Function m represents the number of people in a movie theatre on a Tuesday as a
function of hours since the movie theatre opened.

Here is the graph of function

Based on the graph and the situation, what are the domain and range for function m?

The domain is...

The range is...

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1. Then λ belongs to (0,1).

In the given question, if λ∈R and the domain of f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex] is [1,2)∪(2,3], then λ belong to

The given function is

f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex]

The function is belong in between [1,2)∪(2,3]. So

|x-2| ≠ 0  and  |x| > 0

x ≠ 2       and  x > 0

Since the value of x can not be equal to 2 and x value is always greater than 0. So

[tex]log_{\lambda}|x-2|\geqslant 0[/tex]

The value of |x-2| should be lies between 0 and 1 because x cannot be equal to 2 and greater than 1.

So 0< |x-2| < 1

If the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1.

Hence, 0 < λ < 1.

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In the figure, the angles m∠ 1 and m∠ 2 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

In the question given, m∠ 1 and m∠ 2 are corresponding angles with each other.

This also implies that they are equal with one another using corresponding angle theorem.

Corresponding angle theorem states that : All corresponding angles are equal to one another.

Therefore, m∠ 1 and m∠ 5 are corresponding angles and are equal to one another.

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Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

Relations called functions provide an output for each input. The characteristic that every input is associated to exactly one output defines a function as a relation between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Based on the values listed in the table for the parallelograms' base length and height, you can see that the base length grows by one unit, giving you the numbers 1, 2, 3, and 4. When base length increases by one unit, height reduces by 1/x, as shown in the following example:

Height and base length have the following relation:

[tex]f(x)=\frac{48}{x}[/tex]

where x is the base length and f(x) is the height. 

[tex]f(1)=\frac{48}{1}= 48\\f(2)=\frac{48}{2}=24\\f(3)=\frac{48}{3}=16\\f(4)=\frac{48}{4}=12\\f(6)=\frac{48}{6}==6[/tex]

Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

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The frequency of oscillation for the spring with the constant value of 2.5×10⁴ is 0.0012

The term frequency is defined as the number of waves that pass a fixed point in unit time and it is also known as the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

Here we have given the following values,

Spring constant = 2.5 × 10⁴

And the weight of the cart = 1.4 kg

Now, we have calculated the value of the frequency of oscillation as,

=> v = 1/T

Here T refers the time period.

Where it can be rewritten as,

=> 1/2π x √(k/m)

Now, we have to apply the values on it then we get

=> 1/2π  x √(1.4/2.5 x 10⁴)

=> 0.1592 x 0.0074

=> 0.0012

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The distance the 12 centimeters minute hand moves in 20 minutes obtained by converting the angular motion to translational motion is about 25.133 centimeters

Angular motion is the circular motion of an object around a point or location.

The complete 360° rotation of the minute hand = 60 minutes

Therefore;

60 minutes is equivalent to 360°

1 minute is equivalent to 360°/60 = 6°

20 minutes is equivalent to 20 × 6° = 120°

The circular path motion following an angular rotation of angle theta = Radius × Theta

Where, theta is in radians

The radius of the minute hand = 12 centimeters

360° = 2•π radians

120° = 360°/3 = (2•π/3) radians

The distance moved by the the minute hand = 12 cm × (2•π/3) radians = 8•π cm

8•π cm ≈ 25.133 cm

The distance the minute hand moves in 20 minutes is about 25.133 cm

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A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.

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Answer: The second one.

The equation of the line that passes through the given points in the slope-intercept form is y = (-5/2)x - 1

From the question, we are to determine the equation of the line that passes through the given points

We will pick two value pairs from the table

Picking (-4, 9) and (-2, 4)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Then,

(y - 9) / (x - (-4)) = (4 - 9) / (-2 - (-4))

Simplify

(y - 9)/(x + 4) = -5/(-2 + 4)

(y - 9)/(x + 4) = -5/2

Cross multiply

2(y - 9) = -5(x + 4)

2y - 18 = -5x - 20

2y = -5x -20 + 18

2y = -5x - 2

Divide through by 2

y = (-5/2)x - 1

Hence, the equation is y = (-5/2)x - 1

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Answer:

$1.41

Step-by-step explanation:

0.20 * 5.8 ounces = $1.16

0.25 * 1.16 = $1.41

The mail  weighing 6.8 ounces cost 145 cents

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here, the first ounce cost 25 cents and all subsequent ounces or parts of an ounce cost 20 cents each

therefore cost of the first ounce = 25

        and cost of 5.8 ounces = 20× 6

                                                = 120 cents

thus total cost is 120+25 =145 cents

Hence, the  total cost to mail a package is 145 cents

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We need 6 cans of paint are needed to cover an area of 2 200 square units.

In this question we need to find the number of cans of paint needed to cover an area of 2 200 square units.

We have been given one can of paint covers an area of 400 square units.

Let x cans of paint are needed to cover an area of 2200 square units..

1 can = 400 square units

x cans = 2200 square units

Bu Unitary method,

x = 2200/400

x = 22/4

x = 11/2

x = 5.5

x ≈ 6

Therefore, six cans of paint are needed to cover an area of 2 200 square units.

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A complete question is:

How many cans of paint are needed to cover an area of 2 200 square units if one can of paint covers an area of 400 square units?

The total mileage on Joe's shoes after the 21 weeks is 2,457 miles.

The total mileage of Joe's shoes is the sum of all the distance travelled by Joe within the given time of period of 21 weeks.

The distance travelled by Joe in 1 week is calculated as follows;

distance travelled by Joe in 1 week = 1 mile/day  x  7 days = 7 miles

The distance travelled by Joe in 21 weeks is calculated as follows;

distance travelled in 21 weeks = ( 7 miles / week ) x ( 21 weeks )

distance travelled in 21 weeks = 147 miles

the number of additional mile added each week = 110 mile

for 21 weeks = 21 x 110 mile = 2,310 miles

The total mileage on Joe's shoes after the 21 weeks is calculated as follows;

total mileage = 2,310 miles  +  147 miles

total mileage = 2,457 miles

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The graph of y² 4x is a parabola with vertex (0,0) and x- and y-intercepts (0,0). The graph opens downward and can be written as y=4x².

The graph of y² 4x is a parabola in the shape of a "U" that opens downward. This parabola can be written in the standard form of y=a(x-h)²+k. In this case, a=4, h=0, and k=0. This means that the equation for the graph of y² 4x is y=4x².

To calculate the graph, we must first determine the vertex, which is the point of the parabola that has the maximum or minimum value. To do this, we use the formula for the vertex of a parabola, which is (h,k)=(-b/2a,f(h)). With a=4 and b=0, the vertex of the parabola is (0,0).

We can then calculate the x-intercepts, which are the points at which the graph of y² 4x crosses the x-axis. To do this, we set y=0 in the equation y=4x² and solve for x. This gives us x=±√(0/4) or x=0. This means that the x-intercepts of the graph of y² 4x are (0,0).

Finally, we can calculate the y-intercept, which is the point at which the graph of y² 4x crosses the y-axis. To do this, we set x=0 in the equation y=4x² and solve for y. This gives us y=0. This means that the y-intercept of the graph of y² 4x is (0,0).

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The probability that the shipment will be rejected is 0.724.

Given :

Since we have given that

n = 125

p' = 8 % = 0.08

p = 10 % = 0.10

Test statistic value :

z = p' - p / [tex]\sqrt{p(1-p)/n}[/tex]

= 0.08 - 0.10 / [tex]\sqrt{0.10 * 0.90 / 125}[/tex]

= -0.75

p value at z = -0.75

p = 0.226

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability of shipment will be rejected = 1 - 0.226

= 0.724

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There is major 3 types of expression. Numerical expression, algebraic expression and fractional expression.

This expression contains only two or more numbers along with symbols or operator. There is no variable present.

such as 226÷113+2×22-11

or (44÷88) ×100%

the above sign is percentage sign we can determine a percent value

or∛ (64)

the above sign represents a cubic root

we get the value 4

The expression having two or more fractional terms along with symbols are called fractional expression. There are numerator and denominator from which we need to determine a common denominator to obtain a result.

such as, 4/5+3/4

we have 2 different denominators 5 and 4. we need to find a common denominator by multiplying both. 5x4

                                                           20

In the next, common denominator is divided by each denominator and the result is multiplied with each numerator.

                 (4×4+3×5)/20

       hence, the result is 31/20

The expression contains both variables and numbers along with symbols are called algebraic expression. The algebraic expression having equal sign are termed as equation. Tha main purpose of using equation is to determine unknown value.

Algebraic expression are different types such as linear expression

2x+3-4y

2 and 4 are coefficient, 3 is constant

Polynomial expression as example 2x²-3y+4

Besides, we have other algebraic expression such as 3y+4 or x/4+y/3

and so on.

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Answer:

5x + 8y = 24

Step-by-step explanation:

y = [tex]\frac{-5}{8}[/tex]x + 3  Add [tex]\frac{5}{8}[/tex]x  to both sides

[tex]\frac{5}{8}[/tex]x + y = [tex]\frac{-5}{8}[/tex]x + [tex]\frac{5}{8}[/tex]x + 3

[tex]\frac{5}{8}[/tex]x + y = 3  Multiply all the way through by 8 to clear the fraction

[tex](\frac{8}{1})[/tex][tex](\frac{5}{8})[/tex]x + (8)y= (8)(3)

5x + 8y = 24

The theorem that is a valid triangle congruence theorem is the: ASA

A triangle congruence theorem is a set of conditions that must be met by a set of triangles before both triangles can be said to be congruent to each other.

Some of the valid triangle congruence theorem are:

Therefore, from the option given, the only valid triangle congruence theorem is: ASA.

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Complete Question:

Which of the following is a valid triangle congruence theorem?

AAA

SSA

ASA

none of the above

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

What are Corresponding Sides ?

Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure. For any two polygons to be similar, the ratios of the lengths of each pair of corresponding sides must be equal.

In the below-given images, the two triangles are congruent and their corresponding sides are color-coded.

In the above two triangles ABC and XYZ,

AB is the corresponding side to XY

BC is the corresponding side to YZ

CA is the corresponding side to ZX

Similarly , if ΔFAR is similar to ΔSUN

then ,

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

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On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

The factors of 5 are -

5

and 1

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Answer:

  3x -y = -4

Step-by-step explanation:

You want the equation of the line parallel to 3x-y=5 through point (0, 4).

The equation for the parallel will differ only in the constant. To find the new constant, use the given point coordinates for x and y.

  3x -y = 3(0) -(4) = -4

The equation of the line is ...

  3x -y = -4

Answer:

Neither

Step-by-step explanation:

It is not opposite to each other (perpendicular) or the same slope (parallel)

Answer:

m = 3

Step-by-step explanation:

rise over run

Answer:

Hope it helps you ...........

The theoretical and experimental probabilities are equal.

Probability determines the likelihood of a random event occurring. The ratio of the number of favorable outcomes to the total number of possible outcomes is known as theoretical probability.

Theoretical probability = number of odd sides/ die sides

Here given that the numbers that are odd comes 6

So,

6/20 = 3/10 theoretical probability

The outcome of an experiment that has been repeated multiple times is used to calculate experimental probability.

Experimental probability = number of times Tani landed on a odd number  divided by the number of times the experiment was performed

6/ 20= 3/10.

Therefore here , both experimental and theoretical probabilities are equal.

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Answer:

  (c)  The range of the function is all real numbers less than or equal to 0

Step-by-step explanation:

You want the true statement describing the domain or range of f(x) = -√x.

The domain of the function is the set of values x for which the function is defined. The square root is only defined for non-negative arguments:

  x ≥ 0 . . . . . . not an answer choice

The range is of the function is the set of values f(x) that the function can produce. The square root function can produce any non-negative value, so the opposite of the square root function will produce any non-positive value:

  f(x) ≤ 0 . . . . . the range is real numbers less than or equal to zero

Answer:

θ = 15°

Step-by-step explanation:

The wheelchair ramp creates a right triangle figure. Look at the image I have attached to this response to see the figure.

⭐ What is the "angle of inclination"?

The angle of inclination is the base angle adjacent to the 90-degrees. The angle of inclination is often denoted as θ.

To solve for the angle of inclination, θ, we have to use the inverse of a trigonometric function.

⭐ What trigonometric function do we use?

Look at the side lengths you are given. Are they opposite of θ? Are they adjacent to θ? Are they the hypotenuse of the triangle? Whatever combination of 2 side lengths you have, see what trigonometric function uses those 2 side lengths.

We are given the side length opposite of θ and a side length that is the hypotenuse of the triangle. Therefore, we are going to use the sine function.

⭐ What is the sine function?

sin(θ) = opposite/hypotenuse

Now, we are going to create an equation of the wheelchair ramp using the sine function.

sin(θ) = 5.1/20

Next, find the inverse of the equation. Here is the inverse of the sine function:[tex]sin^{-1} (opposite/hypotenuse) =[/tex]

Let's substitute the opposite and hypotenuse into the inverse of the sine function and solve using a scientific calculator. Make sure to round to the nearest degree.

[tex]sin^{-1}(5.1/20) =[/tex]

∴ [tex]sin^{-1}(5.1/20)[/tex] ≈ 15°

The number of 5 digit numbers that can be formed is 3125

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

Digits = 0, 1, 2, 3, 4

These digits can be repeated

So, we have

n = 5 i.e. the count of digits in 0, 1, 2, 3, 4

The number of 5 digit numbers  is then calculated as

Count = n⁵

So, we have

Count = 5⁵

Evaluate

Count = 3125

Hence, the count is 3125

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The slope of the situation means: B. after the initial rental fee, the paddleboard costs an additional $12 every hour

If a situation is modeled as a linear relationship between two variables, the slope of the relationship is a measure of the strength and direction of the relationship between the two variables in that particular situation.

The slope is calculated as the change in the value of one variable (the "rise") over the change in the value of the other variable (the "run").

For example, consider a situation in which the number of hours that a student studies is related to their grades in a class. The slope of this relationship would indicate the strength and direction of the relationship between hours of study and grades in this particular situation.

A positive slope would indicate that as the number of hours of study increases, the grades also increase, while a negative slope would indicate that as the number of hours of study increases, the grades decrease.

To find the slope of the situation that is represented in the graph given, use two points on the line to calculate the slope.

Using (0, 10) and (2.5, 40)

Slope (m) = change in y / change in x = (40 - 10) / (2.5 - 0)

= 30/2.5

Slope (m) = 12

Therefore, this means that, B. after the initial rental fee, the paddleboard costs an additional $12 every hour.

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There are countless possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable. If we try to solve an equation and receive a variable or a number equal to itself, there are infinitely many solutions to the equation.

Single-solution equations:

Some equations only have one precise solution. The variable in these equations can only take on one value in order for the equation to be true. When you solve an equation and the result is a variable equal to a number, you know that the equation only has one solution.

Example: For x, find the solution to the equation 6x-3=21.

6x \s= 24

To both sides, add 3.

x \s= 4

Subtract 6 from both sides.

For a single value of the variable, x=4, the equation is true. Consequently, there is only one solution to the equation 6x-3=21

Non-solvable equations:

There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.

Example: Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides.

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

Equations that have infinitely many solutions:

The number of solutions to some equations is limitless. When a variable is used in these equations, any value makes the equation true. If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions.

Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

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Children who are 4 years old frequently count up to 1,0and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.

Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

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The constraints for this situation are x>0, y>0, 340x + 670y < 5650 and x>1/3y

Let the number of bicycles = x

and the number of treadmills = y

Since the number of new bicycles must be more than 1/3 times of the new treadmills.

Inequality representing the statement will be,

x>1/3y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y

(Refer to the image attached for the complete question)

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Let the number of bicycles = x

and the number of treadmills = y

Inequality representing the statement will be,

x>1/3y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y