Theorem: For any real number x, x+∣x−5∣≥5 In a proof by cases of the theorem
A. x≤0 B. x≤5 C. x<5 D. x<0

Domain: [-6,-2], Range: [-4,3) and Function: Yes, this graph can be expressed as a function as it passes the vertical line test.

A function is a set of instructions used to perform a specific task. It is a fundamental building block of computer programming, and it is used to create programs that can perform specific tasks. A function is a named block of code that performs a specific task. It can take one or more arguments as input and return a value as output. Functions can be used to divide a large program into smaller, more manageable pieces. Functions are also useful for code reuse, since the same code can be used multiple times within a program. In addition, functions can help improve program efficiency since code does not need to be written multiple times.

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The domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).

Function is an operation that takes one or more input values and produces one or more output values. It is a mathematical concept that is used in programming to create programs that can be used to solve problems. Functions can be used to organize code blocks into reusable pieces, making it easier to debug and maintain the code. A good example of a function is the mathematical function f(x) = x2, which takes an input value x and produces an output value of x2.

The domain of the inverse of a function is the range of the original function, and the range of the inverse is the domain of the original function. Therefore, since the domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).

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Complete Question is attached below:

Answer:30

Step-by-step explanation:

(a) The probability of a car accident occurring in the two hours is 0.3679.(b) The probability of a car accident occurring between 45 and 75 minutes is 0.3935 (c) The variance of the time until a car accident occurs is 0.0167 d) If a car accident has not happened in 3 hours, the probability it will happen in the next two hours is 0.7385

Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-120/60) * (120/60)^1) / 1! = 0.3679[/tex]
So the probability of a car accident occurring in the two hours is 0.3679.

Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-30/60) * (30/60)^1) / 1! = 0.3935[/tex], So the probability of a car accident occurring between 45 and 75 minutes is 0.3935.

The variance of a Poisson distribution is equal to the average rate, so the variance of the time until a car accident occurs is: [tex]Var(X) = 1/60 = 0.0167[/tex]Given that no car accident has occurred in the previous 180 minutes. We can use the conditional probability formula to find this probability:

[tex]P(X = 1 | X = 0) = P(X = 1 and X = 0) / P(X = 0) = (e^(-120/60) * (120/60)^1) / (e^(-180/60) * (180/60)^0) = 0.3679 / 0.0498 = 0.7385[/tex]
So the probability of a car accident occurring in the next two hours, given that no car accident has occurred in the previous 3 hours, is 0.7385.

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Any given expressions in the οptions that simplifies tο  -9.9999 are equal tο [tex]6^{-10}\times6 -10[/tex]   ( since the expressiοns in the οptiοns are nοt clear, mentiοning the value)

An expressiοn in math is a sentence with a minimum οf twο numbers/variables and at least οne math οperatiοn in it.

An expressiοn that includes variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn in mathematics (additiοn, subtractiοn, etc.). Terms cοmbine tο fοrm expressiοns.

Given expressiοn :

[tex]6^{-10}\times6 -10[/tex]

This simplifies tο -9.9999

Any given expressiοns in the options that simplifies to  -9.9999 are equal to [tex]6^{-10}\times6 -10[/tex]   ( since the expressions in the οptions are not clear, mentiοning the value)

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Answer:

[tex]2^{6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]

then

[tex]2^{15}[/tex] ÷ [tex]2^{9}[/tex] = [tex]2^{(15-9)}[/tex] = [tex]2^{6}[/tex] ( with k = 6 )

Alexis made 63 foul shots during the season.

If Alexis made 73% of her foul shots, then she made 0.73 * 86 = 62.78 foul shots during the season.

However, since foul shots must be whole numbers, Alexis would have made either 62 or 63 shots.

We know that Alexis and her team won 15 out of 17 games during the season. This means that Alexis made foul shots in each of these 15 games, for a total of 15 * 2 = 30 foul shots.

If Alexis made a total of 62 foul shots during the season, she would have had to make an additional 32 foul shots in the two games they lost (17 games - 15 games they won = 2 games they lost). That would mean she made 16 foul shots in each of the two games they lost, which is unlikely.

Therefore, Alexis must have made 63 foul shots during the season, leaving only 23 foul shots missed (86 total foul shots - 63 made foul shots).

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The probability of X = 2 can be found using the binomial probability formula, with p ≈ 0.119 obtained by solving for p using the equation P(X = 4) = 0.9724. The resulting probability is approximately 0.193.

We can use the binomial probability formula to find P(X = 2):

P(X = 2) = (7 choose 2) * p² * (1-p)⁽⁷⁻²⁾

We know that P(X = 4) = (7 choose 4) * p⁴ * (1-p)⁽⁷⁻⁴⁾ = 0.9724

Solving for p in this equation, we get p ≈ 0.119

Substituting this value of p in the formula for P(X = 2), we get:

P(X = 2) = (7 choose 2) * 0.119² * 0.881⁽⁷⁻²⁾ ≈ 0.193

Therefore, the probability that X = 2 is approximately 0.193.

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Answer:

24.5

Step-by-step explanation:

we know that x=7

so 7x/2 (just a fancy way of saying x multiplied by 7/2)=

7*7/2= 24.5

Hope this helps! :)

The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.

First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:

Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]

Distance Yq = [tex]\sqrt{8 + 25 }[/tex]

Distance Yq =[tex]\sqrt{ 33}[/tex]

Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]

Distance 5B = [tex]\sqrt{2}[/tex]

Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:

x = (33/2)

Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,

Slοpe Yq = (10-5)/(8-10) = -5/2

Slοpe B-missing vertex = -5/2

write the equatiοn οf the line passing thrοugh B and the missing vertex:

y - 2 = (-5/2)(x - 3)

Simplifying, we get:

y = (-5/2)x + (19/2)

Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.

Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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Answer:

There is no pie chart to answer it

Step-by-step explanation:

The total number of residents in the project is 17,664.

The total number of residents in the project can be calculated by using the following formula:

Number of residents = Number of apartments x Average number of persons per apartment

In this case, the calculation would be:

Number of residents = 4,416 x 4

Number of residents = 17,664

Therefore, the total number of residents in the project is 17,664.

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Answer:add pic

Step-by-step explanation:

The chord of the sphere is represented by OT.

The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.

So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.

Hence, the chord of the sphere is represented by OT.

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Answer:  -4 to the 7th power.

Step-by-step explanation:

Answer:

-45,000

Step-by-step explanation:

The evidence which supports the fact that the shape ABCD is a parallelogram is; ABCD is a parallelogram because both pairs of opposite sides are parallel.

From the features of parallelograms, it can be inferred that the opposite sides of a parallelogram are parallel.

Also, parallel lines are lines whose slopes are equal.

On this note;

slope of AB-2/5 slope of BC = -4

slope of CD-2/5 slope of AD = -4

Hence, it can be inferred that opposite sides AB and CD as well as BC and AD are parallel.

Ultimately, ABCD is a parallelogram because both pairs of opposite sides are parallel.

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Answer:

First choice, y = -2x+6

Step-by-step explanation:

Convert the original equation to slope-intercept form, where y = mx + b.
We are looking for a parallel line so keep x, y, and the slope. turn the 7 into an intercept variable. Plug in (2,2) for (x,y). Solve for b. b = 6. Rewrite the equation with the same slope and the new y-intercept.

y = -2x + 6

Answer:

216 cubic cm

Step-by-step explanation:

Answer:

3174.538707cm³

Step-by-step explanation:

SurfaceArea of Cube=S²

volume of cube=S³

SA=216cm²

S=

[tex] \sqrt{216} [/tex]

S=

[tex]6 \sqrt{6} [/tex]

Volume of cube =S³

V=

[tex](6 \sqrt{6} )^{3} [/tex]

: . V= 3174.538707cm³

well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.

so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x[/tex]

so "x" plus the tax will just be x + 0.08x = 1.08x.

The tip was 15% of that 1.08x, and we happen to know that was $1.05.

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48[/tex]

According to the given information, the value(s) of x for which[tex]$f(G(x)) = g(f(x))$[/tex] is x = 1 or x = -2/3.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

[tex]To find the inverse of $G(x)$:Replace $G(x)$ with $y$: $y = x - x^2 + 1$Solve for $x$: $x^2 - x + (1 - y) = 0$Apply the quadratic formula: $x = \frac{1 \pm \sqrt{1 - 4(1)(1-y)}}{2} = \frac{1 \pm \sqrt{-3 + 4y}}{2}$The inverse of $G(x)$ is therefore: $G^{-1}(x) = \frac{1 \pm \sqrt{-3 + 4x}}{2}$To find the value of $x$ for which $f(G(x)) = g(f(x))$:Start with $f(G(x))$: $f(G(x)) = f(x^2 - x + 2)$[/tex]

[tex]Replace $f(x)$ with $3 - 2x$: $f(G(x)) = 3 - 2(x^2 - x + 2) = -2x^2 + 2x - 3$Replace $G(x)$ with $y$: $y = x^2 - x + 2$Replace $g(y)$ with $y - x^2 + 1$: $g(y) = y - x^2 + 1$Set $f(G(x))$ equal to $g(f(x))$ and solve for $x$:$-2x^2 + 2x - 3 = (3 - 2x) - x^2 + 1$Simplify and solve for $x$: $x = 1$ or $x = -\frac{2}{3}$[/tex]

Therefore, according to the given information, the value(s) of x for which [tex]$f(G(x)) = g(f(x))$[/tex]is x = 1 or x = -2/3.

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The total percentage increase in the investor's stock account is 3.7%.

What is the percentage increase?

Percentage increase refers to the amount by which a value or quantity has grown or increased, expressed as a percentage of its original value. It is calculated by dividing the difference between the new value and the original value by the original value, and then multiplying by 100 to express the result as a percentage. The formula for calculating percentage increase is:

Percentage increase = [(New value - Original value) / Original value] x 100%

To find the total percentage increase in the investor's stock account, we need to first calculate the new value of each stock and then add them together.

For Company A:

The stock has increased by 1%, which means its new value is 1% higher than $2000.

The increase in value is 0.01 * $2000 = $20.

The new value of the stock in Company A is $2000 + $20 = $2020.

For Company B:

The stock has increased by 5%, which means its new value is 5% higher than $4240.

The increase in value is 0.05 * $4240 = $212.

The new value of the stock in Company B is $4240 + $212 = $4452.

Now, we can find the total value of the investor's stock account by adding the new values of both stocks:

$2020 + $4452 = $6472

To find the percentage increase, we need to compare the total new value to the original total value:

The original total value was $2000 + $4240 = $6240

The total percentage increase is [(New total value - Original total value) / Original total value] x 100%

Plugging in the numbers: [(6472 - 6240) / 6240] x 100% = 3.7%

Therefore, the total percentage increase in the investor's stock account is 3.7%.

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After 71 years we will no longer have enough natural resources to support the growing population.

What is a population?

The population of a given place is the total number of people who typically reside there as of January 1 of a given year.

Total population supported by resources = 9 billion = 9 x [tex]10^9[/tex]

Because resources are being depleted 1% per year = 90000000000 x 1%

= 9 x [tex]10^7[/tex]

Total world population = 6.4 x [tex]10^9[/tex]

Now, for to find time of resource depletion,

Resource problem = 6.4 x [tex]10^9[/tex] ÷ 9 x [tex]10^7[/tex]

On solving we get 71 years

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The area of the composite figure is the sum of the whole area of each shape. Therefore, the area of the figure is 151.585 ft².

The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.

Therefore, the composite figure can be divided into two rectangles and a quarter circle.

Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.

Hence, the area of the composite figure is the sum of the area of the two rectangle and area of the quarter circle.

area of the composite figure = area of rectangle + area of rectangle + area of quarter circle

area of the composite figure = 5 × 8 + 8 × 6 + 1 / 4 × π × 9²

area of the composite figure =  40 + 48 + 81π / 4

area of the composite figure = 88 + 254.34 / 4

area of the composite figure = 88 + 63.585

area of the composite figure = 151.585 ft²

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A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

For hamburguers, the outcomes are given as follows:

Hence:

58/300 x 100% = 19.33%.

For cheeseburger and onion rings compared to the total amount of orders for onion rings, the outcomes are given as follows:

Hence:

74/103 = 71.84%.

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Based on the given scenario, the expected profit if the price is $4 is $11.91, while the price that maximizes the profit is $5.47.

What is the Newsvendor problem?

The Newsvendor problem is a problem in inventory theory that tries to answer the question of how much inventory should be ordered to maximize profit, given limited shelf space or warehouse space, uncertain product demand, and a fixed order quantity. This problem is often encountered in newspaper, magazine, and perishable food industries, and the answer lies in balancing the risk of stocking out (not having enough inventory to meet demand) with the cost of holding excess inventory.

Newsvendor problem with a single product that sells at a price of p and costs $3 per item. Assuming that the store holds 5 products and that the demand is a Poison random variable with rate 10€-(P-3), let’s answer the two questions.

The expected profit (EP) is given by:

EP = Revenue - Cost =

EP = (p*min{Demand, Quantity}) - (3*Quantity)

For the given problem, Quantity is 5, and Demand is a Poison random variable with rate 10€-(P-3). Therefore:

EP(p) = (p*min{Demand, 5}) - (3*5)EP(p)

EP(p) = {p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15.

Using p = $4:

EP(4) = {(4*(1 - exp[-7])) + (5*(1 - exp[-7]))} - 15EP(4)

EP(4) = $11.91

Therefore, the expected profit is $11.91 when the price is $4.

The profit function is given by:

P(p) = (p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15

To maximize the profit, we need to take the derivative of the profit function with respect to p, set it equal to zero, and solve for p:

P'(p) = {1 - exp[-10€-(p-3)]} + p*{10€-(p-3)}*exp[-10€-(p-3)] - 5*{10€-(p-3)}*exp[-10€-(p-3)] = 0

Rearranging and using numerical methods to solve for p, we find:

p = $5.47

Therefore, the price that maximizes the profit is $5.47.

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Step-by-step explanation:

Find unit rate :

90 miles  in 1.5 hrs

90 /1.5 = 60 miles/hr

    that is one mile per minute     20 miles takes 20 minutes

            120 miles takes 120 minutes = 2 hours

The correct option is No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.

What is Side-Angle-Side (SAS) criterion?

The Side-Angle-Side (SAS) criterion is a rule used in geometry to determine whether two triangles are congruent, which means they have the same size and shape. The SAS criterion states that if two sides and the angle between them in one triangle are equal to two corresponding sides and the angle between them in another triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the two triangles are equal in length and measure.

To determine whether the two triangles are congruent, we can use the side-angle-side (SAS) congruence criterion. We can see that triangle PQR has sides PQ, QR, and RP, and angle QPR, while triangle STU has sides ST, TU, and US, and angle TSU. We can compare the corresponding sides and angles:

PQ is of length 4, and ST is of length 4.

QR is of length 1, and TU is of length 4.

RP is of length 2, and US is of length 2.

Angle QPR is a right angle, while angle TSU is an acute angle.

Therefore, the two triangles do not have the same corresponding sides and angles, and we cannot conclude that they are congruent.

The correct option is:

No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.

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The probability that exactly 3 employees are absent during a given week is 0.25.

The probability that at least 3 employees are absent during a given week is 0.19 + 0.09 + 0.25 = 0.53.

The probability that at most 3 employees are absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 + 0.25 = 0.72.

The probability that at most 2 employees are absent during a given week is P(X ≤ 2) = 0.12 + 0.15 + 0.20 = 0.47.

The probability that between 2 and 4 employees inclusive are absent during a given week is P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.19 = 0.64.

The probability that strictly between 2 and 4 employees are absent during a given week is P(2 < X < 4) = 0.25 + 0.19 = 0.44.

The probability that more than 3 employees are not absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 = 0.47, and the probability that more than 3 employees are absent during a given week is P(X > 3) = 0.19 + 0.09 = 0.28. The probability that more than 3 employees are not absent is the complement of the probability that more than 3 employees are absent. Therefore, the probability that more than 3 employees are not absent during a given week is 1 - 0.28 = 0.72.

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The required diameter of the actual Ricoffy tin container is approximately 92 mm.

By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).

Let the diameter of the actual Ricoffy tin container be d mm.

Since the volume of the tin container is proportional to the cube of its dimensions, and the tin container is 2.5 times smaller than its actual size, we have:

[tex]$(\frac{d}{2.5})^3 = \frac{1}{2.5} \times d^3 = \frac{3}{4} \times 750\text{ g} = 562.5\text{ g}$$[/tex]

where we have used the fact that the actual weight of the coffee is 750g.

Solving for d, we get:

[tex]$$d = \sqrt[3]{\frac{562.5\text{ g}}{\frac{1}{2.5}}} \approx 91.98\text{ mm}$$[/tex]

Therefore, the diameter of the actual Ricoffy tin container is approximately 92 mm.

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Answer:

x(x - 5)(x + 2)

Step-by-step explanation:

[tex]x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)[/tex]

x² - 3x - 10

Now, we look for two integers which when added give (-3) and when multiplied give (-10). The factors are 2 and (-5).

Sum = -3

Product = -10

Factors = 2 , (-5)       {2*(-5) = -10 and 2 + (-5) = -3}

x² - 3x - 10 = x² - 5x + 2x - 10   {Rewrite the middle term using the factors}

From the first and second term, take out the common factor 'x' & take out the common factor 2 from the third and fourth term.

                 = x(x - 5) + 2(x - 5)

                 = (x -5)(x + 2)

[tex]x^3 - 3x^2 - 10x = x(x -5)(x + 2)[/tex]