1. Let (X, d) be a metric space. Define e : X × X −→ R by
e(x, y) = min {1, d(x, y)}, ∀ x, y ∈ X

Answer: The probability of picking each type of player at random depends on the number of players of each type on the field. If the number of players of each type is not specified, it is not possible to determine the probability of picking each type of player at random.

Step-by-step explanation:

Answer: To find the principal value of arctan(-1.44) to the nearest minute, we first need to find the value of arctan(-1.44) in radians.

We can use the arctan function in a mathematical software or calculator to find the result. The value of arctan(-1.44) in radians is approximately -0.8623.

Next, we convert the result from radians to minutes, by multiplying the radians by 180/π and then multiplying the result by 60.

-0.8623 * 180/π * 60 = -50.47 minutes

So the principal value of arctan(-1.44) to the nearest minute is approximately -50 minutes.

Step-by-step explanation:

Therefore, we have proved that the value of the expression

(3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.

In mathematics, addition, multiplication, and division are necessary. They result in the following when combined: An equation, some data, and a mathematical function Values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions can all be found in a declaration of fact. Different phrases and words can be compared and evaluated.

Here,

To prove that the value of the expression doesn't depend on x, we need to show that the x-term disappears when we simplify the expression.

Starting with:

(3/5x² - 0.4cy - 1.5y + 1) - (y² - 2/5xy + 0.6x²)

Distributing the negative sign in the second set of parentheses:

3/5x² - 0.4cy - 1.5y + 1 - y² + 2/5xy - 0.6x²

Rearranging the terms by collecting like terms, we get:

(3/5 - 0.6)x² + (2/5y - 0.4c)y - y²- 1.5y + 1

Simplifying further, we get:

(-0.1)x² + (0.4y - 0.4c)y - (y² + 1.5y - 1)

Notice that there is no x-term in the final expression, which means that the value of the expression doesn't depend on x.

Therefore, we have proved that the value of the expression (3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.

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Using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and sometimes "pc" is also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without boundaries and without a standard measurement.

So, calculate as follows:

5880/100 * 11.5 = 676.2

Now,

5880 - 676.2 = 5,203.8

Now, calculate the percentage as follows:

806.59/5,203.8 * 100

15.5%

Therefore, using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.

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Answer:

The domain for the interval of decrease is 3 ≤ x ≤ 5

Answer:

[tex]y=-105x+1300[/tex]

Step-by-step explanation:

Define the variables:

Given information:

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The initial purchase price of the computer was $1,300. So when x = 0, y = 1300.  Therefore, the y-intercept is 1300.  

We have already calculated the slope as -105.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

[tex]y=-105x+1300[/tex]

Mike buys 3 oranges and 1 lemon at the

farmers market. What fraction of his

purchase were oranges?

answer :

3/4

Answer: 3/4

Step-by-step explanation:

there are a total of four purchases and three of them were purchases we can represent this with the fraction 3/4

The most accurate comment about the graph  data is: "China's steel production is increasing while its major competitors' production is declining."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."

This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.

While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.

The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.

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93,101,109,117,125,133,141,149,157,165

Answer:

Step-by-step explanation:

You want the domain and range of the relation {(-4,-4),(-1,3),(0,5),(3,9)}.

The domain is the set of first numbers of the ordered pairs:

  {-4, -1, 0, 3}

The range is the set of second numbers of the ordered pairs:

  {-4, 3, 5, 9}

Answer:

Domain: {-4, -1, 0, 3}

Range: {-4, 3, 5, 9}

Step-by-step explanation:

The Domain is the number that is on the x-axis.

The Range is the number on the y-axis.

Its quite simple. Hope this HELPED! HAVE A GOOD DAY AND NIGHT!!!!!!!!!!

The required answers are:

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

Given image has a graph of the function f(x)

To find [tex]\lim_{x\rightarrow 2^-}f(x), lim f(2) 12+, lim f(x) 12 and f(2)[/tex]

We have from the image of the graph the function f(x) is a discontinuous function with x=2 is the point of discontinuity.

Now from the graph the value of f(x) at x=2 i.e. f(2) = -3 as the graph has a bold dot at y=-3.

Next [tex]\lim_{x\rightarrow 2^-}f(x)=\lim_{x\rightarrow 2^+}f(x)=-1[/tex] as in the graph of f(x) it has a small circle at y = -1.

As f(2) = -3 so [tex]\lim_{x\rightarrow 2}f(x)=f(2)=-3[/tex]

Thus the required answers are

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

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The three criteria that binomial experiments meet are :

The experiment is referred to as a binomial experiment since there are only two possible output values in a binomial experiment. In the case of binomial experiments, the number of independence variables is fixed.

In the case of binomial experiments, the number of independence variables is fixed. The total number of output values for the binomial experiment is 2. For the binomial experiment, each of the two outputs has a 50% chance of happening—50% for success and 50% for failure.

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Answer:

B. The trials are independent.

C. There are only two outcomes per trial.

E. The probability of success is the same for each trial.

Step-by-step explanation:

and then

B. a survey asking 50 people if they like pizza

C. a survey measuring 50 people to see if they are over 6 feet tall

The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = | x³ -3x² + 2|

Now, We know that;

⇒ All the critical points are find as;

⇒ f '(x) = 0

⇒ 3x² - 6x = 0

⇒ 3x(x - 2) = 0

⇒ x = 0

⇒ x = 2

Thus, The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.

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Answer:

5000

Step-by-step explanation:

10×16=160

160 Btu?

is 5000

because the closesd value in the graph is 5000

for 160

Lourdes will spend an amount of  $1.50 more if she buys only 3-packs of paper.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

If Lourdes buys only 3-packs of paper, she will need to buy 12 / 3 = 4 sets of paper.

At $10.50 per set, this will cost her 4 x $10.50 = $42.

If Lourdes buys only 4-packs of paper, she will need to buy 12 / 4 = 3 sets of paper.

At $13.50 per set, this will cost her 3 x $13.50 = $40.50.

So, Lourdes will spend $42 - $40.50 = $1.50 more if she buys only 3-packs of paper.

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The number of bouts that Andrew won during the last would be = 20 bouts.

The number of fencing bouts that Andrew won = 4

The number of bouts he losses every 4 wins = 3 bouts

The total number of bouts he is having this year = 35 bouts.

The number of bouts he won amongst the number that he lost would be calculated as;

= 4+3 = 7

= 4/7 × 35/1

= 4× 5 = 20 bouts.

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Answer:

y = 4x - 3

Step-by-step explanation:

y = mx + b

The m is the slope and the b is the y-intercept.

The slope is 4.  If you start at the point (0,-3) and go up 4 units and then 1 unit to the right, you will be back on the line at point (2,4) The slope is the rise over the run.  The rise is 4 and the run is 1.  4/1 = 4.

The slope (m) is 4.

The y-intercept is where the line crosses the y axis.  It crosses at (0,-3)

The y-intercept (b) is -3

Plug 4 in for m and -3 in for b

y = mx + b

y = 4x -3

Answer:

[tex]y = 4x - 3[/tex]

Step-by-step explanation:

we need to find out the equation of the function that is graphed. From the given graph we can see that the line passes through points (0,-3) and (2,5) . So we can find out the slope of the line as ,

[tex]\implies m =\dfrac{y_2-y_2}{x_2-x_1}=\tan\theta\\[/tex]

[tex]\implies m =\dfrac{-3-5}{0-2} \\[/tex]

[tex]\implies m =\dfrac{-8}{-2} \\[/tex]

[tex]\implies \mathfrak{ m = 4 }\\[/tex]

Now we may use point slope form of the line to find out the equation of the line as,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

[tex]\implies y -(-3) = 4(x-0) \\[/tex]

[tex]\implies y +3 = 4x\\[/tex]

[tex]\implies \underline{\underline{ y = 4x -3}} \\[/tex]

And we are done!

-TσηγSтαяκ

The value for variable m in equation Z = m + mwg is m = Z - mwg.

What are variables?

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The equation is given as -

Z = m + mwg

To get the value for variable m, subtract mwg from Z and take it to left-hand side.

Z - mwg = m

Reverse the equation and get it in right form -

The equation obtained is -

m = Z - mwg

Therefore, the value is m = Z - mwg .

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Answer:

Below

Step-by-step explanation:

I suppose you are looking for a solution to the system of equations

  since both equations are equal to 'y' they are equal:

 2x+3  = -3x+3       add 2x to both sides of the equation

 5x + 3 = 3              subtract 3 from both sides

 5x = 0            so x = 0

  if x =0 then find y    y = 2(0) + 3 = 3

       the solution is (0,3)

Answer:

1) {2,0,-2}

2) {1,-3,1}

3) {1,3,5}

4) {0,1,2}

Answer: 4 7/12

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8\dfrac{1}{6} - 3 \dfrac{7}{12}}[/tex]

[tex]\mathsf{= \dfrac{8\times6 + 1}{6} - \dfrac{3\times12 + 7}{12}}[/tex]

[tex]\mathsf{= \dfrac{48 + 1}{6} - \dfrac{36 + 7}{12}}[/tex]

[tex]\mathsf{= \dfrac{49}{6} - \dfrac{43}{12}}[/tex]

[tex]\mathsf{= \dfrac{49}{6}\times\dfrac{2}{2} - \dfrac{43}{12}\times\dfrac{1}{1}}[/tex]

[tex]\mathsf{= \dfrac{49\times2}{6\times2} - \dfrac{43\times1}{12\times1}}[/tex]

[tex]\mathsf{= \dfrac{98}{12} - \dfrac{43}{12}}[/tex]

[tex]\mathsf{= \dfrac{98 - 43}{12 - 0}}[/tex]

[tex]\mathsf{= \dfrac{55}{12}\rightarrow 4\dfrac{7}{12}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{4\dfrac{7}{12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The dilated coordinates:

D(-7, 0) → D' (-7/5, 0)

E(-7, -5) → E' (-7/5, -1)

F(-2, -5) → F' (-2/5, -1)

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.

Given:

Coordinates: D(-7, 0), E(-7, -5), F(-2, -5).

The shape is dilated by the scale factor of 1/5.

The dilation rule:

D(-7, 0) → D' (-7/5, 0)

E(-7, -5) → E' (-7/5, -1)

F(-2, -5) → F' (-2/5, -1)

Hence, the dilated coordinates are given above.

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The complete question:

Find the dilated coordinates with the scale factor of 1/5,

D(-7, 0), E(-7, -5), F(-2, -5).

Answer:

Tax amount: $7.36

Tax rate: 5.84%

Step-by-step explanation:

First, we have to find the tax amount by taking

$133.36 - $126 = $7.36

Tax amount: $7.36

To find the tax rate, we take

7.36 divided by 126, times 100 = 5.84%

Tax rate: 5.84%

So,

Tax amount: $7.36

Tax rate: 5.84%

The given expression "4 divided by 2 left square brackets 2 plus 2 right square brackets equals" gives the solution one divided by 2.

4 divided by 2 left square brackets 2 plus 2 right square brackets equals?

4 ÷ 2(2 + 2)

based on the concept of PEMDAS

P = parenthesis

E = Exponent

M = Multiplication

D = Division

A = Addition

S = Subtraction

= 4 ÷ 2(4)

= 4 ÷ 8

= 4/8

= 1/2

Therefore, the correct answer is 1/2(one divided by two

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Answer:

p = 1

Step-by-step explanation:

since (p, 2p + 1) is a solution then it makes the equation true.

substitute x = p and y = 2p + 1 into the equation and solve for p

11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side

11p - 4p - 2 = 5

7p - 2 = 5 ( add 2 to both sides )

7p = 7 ( divide both sides by 7 )

p = 1

The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603

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

Base fee = $85.00

Rate = $2 off

Using the above as a guide, we have the following:

R(n) = n(85 - 2n)

Where n is the number of rooms

This means that

n = 9

So, the notation is

R(9)

The value is

R(9) = 9 *(85 - 2 * 9)\

R(9) = 603

Hence, the value is $603

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Answer:

a $12 discount like what is it soupoust to be

Kelly can run 1/2 mile in 3 minutes. 1/6 mile Kelly run in 1 minute if he runs at the same pace the entire time.

The word "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards.

Kelly can run 1/2 mile in 3 minutes so the ratio is 1/2 mile per 3 minutes

= [tex]\frac{\frac{1}{2} }{3}[/tex]

For transforming 3 to 1 we need to divide by 3 because we have to keep the ratio value, we have to divide also the numerator by 3 :

= [tex]\frac{\frac{1}{2} }{3} \times \frac{\frac{1}{3} }{\frac{1}{3}}[/tex]

[tex]= \frac{\frac{1}{2} \times \frac{1}{3} }{3 \times \frac{1}{3} }[/tex]

= 1/6 / 1

= 1/6

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By the inverse of a number, 0.3⁻¹ = 10/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 0.3⁻¹ = 10/3

Now, We can simplify as;

⇒ 0.3⁻¹

⇒ (3/10)⁻¹

⇒ 10/3

Thus, By the inverse of a number, 0.3⁻¹ = 10/3

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