex]]

⇒ [tex]2 \times \frac{7}{2} = a-1[/tex]      [Dividing by a fraction is the same as multiplying by its reciprocal]

⇒  [tex]\frac{14}{2} = a - 1[/tex]

⇒ [tex]7= a - 1[/tex]

⇒ [tex]a = 7 + 1[/tex]            [Adding 1 to both sides]

⇒ [tex]a = \bf 8[/tex]

Therefore, the value of a is 8.

The volume of the cone is,

V = 28.1 millimeters

We have to give that,

An oblique cone with a height of 10.5 millimeters and a radius of 1.6 millimeters.

Since the Volume of the cone is,

V = πr²h/3

Here, r = 1.6 millimeters

h = 10.5 millimeters

Substitute all the values,

V = 3.14 × 1.6² × 10.5 / 3

V = 80.4/3

V = 28.1 millimeters

Therefore, The volume is,

V = 28.1 millimeters

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Answer:

In any polygon, the sum of the exterior angles' measures is 360°.

59° + 68° + 75° + 37° + 63° + g = 360°

302° + g = 360°

g = 58°

The value of x that makes ABCD an isosceles quadrilateral is x = 11.

To determine the value of x that makes ABCD an isosceles quadrilateral, we need to find the condition where AB is congruent to CD and BC is congruent to AD.

In an isosceles quadrilateral, opposite angles are congruent.

So, we can set up an equation based on the given angle measures:

m∠ABC = m∠CDA   (opposite angles)

4x + 11 = 2x + 33   (substituting the given angle measures)

4x - 2x = 33 - 11

2x = 22

x = 11

Hence, the value of x that makes ABCD an isosceles quadrilateral is x = 11.

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The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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The solution of number after multiplication is,

⇒ [tex]2^{29/12}[/tex]

We have to give that,

An expression to simplify,

⇒ ⁴√8 × ∛32

Now, Multiplying numbers is not possible without simplifying because the nth power of numbers is not the same.

Hence, We can simplify the numbers as,

⇒ ⁴√8 × ∛32

⇒ ⁴√(2×2×2) × ∛(2×2×2×2×2)

⇒ ⁴√(2)³ × ∛2⁵

⇒ [tex]2^{3/4} * 2^{5/3}[/tex]

⇒ [tex]2^{\frac{3}{4} + \frac{5}{3} }[/tex]

⇒ [tex]2^{29/12}[/tex]

Therefore, The solution of number after multiplication is,

⇒ [tex]2^{29/12}[/tex]

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Answer:

Step-by-step explanation:

To apply the Rational Root Theorem to the equation 2x³ - 5x + 4 = 0, we need to determine the possible rational roots. The Rational Root Theorem states that any rational root of a polynomial equation with integer coefficients must be of the form p/q, where p is a factor of the constant term (in this case, 4) and q is a factor of the leading coefficient (in this case, 2).

The factors of 4 are ±1, ±2, and ±4.

The factors of 2 are ±1 and ±2.

Therefore, the possible rational roots can be expressed as:

±1/1, ±1/2, ±2/1, ±2/2, ±4/1, ±4/2.

Simplifying these fractions:

±1, ±1/2, ±2, ±1, ±4, ±2.

Now, we need to check if any of these possible rational roots are actual roots of the equation. We can do this by substituting each value into the equation and checking if the equation equals zero.

Checking ±1:

For x = 1:

2(1)³ - 5(1) + 4 = 2 - 5 + 4 = 1 ≠ 0

For x = -1:

2(-1)³ - 5(-1) + 4 = -2 + 5 + 4 = 7 ≠ 0

Checking ±1/2:

For x = 1/2:

2(1/2)³ - 5(1/2) + 4 = 1/4 - 5/2 + 4 = -3/4 ≠ 0

For x = -1/2:

2(-1/2)³ - 5(-1/2) + 4 = -1/4 + 5/2 + 4 = 15/4 ≠ 0

Checking ±2:

For x = 2:

2(2)³ - 5(2) + 4 = 16 - 10 + 4 = 10 ≠ 0

For x = -2:

2(-2)³ - 5(-2) + 4 = -16 + 10 + 4 = -2 ≠ 0

Checking ±4:

For x = 4:

2(4)³ - 5(4) + 4 = 128 - 20 + 4 = 112 ≠ 0

For x = -4:

2(-4)³ - 5(-4) + 4 = -128 + 20 + 4 = -104 ≠ 0

None of the possible rational roots ±1, ±1/2, ±2, ±4 are actual roots of the equation 2x³ - 5x + 4 = 0.

Therefore, this equation does not have any rational roots.

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The sum and product of the roots of a given quadratic equation,

2x²+3x-2 =0, are -3 and -1 respectively.

The given quadratic equation is,

2x²+3 x-2=0

Since we know that,

if ax² + bx + c have roots x and y then

Sum of roots: x+y = -b/a

Product of roots: xy = c/a

Here we have,

a = 2, b = 3, c = -2

Therefore,

Sum of roots = -3/2

                     = -3

Product of roots = -2/2

                           = -1

Hence the sum and product of roots are -3 and -1 respectively.

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The measure of variability that is based upon the absolute values of the deviations from the mean is the **mean absolute deviation (MAD)**.

The mean absolute deviation is calculated by finding the average of the absolute values of the deviations from the mean. The absolute value of a number is its distance from zero, regardless of whether it is positive or negative. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.

To calculate the mean absolute deviation, we first find the deviation from the mean for each data point. Then, we take the absolute value of each deviation and average them. The formula for the mean absolute deviation is:

```

MAD = \frac{\sum\limits_{i=1}^{{n}} |x_i - {\mu}|}{{n}}

```

where:

* MAD is the mean absolute deviation

* $x_i$ is the $i$th data point

* ${\mu}$ is the mean of the data set

* $n$ is the number of data points

The mean absolute deviation is a measure of how spread out the data is around the mean. A small mean absolute deviation indicates that the data points are clustered closely around the mean, while a large mean absolute deviation indicates that the data points are more spread out.

The mean absolute deviation is a robust measure of variability, meaning that it is not as sensitive to outliers as other measures of variability, such as the standard deviation. Outliers are data points that are much larger or smaller than the rest of the data set. The standard deviation can be artificially inflated by outliers, while the mean absolute deviation is less affected.

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The two-column proof shows that if CD ≅ EF, then y=8. This is because the definition of congruent segments states that if two segments are congruent, then they have the same length. In this case, CD ≅ EF, so CD and EF have the same length, which is 4. Since CD = 4, then y = 4, as shown in the proof.

The first step in the proof is to state the given information. In this case, we are given that CD ≅ EF. The second step is to use the definition of congruent segments to show that DE = EF. The third step is to use the Segment Addition Postulate to show that DE + EF = 8. The fourth step is to simplify the expression DE + EF = 8 to 2EF = 8. The fifth step is to divide both sides of the equation 2EF = 8 by 2 to get EF = 4. The sixth step is to substitute EF = 4 into the equation CD = EF to get CD = 4. The seventh and final step is to use the definition of congruent segments to show that y = 4.

As shown in the proof, if CD ≅ EF, then y=8. This is because the definition of congruent segments states that if two segments are congruent, then they have the same length. In this case, CD ≅ EF, so CD and EF have the same length, which is 4. Since CD = 4, then y = 4, as shown in the proof.

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The two constructions for determining the type of triangle are the construction of medians and the construction of perpendicular bisectors.

To construct the medians of a triangle, draw a line segment from each vertex of the triangle to the midpoint of the opposite side. The point where the medians intersect is called the centroid. By observing the lengths of the medians, you can determine the type of triangle. If all three medians are of equal length, the triangle is an equilateral triangle. If two medians are of equal length and one is shorter, it is an isosceles triangle. If all three medians have different lengths, it is a scalene triangle.

To construct the perpendicular bisectors of a triangle, draw a line segment perpendicular to each side of the triangle at its midpoint. The point where the perpendicular bisectors intersect is called the circumcenter. By analyzing the lengths of the perpendicular bisectors, you can determine the type of triangle. If all three perpendicular bisectors are of equal length, the triangle is an equilateral triangle. If two perpendicular bisectors are of equal length and one is shorter, it is an isosceles triangle. If all three perpendicular bisectors have different lengths, it is a scalene triangle. These constructions provide geometric methods for classifying triangles based on their side lengths and help identify their respective types.

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The next time the red line and blue line trains will arrive at the station at the same time will be in 40 minutes.

To determine the next time the red line and blue line trains will arrive at the station simultaneously, we need to find the least common multiple (LCM) of the time intervals between their arrivals. The red line arrives every 8 minutes, and the blue line arrives every 10 minutes.

The LCM of 8 and 10 is 40. Therefore, it will take 40 minutes for both trains to arrive at the station at the same time again.

As for the blue line and yellow line trains, their time intervals between arrivals are 10 minutes and 12 minutes, respectively. To find the next time they will arrive at the station simultaneously, we again need to find the LCM of these time intervals.

The LCM of 10 and 12 is 60. Therefore, it will take 60 minutes for both the blue line and yellow line trains to arrive at the station at the same time again.

Finally, to determine when all three trains (red line, blue line, and yellow line) will arrive at the station simultaneously, we need to find the LCM of their respective time intervals. The time intervals are 8 minutes, 10 minutes, and 12 minutes.

The LCM of 8, 10, and 12 is 120. Thus, it will take 120 minutes for all three trains to arrive at the station at the same time.

In summary, the next time the red line and blue line trains will arrive at the station at the same time is in 40 minutes, the next time the blue line and yellow line trains will arrive simultaneously is in 60 minutes, and the next time all three trains will arrive together is in 120 minutes.

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The result is infinity ([tex]\infty[/tex]), which implies that the volume of the solid is infinite when revolving the region bounded by the given curve and lines about the y-axis.

The region is bounded by the curve x = 6/y, the x-axis (x = 0), and the lines y = 0 and y = 1.

To find the volume using cylindrical shells, we integrate along the y-axis.

The radius of each cylindrical shell is given by the x-coordinate of the curve x = 6/y, which is x = 6/y. The height of each cylindrical shell is given by the difference between y = 1 and y = 0, which is 1 - 0 = 1.

The volume element of a cylindrical shell is given by the formula:

[tex]dV = 2\pi rh dy[/tex]

where r is the radius and h is the height.

Substituting the values, we have:

[tex]dV = 2\pi (6/y)(1) dy\\= 12\pi /y dy[/tex]

Now, we integrate the volume element over the interval [0, 1]:

[tex]V = \int [0,1] 12\pi /y dy[/tex]

To evaluate the integral, we have:

[tex]V = 12\pi \int [0,1] (1/y) dy\\= 12\pi [ln|y|] [0,1]\\= 12\pi (ln|1| - ln|0|)\\= 12\pi (0 - (-\infty))\\= 12\pi (\infty)[/tex]

Since the result is infinity ([tex]\infty[/tex]), it implies that the volume of the solid is infinite when revolving the region bounded by the given curve and lines about the y-axis.

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The levels of factor is 4 when the degree of freedom is 3 .

Given,

Degree of freedom = 3

Now,

If factor A has a levels, then numerator degree of freedom for factor A is

df  = A - 1

Here,

In the given case degree of freedom is 3 so levels of factors,

A = 3+1 = 4.

Therefore given statement is false.

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Complete question :

A two-factor analysis of variance produces an f-ratio for factor a that has df = 3, 36. this analysis is comparing three different levels of factor A. True False.

Answer:

c. A point reduces the interest rate by 1%.

Step-by-step explanation:

The value of the of expression that can be found by the data given in the question that is (g∘h)(-2) is quat to 16.

Composition of functions:

The composition of functions is an operation that combines two functions to create a new function. It is denoted by the symbol "[tex]\circ[/tex]" (a small circle).

If we have two functions, f(x) and g(x), the composition of f and g is written as (f∘g)(x), and it represents the result of applying the function g to x first and then applying the function f to the result.

To find the value of (g[tex]\circ[/tex]h)(-2), we need to evaluate the composition of functions g and h at the input value -2.

First, we evaluate h(-2):

h(-2) = (-2)² + 4 = 4 + 4 = 8

Next, we substitute the result of h(-2) into g(x):

g(8) = 2 * 8 = 16

Therefore, (g∘h)(-2) = 16.

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To determine which plan offers Benito the better rate, let's compare the costs of both plans based on the given information.

Plan Y:

Monthly fee: $44

Cost per text message: $0.02

To calculate the total cost of Plan Y, we need to consider the monthly fee plus any additional charges for text messages.

Let's compare this to an alternative plan, Plan Z, which we'll define:

Monthly fee: $50

No additional charges for text messages

With Plan Z, Benito has a fixed monthly fee of $50 and does not incur any additional charges for text messages.

To determine which plan offers a better rate, we need to consider Benito's text messaging habits. If Benito sends a large number of text messages per month, Plan Y's additional charge of $0.02 per text message could quickly accumulate and result in a higher overall cost compared to Plan Z.

On the other hand, if Benito sends only a few text messages per month, the additional charge for text messages in Plan Y might not significantly impact the total cost.

Ultimately, the better rate depends on Benito's text messaging usage. If Benito sends a high volume of text messages, Plan Z with its fixed monthly fee of $50 may be more cost-effective. However, if Benito sends very few text messages, Plan Y could potentially offer a better rate.

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The total production after specialization would be 3F + 6C = 3 + 6 = 9 units.

Betty: F = 3 - 3C

Ann: F = 6 - 1.5C

Let's calculate the opportunity costs for both Betty and Ann for Fish and Coconuts:

The opportunity cost of Fish for Betty is the slope of her PPF, which is the negative of the coefficient of C in her equation. So, the opportunity cost of Fish for Betty is -(-3) = 3 Coconuts.

The opportunity cost of Coconuts for Betty is the inverse of the slope, which is 1/3 Fish per Coconut.

Similarly, the opportunity cost of Fish for Ann is the negative of the coefficient of C in her equation, which is -(-1.5) = 1.5 Coconuts.

The opportunity cost of coconut for Ann is the inverse of the slope, which is 2/3 Fish per Coconut.

Comparative advantage in Fish:

Betty has a lower opportunity cost of Fish (3 Coconuts) compared to Ann (1.5 Coconuts). Therefore, Betty has a comparative advantage in Fish production.

Comparative advantage in Coconuts:

Ann has a lower opportunity cost of Coconuts (2/3 Fish) compared to Betty (1/3 Fish). Therefore, Ann has a comparative advantage in Coconut production.

Absolute advantage:

Betty has an absolute advantage in Fish production since she can produce 3 Fish per day compared to Ann's 1 Fish per day. Ann has an absolute advantage in Coconut production since she can produce 2 Coconuts per day compared to Betty's 1 Coconut per day.

If in Autarky (without trade) Betty produces 1F and 1C, and Ann produces 1F and 2C, the total production would be:

Betty: 1F + 1C = 2 units

Ann: 1F + 2C = 3 units

If each specializes in the production of the good in which she has a comparative advantage, Betty would produce only Fish and Ann would produce only Coconuts. The total production would be:

Betty: 3F (since she has a comparative advantage in Fish)

Ann: 6C (since she has a comparative advantage in Coconuts)

The total production after specialization would be 3F + 6C = 3 + 6 = 9 units.

The gain from specialization is the increase in total production compared to Autarky, which is 9 units - 5 units (total production in Autarky) = 4 units.

The range for the terms-of-trade (TOT) represents the rate at which Fish and Coconuts can be exchanged between Betty and Ann. Since we have only the information about their individual production, we cannot determine the exact range of the TOT.

The social PPF for this society, considering only Betty and Ann, would be the sum of their individual PPFs.

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The calculated depth of the well in feet is 402.5 feet

From the question, we have the following parameters that can be used in our computation:

Time, t = 5 seconds

The depth of the well in feet is calculated as

d = 1/2gt²

substitute the known values in the above equation, so, we have the following representation

d = 1/2 * 32.2 * 5²

Evaluate

d = 402.5

Hence, the depth is 402.5 feet

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The volume of a cylinder with a radius of 3 cm and height of 8 cm is approximately 226.1 cubic centimeters. This is calculated using the formula V = πr²h, where π is approximately 3.14.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder.

In this case, the radius is 3 centimeters and the height is 8 centimeters. Substituting these values into the formula, we get V = π(3)²(8) = π(9)(8) = 72π.

To find the approximate value, we can use the approximation π ≈ 3.14. So, the volume is approximately V ≈ 72(3.14) = 226.08 cubic centimeters. Rounding to the nearest tenth, the volume is approximately 226.1 cubic centimeters.

To find the volume of a cylinder, we multiply the area of the base (which is a circle) by the height of the cylinder. In this case, the radius of the cylinder is given as 3 centimeters. Therefore, the area of the base (circle) is calculated as πr² = π(3)² = 9π square centimeters.

The height of the cylinder is given as 8 centimeters. Multiplying the area of the base by the height gives us the volume: V = 9π * 8 = 72π cubic centimeters.

To find the approximate value, we can use the approximation π ≈ 3.14. So, the volume is approximately 72 * 3.14 = 226.08 cubic centimeters. Rounding to the nearest tenth, we get approximately 226.1 cubic centimeters.

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To determine the number of gold atoms in the coin, we need to use the molar mass of gold and Avogadro's number. The number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

1. Find the molar mass of gold (Au):

The molar mass of gold is the atomic mass of gold, which can be found on the periodic table. The atomic mass of gold is approximately 197 g/mol.

2. Convert the mass of the coin to moles:

Number of moles = Mass / Molar mass

Number of moles = 3.5 g / 197 g/mol ≈ 0.01777 mol

3. Calculate the number of atoms:

Number of atoms = Number of moles × Avogadro's number

Number of atoms = 0.01777 mol × 6.022 × 10^23 atoms/mol ≈ 1.068 × 10^22 atoms

Therefore, the number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

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if the linear correlation between two variables is​ negative,  correlation between two variables corresponds to a negative slope in the regression line.

If the linear correlation between two variables is negative, it indicates that there is a negative relationship between the variables. In other words, as one variable increases, the other variable tends to decrease.

In terms of the slope of the regression line, when the correlation is negative, the slope of the regression line will also be negative. This means that for every unit increase in the independent variable, the dependent variable is expected to decrease by the value of the slope.

The slope of the regression line represents the change in the dependent variable for a one-unit change in the independent variable. In the case of a negative correlation, the slope will be negative to reflect the negative relationship between the variables.

Therefore, a negative correlation between two variables corresponds to a negative slope in the regression line.

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The equation of a line perpendicular to y=-2 x+6 containing (3,2) in slope-intercept form: y = 0.5 x - 0.5

Two lines are perpendicular if their slopes are negative reciprocals of each other. The slope of y=-2 x+6 is -2, so the slope of the perpendicular line will be 1/2.

We can plug the point (3,2) into the slope-intercept form of a line, y = mx + b, to solve for b, the y-intercept.

```

2 = (1/2) * 3 + b

```

```

2 = 1.5 + b

```

```

b = 2 - 1.5 = 0.5

```

Therefore, the equation of the perpendicular line is y = 0.5 x + 0.5.

Here is a graph of the two lines:

```

[asy]

unitsize(1 cm);

draw((-1,0)--(6,0));

draw((0,-1)--(0,4));

draw((3,2)--(3,0.5));

draw((-0.5,4)--(5.5,-0.5),dashed);

label("y = -2 x + 6", (6,4), E);

label("y = 0.5 x + 0.5", (3,0.5), NE);

dot("(3,2)", (3,2), SW);

[/asy]

```

As you can see, the two lines intersect at the point (3,2), and their slopes are negative reciprocals of each other.

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The population median commute time of the employees of Asons is 40 minutes.

The median is a measure of central tendency that represents the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the commute times provided are 47.4, 45, 35, and 40 minutes.

To determine the median, we arrange the commute times in ascending order: 35, 40, 45, 47.4. Since there are four values in the dataset, the middle value is the average of the two central values, which are 40 and 45. Taking the average of these two values gives us the median of 40 minutes.

Therefore, the population median commute time of the employees of Asons is 40 minutes, indicating that half of the employees have a commute time of 40 minutes or less, while the other half have a commute time of 40 minutes or more.

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The system will be consistent and will have unique solution.

Given,

Coefficient matrix of 5 equation in 5 variables.

Here,

Let A be a 5x5 coefficient matrix such that its each column has a pivot element, then

Rank A = 5, rank of augmented matrix [A|b] = 5 and number of unknowns = 5

Rank A = rank of augmented matrix [A|b] = number of unknowns = 5

Hence , System is consistent

There is a unique intersection point of all three lines, so values of variables is unique.

Hence, solution of system if unique.

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The explicit formula for the given sequence is aₙ = 1 * 3^(n-1), and the tenth term is 19683. This formula can be used to find any term in the sequence by plugging in the corresponding term number.

The given sequence seems to be a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio. In this case, the common ratio appears to be 3 because each term is three times the previous term.

To find the explicit formula for the sequence, we can use the general formula for a geometric sequence: aₙ = a₁ * r^(n-1), where aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the term number.

For the given sequence, the first term (a₁) is 1, and the common ratio (r) is 3. Plugging these values into the formula, we have:

aₙ = 1 * 3^(n-1)

Now, to find the tenth term (a₁₀), we substitute n = 10 into the formula:

a₁₀ = 1 * 3^(10-1)

    = 1 * 3^9

    = 1 * 19683

    = 19683

Therefore, the tenth term of the given sequence is 19683.

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The triangle with side lengths 11, 12 and 24 is a obtuse triangle.

Let us assume a, b and c are three sides of a triangle in such a way that c is the longer side.

if c²=a²+b² then the triangle is a right triangle.

if c²>a²+b² then the triangle is a obtuse triangle.

if c²<a²+b² then the triangle is a acute triangle.

Let us take c=24, a=11 and b=12.

24²=11²+12²

576=121+144

576>265

Since, 576>265 the triangle is a obtuse triangle.

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To deposit enough today to buy a $22,000 Harley in four years at 5.14% interest, you would need to deposit approximately $17,928.09.

To calculate the present value of a future amount, we can use the formula:

PV = FV / (1 + r)^n

Where:

PV = Present Value (the amount you need to deposit today)

FV = Future Value (the cost of the Harley)

r = Interest rate per period (converted to decimal form)

n = Number of periods (years)

In this case, FV = $22,000, r = 5.14% (or 0.0514), and n = 4. Plugging these values into the formula, we get:

PV = 22,000 / (1 + 0.0514)^4

  = 22,000 / (1.0514)^4

  ≈ 17,928.09

Therefore, you would need to deposit approximately $17,928.09 today to have enough to buy the Harley in four years, considering the given interest rate.

Please note that this calculation assumes compound interest, where the interest is compounded annually.

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The value of f(g(-3))  is 8.

The correct answer is b) 8.

Given:

f(x) = x² + 4

g(x) = √(1 - x)

First, let's find g(-3),

g(-3) = √(1 - (-3))

      = √(1 + 3)

      = √4

      = 2

Now, substitute g(-3) into f(x):

f(g(-3)) = f(2)

        = 2² + 4

        = 4 + 4

        = 8

we need to substitute -3 into the function g(x) and then substitute the result into the function f(x).

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