Write a rational function with the given characteristics.
A vertical asymptote at x=8 and a horizontal asymptote at y=0

The maximum occupancy of the commuter train is 568 passengers

The given parameters can be represented using the following table of values

                         1              2

Passenger       56            40

Cars                  8              3

The maximum occupancy of the commuter train is then calculated as

Maximum occupancy = Sum of (Passengers * Cars)

So, we have

Maximum occupancy = 56 * 8 + 40 * 3

Evaluate the products in the above equation

So, we have

Maximum occupancy = 448 + 120

Evaluate the sum in the above equation

So, we have

Maximum occupancy = 568

Hence, the maximum occupancy of the commuter train is 568 passengers

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Answer:

(2, 1 )

Step-by-step explanation:

2x + 3y = 7 → (1)

3x + 2y = 8 → (2)

multiplying (1) by 3 and (2) by - 2 and adding will eliminate x

6x + 9y = 21 → (3)

- 6x - 4y = - 16 → (4)

add (3) and (4) term by term to eliminate x

0 + 5y = 5

5y = 5 ( divide both sides by 5 )

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

2x + 3(1) = 7

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

solution is (2, 1 )

'x' in each expression is as follows:

So, the value of 'x' in each expression:

Therefore, 'x' in each expression is as follows:

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Answer:

0.0606060606 hope that's right if not I'm sorry

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{\log(2)}{2}+\cfrac{\log(4)}{3}\implies \cfrac{1}{2}\log(2)+\cfrac{1}{3}\log(4)\implies \log(2^{\frac{1}{2}})+\log(4^{\frac{1}{3}}) \\\\\\ \log(2^{\frac{1}{2}})+\log( ~~ (2^2)^{\frac{1}{3}} ~~ )\implies \log(2^{\frac{1}{2}})+\log(2^{\frac{2}{3}})\implies \log( ~~ 2^{\frac{1}{2}}\cdot 2^{\frac{2}{3}}~~) \\\\\\ \log( ~~ 2^{\frac{1}{2}+\frac{2}{3}} ~~ )\implies \log( ~~ 2^{\frac{3+4}{6}} ~~ )\implies \log (~~ 2^{\frac{7}{6}} ~~ )\implies {\LARGE \begin{array}{llll} \log(\sqrt[6]{128}) \end{array}}[/tex]

Based on the given task content; the value of v from the points (5,6) and (6,v) which has a slope of –9 is -3

Slope refers the change in y over the change in x.

Slope = Change in y / Change in x

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Slope m = -9

Point 1( 5, 6 )

x₁ = 5

y₁ = 6

Point 2( 6,v )

x₂ = 6

y₂ = v

Substitute the given values into the formula and solve for v.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )-9

= ( v - 6 ) / ( 6 - 5 )-9

= ( v - 6 ) / ( 1 )

-9( 1 ) = ( v - 6 )

-9 = v - 6

v = -9 + 6

v = -3

Therefore, the value of v from the points (5,6) and (6,v) which has a slope of –9 is -3

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The numerical value of v in the coordinates of a line that passes through (5,6) and (6,v) with a slope of –9 is -3

Slope is simply the change in y over the change in x.

Slope = Change in y / Change in x

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Slope m = -9

Point 1( 5, 6 )

Point 2( 6,v )

Plug the given values into the slope formula and solve for v.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

-9 = ( v - 6 ) / ( 6 - 5 )

-9 = ( v - 6 ) / ( 1 )

Cross multiply

-9( 1 ) = ( v - 6 )

-9 = v - 6

v = -9 + 6

v = -3

Given the slope and coordinates of the two points of the line, the numerical value of v is -3.

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Is there an attachment? I don't get the worksheet!

The percentage of decay for the exponential function: y = 104(2.05) x is 105%.

This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 2.05 which is 1.05 than 1, representing growth.

The formula for exponential decay is y=a(1-r)x.

r is the decay rate, expressed as a decimal.

In this case, r = 2.05 - 1 = 1.05 which represents 105%.

Therefore, the percentage of decay for the exponential function is 105%.

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Answer:

[tex] \large \bf \implies{(6,10)}[/tex]

Step 1) : Solve the inequality

[tex] \bf \longrightarrow{8 \leqslant 2m - 4 < 16}[/tex]

Separate compound inequalities into system of inequalities

[tex] \begin{cases}2m - 4 \geqslant 8 \\2m - 4 < 16\end{cases}[/tex]

[tex]1) \: \: \: \: \: \large\boxed{ \tt2m - 4 \geqslant 8}[/tex]

[tex] \bf \longrightarrow2m \geqslant 8 + 4[/tex]

[tex] \bf \longrightarrow2m \geqslant 12[/tex]

[tex]\bf \longrightarrow \: m \geqslant \frac{12}{2} [/tex]

[tex]\bf \longrightarrow \: m \geqslant 6[/tex]

[tex]2) \: \: \: \: \: \large \boxed{ \sf2m - 4 < 16}[/tex]

[tex]\bf \longrightarrow2m < 16 + 4[/tex]

[tex]\bf \longrightarrow2m < 20[/tex]

[tex]\bf \longrightarrow \: m < \frac{20}{2} [/tex]

[tex]\bf \longrightarrow \: m < 10[/tex]

[tex] \pink{ \rule{7cm}{0cm}}[/tex]

[tex]\bf \longrightarrow \: m \geqslant 6 \: and \: m < 10[/tex]

[tex]\bf \longrightarrow \boxed{ \sf6 \leqslant m < 10}[/tex]

Step 2) : Graph on a number line attached above

Step 3) : Express solution set in interval notation

[tex]\bf \longrightarrow {\boxed {\underline {\underline{{( \bold{6,10)}}}}}}[/tex]

There are 256 ways to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among $4$ people

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

We are given that for bracelet Yellow, green,black  and red

We need to find the number of ways in which

Each person receive any number of bracelet.

Number of peoples=4

If each person receive exactly one bracelet then , the number of ways= 4 x 3 x 2 x 1 = 24

If all bracelet received by one person and other have no bracelet 4 ways

If one person receive 2 bracelet and other two received by any other=

144 way.

If two person gets  two bracelet each and other two have no bracelet= 36 ways

Same, one person received three bracelet and one received by any of them =48 ways

So Total number of ways=24+4+144+48+36=256 ways

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Answer:

the answer

Step-by-step explanation:

you got to write the answer in the blank boxes

According to the question, to calculate the relationship function model of the given equations which are as follows:

[tex]x=13[/tex] and [tex]y=17[/tex]

And the condition is the function is inverse in nature that means they vary inversely. And it can be represented as:

Equation: [tex]y = \frac{k}{x}[/tex]

[tex]17 = \frac{k}{13}[/tex]

[tex]k = 221[/tex]

Substituting the values to get the final expression:

[tex]y = \frac{221}{x}[/tex]

[tex]xy = 221[/tex]

Substitute the value of 'k' in the original equation. And the final expression is: [tex]xy =221[/tex]

What is function?

In mathematics, function can be defined as an expression or the rule or the law. It defines the relationship between dependent variable and the independent variable.

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The correct was done by Jason

Geometric construction is a process of constructing geometric figures using geometric tools such as a straightedge (ruler), a compass, and a pencil.

Given:

We have some sequence to construct an equilateral triangle

So, Jason are more relatable in constructing an equilateral triangle.

1. Use a compass to draw circle O

2. Use a straightedge to draw a diameter of the circle. Label the endpoints P and S.

3. Without changing the compass width draw a full circle centered at S

4. Label the points of intersection of the two circles R and Q

5. Use a straightedge to draw segments joining points P, Q, and R to form the equilateral triangle PQR.

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Answer:

Two and three

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

Take 56 away from 306

306 - 56

=250

Answer:

BD = [tex]\sqrt{82}[/tex]

Step-by-step explanation:

calculate BD using the distance formula

BD = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = B (- 4, 6 ) and (x₂, y₂ ) = D (- 3, - 3 )

BD = [tex]\sqrt{(-3-(-4))^2+(-3-6)^2}[/tex]

     = [tex]\sqrt{(-3+4)^2+(-9)^2}[/tex]

     = [tex]\sqrt{1^2+81}[/tex]

     = [tex]\sqrt{1+81}[/tex]

     = [tex]\sqrt{82}[/tex]

     ≈ 9.1 ( to 1 dec. place )

Answer:

9.055385 rounded to 6 decimal places

Step-by-step explanation:

The distance between 2 points in a 2_D Cartesian coordinate can be determined by the distance formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

where [tex](x_1, y_1) \mathrm{\;and\:} (x_2, y_2)[/tex] are the coordinates of the two points

This is also called Euclidean distance between the two points

Here coordinates of B are (-4, 6)  and those of D are (-3, -3)

So distance between them

[tex]d = \sqrt {(-3 - (-4))^2 + (-3 - 6)^2}[/tex]

[tex]= \sqrt {(1)^2 + (-9)^2}[/tex]

[tex]= \sqrt {{1} + {81}}[/tex]

[tex]= \sqrt {82}[/tex]

[tex]= 9.055385[/tex]  rounded to 6 decimal places

Two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.

The two given rational numbers are −7/2 and 4/3.

A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.

Now, two rational numbers between −7/2 and 4/3 can be found as follows:

Make denominators the same by taking the LCM of denominators.

LCM of 2 and 3 is 6.

Change denominators of both the rational numbers to 6 by multiplying the same number by numerator and denominator.

So, the rational numbers become −21/6 and 8/6.

Now, two rational numbers between −21/6 and 8/6 are -20/6 and 7/6.

Therefore, two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.

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Answer:

Kinetic energy = 2500 J

Step-by-step explanation:

To calculate the kinetic energy of an object, we can use the following formula:

[tex]\boxed{E_k = \frac{1}{2}mv^2}[/tex],

where:

[tex]E_k[/tex] = kinetic energy

m = mass of the object

v = speed of the object

In this question, we are told that Carlo's mass is 50 kg and his speed is 10 m/s. Using this information and the formula above, we can calculate Carlo's kinetic energy:

[tex]E_k = \frac{1}{2} \times 50 \times (10)^2[/tex]

     [tex]= \frac{1}{2} \times 50 \times 100[/tex]

     [tex]= \bf 2500 \: J[/tex]

Therefore, Carlo's kinetic energy is 2500 J.

Answer:

36

Step-by-step explanation:

36÷12=3

36÷18=2

The  equation in logarithmic form is log₁₀(0.01)=−2.

Given the equation is:

10⁻²=0.01

The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).

Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).

A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form

Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.

log₁₀(0.01)=−2

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The volume of the sports drink that they have with them, in whole liters is: d. 30 liters

The volume of a rectangular shape, just like the rectangular block in the given problem, can be calculated using the formula:

Volume = (length)(width)(height).

From the information given, the rectangular block's dimensions are:]

Volume of one rectangular block = (6.0)(4.0)(10.5)

Volume of one rectangular block = 252 cm³

Convert 252 cm³ to liters:

1,000 cm³ = 1 liters

252 cm³ = 252/1,000 = 0.252 liters

120 packs of 0.252 liters = 120 × 0.252

= 30.24 ≈ 30 liters

Therefore, the volume of the sports drink that they have with them, in whole liters is: d. 30 liters

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Mackenzie can find the amount of flour used by using subtraction. She should subtract the flour left in the bag from 10 pounds.

Subtraction is one of the four basic mathematical operations.

It is used to calculate the amount left after a quantity is reduced.

When two variables are subtracted we use the following notation '-' .

Let us consider two variables x and y such that x is subtracted from y then mathematically it is denoted by y - x .

Mackenzie used some flour to bake bread. To calculate the amount she used from 10 pound bag , first she will have to find the amount of flour left in the bag.

Let a pounds of flour is left (a<10).

So to calculate the amount of flour used by her we simply subtract a from 10 pound.

Hence flour left is (10 - a) pounds.

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Answer:

1.954

Step-by-step explanation:

4 is the thousandth and we wouldn’t round up because of 1

Answer: 1.954

1.9541 is to low to round up to the thousandths so it needs to be rounded down, giving the answer 1.954.

odd Answer:

make icecubes then drop them in hydrochloric acid

Step-by-step  Step-by-step  Step-by-step Step-by-step explanation

Answer:

See below

Step-by-step explanation:

Lindsey height = 190 + 130 m       ( m = minutes)

Eduardo height = 240 m

Equate them

190 + 130 m  = 240 m

190 = 110 m

190/ 110 =  1  8/11 minutes  after Eduardo starts

Domain: -4 is less than x which is less than or equal to 4

Range: -2 is less than or equal to y which is less than 5

What is domain and range ?

The bis the set of possible input values, and the range is the set of all possible output values of the graph

The completed inequality representing the set of the domain and range are presented as follows;

Given:

Question The graph of the question appear missing and the required graph to complete the question is attached here

Solution:

From the attached graph, we have that there is an open circle at the point (-4, 5), which represents that there is no value at the point

However, at the other end of the graph, which is the point (4, -2), we have a closed circle, which represents that the graph has a value at the point (4, -2)

Part A

The domain of a graph are the possible input (x-values) of the graph, in inequality format, the domain of the attached graph is -4 < x ≤ 4

Therefore;

To complete the inequality for the domain, gives;

Domain: -4 is less than x which is less than or equal to 4

Part B

The range of a graph are the possible output (y-values) of the graph, in inequality format, the domain of the attached graph is -2 ≤ y < 5

To complete the inequality for the domain gives;

Range: -2 is less than or equal to y which is less than 5

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Answer:

p + 3.6 > −5.8?​

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

12 divided by 3/4. You write 12 and change to multiplication and flip 3/4 to 4/3 and the answer will be 48/3 which equals 16.