eric walks around a man-made circular lake (pictured above) four times. how far (in miles) has he walked?

The value of RS would be 10.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It represents a value or a computation and can be evaluated to obtain a numerical result. For example, "2x + 3" is an expression where x is a variable and 2 and 3 are numbers, and the + and * symbols represent mathematical operations.

RS + ST = RT
x + 4 + 8 = 3x
3x - x = 12
2x = 12
x = 6

RS = x + 4
RS = 6 + 4

RS = 10

Hence, the value of RS would be 10.

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The velocity of the car is given as follows:

2.83 m/s.

The kinetic energy is obtained as half the multiplication of an object's mass by the velocity squared of the object, that is:

K = 0.5mv².

The parameter values for this problem are given as follows:

K = 40000, m = 10000.

Hence the velocity of the car is obtained solving the equation for v as follows:

40000 = 0.5 x 10000v²

5000v² = 40000

v² = 8

v = square root of 8

v = 2.83 m/s.

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The number of three digits positive integers contain two (but not three) different digits is 243 .

In a 3 digit number the first digit cannot be zero ,

So , the total 3 digit number  is = 9 × 10 × 10 = 900 ;

the total three digit number with all different digit is = 9 × 9 × 8 = 648 different digits ;

and total three digits numbers with all same digits are {111 , 222 , ..., 999}

= 9 numbers ;

Therefore  , the number of three digits numbers with two but not three different digits is = 900 - 648 - 9 = 243 .

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Answer:

2

Step-by-step explanation:

Given expression is

[tex]\mbox{\large \left(\dfrac{4^{\frac{5}{4}}\cdot \:4^{\frac{1}{4}\:}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}}[/tex]

Let's take the term in parenthesis and simplify

[tex]\dfrac{4^{5/4} \cdot 4^{1/4}}{4^{1/2}}[/tex]

Numerator [tex]4^{5/4} \cdot 4^{1/4}[/tex] can be simplified to [tex]4^{5/4 + 1/4} = 4^{6/4} = 4^{3/2}\\\\[/tex]

The entire expression on parentheses becomes:
[tex]\dfrac{4^{3/2}}{4^{1/2}} = 4^{3/2 - 1/2} = 4^1 = 4\\[/tex]

Therefore
[tex]\left(\dfrac{4^{\frac{5}{4}}\cdot \:4^{\frac{1}{4}\:}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}} = (4)^\dfrac{1}{2} }= \sqrt{4} = 2[/tex]

So the entire expression simplifies to 2

The expression  [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex] is equivalent to 2, option C is correct.

An expression is combination of variables, numbers and operators.

The given expression is [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex]

Let us solve the numerator in parenthesis

[tex]4^\frac{5}{4}.4^\frac{1}{4}[/tex]

When bases are same then powers will be added

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

So the expression will be [tex](\frac{4^\frac{3}{2}}{4^\frac{1}{2} })^\frac{1}{2}[/tex]

[tex](4^\frac{3}{2}} ^-^\frac{1}{2} )^\frac{1}{2}[/tex]

We get [tex]4^\frac{1}{2}[/tex]

√4=2

Hence, the expression  [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex] is equivalent to 2, option C is correct.

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The output of the given code will be: 15, 2, 15, -5.

The given code declares two integer variables max and min, with min initialized to 10. The expression 17 - 4 / 10 is evaluated as 17 - 0, since integer division returns the floor value, which is 0 in this case.

The expression max = max - 6 then sets max to 17 - 0 - 6, which is equal to 11. The expression min = max - min then sets min to 11 - 10, which is equal to 1. Finally, the println statements print out the values of max * 2, max - min, max, and min. These values are 15, 2, 11, and 1, respectively.

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The equation of the Linear Graph in slope intercept form is;

y = 15x + 20

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, we see that the y-intercept is c = 20

Slope is gotten from the formula;

m = (y2 - y1)/(x2 - x1)

(-1, 5) and (0, 20)

m = (20 - 5)/(0 - (-1))

m = 15/1

m = 15

Thus, the equation is; y = 15x + 20

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Answer:

The radius of the circle when 0 = 90°, A = 20 cm² and when 0 = 30°, A = 35 cm² is 7 cm. This can be determined by using the information from byjus.com, which states that the Find the Value of X calculator is a free online tool that can be used to calculate the radius of a circle. Using the calculator, the radius of the circle when 0 = 90°, A = 20 cm² and when 0 = 30°, A = 35 cm² is 7 cm.

Step-by-step explanation:

Ratio: Because it has a meaningful zero point and allows for meaningful comparison of value differences, the volume of a backpack is a ratio level of measurement.

Ratio: A backpack's capacity is a ratio level of measurement because it has a meaningful zero point, or when an item (in this case, capacity) is absent, it has a value of zero. Additionally, it is possible to meaningfully compare value differences. As opposed to other levels of measurement like nominal or ordinal where the differences between two values may not be relevant, this means that differences in capacity between two backpacks may be compared properly.

For instance, the difference between two backpacks can be considered to be twice as great if one backpack has a capacity of 20 litres and the other has a capacity of 40 litres (20 liters). Ratio is the most suitable level of measurement for a backpack's capacity since other levels of measurement cannot account for this disparity.

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The conversion of inches to yards is an important calculation in the field of measurement, especially in the United States where both units are widely used. To convert inches to yards, you must divide the number of inches by 36. This is because there are 36 inches in a yard.

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Twelve dozen is referred to as a gross (122 = 144) and twelve gross (123 = 1,728, the duodecimal 1,000) is referred to as a great gross, a word most frequently used when shipping or purchasing products in bulk. The equivalent of 120 or ten dozen is a great hundred, commonly referred to as a small gross.

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The length of the other sides are 5cm and 12cm

Let the legs of the right triangle be 'a' and 'b'. Let the hypotenuse be 'h'.

We have the formula for perimeter as;

Perimeter, p = a + b + h = 30 cm

p = a + b + 13 cm = 30 cm

a + b = 30 - 13 = 17 cm

a = 17 - b …………… (1)

Using the Pythagorean Theorem

a² + b² = h²

(17 - b)² + b² = 13² ................ From equation (1)

b² + 17² - 34b + b² = 169

2b² - 34b + 289 - 169 = 0

collect like terms

2b² - 34b + 120 = 0

b² - 17b + 60 = 0

solve the quadratic equation

b² - 12b - 5b + 60 = 0

b(b - 12) - 5(b - 12) = 0

Factor the like terms

(b - 12)(b - 5) = 0

b = {12, 5}

From equation (1), we have;

a = 17 - 12 = 5 cm, or a = 17 - 5 = 12 cm

a = {5,12}

Hence, the values are 5cm and 12cm

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Answer:

I may be wrong but I  believe it could be (−∞, ∞).

Step-by-step explanation:

Depending on the polynomial is what the rage would be. I'm beyond sorry if it is wrong.

The volume of the parallelepiped is 63 cubic units.

The volume of a parallelepiped is the amount of space it takes up. It is calculated by multiplying the lengths of its three sides together.

In this case, the parallelepiped has three sides: i+0j+0k, 0i+7j − k, and 9i+6j − k.

To find the volume, we will use the cross product of two of the vectors. The cross product of two vectors results in a third vector that is perpendicular to both.

The cross product of the first two vectors,

=> (i+0j+0k) x (0i+7j − k) = 7i − 7j − 0k.

The cross product of this vector and the third vector,

=> 9i+6j − k,

results in the vector

=> 63i + 63j − 63k.

The magnitude of this vector is the volume of the parallelepiped.

To calculate the magnitude, we use the Pythagorean theorem and find that it is equal to 63.

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Data categorization is a process of organizing and grouping data into meaningful classes or categories.

This process is often used to simplify data and make it easier to understand and analyze. Data categorization involves breaking down a large set of data into smaller, more manageable groups. For example, a company may group customers into categories based on their age, income, or location. Each group can then be analyzed separately to better understand customer behavior. Categorizing data can also help identify trends or patterns that may not be visible when looking at the data as a whole. Categorization can also be used to identify outliers or anomalies in the data. By breaking down the data into smaller groups, it becomes easier to see which elements don’t fit the pattern or are not part of the normal range. Categorizing data can be done using a variety of methods. For example, data can be divided into numerical ranges or grouped into categories such as low, medium, and high. Data can also be grouped using descriptive terms, such as customer type or product type. Once the data is categorized, calculations such as averages, medians, and modes can be used to analyze the data. This can help to identify patterns or trends that can be used to make decisions or draw conclusions.

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Answer:

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°

so

4x + 21x + 13 + 3x - 1 = 180

28x = 180 - 13 + 1

28x = 168

x = 168 : 28

x = 6

21x + 13 =

21 x 6 + 13 =

126 + 13 =

139°

--------------------------

check

4 x 6 = 24°

3 x 6 - 1 = 17°

139 + 24 + 17 =

180°

the answer is good

The value of x is  log(49)/log(7³) in the equation  7³x+1 =49ˣ - 1

Two or more expressions with an Equal sign is called as Equation.

The given equation is 7³x+1 = 49^x-1​

7³ˣ + 1 = 49ˣ - 1

Take log on both sides

log(7³)ˣ + 1 = log(49)ˣ - 1

x log(7³) = x log(49)

x = log(49)/log(7³)

Hence, the value of x is  log(49)/log(7³) in the equation  7³x+1 =49ˣ - 1

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By using the concept of permutations and combinations, we can conclude that the shop can create 150 different sandwiches

We are given a deli that offers 5 fillings, 6 types of bread, and 5 condiments. Also, each sandwich consists of a filling, a type of bread, and a condiment.
We are asked to find the number of different sandwiches that the shop can create.

Here, we are gonna use the concept of permutations and combinations.

Number of different fillings = 5

Number of different beads = 6

Number of different condiments = 5

Number of different sandwiches = Number of different fillings x Number of different beads x Number of different condiments = 5

                                     = 5 x 6 x 5

                                     =  150 sandwiches

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The measurement of angle 5 is given as follows:

m < 5 = 150º.

In this problem, we have that two parallel lines are cut by a transversal line.

Angles 5 and 8 are on the same position relative to the transversal line, separated by one of the parallel lines, hence they form a linear pair, meaning that they are supplementary.

Supplementary angles have the sum of their measures with a result of 180º, hence the measurement of angle 5 is obtained as follows:

m < 5 + 30º = 180º

m < 5 = 150º.

The diagram is given by the image presented at the end of the answer.

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Answer:

5x10^-19/x^3

Step-by-step explanation:

The Logarithmic function is a mathematical operation that is used to determine the logarithm of a number.

The logarithm of a number x is the exponent to which a fixed number, the base, must be raised to produce x. The most common bases used are 10 and e. The formula for determining the logarithm of a number x base d is: log base d of x = (log base d of x)/(log base d of b).

For example, if we want to calculate the log base 10 of a number x, we would use the formula: log base 10 of x = (log base 10 of x)/(log base 10 of b). We can calculate the log base 10 of a number x by taking the logarithm of x and dividing it by the logarithm of the base, 10. The result will be the log base 10 of x.

For example, if we want to calculate the log base 10 of 25, we would calculate the logarithm of 25 and divide it by the logarithm of 10. The calculation would be: log base 10 of 25 = (log base 10 of 25)/(log base 10 of 10) = (1.3979)/(1) = 1.3979. This means that the log base 10 of 25 is 1.3979.

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The United States has the comparative advantage in producing footballs, while Canada has the absolute advantage in producing lumber. If the two countries specialize and trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(a)US Production Possibility Frontier:

Football (1000)  |  0  |  200  |  400  |  600  |  800  |  1000

Lumber (10)     | 10  |  8   |   6   |   4   |   2   |    0

Canadian Production Possibility Frontier:

Football (400)  |  0  |  100  |  200  |  300  |  400

Lumber (8)      | 8   |  7   |   6   |   5   |   4

(b) In autarky, if the United States wants to consume 500 footballs, it can consume at most 4 tons of lumber. This point is labeled A in the diagram. Similarly, if Canada wants to consume 1 ton of lumber, it can consume at most 300 footballs. This point is labeled C in the diagram.

(c) Canada has the absolute advantage in lumber production.

(d) The United States has the comparative advantage in lumber production.

(e) If each country specializes in the good in which it has the comparative advantage and there is trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(f) Yes, it is possible for the United States to consume 500 footballs and 7 tons of lumber. This point is labeled B in the diagram. It is not possible for Canada to consume 500 footballs and 1 ton of lumber at the same time. This point is labeled D in the diagram.

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The probability of finding an average in excess of 4. 3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline is approximately 0.7972.

We may use the normal distribution and the Z-score to determine the likelihood that 100 randomly selected 1-gallon samples of standard unleaded gasoline will have an average of more than 4.3 ounces of the component. A value's Z-score indicates how many standard deviations away from the mean it is.

We must first get the average of 100 randomly chosen samples' mean and standard deviation. The average's mean will be 4 ounces, which is also the mean of the individual samples. The sample size is divided by the square root of the standard deviation to get the average standard deviation, which is 1.2/100 = 0.12 ounces.

Next, we calculate the Z-score for the value of 4.3 ounces:

Z = (4.3 - 4) / 0.12 = 0.83

Finally, we use a Z-score table or a normal distribution calculator to find the probability of finding an average in excess of 4.3 ounces. The result will be the area under the standard normal distribution curve to the right of 0.83.

There is a 79.72% chance of finding an average in excess of 4.3 ounces of the ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline.

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E(aX + b) = aE(X) + b, which shows that E(ax + b) = aE(X) + b, as stated.

What is integration ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

This statement can be shown using the linearity property of expectation. According to this property, if X is a random variable and a, b are constants, then E(aX + b) = aE(X) + b.

Applying this property, we have:

E(aX + b) = aE(X) + b

= a(E(X) + b/a)

= aE(X) + ab/a

= aE(X) + b

So, E(aX + b) = aE(X) + b, which shows that E(ax + b) = aE(X) + b, as stated.

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The student made the following mistake: The use of operator "+" in binomial (x - 4) instead of "-" when factoring the quadratic equation x² - 3 · x - 4.

In this problem we find the case of a quadratic equation that must factorized by algebra properties. We present the complete procedure to show what mistake the student did. First, write the original expression:

x² - 3 · x - 4

Second, use definition of addition, associative and distributive properties:

x² - 4 · x + x - 4

Third, use conmutative property:

x² + x - 4 · x - 4

Fourth, use distribute property:

x · (x + 1) - 4 · (x + 1)

Fifth, apply commutative and distributive properties:

(x - 4) · (x + 1)

Sixth, use commutative property:

(x + 1) · (x - 4)

The student wrote the operator "+" instead of "-" in binomial (x - 4) of the quadratic equation x² - 3 · x - 4.

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The critical point (0, 9) is a minimum and (0, -9) is a maximum.

Lagrange multipliers are a method used to find the maximum and minimum values of a function subject to a constraint.

To use Lagrange multipliers, we first write the function and constraint as a system of equations.

For the function

=> f(x, y) = y² − x²

and the constraint

=> 14x²y² - 81,

the system becomes:

y² − x² = λ(14x²y² − 81)

Next, we find the partial derivatives of both equations with respect to x and y and set them equal to zero to find the critical points.

Solving for x and y, we find that (0, ±9) are the critical points.

If the value is zero, the critical point is a saddle point.

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The population of interest in the study is asthma patients aged 18-69 who relied on medication for treatment.

The population of interest in the study is adult individuals (aged 18-69) who have been diagnosed with asthma and are currently using the medication as a form of treatment for their condition. This group of people is the focus of the research, as the aim of the study is to assess the effectiveness of the Buteyko shallow breathing technique on reducing asthma symptoms and improving the quality of life for this specific population.

By randomly assigning the participants to two groups and observing the outcomes of each group, the researchers aim to determine if the Buteyko method can offer any additional benefits to asthma patients who are already taking medication.

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The general solution would be (y).e = C.

A differential equation is an equation that connects some independent variables to an unknown function and its derivatives. It is used to describe a system's behaviour that changes over time or in response to an outside factor.

There are many ways to solve the differential equation (x2 - y2) dy - 2xy dx = 0, including variable separation, integrating components, and substitution.

One possible method is separation of variables, where we separate the variables x and y by dividing both sides by x² -y2

dy/dx = 2xy/(x² -y²)

We can then integrate both sides:

[(dy/dx) dx = √(2xy/(x²-y²)) dx

y = √2xy/(x²-y²²) dx + C, where C is an arbitrary constant. solving this, (y-x).ec"

Hence, the general solution would be (y-x).e=C".

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49 inches in feet is 4.08333.

You can easily convert 49 inches into feet using each unit definition:

Inches

inch = 2.54 cm = 0.0254 m

Feet

foot = 12 inch = 0.3048 m

Performing the inverse calculation of the relationship between units, we obtain that 1 foot is 0.24489796 times 49 inches.

A foot is zero times forty-nine inches.

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Answer:

Step-by-step explanation:

y=-1x+5