What is range of function f/x )= x 1 which is defined everywhere on its domain?

The equation that shows the situation is; 3.5x + 2y = 42.

We know that sometimes in mathematics, the problem can be given in the form of a sentence and then the first step in the solution of the problem would be to rewrite the sentence into an equation.

In this case, we have that; Francis is at the state fair. A fair concession stand is selling funnel cakes for $3.50 and deep-fried Oreos for $2.00. Given that the total amount spent is $42.00 when  number of funnel cakes x and the number of deep-fried Oreos y. The equation is; 3.5x + 2y = 42.

We now see that;

Total number= 42

Each deep-fried Oreos cost $ 3.5 and we have y number of it

Each funnel cake cost $2.00 and we have x of it.

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The slope of the line whose equation 3x + 4y = 12 is -3/4.

In the given question, we have to find the slope of the line whose equation 3x + 4y = 12.

The given equation is 3x + 4y = 12.

We need the equation of the line with slope-intercept form. To put it another way, we need y=mx+b to take the form ax+by=c. In the slope-intercept form, M is the slope and b is the y-intercept.

By isolating the y, the preceding equation can be transformed into the general form of a line to get the line's slope.

Subtract 3x on both side, we get

4y = -3x + 12

Divide by 4 on both side, we get

y = -3/4 x + 12/4

y = -3/4 x + 3

By comparing the equation y = mx + c

m = -3/4

Hence, the slope of the line whose equation 3x + 4y = 12 is -3/4.

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The inequality that would represent given condition will be

t + b <= 126 (linear inequality).

What is a linear inequality ?

In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols "< and '>' represent strict inequalities, whereas  ‘≤’ and ‘≥’ represent slack inequalities. A linear inequality appears to be a linear equation, however there is a difference in the formula.

Now,

As,  we know that the total of the tacos and burritos cannot exceed 126, we know that that total must be less than or equal to 126, giving us our linear inequality:

t + b <= 126

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Answer:

The first one. (A)

Step-by-step explanation:

A easy way to find these answers is to type the problem exactly the way it is into demos.

The volume of the cake is 198 cubic inches.

We are given that the volume of the cake is a function of its width:

V(w) = 1/2w^3 + 5/2w^2

To find the volume when the width is 6 inches, we simply substitute 6 for w in the equation:

V(6) = 1/2(6^3) + 5/2(6^2)

Expanding the exponents and simplifying:

V(6) = 1/2(216) + 5/2(36)

V(6) = 108 + 90

V(6) = 198 cubic inches

So the volume of the cake when the width is 6 inches is 198 cubic inches.

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x = 8

m∠V = 89°

m∠W = 90°

m∠V = 11x + 1

m∠U = 12x + 10

m∠X = 75

The sum of all the angles in a quadrilateral is 360°

m∠W + m∠V + m∠U + m∠X = 360°

Plug what you know into the above equation in the appropriate spots

90 + (11x + 1) + (12x + 10) + 75 = 360

Combine like terms

90 + 11x + 1 + 12x + 10 + 75 = 360

176 + 11x + 12x = 360

176 + 11x + 12x = 360

176 + 23x = 360

23x = 184

Isolate x

x = 8

Given: m∠V = 11x + 1

Plug in the x you previously found into the equation above and solve

m∠V = 11(8) + 1

m∠V = 88 + 1

m∠V = 89°

Due to the fact that the x coordinates of any two points allow us to calculate their separation from the y-axis, we may deduce that the distance between (-5, 6) and the y-axis is 5 units.

Both statistical and qualitative methods can be used to calculate the distance between two items or points.

The word "distance" in physics can refer to an exact measurement or, more frequently, to an estimate based on a number of different factors.

The length of the line segment that connects any two points on a plane provides the distance between those spots.

The following formula can be used to calculate the separation between two points:

d=((((x2 - x1)2 + (y2 - y1)2)

So, the given points are:

(-5, 6)

We may conclude that the gap between (-5, 6) and the y-axis is 5 units because the x coordinates of any two points show us how far apart they are from the y-axis.

Therefore, due to the fact that the x coordinates of any two points allow us to calculate their separation from the y-axis, we may deduce that the distance between (-5, 6) and the y-axis is 5 units.

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The fabric used for the different sizes of blankets is 9 and 1

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

Fabric used to make 28 twin-size blankets and 49 queen-size blankets= 469yards of fabric

Fabric used to make 16 twin-size blankets and 36 queen-size blankets=

340yards of fabric

Let, twin-size blankets be x and queen-size blankets be y

So, the equations will become;

28x+49y=469...(1)

16x+36y=340...(2)

Solving for x and y;

28x=469-49y

x=(469-49y)/28

Substituting the value of x in equation 2

16((469-49y)/28)+36y=340

y=9

Substituting the value of y in equation 1

x=1

Therefore, by solving the equations 1yard of fabric is used for twin-size blankets and  9yard of fabric is used for queen-size blankets

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Bayes's Theory is an important tool for understanding probability and for determining the likelihood of certain outcomes occurring.

It states that the probability of an event occurring if another event has already occurred is generally different from the probability of the second event occurring if the first one has already occurred. This is a common mistake made by medical professionals, particularly when interpreting test results.

For example, in a study conducted in both Germany and the United States, researchers asked physicians to estimate the probability that an asymptomatic woman between the ages of 40 and 50 who has a positive mammogram actually has breast cancer. The physicians were told that 7 percent of mammograms show cancer when there is none, the actual incidence of cancer is 0.8 percent, and the false-negative rate is about 10 percent. Through the use of Bayes's Theory, it can be determined that a positive mammogram is due to cancer in only about 9 percent of the cases.

However, in the German group, one-third of the physicians concluded that the probability was about 90 percent, and the median estimate was 70 percent. In the American group, 95 out of 100 physicians estimated the probability to be around 75 percent. This example shows how medical professionals can make mistakes when interpreting test results, due to a lack of understanding of Bayes's Theory.

In order to avoid making such mistakes, medical professionals need to be educated on Bayes's Theory and its importance in determining the probability of certain outcomes occurring. By doing so, medical professionals can increase their accuracy in interpreting test results and make better decisions for their patients.

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The  value of r is 4 , so the line that passes through the pair of points has the given slope. (r, 2), (6, 3), m=1/2.

The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. The terms Y and x, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. where "m" denotes a line's slope. The outcome is that a line's slope is tan.

Two points along the selected line should have their coordinates determined. The difference between these two places' y-coordinates should be determined (rise).

The difference between these two places' x-coordinates should be determined (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

Given Points are (r, 2), (6, 3) , slope m = 1/2

(3 - 2)/(6 - r) = (1/2)

Simplifying the above equation, then we get

6 - r = 2

r = 4

Therefore, (r, 2), (6, 3), m = 1/2 the slope of the line passing through each pair of points is r = 4.

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85 units is the distance between the two points (-1, 4) and (6, -2).

The total velocity of an object defines its distance regardless of direction.

Regardless of where it started or ended, distance is the amount of space that an object has covered.

We can calculate an object's actual size by knowing how far it is from us.

The formula shown below is frequently used to calculate the separation between two points: d=((x2 - x1)2 + (y2 - y1)2)

The distance formula is as follows:

d=((x2 - x1)2 + (y2 - y1)2)

Points are: (-1, 4) and (6, -2)

Now, use the numbers in the formula above to calculate the result given below:

d=((6+1)2 + (-2-4)2)

d=((7)2 + (-6)2)

d=(49+36)

d=85 units

Therefore, 85 units is the distance between the two points (-1, 4) and (6, -2).

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The function of x7 is to multiply a number by 7. For example, if x = 3, then x7 = 21.

x7 = x * 7

x7 = 3 * 7

x7 = 21

The function of x7 is to multiply a number by 7. This means that if you have a number x, then the answer of x7 will be x multiplied by 7. For example, if x = 3, then

x7 = 3 * 7 = 21.

This can be written as an equation,

x7 = x * 7.

This is a useful function because it allows us to quickly multiply a number by 7 without having to do the calculation manually. It can be applied to any number and can be used in a variety of mathematical problems. For instance, it can be used to calculate the area of a rectangle by multiplying its length by 7. It can also be used to solve equations and find the roots of equations. In conclusion, the function of x7 is to multiply a number by 7, which can be used to simplify mathematical calculations and solve equations.

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Answer:

Letter recognition, Letter naming, Letter sound knowledge, Letter writing

The only function in the relations given is graph C which can be determined using vertical line test.

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range.

A function assigns exactly one output to each input, and each input can only have one output. This means that a function will always give the same output for the same input.

Functions can be classified in different ways. For example, some functions are linear, meaning that the graph of the function is a straight line. Other functions are non-linear, meaning that the graph of the function is not a straight line.

The vertical line test is a method used to determine if a graph represents a function. A graph is a visual representation of a set of points, where each point is defined by a pair of coordinates (x, y).

A graph represents a function if and only if no vertical line intersects the graph more than once. In other words, for any value of x, there should be exactly one corresponding value of y. If a vertical line intersects the graph more than once, it means that there are multiple values of y for the same value of x, which violates the definition of a function.

The vertical line test can be used to determine if a graph is a function by drawing a vertical line on the graph and seeing if it intersects the graph at more than one point. If it does, then the graph is not a function. If it doesn't, then the graph is a function.

Using vertical line test for each of the relation given, only graph C is a function which is a quadratic function.

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To obtain the y-intercept of the perpendicular line's b-intercept, she must similarly substitute the slope and the point P into the equation y = mx + b.

The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).

Intercept Form of Equation of a Line: x/a + y/b = 1.

To solve for the y-intercept, b, in the equation y = mx + b, substitute the coordinates of the point P and the slope m.

A P is present in Rosetta. There are lines that cross this location and are both parallel and perpendicular to line g. She is attempting to formulate the equations of the lines in the form of the slope-intercept.

She has already determined the inclinations of these two lines. Similar to line g, the parallel line will also have a slope. The slopes of line g and the perpendicular line will add up to -1.

She must now determine the y-intercepts of each line.

She possesses P, a point on the parallel line, and its slope for the parallel line. In order to find the y-intercept of this line, she only needs to solve for these values in the equation y = mx + b.

Thus, to obtain the y-intercept of the perpendicular line's b-intercept, she must similarly substitute the slope and the point P into the equation y = mx + b.

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Answer:

Andre has more money because he has $120 in his account after four weeks and Elena has $90 in her account after four weeks and $120 in more than $90.

Step-by-step explanation:

$5 * 4 = $20

$20 * 4 = $80

$100 + $20 = $120

$10 + $80 = $90

Andre = $120

Elena = $90

The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

To determine the probability that a lightbulb lasts at least one year, we need to know the failure rate of the lightbulb and its distribution. For example, if the lightbulb follows a exponential distribution with parameter λ, the probability that it lasts at least one year (t = 365 days) can be calculated as:

P(T ≥ 365) = 1 - P(T < 365) = 1 - F(365),

where F(365) is the cumulative distribution function (CDF) of the exponential distribution evaluated at t = 365. The CDF of the exponential distribution is given by:

F(t) = 1 - e^(-λt),

so the probability that the lightbulb lasts at least one year is:

P(T ≥ 365) = 1 - e^(-λ * 365)

The value of λ depends on the specific lightbulb and its failure rate, which needs to be determined from data or from the manufacturer. Once the value of λ is known, the above equation can be used to calculate the probability that the lightbulb lasts at least one year.

Therefore, The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

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The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

To determine the probability that a lightbulb lasts at least one year, we need to know the failure rate of the lightbulb and its distribution. For example, if the lightbulb follows a exponential distribution with parameter λ, the probability that it lasts at least one year (t = 365 days) can be calculated as:

P(T ≥ 365) = 1 - P(T < 365) = 1 - F(365),

where F(365) is the cumulative distribution function (CDF) of the exponential distribution evaluated at t = 365. The CDF of the exponential distribution is given by:

F(t) = 1 - e^(-λt),

so the probability that the lightbulb lasts at least one year is:

P(T ≥ 365) = 1 - e^(-λ * 365)

The value of λ depends on the specific lightbulb and its failure rate, which needs to be determined from data or from the manufacturer. Once the value of λ is known, the above equation can be used to calculate the probability that the lightbulb lasts at least one year.

Therefore, The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

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The function f(x) = -4(x-12)^2+5 yields a value of f(6)=-139.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is f(x) = -4(x-12)^2+5

f(x) = -4(x-12)²+5

Apply the formula for (a - b)²=(a² - 2ab + b²)

f(x) = -4(x-12)²+5

-4[x² - 24x + 144] + 5

To find the value of f(6), substitute the value of x as 6.

= -4[(6)² - 24(6) + 144] + 5

Simplify the expression inside the brackets -

= -4 [36 - 144 + 144] + 5

= -4 (36) + 5

Simplify the expression further to get the value -

= -144 + 5

= -139

Therefore, the value for f(6) is obtained as -139.

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After solving he question, Lin is walking the southwest direction making an obtuse angle.

In the given question, we have to find general direction did Lin walk from the gym to his house and what type of triangle did his walking path form.

To solve this question we have to thoroughly read the question. According to the given question we have to draw one by one with mentioning the distance. If we created the diagram correctly according to the question, then we can easily answer any question without any problem.

Lin walked west 651 feet.

After class, he walked northeast 910 feet to the gym.

Finally, he walked 615 feet back to his house from the gym.

So if we check the diagram that given below, we can say that Lin is walking the southwest direction making an obtuse angle.

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The complete question is:

To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym.

What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

X-axis divides the line segment formed by joining the points A(1,−5) and B(−4,5) in the ratio equals to 1 :1.

As given in the question,

Points A(1,−5) and B(−4,5)  used to form line segment is represented by :

( x₁ ,y₁) = ( 1, -5)

(x₂ , y₂) = (-4 ,5)

Let the ratio that divides the given line segment be m : n.

As x-axis divides the line segment coordinates are ( x, 0).

( x, 0) = [ (mx₂ + nx₁)/ (m+ n) , (my₂ + ny₁)/ (m+ n)]

⇒( x, 0) = [ (-4m + 1n)/ (m+ n) , (5m -5n)/ (m+ n)]

⇒ (5m -5n)/ (m+ n) = 0

⇒ 5m - 5n = 0

⇒ 5m = 5n

⇒ m : n = 1 : 1

Therefore, the x-axis divides the given line segment into the ratio 1 : 1.

The above question is incomplete, the complete question is :

In what ratio does the line segment joining A(1,−5) and B(−4,5) is divided by the x-axis ?

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Answer: In this case, the experimental value is 20 cm (the length that Diego measured) and the theoretical value is 23 cm (the actual length of the pencil). Plugging these values into the formula, we get:

percent error = (|20 - 23| / 23) x 100 = (3 / 23) x 100 = 0.13 x 100 = 13%

So the percent error for Diego's measurement is 13%.

Step-by-step explanation:

The Pearson correlation coefficient of the data is -0.6619

The Pearson correlation coefficient (PCC, for short) is a measure of the linear correlation between two variables. It is a value between -1 and 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. The PCC is calculated as the covariance of the two variables divided by the product of their standard deviations. It is widely used to measure the strength of a linear association between two continuous variables.

From the data given;

X Values

∑ = 28

Mean = 4

∑(X - Mx)2 = SSx = 28

Y Values

∑ = 37

Mean = 5.286

∑(Y - My)2 = SSy = 59.429

X and Y Combined

N = 7

∑(X - Mx)(Y - My) = -27

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -27 / √((28)(59.429)) = -0.6619

r = -0.6619

This is a moderate negative correlation, which means there is a tendency for high X variable scores to go with low Y variable scores (and vice versa).

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-25 is the  difference of outputs of any two inputs that are one value apart

A relation is a function if it has only One y-value for each x-value.

The given table of linear function

x          f(x)

-2         20

-1          -5

0           -30

1            -55

2          -80

The difference of outputs of any two inputs that are one value apart is -5-20=-25

Hence, -25 is the  difference of outputs of any two inputs that are one value apart

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A composite function, also known as f of g of x, is formally denoted as f(g(x)) or (f g)(x), and it requires the substitution of x = g(x) in f. (x). Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, distinct function.

The composite function F of G of X is composed of the two functions f(x) and g. (x). Let's use an actual situation to better comprehend f of g of x. We employ the slicer and the fryer for making french fries. Assume that x is a potato, that the fryer is performing the function f(x), and that the slicer is performing the function g(x) (frying the potato).

A composite function, also known as f of g of x, is formally denoted as f(g(x)) or (f g)(x), and it requires the substitution of x = g(x) in f. (x). Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function. The output of one function becomes the input of another function in f of g of x. It can be compared to a sequence of tools or processes.f(x) = 2x + 3 and g(x) = x2

f of g of x = (f ∘ g)(x) = f(g(x))

g of f of x = (g ∘ f)(x) = g(f(x))

We are aware that anytime we simplify a mathematical equation, we always operate on the elements inside the brackets first. Therefore, in order to obtain f(g(x)), we must first identify g(x), which we must then use as the input for f(x) and simplify. Here is an illustration to help you comprehend. Assume that g(x) = x2 and f(x) = 2x + 3. We'll discover f(g(3)).

g(3) = 32 = 9.

f(g(3)) = f(9) = 2(9) + 3 = 18 + 3 = 21.

Then

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Answer:

(112/56)*77 = $154

Step-by-step explanation:

Answer:

154

Step-by-step explanation:

112/56 = $2 per sq meter. so 77*2 = 154$

Yes, -7 has greater absolute value than 6.

What is a absolute value ?

The absolute value of a number is the distance from the origin of a number line (i.e. 0). It is denoted as |a|, which represents the magnitude of any integer 'a'. Regardless of sign, the absolute value of any integer, positive or negative, will be the real a number. It is denoted by two vertical lines |a| and is known as the modulus of a.

For example, the absolute value of 5 is the same for both 5 and -5.

as |-5| = +5 and |+5| = +5

Now,

As the distance of -7 in magnitude from zero is greater than distance of 6 from zero.

Hence,

          -7 has greater absolute value than 6.

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Answer:

The absolute value of -7 is 7. 7 is greater than 6.

Step-by-step explanation:

Another technique for defining the scope and range of functions is to utilize graphs.

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range. Following the insertion of an x value, the function outputs this sequence of values.

Graphs can be used as a second method to define the domain and range of functions. A graph's domain is the entire set of input values represented on the x-axis because the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.

The set of all possible inputs and outputs is known as a function's domain, and the same is true for its range. It is crucial to consider a function's domain and range. The range contains all of the function's output values, while the domain contains all of the real numbers that can be used as input values.

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The perimeter of the square is 40 meters.

The complete length that a square's edge in a plane covers is known as its perimeter. The route that encircles a form is called the perimeter.

By summing all the sides of a closed geometrical object (two-dimensional), the perimeter is determined. Since a square is a polygon with four equal sides, its perimeter will be equal to the sum of those sides.

Since all the sides of a square are equal, therefore, the perimeter of the square will be 4 times its side, i.e. 4 × Side. It is measured in units, such as m, cm, in, ft, etc.

Because a square has four sides of equal length, the perimeter is 12 m+12 m+12 m+12 m=48.0m

Thus, The perimeter of the square is 40 meters.

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