True or False: An asymptote is a line that a curve gets infinitely close to

True
False

The probability that exactly one of the next three vehicles fail is 0.737 .

Given :

64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another .

probability that exactly one of the next three vehicles fail is :

P = 1 -  probability that all of the next three vehicles passes .

= 1 - 64 % * 64 % * 64 %

= 1 - 64/100 - 64/100 - 64/100

= 1 - 0.64 * 0.64 * 0.64

= 1 - 0.4096 * 0.64

= 1 - 0.262

= 0.737

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There are no crictical numbers of the given function 12-5e^(-x).

Let's Consider

[tex]f(x) = 12 - 5*e^-x[/tex].

What is critical number of a function.

If a number causes the derivative of an expression to equal 0, it is critical.

As a result, we must set the derivative of the expression to 0.

Local Maxima and Local Minima points are also consider as critical number of a function.

f`(x) = 0 or f`(x) =1/0 by solving both equation we can find all the critical points of a function f(x).

Derivative of given funciton f(x) is f`(x).

f`(x) = [tex]0 - 5*(e^-x)*(-1).[/tex]

f`(x) = [tex]5*(e^-x)[/tex].

f`(x) = 0

[tex]5*e^-x[/tex] = 0

[tex]e^-x[/tex] = 0

[tex]e^-x[/tex] never going to zero because e^-x is an exponential decreasing function.

So there are no crictical numbers of the given function f(x).

So We enter none in this question.

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Is there any other information provided in the given question? For instance, is there data showing what each of the given letters represent?

The ordered pair which is a solution to the system of linear equations (0,2).

In mathematics, a system of linear equations refers to a collection of one or more linear equations which involve the same variables. In order to solve the system of linear equations, multiply each equation by a constant such as the coefficient of one variable becomes the same.

Hence, multiply 2x + 3y= 6 by 3 and –3x + 5y = 10 by 2.

3 (2x + 3y= 6)

6x + 9y = 18

2(–3x + 5y = 10)

-6x + 10 y = 20

Adding the two equations

6x + 9y = 18

-6x + 10 y = 20

19y = 38

y = 2

Substitute y in either of the equations:

2x + 3(2)= 6

2x = 6 – 6 = 0

x = 0

Hence, the solution is (0, 2)

The ordered pair (0,0) is not a solution as it will invalid the given linear equation.

Note: The question is incomplete. The complete question probably is Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 and –3x + 5y = 10.  (0,2) (2,0) (3,2) (2,3)

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90% confidence interval for positive difference between means that there is a 90% probability that the confidence interval will contain the true population mean

The difference in sample means is used to calculate the difference in population means. A confidence interval reveals how accurate the estimate is.

We will make three assumptions in order to build a confidence interval:

1. The variance between the two populations is equal. The second assumption of homogeneity of variance is what this premise is known as.

3. The populations are evenly distributed.

4. Each value is sampled separately from every other value.

The following formula is used to construct a confidence range for the mean difference:

[tex]Lower Limit = M_1 - M_2 -(t_{CL})(S_{M1} - S{M2})\\Upper Limit = M_1 - M_2 +(t_{CL})(S_{M1} - S{M2})[/tex]

where [tex]S_{M1} - S{M2}[/tex] is the expected standard error of the difference between sample means, tCL is the desired level of confidence, and M1 - M2 is the difference between sample means.

The given question is incomplete So, I've answered in general according to my knowledge

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y = 3 + tan (π/4)x , this is the equation of transformed graph of tangent with period 4 that has been shifted vertically up 3 units.

Our parent function:

y = tan x

Let's apply the vertical shift now:

y = 3 + tan x

Now the period. This is a little tricky because we have to remember that the period is equal to π/b, because tangent functions normally have a period of π, and the b is the value placed in front of the x.

In this case, that value would have to be π/4

π/(π/4) = 4

Therefore, our b-value is π/4 and our final equation is as follows:

y = 3 + tan (π/4)x

The question is :

write the equation of the transformed graph of tangent with period 4 that has been shifted vertically up 3 units

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Answer:

x=−10,y=−5

Step-by-step explanation:

The simplified cube roots expressions are:

Rational numbers: Rational numbers include terminating decimals, non-terminated with repeating decimals, perfect squares, integers, whole numbers, perfect squares, and fractions.

Example: 2.434343; 5.2; 1/2, -8; √4; etc.

Irrational numbers: Irrational numbers include non-terminated decimals, non-repeated decimals, non-perfect squares, and infinite decimals, and do not form ratios of two numbers.

Example: π = 3.141.....; √2; e/√2; etc.

The given cube root expressions are:

1. [tex]\sqrt[3]{81}[/tex]

2. [tex]\sqrt[3]{-64}[/tex]

Simplifying the first expression, we get

[tex]\sqrt[3]{81}=\sqrt[3]{3\times3\times3}[/tex]

⇒ [tex]\sqrt[3]{81}[/tex] = 3∛3 = 4.3267....

Thus, the cube root of 81 gives an irrational number since it is a non-terminating decimal and has no repeated decimals in it.

Now, simplifying the second expression, we get

[tex]\sqrt[3]{-64}=\sqrt[3]{-4\times-4\times-4}[/tex]

⇒ [tex]\sqrt[3]{-64}[/tex] = -4

Since the result is an integer, the cube root of -64 is a rational number.

Therefore, the given cube root expressions give irrational and rational numbers respectively. They are:

[tex]\sqrt[3]{81} =4.32674...[/tex]  and [tex]\sqrt[3]{-64} = -4[/tex]

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According to the given charges, the mean of the sum would be as follows $1,692.5 and the difference of the amount of money earned by Jennie and Paul would be $-232.5

Mean:

In statistics, mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers

Given,

As Jennie charges $200 per passenger for a sunset sailing tour on her catamaran, while Paul charges $250 per passenger. we can define the amount of money each person earns per cruise as a random variable.

Here we need to find the mean and the difference of the amount of money earned by Jennie and Paul.

Let us consider x be the amount earned by Jennie and y be the amount earned by Paul.

While we looking into the given question , we have identified the value of the following,

=> Money earned by Jennie(A) = 200x

=> Money earned by Paul(B) =  250 X

Here the value of μ = $730 and σ = $ 192.62 for Jennie

And the value of Paul is μ = $962.5 and σ = $253.425

Then the mean of the sum is calculated as,

=> 730 + 962.5 = 1292.5

Similarly, the difference of the amount of money is calculated as,

=> -232.5

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Answer:

D) On average, Jennie makes $232.50 less than Paul in a typical cruise.

Step-by-step explantion

The ways the assignments can be assigned to the students with the condition is 66 ways

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

Total number of questions, n = 12

Total numbers of students, r = 2

The number of ways the assignments can be assigned to the students is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 12 and r = 2

Substitute the known values in the above equation

Total = ¹²C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 12!/10! * 2!

Evaluate

Total = 66

Hence, the number of ways is 66

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The velocity at which the diver hits the water is 45.96 feet/s.

The velocity of an object is in feet per sec after it has fallen a distance of d feet is approximated by the function v(d) = √64.4d

Given that, height of olympic diving platform d = 10 m = 32.8 feet

We know that, v(d) = √64.4d and d = 32.8

So, substituting in the above function, we have

v(d) = √64.4d

⇒ √64.4 * 32.8

⇒ √ 2112.32

⇒ 45.96 feet/s

Thus, the velocity at which the diver hits the water is 45.96 feet/s.

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The exponent in the term 5x⁶ is of the expression 6

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

Expression: 5x6+3yr-7yz2+2y/z

Rewrite the expression properly

So, we have the following representation

5x⁶ + 3yr - 7yz² + 2y/z

From the above expression, the spotlight is on the first term

i.e. 5x⁶

Considering an expression represented as axⁿ

Where x is a variable, the exponent is n

Using the above as a guide, we have the exponent of 5x⁶ to be 6

Hence, the exponent is 6

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Answer: x = 25, y=15, z = 58

Step-by-step explanation:

Answer:

AngleCAB = 44°

AngleHAB = 66°

Step-by-step explanation:

AngleEAF is a right angle, equal to 90°.

EH and DC are just two intersecting lines. They form a couple of pairs of vertical angles. Vertical angles are equal to each other. We'll use the vertical angles, AngleEAD and CAH.

Angle EAD and CAH are equal to each other.

EAD = CAH

90°+20° = 2x + 3x

Combine like terms.

110° = 5x

Divide by 5

110/5 = x

22 = x

Angle CAB

= 2x

= 2(22)

= 44

AngleCAB = 44°

AngleHAB

= 3x

= 3(22)

= 66

AngleHAB = 66°

Answer:

C'(9,5)

Step-by-step explanation:

C(5,6)

Add or subtract how much you translate (move) left/right to the x-coordinate

Add or subtract how much you translate (move) up/down to the y-coordinate

C(5+x, 6+y) = C'

C(5+4, 6-1) = C'

C'(9,5)

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The unknown angle measures are 51.5° and 51.5° respectively.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides.

Given, side DE = side EF

Then, ∠D = ∠F

So, the sum of all angles of the triangle = 180°

or, ∠D + ∠E + ∠F = 180°

or, ∠F + 77° + ∠F = 180°

or, 2∠F = 180° - 77°

or, ∠F = 103/2 = 51.5°

And, ∠D = 51.5°

Hence, the unknown angle measures are 51.5° and 51.5° respectively.

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The statement " when adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree" is true.

A tree is a type of data structure made up of nodes and contains the following features:

1- Every tree has a root node (also known as a parent node) at the top that contains some value (can be any datatype).

2- There are 0 or more child nodes of the root node.

3- There are zero or more child nodes for each child node, and so forth. As a result, the tree gains a subtree. Each node has a separate subtree that consists of its offspring and their offspring, etc. This implies that any node can function as a tree on its own.

In addition, a binary search tree (BST) has the following two features:

1- Each node has a maximum of up to two children.

2-For each node, the values of its left descendent nodes are less than that of the current node, which in turn is less than the right descendent nodes (if any).

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The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

a. Estimate the number of students studying abroad in 2003.

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

In the given question, Decker scientific is considering an investment of $850,000 in a new product line.

The company will make the investment only if it will result in a rate of return of 20% per year or higher.

If the revenue is expected to be between $290,000 and $325,000 per year for each of 5 years, we have to determine if the decision to invest is sensitive to the projected range of income using an annual worth analysis.

AW of investment when expected revenue is

290000 = -1080000*(A/P,20%,4) + 290000

A/P = -1080000*0.386289 + 290000

A/P = -127192.12

A/P = -127192

AW of investment when expected revenue is

369000 = -1080000*(A/P,20%,4) + 369000

A/P = -1080000*0.386289 + 369000

A/P = -48192.12

A/P = -48192

As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

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The appropriate statistical decision that researcher should use is that (d) Reject the null hypothesis with either a = 0.05 or a = 0.01

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.

Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not.

According to the null hypothesis, there is no relationship between the independent variable and the measured event (the dependent variable). To test the null hypothesis, we don't have to think it's accurate. In contrast, you can suppose that a group of variables (dependent and independent) are connected.

According to the question ,

A researcher is testing a null hypothesis stating that for the general population there is no preference between the two leading brands of cola In a sample of n = 100 people, 35 preferred brand A and 65 preferred brand B.

The appropriate statistical decision is (d) Reject the null hypothesis with either a = 0.05 or a = 0.01

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The quadrilateral is a parallelogram if and only if it has two pairs of parallel sides

What is parallelogram?

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

A parallelogram is a quadrilateral with two pairs of parallel sides.

As we know,

The quadrilateral can be defined as the four-sided polygon in geometry having four edges and four corners.

The quadrilateral, has:

Two pairs of congruent sides.

It has one pair of opposite congruent angles.

The diagonals of a kite are perpendicular.

One diagonal is bisected.

The top and bottom angles are bisected but does not have congruent diagonals.

A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.

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So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

Equations go into one of two categories: identities or conditional equations. An identity holds true for each value of the variables. A conditional equation is valid only for certain values of the variables. An equation is represented by the equals sign ("="), which separates two expressions.

Here,

In essence, this can be set up in a proportion.

Two cups of cranberry juice are required per gallon of punch. The quantity of cranberry juice required for one gallon is what you need to determine. So, in order to set up your percentage, do as follows:

Following cross-multiplication, you should have the following:

=> 3x = 2

then division should result in this:

=> x = 2/3

So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

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Answer:

Before we declare what happens, we must have an understanding of outliers and standard deviation. Outliers are certain points that are x deviations away from the mean. Standard deviation is a measurement of dispersion in relations to the mean you are identifying. Given this information, when outliers are removed, the standard deviation becomes a lower amount, because you have to think of standard deviation as a population measurement in a way. So imagine the outliers are a prestigious group of people, and if they leave the community, the population is indeed lower. Outliers affect deviation by a measure of extremity. The more extreme an outlier, the more or less a standard deviation will be affected. When outliers are removed, they will lower the standard deviation, which changes the data in respect to population. A high outlier, however, will increase both mean and median no matter what.

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Using simple percentage rule, the answer is 25%,52% and 16.67%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, %, or the abbreviation "pct" are frequently used to indicate percentages. The term "percent" derives from "percent," a shortened form of "per centum," which meaning per hundred.

The required formula is:

percentage (%) = Change/total * 100

Percentage Decrease = [tex]\frac {80-60}{80} * 100[/tex]

=25%

Percentage Decrease=[tex]\frac {500-240}{500} * 100[/tex]

=52%

Percentage Decrease = [tex]\frac {144-120}{144} * 100[/tex]

=16.67%

We calculated the percentage decrease using the above-mentioned formula.

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By using Euclidean geometry, the set of side lengths  2.5 cm, 1.8 cm, 4 cm can form a triangle.

The sum of the lengths of any two sides must be greater than the length of the third side.

a + b ≥ c

A triangle is a three-sided polygon with three straight sides. It is a basic geometric shape that is found in many areas of mathematics and geometry.

Using this rule, we can determine which of the given sets of side lengths can form a triangle:

(a) 3 cm, 4 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (3 cm + 4 cm = 7 cm) is equal to the length of the third side.

(b) 2 cm, 3 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2 cm + 3 cm = 5 cm) is less than the length of the third side.

(c) 2.5 cm, 1.8 cm, 4 cm: It is possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2.5 cm + 1.8 cm = 4.3 cm) is greater than the length of the third side.

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After converting Cartesian into polar form, ∂S = (3cost, 3sint, -3) at t=0→2π. So option d is correct.

In the given question, we have to find a parametrization of the boundary curve as with positive orientation if

1. S is the part of the surface of the paraboloid z = 6-X^2-y^2 above the plane z=-3 with a normal vector pointing upward.

a. (√6 cos(t), √6 sin(t), 0)

b. (√6 cos(t), √6 sin(t), -3)

c. (3 cos(t), – 3 sin(t), -3)

d. (3 cos(t), 3 sin(t), -3)

e. (3 cos(t), 3 sin(t),0)

The given paraboloid is z = 6-X^2-y^2 above the plane z=-3.

Now convert Cartesian form to the polar equation.

In polar form x=rcost, y=rsint z=z and x^2+y^2=r^2

Now z = 6-X^2-y^2

z = 6-(X^2+y^2)

z = 6-r^2

Now put z=-3

-3 = 6-r^2

Subtract 6 on both side, we get

-r^2 = -9Now r^2 = 9

Taking square root on both side, we get

r=3

Now x=3cost, y=3sint, z= -3

So ∂S = (3cost, 3sint, -3) t=0→2π

So option d is correct.

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The flagpoles are 40 feet, and the wires cross at E, which is directly above point F on the ground. Then EF is 5.142 feet.

The maximum height for flagpoles is twenty (20) feet. (3) When next to or encircled by residential lots, the flagpole may not be erected in any side or rear yard setback.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

by applying similar triangles on triangles we get the equation on ABC and EFC

40y+9x=360

by applying similar triangles on triangles, we get the equation on DBC and EBF

y=3/10x

x=120/7

putting values in the very first equation we get

y=3/10x(120/7)

y=5.142

EF=5.142 feet.

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The perimeter of the parallelogram will be D. 2✓26 i+ 8.

It should be noted that the perimeter of the parallelogram will be calculated by using the formula for distance between point.

For WX, the coordinate are (-2, 4)(2, 4)

d = ✓2 - (-2)² + (4 - 4)²

= ✓16 - 0.

= ✓16

= 4

For XY, this will be illustrated as:

d = ✓(1 - (2)² + (-1 - (4)²

= ✓1² + 5²

= ✓1 + 25.

= ✓26

Since the other sides are parallel, the perimeter of the parallelogram will be:

= 2(4) + 2✓26

= 2✓26 + 8

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