exercise 3.1.8: find example functions f and g such that the limit of neither f (x) nor g(x) exists as x!0, but such that the limit of f (x) g(x) exists as x!0.

Answer:

The percentage of boys is 57.1%.

Step-by-step explanation:

I don't have to explain.

Hope this just helps!

Have a great day/night!

The amount of paint needed to apply a coat of paint is 1.00 m³.

Given:

a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m.

we are asked to  estimate the amount of paint needed to apply a coat of paint.

The amounts

Volume of a hemisphere, V = (2/3)πr³

r = 40/2

= 20 m

dr = 0.04 cm = 0.0004 m

dV≈2πr²dr

= 2π(20)²(0.0004) m³

=  1.0048 m³

rounding it of to two decimal places.

= 1.00 m³

Hence the amount of paint needed is 1.00 m³

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the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300 P(10000 ≤ x ≤ 10300) = 0.54

We would assume a normal distribution for the breaking strength of a rivet. We would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ/√n

Where

n = number of samples

x = Breaking strengths of rivet.

µ = mean breaking strength

σ = standard deviation

From the information given,

µ = 10,100 psi

σ = 499 psi

n = 40

The probability that the sample mean breaking strength for a random sample of 40 rivets is between 10000 and 10,300 is expressed as

P(10000 ≤ x ≤ 10300)

For x = 10000,

z = (10000 - 10100)/499/√40 = - 0.13

Looking at the normal distribution table, the probability corresponding to the z score is 0.45

For x = 10300,

z = (10300 - 10100)/499/√40 = 2.54

Looking at the normal distribution table, the probability corresponding to the z score is 0.99

Therefore,

P(10000 ≤ x ≤ 10300) = 0.99 - 0.45 = 0.54

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(a) The probability that two radios are being defective= 0.035

(b) The probability that all radios are not defective = (11/12)^4

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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Three common failures in a distributed system include

Host failure and storage medium failure are failures that could also occur in a centralized system, whereas a network link failure can occur only in a networked-distributed system.

CENTRALIZED SYSTEMS

Centralized systems are systems that use client/server architecture where one or more client nodes are directly connected to a central server. This is the most commonly used type of system in many organizations where a client sends a request to a company server and receives the response.

DECENTRALIZED SYSTEMS

These are other types of systems that have been gaining a lot of popularity, primarily because of the massive hype of Bitcoin.

In decentralized systems, every node makes its own decision. The final behavior of the system is the aggregate of the decisions of the individual nodes.

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the regression equation:

y = 0.9x+ 7.5

given that:

Xi: 2; 6; 9; 13; 20

Yi: 7; 18; 9; 26; 23

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑XY = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] +  [tex]6^{2}[/tex]+[tex]9^{2}[/tex]  +  [tex]13^{2}[/tex]+ [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]=  [tex]7^{2}[/tex]+ [tex]18^{2}[/tex]  + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] +[tex]23^{2}[/tex]  = 1659

the slope b is calculated:

b = ∑XY - ∑x × ∑y/n ÷ ∑ - (∑x)^2 /n

now we need to substitute the above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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Answer: 225

Step-by-step explanation:

He paid 0.0012% of his total wealth increase as federal tax.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -

y = f(x)

y' = dy/dx = (d/dx)[f(x)]

We have Mr. Bezos, who paid 1.4 million in federal taxes between 2006 -2018. His net worth increased by 127 billion dollars during this time span.

Assume that he paid [x]% of money to federal taxes. Then, we can write -

1.4 x 1,000,000 = (x/100) x 127 x 1000,000,000

1.4 = (x/100) x 127000

x = (1.4 x 100)/(127000)

x = 1.4/1270

x = 14/12700

x = 0.0012%

Therefore, he paid 0.0012% of his total wealth increase as federal tax.

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There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling

Let S represent the set for donut with Sprinklers.

Let F represent the set for donut with Filling.

To find :- How many have sprinkles or filling?

i.e. n ( S ∪ F )

Formula,

n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )

Given,

n ( S ) = 6

n ( F ) = 7

n ( S ∩ F ) = 3

Putting in formula

n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )

                = 6 + 7 - 3

                = 10

Donuts with Sprinklers or Filling = 10

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Step-by-step explanation:

x + 1/2y = 18

2x + y = 36

x = 36 - y

18 = 36 - y + 1/2y

18 = 36 - 1/2y

36 - 18 = 1/2y

18 = 1/2y

y = 36

x = 18 - 1/2(36)

x = 18 - 18

x = 0

Therefore, you can spend 0 hours on the phone and 36 hours on the internet.

Answer:

I don't think there would be any asymptotes because there are no denominators.

Step-by-step explanation:

The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, △ ABC is transformed in to △ A′B′C′

Firstly,  △ ABC is being rotated 90° counterclockwise about the origin, and then it translated 3 units up.

Hence, The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.

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if it produced 500 units per day, its total cost would be $425. then average total cost is $0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 1,000 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/1000

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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The average profit is positive if the number of snowboards is less than 67418 .

Given:

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = (Px)/x, where P(x) is the profit function.

The profit is P ( x ) = R ( x ) - C ( x )

= -x^2 + 10x - ( 4x + 5 )

= -x^2 + 10x - 4x + 5

= -x^2 + 6x + 5

Then AP( x ) = ( P( x )) / x

= -x^2 + 6x + 5 / x > 0

As x > 0 then the sign of AP(x) depends on numerator only.

-x^2 + 6x + 5 > 0

D = 36 + 20

= 56

x = 6.7417

Therefore AP(x) > 0 if 0 < x < 6.7417

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Full question:

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x)/x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.

Answer:

19

Step-by-step explanation:

therefore the answer is 19

Answer:

4

Four subsets of {w, x, y} contain w.

Step-by-step explanation:

There are four subsets that have w in it:

{w} has w in it.

{w, x} has w in it.

{w, y} has w in it.

{w, x, y} has w in it.

The answer is 4.

The scenario assumed to be the number of flips until you land on a head is P(x) = 1 + (1 - p)/p.

Given info,

If you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head,

To solve the above condition, have a formula;

P(x) = 1 + ( 1 - p )/p

Hence, P(x) = 1 + ( 1 - p )/p is the case expected to number of flips before you end up with a head.

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Illinois city-to-airport distances can be discovered using a distance spatial join. The utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

A system called a geographic information system (GIS) is one that collects, organizes, processes, and maps all kinds of data.

Illinois city-to-airport distances can be discovered using a distance spatial join.

Thus, the utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

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Answer:

f X varies directly with Y, then the relationship between them can be expressed as Y = kX, where k is a constant. Therefore, we can calculate the value of Y when X is 3 by substituting the values into the equation: Y = (20/30) * 3 = 2

Step-by-step explanation:

The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.

For the stated question -

The formula for the z score -

z = (x - μ)/σ

In which,

μ = 140  and σ = 20

Put the values-

z = (150 - 140)/20

z = 0.5

p(x > 105.0) = p(z > 0.5)

p(x > 105.0) = 0.6915

Thus, the value of the probability p(x > 105.0) for the given  normal random variable is found as 0.6915.

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The complete question is-

suppose x is a normal random variable with μ = 140  and σ = 20 and find p(x > 105.0).

When 200ft of string has been let out, the angle is decreasing at a rate of 0.015 radians per second.

In this question, we have been given the height of the kite from the ground is y = 75 ft.

The kite moves horizontally at a speed of 8 ft/s

So, dx/dt = 8 ft/s

The length of the string is 200 ft

so, L = 200 ft

Consider the following figure for this situation.

Now consider the sine of angle theta.

sin(θ) = 75/200

sin(θ) = 3/8

Now consider the tangent of angle theta.

tan(θ) = 75/x

1 / tanθ = x/75

cot(θ) = x/75

Differentiating the above equation with respect to t.

-csc²(θ) * dθ/dt  = 1/75 * dx/dt

- csc²(θ) * dθ/dt  = 1/75 * 8

- csc²(θ) * dθ/dt = 8/75

We know that, csc(θ) = 1/sin(θ)

csc(θ) = 8/3

So above equation becomes,

-(8/3)² × dθ/dt = 8/75

dθ/dt = - (8/75 * 9/64)

dθ/dt = 0.015

Therefore, the angle is decreasing at a rate of 0.015 radians per second.

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The population grows according to the recursive rule is-

For the stated question-

Then,

P1 = P0 + 80

P1 = 60 + 80 = 140

P2 = P1 + 80

P2 = 140 + 80 = 220

Thus, an explicit formula for the population

Pn = P0 + n×80 = 60 + n×80

P100 = 60 + 100×80 = 8060

Thus, explicit formula for the  population growth is

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The complete question is-

Consider a population that grows according to the recursive rule pn = p

(n − 1) + 80 , with initial population p0 = 60

Find an explicit formula for the population. Your formula should involve  n  (use lowercase n)

Pn=    

Use your explicit formula to find

P100  =

The equation of the circle with center (−1,−2) containing the point (0,6).

(x + 1)^2 + (y + 2)^2 = 65

Remember that the equation of a circle with radius R and center (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is (-1, -2), then our equation is something like:

(x + 1)^2 + (y + 2)^2 = R^2

We know that our circle contains the point (0, 6), replacing these values in the equation above we get:

(0 + 1)^2 + (6 + 2)^2 = R^2

1 + 8^2 = R^2

65 = R^2

Then the circle equation is:

(x + 1)^2 + (y + 2)^2 = 65

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Answer:

25

Step-by-step explanation:

450 divided by 18 is 25

Answer: 25 miles

Step-by-step explanation:
450/18 = 25
25 miles with 1 gallon of gas

Answer:

-40

Step-by-step explanation:

Given that,

c = -6

d = 2

To find the value of the given expression, replace c & d with 6 & 2 respectively.

Let us solve it now.

10c - cd + d³

( 10 × -6 ) - ( -6 × 2 ) + 2³

- 60 - ( -12 ) + 8

- 60 + 12 + 8

- 40

Segment US and segment JH are congruent is correct.

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given:

ΔSTU ≅ ΔHIJ

⇒ All three sides of ΔSTU are equal to all three sides of ΔHIJ.

⇒  ST ≅ HI, TU ≅ IJ and US ≅ JH.

Also all three angles of ΔSTU are same as the angles of  ΔHIJ

⇒   ∠S ≅ ∠H, ∠T ≅ ∠I, and ∠U ≅ ∠J

So, from the given options segment US and segment JH are congruent is correct.

Hence, segment US and segment JH are congruent is correct.

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The equation of g(x) = y=[tex]3^{x+1}[/tex]+1 is if the function f(x)=3ˣ

A graph is a visual depiction or diagram that organizes facts or values. The points on the graph frequently reflect the relationship between two or more objects.

A function graph is a subset of a relation. In the current foundations of mathematics, and most notably in set theory, a function is truly equivalent to its graph. However, it is frequently beneficial to consider functions as mappings, which include not only the relationship between input and output, but also which set is the domain and which set is the codomain. For example, while determining whether a function is onto (surjective) or not, the codomain must be considered. The graph of a function does not determine the codomain on its own.

The graph is as follows: f(x) =[tex]3^{x}[/tex]

The graph g(x) represents a transformation of the graph f(x).

The g(x) curve travels through (-2,2) and (-1,4).

Let (a, b) represent any point on f(x).

After translation, a new curve g(x) is obtained that is parallel to the line, y=1 or asymptode is, y=1 or the graph becomes parallel to the x axis when y reaches 1.

g(x)= y-1=[tex]3^{x+1}[/tex]

g(x) = y=[tex]3^{x+1}[/tex]+1

The graph of the translated curve is +1.

The two graphs are shown below.

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The analyst should provide a report addressing the following

A sale’s affect on subscription purchases is an example of customer buying behavior analysis.

Data analysis is the process of modifying, processing, and cleaning raw data in order to obtain useful, pertinent information that supports commercial decision-making. The process offers helpful insights and statistics, frequently presented in charts, graphics, tables, and graphs, which lessen the risks associated with decision-making.

Every time we make a decision in our daily lives, we can see a basic example of data analysis by assessing what has happened in the past or what will happen if we take that action. In its simplest form, this process involves looking at the past or future and making a choice based on that analysis.

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