1) The end behavior of a rational function is equal to

A) Holes

B) Horizontal Asymptote

C) Vertical Asymptote

D) Domain

The point(s)) where the fire road intersects the outer boundary of the service area is found using the equation of circle which is (0,20) and (-12,-16).

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

The equation of the circle is given as - x² + y² = 400 .... (1)

The equation of the fire road is given as - y - 3x = 20 .... (2)

Write the equation of fire road in slope-intercept form - y = mx + b

y = 3x + 20

Substitute the value of y in equation (1) -

x² + y² = 400

x² + (3x + 20)² = 400

Follow the (a + b)² rule, (a + b)² = a² + 2ab + b²

x² + (3x + 20)² = 400

x² + 9x² + 120x + 400 = 400

10x² + 120x + 0 = 0

x² + 12x = 0

x(x+12) = 0

x = 0, x = -12

Substituting the values of x in equation (2).

First calculate for x = 0.

y - 3x = 20

y - 3(0) = 20

y = 20

Now, calculate for x = -12.

y - 3x = 20

y - 3(-12) = 20

y + 36 = 20

y = 20 - 36

y = -16

Therefore, the points of intersection are (0,20) and (-12,-16).

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Answer: 70

Step-by-step explanation:

70 kilometers if 3.5 centimeters is the distance and each centimeter represents 20 kilometers, 3.5 times 20 is equal to 70

There are 5040 ways to place 8 rooks on an 8 x 8 chessboard.

A permutation is a systematic grouping of objects or numbers. Combinations allow you to select objects or numbers from a group of items without having to worry about the order in which they were collected. Contrary to permutations, when selecting components from a collection using the combination method, the order of selection is unimportant.

There are 8! ways to place 8 rooks on an 8 x 8 chessboard such that no two rooks are in the same row or column.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

   = 5040

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The value of y is multiplied by 6 when x is divided by 6

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

y = 3/x

Also, from the question we understand that

x is divied by 6

This means that the new equation is

y = 3/(x/6)

Evaluate

y = 6 * 3/x

This means that the new value of y is  multiplied by 6

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Answer:

what is the question the website is blocked

Step-by-step explanation:

The intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric function is given below.

3 sec2x − 2 tan 2x − 4 = 0

Simplify the equation, then we have

3 sec2x − 2 tan 2x − 4 = 0

3 / cos 2x − 2 sin 2x / cos 2x = 4

3 − 2 sin 2x = 4 cos 2x

(3 − 2sin 2x)² = 16 cos² 2x

The graph of the functions is drawn below.

From the graph, the intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

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Answer:

0.1

Step-by-step explanation:

1.distribute the 6 to 1 and 10

2.now its 6+60m

3. divide 60 on both sides

4. 60/60 cancels out.

5.  6/60 =0.1

If Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden then the number of packs of seeds were planted is 2.74 pack for each garden  .

the number of packs of seed planted by Jason is = 11 packs  ;

the number of gardens in which the seeds are planted is = 4 garden ;

the amount of packs planted in each garden can be calculated by the expression on dividing "number of seed packs" by "number of gardens" ;

⇒ (number of seed packs)/(number of gardens) ;

Substituting values of number of seed pack and number of garden ,

we get ;

= 11/4 = 2.74 .

Therefore , Jason planted 2.74 packs of seed in each garden .

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The statement that is true about the rental company’s charges is A. The deposit fee is $ 25 and the rental fee per day is $ 45.

The total cost function is given as C = 45d + 25. This means that the slope is 45 and the y - intercept is 25.

This also means that the rental per day is $ 45 because the slope is the amount that the total cost changes by per day which must be the daily rental cost.

The $ 25 would be the cost that a person pays as a down payment when they rent the car because this amount does not change.

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Options for this question include:

A. The deposit fee is $ 25 and the rental fee per day is $ 45.

B. The deposit fee is $ 45 and the rental fee per day is $ 25.

C. The car can be rented for $ 45 and then given back to the company at $ 25

Answer: $960

Step-by-step explanation:

Regular Price = x

x*0.5 = 480

x = 960

Answer:

$960

Step-by-step explanation:

Since 480 dollars is half (50%) of the regular price...

you can find the total price by dividing 480 by 0.50 (50%)

or multiplying 480 by 2. You end up getting an answer of $960.

well, the selling price is simply $30 plus 120% of that, hmmm what's 120% of 30 anyway?

[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{120\% of 30}}{\left( \cfrac{120}{100} \right)30}\implies 36~\hfill \underset{selling~price}{\stackrel{30~~ + ~~36}{\text{\LARGE 66}}}[/tex]

To earn at least $640 in revenue, the ticket prices should be $8 or $2

An equation is an expression that shows the relationship between two or more variables and numbers.

Revenue = number of tickets sold * price per ticket  R(p) = -40p^2 +400p-640

p² -10p +16

Factorizing the function to have

(p²-8p)-(2p+16)

p(p-8)-2(p-8)

p-2 = 0 or p-2=0

This implies that

p=8 or p=2

p = $8 or p = $2

To earn at least $640 in revenue, the ticket prices should be $8 or $2.

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Kelly's brothers age after 4 2/3 is 23 12/24 years.

What is Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

We have  ;

Kelly's Brother is 18 7/8 year old.

We have to calculate;

His age after 4 2/3 years.

So,  

⇒ 18 7/8 + 4 2/3

⇒ 151/8 + 14/3

⇒151 x 3 + 14 x 8/24

⇒453 + 112 /24

⇒565/24

⇒23 13/24 year old

Hence , his age after 4 2/3 is 23 13/24 years.

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The time that it would take for the population to decrease by one fourth is 3 years. Option C

We know that when we talk about population growth, we are talking about the increase in the population of the species and this can be regarded as a kind of an exponential growth problem.

We know that we can write;

P = Poe^-rt

P = population at time t

Po = initial population

r = population growth rate

t = time taken

Then we have that at the said time, P = 1/4Po

Hence;

1/4Po = Poe^-0.365t

1/4 = e^-0.365t

0.25 = e^-0.365t

ln0.25=ln e^-0.365t

-1.386 = -0.365t

t = 3 years

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The possible prices of the new dress must be any value less than or equal to $45.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Start with the inequality x ≤ 45

This inequality states that x must be less than or equal to 45.

Therefore, the possible prices of the new dress must be any value less than or equal to $45.

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The probability that at least 30% of the items in the shipment are defective is 0.7360.

The beta distribution with parameters (3,3) is the conjugate prior for the binomial distribution with a probability of success of p, where 0<p<1.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of Bernoulli trials. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. In the context of the problem you presented, success would be a defective item, and failure would be a non-defective item.

To find the probability that at least 30% of the items in the shipment are defective, we can use the cumulative distribution function (CDF) of the beta distribution. The CDF of the beta distribution is given by:

F(x;a,b) = (x^(a-1) * (1-x)^(b-1)) / B(a,b)

where x is the proportion of defective items, a and b are the shape parameters, and B(a,b) is the beta function.

We want to find P(X >= 0.3) where X is the proportion of defective items. Substituting the values for a, b, and x we get

P(X >= 0.3) = 1 - P(X < 0.3)

= 1 - F(0.3;3,3)

= 1 - ((0.3^(3-1) * (1-0.3)^(3-1)) / B(3,3))

= 1 - ((0.3^2 * 0.7^2) / (1/6))

= 1 - ((0.09 * 0.49) / (1/6))

= 1 - (0.044/0.1666)

= 1 - 0.2640

= 0.7360

Therefore, The probability that at least 30% of the items in the shipment are defective is 0.7360.

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In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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The average rate of rain displayed in the graph is 2.5 inches per day.

1. The C.R.O.C is 2.5.

2. The equation that can be used to find y, is y = 2.5x.

3. Yes, this is a proportional relationship.

4. Yes there is a C.O.P of 2.5.

5. The unit rate is 2.5 inch rain in 1 day.

6. The amount of rain that would fall in 15 days is 37.5 inches.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

In the graph the x-axis represents the number of days.

In the graph the y-axis represents the rain in inches.

The first point is (2,5) which tells that in 2 days the rain fell 5 inches.

So, the average rain will be 5/2 = 2.5 inches.

CROC stands for constant rate of change. The formula for constant rate of change is -

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

= (10 - 5)/(4 - 2)

= 5/2

= 2.5

Therefore, the constant rate of change is 2.5

The first point in the graph is (2,5), the x-intercept being 2 and y-intercept being 5. The CROC is obtained as 2.5.

So the equation for y can be given as -

y = 2.5 x

A proportional relationship between two variables x and y  is when one variable is always some constant value multiplied by the other.

So, yes the relationship between the x and y value in this graph is proportional.

The “constant of proportionality” is the name given to this constant. All proportional relationships can be represented by the equation y =kx  , where k  is the proportionality constant.

Since, the equation is y = 2.5x.

Therefore, the constant of proportionality is 2.5.

The unit rate is 2.5 inches of rain in one day.

The amount of rate that would fall in 15 days is -

y = 2.5 x

y = 2.5 (15)

y = 37.5

Therefore, the amount of rain will be 37.5 inches.

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A counter example to the statement that the difference of two positive numbers is always positive is 4 - 7.

Any exception to a generalization is a counterexample. A counterexample refutes the generalization in logic, and it does so firmly in the disciplines of math and philosophy.

A formal proof is necessary to establish the veracity of a mathematical assertion. Finding just one instance where a mathematical assertion is incorrect suffices to disprove it, though. An example like this is referred to as a counterexample because it contradicts or goes against the conclusion of the statement.

Here, a counter example to the statement that the difference of two positive numbers is always positive is:

= 4 - 7.

= -3

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subtract 22 from 27 the results is=5

Answer: C.

Step-by-step explanation:

since the four friends are SPLITTING the rental cost, it would be dividing.

Then, since it says NO MORE THAN it would be less than or equal to as the symbol for the inequality.

The statement "the maximum likelihood estimator is an unbiased estimator of " is False.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

It depends on the specific probability density function (pdf) of the distribution. An estimator is unbiased if its expected value is equal to the true value of the parameter being estimated. For a given pdf, the maximum likelihood estimator (MLE) may or may not be an unbiased estimator of the true parameter value.

The MLE is the value of the parameter that maximizes the likelihood function, which is the probability of the observed sample under the assumed pdf. In general, the MLE is a consistent estimator, meaning that as the sample size increases, the MLE will converge to the true parameter value with probability 1. However, it may not always be unbiased.

The statement "the maximum likelihood estimator is an unbiased estimator of " is False.

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For the given distance the time taken for the company plan to replace the machine in order to receive this trade in value is 4 years.

The term called distance is defined as the two points lie on the same horizontal or same vertical line and it is the distance can be found by subtracting the coordinates that are not the same.

Here we have know that the company buys a digital scanner for $12,000 the value of the scanner is $12,000 (1-n/5) after n years.

And here we also know that the company has budget to replace the scanner when the trade-in value is 2400.

By Using the given expression for the value of scanner after n years, we equate it to $2400 and solve for n is written as,

=> 12000 (1 - n/5) = 2400

When we simplify this one then we get,

=> 1 - n/5 = 2400/12000

=> 1 - n/5 = 0.2

=> n/5 = 0.8

=> n = 4.

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The height of the CN tower found using the trigonometric function to the nearest metre is 555m.

What are the different trigonometric functions?

Trigonometric functions are used to determine the relationship between

angles and sides of a triangle.

The basic functions are sine, cosine and tangent.

sine = perpendicular/hypotenuse

cosine = base/hypotenuse

tangent = perpendicular/base

From the figure, we can see the right-angled triangles made by both the model and real CN towers.

Since the shadow is cast at the same time of the day, we can say that the angles θ and Φ formed are the same angles.

So from the figure,

tan θ = tan Φ

  0.9/0.2 = h/ 123.3

h = 554.85 m

Therefore the height of the CN Tower to the nearest metre is 555m.

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The balance will be $15,036.30 after 7 years.

Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.

We have,

P = $10,000

R= 6%

T= 7 years

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n[tex])^{nt[/tex]

A = 10,000.00(1 + 0.06/1)⁷

A = 10,000.00(1 + 0.06)⁷

A = $15,036.30

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The time it takes for the country's population to double is 1000 years. The total population would be 10 million people.

We can calculate the population growth by

P = P₀ × r × t

Where

Suppose that immigration is the only factor of population growth. We have

Find the time that takes the country's population to double!

To make the country's population double, the population growth should be also 5 million people.

The formula would be

5,000,000 = 5,000,000 × 1/000 × t

t = 1,000/1

t = 1,000 years

Hence, the country's population will be double after 1,000 years.

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The function represents exponential growth and the y-intercept is 4

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

f(x) = 4(3)^x

An exponential function is represented a

f(x) = ab^x

Where

y-intercept = a

rate = b

This means that

y-intercept = 4

b = 3

Since the value of b is greater than 1, then the function is a growth function

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Using the trigonometry ratio, at angle 50.81° should the arm be set.

We have to determine the angle x should the arm be set.

A crane has a 200-foot arm whose lower end is 5 feet off the ground.

The arm has to reach the top of the dome 80 feet high.

The length of crane arm = 200ft

The height of building = 160ft

The initial height of the crane = 5ft

As a result, the height of the building in relation to the crane can be expressed as;

h = 160ft - 5ft

h = 155ft

The angle x the crane makes with the horizontal can be expressed mathematically as;

sin x = opposite/hypothesis

sin x = 155ft/200ft

sin x = 0.775

Taking [tex]\sin^{-1}[/tex] on both side, we get

x = [tex]\sin^{-1}[/tex](0.775)

Using the calculator

x = 50.81°

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Answer:

$4.38

Step-by-step explanation:

17.52/4=4.38

Answer:

h = [tex]\frac{S-2\pi r^2}{2\pi r}[/tex]

Step-by-step explanation:

S = 2πr² + 2πrh ( subtract 2πr² from both sides )

S - 2πr² = 2πrh ( isolate h by dividing both sides by 2πr )

[tex]\frac{S-2\pi r^2}{2\pi r}[/tex] = h