Calculate the limit:

lim[(x,y) -> (0,0)] [3(x^2)y / (x^2 + y^2)]

Answer:

  a1 = 16

  a(n) = a(n-1) -3   for n ≥ 2

Step-by-step explanation:

You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....

The given sequence has a first term of 16. The common difference is ...

  13 -16 = -3

Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.

  [tex]\begin{cases}a_1=16\\a_n=a_{n-1}-3&\text{for $n\ge2$}\end{cases}[/tex]

The records about colors of automobiles on a car lot is a type of qualitative data.

Qualitative data consists of descriptions and characteristics that are difficult to quantify but easy to perceive in the human senses, such as smell, food, gender, country, and color. Observations, individual interviews, focus groups, and other similar procedures are used to get this information. Categorical data is another name for qualitative data in statistics; it refers to information that may be sorted into groups based on the characteristics of a given entity or event. Qualitative data are also known as categorical data since they may be sorted into categories.

When trying to determine the exact frequency of certain features or attributes, qualitative data is a very useful tool. It gives the statistician or the researcher the ability to generate parameters that can be used to examine larger data sets.

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If we assume that the average rate of arrivals is 5 minutes, then this means that the Poisson distribution will have a mean of 5 customers/minutesThis means that the probability that a customer arrives in the next minute is 0.2 (1/5).

The exponential distribution will have a mean of 4 minutes, meaning that the probability that the customer is served in the next minute is 0.25 (1/4).

Therefore, the expected number of customers that the barber can serve in an hour is 15 (5*4). The expected number of customers served in a given minute is 0.2 (1/5) * 0.25 (1/4) = 0.05. This means that the barber can expect to serve an average of 3 customers per hour.

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The value of a4 would be equal to -666.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that [tex]a_0=10[/tex] and [tex]a_n+1=-5a_n[/tex]

This is a recursive formula. So we can simply substitute in each value. For instance, a₂

Use the recursive definition repeatedly.

a2 = -5(6) +4 = -26

 a3 = -5(-26) +4 = 134

 a4 = -5(134) +4 = -666

Therefore, the value of a4 is -666

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To make the dough, he'll need 5 3/4 cups of floor.

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.

Here,

10 1/4 cups of flour needed to make a batch=41/4 cups

4 1/2 cups of floor is there=9/2 cups

flour does he need to make the dough,

=41/4-9/2

=(41-18)/4

=23/4

=5 3/4 cups

He needs 5 3/4 cups of floor to make the dough.

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The observational unit is Harley and the variable is 0, 1, 2, ..., 10.

When gathering statistical data, information is gathered and statistics are compiled on an observation unit, which is also known as a statistical unit occasionally. An observation is the value of a certain variable at a specific time.

The observational unit in this scenario is Harley and the variable is the number of times Harley chose the correct cup out of 10 trials. The variable can take on the values of 0, 1, 2, ..., 10, where 0 represents the number of incorrect choices and 10 represents the number of correct choices.

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For the given system of inequalities y < -x + a and y > x + b in the xy-plane , the solution represents the relation between a and b is given by :

Option A. a > b.

In the xy -plane given system of inequalities are :

y < -x + a

y > x + b

⇒ x + b < y < -x + a

⇒ x + b < -x + a

⇒ 2x < a - b

Now ( 0, 0 ) is the solution of the given system of inequalities represents :

2(0) < a - b

⇒ a - b > 0

⇒ a > b

Therefore, the relationship between the  'a' and 'b' for the given system of inequalities is given by :

Option A. a > b

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Answer:

66

Step-by-step explanation:

32+44=66

32

+42

____

66

Erick and Mia both live the same distance from the park and decided to meet there one afternoon.

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1.33 cm/s

Step-by-step explanation:

The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:

Replacing all values we have:

Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.

Is this what your looking for if not let me know

Answer:

1.33 cm/s

Step-by-step explanation:

The probability that a randomly selected subject in this is Male or answered 'No' is A: 0.18.

The probability that a randomly selected subject in the study is Male or answered "No" is the sum of the probability that the subject is Male and the probability that the subject answered "No", which is a measure of the overlap between these two events.

To find the probability that a subject is Male, we take the number of Male subjects (50) and divide it by the total number of subjects (100):

P(Male) = 50/100 = 0.5

To find the probability that a subject answered "No", we take the number of subjects who answered "No" (48) and divide it by the total number of subjects (100):

P(No) = 48/100 = 0.48

We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected subject is Male or answered "No"

P(Male or No) = P(Male) + P(No) - P(Male and No)

We know that 18 out of 50 Male subjects answered No and 16 out of 50 Female subjects answered no, so the probability that a Male subject answered No is 18/50 = 0.36, and the probability that a Female subject answered No is 16/50 = 0.32

P(Male and No) = P(Male) * P(No|Male) = 0.5 * 0.36 = 0.18

P(Female and No) = P(Female) * P(No|Female) = 0

Hence, the probability that a randomly chosen subject in this is male or answered 'no' is A: 0.18.

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Here we are given that the distance between city A and B is 39miles and that between city B and C is 99miles . in order to find after how many miles we would reach the midpoint of city A and C , divide the total distance between A and C by 2 as ,

Total distance between A and C =[tex] d_{AB}+d_{BC}[/tex] = 39mi. + 99mi. = 138 miles

Divide this distance by 2 ,

138/2 = 69miles [ answer to Part A ]

_______________

Now the speed is 46miles/hr . In order to find time , use relation,

Speed * time = distance

So that,

time = distance/speed

time = 138/46

time = 3hrs [ answer to Part B ]

and we are done!

The domain and range of the relation are { -2 } and { 4, 5, 6, 7 } respectively. The relation is not a function.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the relation in the question;

(-2,7), (-2,6), (-2,5), (-2,4)

For a relation to be a function, every x-value must have only one y-value mapped to it.

-2 appeared twice and its corresponding y-values are different.

Hence, the relation is Not a Function.

The Domains are the x-values and the Range are the y-values,

Domain: { -2 }

Range: { 4, 5, 6, 7 }

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The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number.

The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number, is a set of points that can be found by taking the given continuous function and evaluating it at each point in the open subset of the complex plane. This set of points can be expressed as a set of the form [tex]$\{z \in u: |f(z)|=c\}$[/tex] where u is the open subset of the complex plane and f  is the given continuous function. The absolute value of the function must be equal to some number c in order for the point to be included in the set. This set of points is useful for understanding the behavior and properties of the given continuous function on the open subset of the complex plane.

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As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.

The numeral is said to be in this simplest form when divided into its smallest equivalent fraction. How to do to find the most basic form. Find common factors in the denominator and numerators. Verify a fractional integer to verify if it passes as a prime number. A statement having two collinear and an equally sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The normal form of a linear function is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorised as identities or conditional equations. An identity holds true regardless of the value given to the variables.

given

Let the boat's speed in calm water be x km/h.

Boat speed downstream is equal to x plus 5.

Upstream boat speed is equal to x - 5

Distance x time speed

Time is therefore determined by speed and distance.

Boat travel time is equal to 30/km upstream (x – 5)

50/(x + 5) is the time it takes a boat to travel 50 kilometres downstream.

Since the boat takes the same amount of time in both scenarios, 30 (x + 5) = 50 (x -5), 30 x +150 = 50 (x -250), 20 (x = 400), and 20 (x = 20).

As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.

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The solution to the given equation x² + 7x = 0 is x = 0, -7.

The quadratic equation is defined as a function containing the highest power of a variable is two.

The quadratic equation is given in the question, as follows:

x² + 7x = 0

We have to determine the solution to the given equation.

As per the question, we have

x² + 7x = 0

x(x + 7) = 0

Equating factors to zero, we get

x = 0 and (x + 7) = 0

x = 0 and x = -7

Thus, the solution to the given equation is x = 0, -7.

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In the given right-angled triangle, the sides are 21.3617 and 22.8815.

The given figure is a right-angled triangle. Hence, sides can be determined by using trigonometric function and/or the Pythagorean theorem. It is known that angle A = 69 and side b = 8.2. The side b is an adjacent side to angle A. Using the trigonometric function of tangent

tan Ɵ = opposite side/adjacent side

tan A = a/b

a = b tan A = 8.2 tan 69 ≈ 21.3617

As the two sides a and b are known, the remaining side c can be determined by using Pythagorean theorem,

Hypotenuse^2 = Opposite^2 + Adjacent^2

c^2 = a^2 + b^2

c^2 = (21.3617)^2 + (8.2)^2

c^2 = 523.3635

c =√523.3635

c ≈ 22.8815

Note: The question is incomplete. The complete question probably is: Use a calculator to find the length of each side to four decimal places. (Assume triangle ABC where side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.) side length b = 8.2 and angle A = 69 degrees.

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As per the given scatter plot, if the outlier were removed, r would get closer to 1.

The term scatter plot in math is used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another

Here we have given that a local ice cream shop kept track of the number of cans of cold soda it sold each day and the temperature that day, for two months during the summer by using the scatter plot.

Here we have also know that X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees and the value of Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans.

While we take into consideration that a reasonable value of the correlation coefficient r for these data is 1.2.

Where as if the temperature were measured in degrees Celsius (C = 5/9 * (F - 32)), then the value of r would change accordingly.

Thus makes that the correlation coefficient would increase and be closer to 1.

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The function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output.

The vector is a 1-dimensional array. The formula for this function is:

For i = 0 to length-1

   Print ( ptr[i] )

End

The calculation for this function is as follows:

The function starts with a for loop, where the initial value of i is set to 0, and the condition for the for loop is i < length, and the increment value of i is 1. The body of the for loop prints the value of ptr[i], which is the value at the i-th position in the vector. This loop is repeated until the condition i < length is false, at which point the function terminates.

In summary, the function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output. The formula for this function is a for loop, where the initial value of i is set to 0 and the condition for the for loop is i < length. The body of the for loop prints the value of ptr[i], and the loop is repeated until the condition i < length is false.

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Answer:0, 18, 36, 54, 72, 90, 108, 126, 144, 162

Step-by-step explanation:0 es múltiplo de 18, pues 18 x 0 = 0

18 es múltiplo de 18, pues 18 x 1 = 18

36 es múltiplo de 18, pues 18 x 2 = 36

54 es múltiplo de 18, pues 18 x 3 = 54

72 es múltiplo de 18, pues 18 x 4 = 72

90 es múltiplo de 18, pues 18 x 5 = 90

108 es múltiplo de 18, pues 18 x 6 = 108

126 es múltiplo de 18, pues 18 x 7 = 126

Answer:

Step-by-step explanation:

18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162

27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270

The number of solutions for given three system of linear equations.

We can simply solve this numerical problem by using the following process.

3x - y = 4 ==> a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

What is meant by numerical?

Based on the formula is:

Let the system of equations be a₁x + b₁y = c₁ and  a₂x + b₂y = c₂ then

Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

Condition for No Solution:  a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Condition for infinitely many solutions:  a₁/a₂ = b₁/b₂ = c₁/c₂

Now in the given question:

a.) 3x - y = 4

6x - 2y = 8

⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2

⇒  a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

The given system of equations is coincident lines, hence has infinitely many solutions.

b.) -3x + y = 7

     2x - 4y = -8

⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8

⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

The given system of equations is intersecting lines, hence having a single solution.

c.) y = -4x - 5

y = -4x +1

⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5

⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂

The given system of equations is parallel lines, hence having no solution.

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Answer:

1 1 1 1 to base two

Step-by-step explanation:

1 0 1 base two

× 1 1 base two

+ 1 0 1

1 0 1

=1 1 1 1 base two

a. Taxpayer having a taxable income of $39,800 has $5,448 as the income tax.

b. The taxable income of taxpayer owing $21,197 is $102,800.

What is Income Tax?

Income tax is the tax which is levied on all individuals and businesses. The individual income taxes are calculated on the basis of the income received by the individual. Typically, it is categorized as a direct tax because the burden is thought to fall on the people who pay it. Net profits, calculated as the excess of receipts over permitted costs, are subject to corporate income tax.

We are given graph of a piecewise function with three equations which is attached below.

From the graph, it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.

Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.

His taxable income is $102,800 as shown in the graph  below.

Hence, taxpayer having a taxable income of $39,800 has $5,448 as the income tax and the taxable income of taxpayer owing $21,197 is $102,800.

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The function f(x) = (x - 3)² is invertible on the interval [1,2], as each output is related only with a single input.

The inverse of the function is given as follows:

[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]

The function for this problem is defined as follows:

f(x) = (x - 3)²

The x-coordinate of the vertex of the quadratic function is given as follows:

x = 3.

Hence the function is invertible on the domain [1,2], which is entirely on one side of the vertex, and thus each output is related only with a single input.

The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:

x = (y - 3)²

[tex]y - 3 = -\sqrt{x}[/tex]

[tex]y = -\sqrt{x} - 3[/tex]

[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]

The negative symbol is because the function is on the left side of the vertex.

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It will take 28 minutes for them to fill the tank.

Work done is defined as the amount of force needed to move and object a certain distance. In essence, it is a measure of an energy transferred to or from an object which allows it to be moved.

Given that, an aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself.

Work done by first pipe in 1 minute = 1/84

Work done by second pipe in 1 minute = 1/42

The time taken by both the pipes together =

1 / 84 + 1 / 42 = 3 / 84

= 1/28

Therefore, time taken by  both the pipe = 28 minutes.

Hence, it will take 28 minutes for them to fill the tank.

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Answer:

1.247 then 1.244 and finally 1.234

Step-by-step explanation:

The vertical scales for each type of vehicle are:

The rationale is to choose a vertical scale that represents the relative frequencies, or the proportion of each type of vehicle sold compared to the total number of vehicles sold. The calculation for each type of vehicle is as follows:

Here, the total number of vehicles sold (150) is calculated by adding up the sales for each type of vehicle. The relative frequency for each type of vehicle is then calculated by dividing the sales for that type of vehicle by the total number of vehicles sold.

This question should be provided as:

A car dealer is deciding what kind of vehicles he should order from the factory. he looks at his sales report for the preceding period. choose the vertical scale so that the relative frequencies are represented:

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Answer:

Step-by-step explanation: