the rotational speed of a driven gear is inversely proportional to the number of teeth on a gear. you are replacing a gear having 200 teeth with one that has 50 teeth and turns 2,000 rpm. what was the rpm of the gear having 200 teeth?

The volume of the given shape is  392.7hr² sq. units.

Given, the base of S is a circular disk with radius 5r.

Parallel cross-sections perpendicular to the base are isosceles triangles with height 5h and unequal side in the base.

we have to find the volume of the shape we are given,

As, Volume = area × height

Now, area = πr²

area = 3.14×(5r)²

area = 78.54r²

as, height = 5h

then, Volume = 78.54r²×5h

Volume = 392.7hr²

Hence, the volume of the given shape is  392.7hr² sq. units.

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Answer:

5 units

Step-by-step explanation:

The formula is [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

You have to plug in the information you are given, into the formula, and you will have: [tex]d=\sqrt{(2-(-1))^2 + (0-4)^2}[/tex]

Then simplify.

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

[tex]d=\sqrt{9+16}[/tex]

[tex]d=\sqrt{25}[/tex]

And the square root of 25 is 5.

Place value of 432 is 400 +30+02 .

What is place value?

In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.

Main body:

The place value of a digit will increase by 10 times as we move  left on the place worth chart and reduces by ten times as we tend to move right.

The place of digit 4 will be hundreds.

The place of digit 3 will be tens.

The place of digit 2 will be ones.

Hence place value of 432 is  400 +30+02 .

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For the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, P equals atmospheric pressure (atm), V equals liters of volume (L), n equals the number of moles, R is the gas constant (0.0821 Latm/(molK)), and T equals Kelvins of temperature (K).

Take into account the following circumstances: a 3,500 mL tank containing 27 moles of argon gas was pressurized to 12 atm.

The ideal gas equation is,

PV=nRT

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, for the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

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A Connected Graph is the one in which every two pairs of vertices are connected.

The correct option is (d)

Given,

In the question:

A_____ is the one in which every two pairs of vertices are connected.

a. directed graph

b. weighted graph

c. complete graph

d. connected graph

To choose the correct answer.

What is connected graph with example?

A graph is said to be connected if there is a path between every pair of vertex. From every vertex to any other vertex, there should be some path to traverse. That is called the connectivity of a graph. A graph with multiple disconnected vertices and edges is said to be disconnected.

Now According to the question:

The right option is :

Connected Graph.

Hence, A Connected Graph is the one in which every two pairs of vertices are connected.

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The vertical traces of the functions at the indicated values of x and y have been represented on the graph attached.

The trace of a graph can be defined as the point where the graph intersects any single plane. Vertical traces are the traces where the lines meet and intersect at the vertical plane.

We have been given the values of the functions as such =

= x = 2

= z = 4 - x- y

If we solve these for the value of x and y, we will get -

= x = 2

= z= 2 - y

Hence, on equating these values, we get the following graph.

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Among smokers, the etiologic fraction of disease due to smoking is: a score of 0.83 for lung cancer and 0.18 for coronary thrombosis.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The death rate per 100,000 for lung cancer is 7 among nonsmokers and 71 among smokers.

The death rate per 100,000 for coronary thrombosis is 422 among nonsmokers and 599 among smokers.

Lung cancer's relative risk (RR) is equal to 71/7 =  10.1

Lung cancer population etiological factor (PEF) =

0.55(10.1 -1) /0'.55 (10,1 -1)+1

= 0.83

Coronary thrombosis' relative risk (RR) is 599/422, or 1.42.

The population etiological factor (PEF) for coronary thrombosis

= 0.55 (1.42-1)/0'.55. (1.42 -1)+1

= 0.18

Hence, Among smokers with a score of 0.83 for lung cancer and 0.18 for coronary thrombosis.

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The eigen values of the given matrix [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] is 1 , 2 and 2  .

In the question ,

the matrix is given as [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] .

The eigen values can be determined by using the characteristic equation ,

|A - λI | = 0

So , [tex]\left|\begin{array}{ccc}0-\lambda&0&-2\\1&2-\lambda&1\\1&0&3-\lambda\end{array}\right| = 0[/tex]

simplifying the above determinant , we get

-λ [(2-λ)(3-λ) - 0| - 0 -2[0 -(2-λ)] = 0

-λ[λ² - 5λ + 6] + 4 - 2λ = 0

-λ³ [tex]+[/tex] 5λ² -8λ [tex]+[/tex] 4 [tex]=[/tex] 0

λ³ - 5λ² + 8λ -4 = 0

Substituting λ = 1 in the above equation ,

we get ,

1 - 5 + 8 - 4 = 0

0 = 0

So , yes λ = 1  is a factor of the equation.

So , the characteristic equation can be written as

(λ - 1)(λ² - 4λ + 4) = 0

(λ -1)(λ² - 2λ -2λ + 4) = 0

(λ - 1)(λ - 2)(λ - 2) = 0

So , λ = 1 , λ = 2 and λ = 2 .

Therefore , the eigen values are λ = 1 , λ = 2 and λ = 2 .

The given question is incomplete , the complete question is

Consider the matrix [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] . Find the eigen values of A .

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Answer:

The required function formula is,

D(t) = 160 - 25 t

Given,

The total distance of her from the safe zone = 160 meters,

And, after 3 seconds she is 85 meters far away from the safe zone,

Thus, the total distance she covered in 3 seconds = 160 - 85 = 75 meters, Since, she drove at a constant speed,

Also,

Thus, the distance she will cover in t seconds = 25 t

( Because, Distance = Speed × Time )

Hence, the total distance of her from the safe zone after t seconds, D(t) = 160 - 25t

Which is the required function formula.

Step-by-step explanation:

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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Answer:

X = 15 = Erin's age

Y = 18 = Alex's age

Step-by-step explanation:

X = Erin's age

Y = Alex's age

33 (combined ages) - 3 (how many years Erin is younger than Alex) = 30

30 ÷ 2 = 15

15 + 0 = 15 (Erin's age)

15 + 3 = (Alex's age)

X = 15 = Erin's age

Y = 18 = Alex's age

The value of a home in San Diego will increase by 80.6% in 20 years.

Here, we are given that the value of a home in San Diego increases by 3 percent each year.

This means that suppose the value of a home today is V, then its value in a year from now will be V(1 + 0.03)

Thus, its value in 20 years will be-

V(1 + 0.03)(1 + 0.03).......(1 + 0.03)

This, can be written as-

[tex]V(1 + 0.03)^{20}[/tex]

= V × [tex]1.03^{20}[/tex]

= V(1.806)

= 1.806V

Thus, we see that the value of the home increases from V to 1.0806V in 20 years. The percentage change will be-

100(1.806V - V)/V

= 100 × 0.806V/V

= 80.6%

Thus, the value of a home in San Diego will increase by 80.6% in 20 years.

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Answer:

Step-by-step explanation

33

Answer:

Step-by-step explanation:

In the pic below:-

The quotient is (x + y) (3x -y) for the expression[tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex]    .

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is

[tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex]      

The factor of equation 3x³-7x2y-7xy²+3y³ are,

(x + y) (3x - y) (x - 3y)

The given expression can be written as,

[tex]\frac{(x + y) (3x - y) (x -3y)}{x-3y}[/tex]

=(x + y) (3x -y)

The required quotient for the given expression [tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex] is (x + y) (3x -y).

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No matter what the shape of the parent population is, as long as our sample size is 10 or greater, we can conclude that the sampling distribution of the sample mean is approximately normally distributed. This statement is False.

We know that,

the Central limit theorem says that no matter what the distribution of the population is, as long as the sample is "large", meaning of size 30 or more, the sample mean is approximately normally distributed. If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size.

So therefore we need sample size greater than 30 and we have given 10 or greater.

Hence the given statement is false.

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The average rate of change of g(x) over the interval [-3, 3] is 2.

For a function f(x), we define the rate of change over an interval (a, b) as:

(f(b) - f(a))/(b - a)

Here we have the interval [-3, 3] and the function:

g(x) = x^2 + 2x + 8

Then the average rate of change over that interval will be:

[ g(3) - g(-3)]/(3 - (-3))

The values in the denominator are:

g(3) = 3^2 + 2*3 + 8 = 9 + 6 + 8  =23

g(-3) = (-3)^2 + 2*-3 + 8 = 9 - 6 + 8 = 11

Replacing that we get:

[23 - 11]/(3 + 3) = 12/6 = 2

The average rate of change over that interval is 2.

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The farmer will produce 700kg of rice this year, which is 30%(percentage) less

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

A farmer produces 1000kg of rice.

This year the production of rice decreased by 30%

30% of 1000 will be 1000*30/100 = 300

So total production this year will be 1000-300 = 700KG

Hence, the farmer will produce 700kg of rice this year.

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The solutions to the equation 5x³=405x are x=0, x=9, x=-9.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions related with an equals sign.

An equation is similar to a scale into which weights are placed. When equal weights of material  are placed in the two pans, the scale is balanced and the weights are said to be equal.

Solving an equation with variables entails determining which variables values make the equality true.

Given, 5x³=405x

5x³-405x=0

5x(x²-81)=0

5x=0 and x²-81=0

If 5x=0 then,

x=0

If x²-81=0

x²=81

x=±9

Therefore, x=0, x=±9

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We can determine if a function is linear or quadratic by, if the function is exponential if the variable is in the exponent. It is a quadratic equation if the variable is not in the exponent. The function is a linear function if it lacks an exponent.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

We can determine if a function is linear or quadratic by,

For data presented as ordered pairs, you can calculate the model's degree by identifying differences between dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.

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As per the given standard deviation, the standard error is 5

Standard deviation:

Basically, standard deviation means the root-mean square deviation as it is the square root of means of the squared deviations from the arithmetic mean.

Given,

A sample of size 16 is randomly selected from a population of size 90.

Here we need to determine the standard error of the mean if the population standard deviation equals 20.

As per the given question, we know that,

Number of population is 16

And the standard deviation = 20

So, the standard error is calculated as,

=> Error =  20/√16

=> error = 20/4

=> error = 5

Therefore, the standard error is 5.

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The expression for the number of paintings Sergio will have in his art collection after his donation is p - 4

Number of Sergio's paintings = p

Total number of paintings to donate = 48

Number of collectors to donate (including Sergio) = 12

Number of paintings donated by each collector = Total number of paintings to donate ÷ Number of collectors to donate

= 48 ÷ 12

= 4 paintings per collector

Therefore,

Number of paintings Sergio will have in his art collection after his donation = Number of Sergio's paintings - Number of paintings donated by each collector

= p - 4

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Complete question

Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression

Answer:

Step-by-step explanation:

76

The coordinate will make perpendicular AB to CD is D(x, x/3 + 3). We have used the slope concept to solve this problem.

The slope of a line segment between two points (x1,y1) and (x2,y2) is given by the ratio of change in the y coordinate to the change in the x coordinate.

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

Slope of line AB = (-5-4)/(2-(-1)) = -9/3 = -3

Let the slope of another segment CD be m.

As the product of two perpendicular segments is equal to -1.

So,

-3m = -1

m = 1/3.

Let,s assume point D is (x,y)

Slope of segment CD = (y - 4) / (x-3)

(y - 4) / (x-3) = 1/3

3(y-4) = (x-3)

3y = x+9

y = x/3 + 3

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The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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The equation which represents this scenario would be y = 2x + 1.

What is a linear function?

The term linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

Miguel runs 1 mile in the first week and in the second week he runs 2 runs farther than his distance for the previous week,

Let the distance covered in the previous week be 'x' distance then his goal can be represented as '2x'.

Then the given scenario can be represented by

                 y = 2x + 1.

Hence, the equation which represents this scenario would be y = 2x + 1.

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your slope is -50 and your equation of x = mp + b becomes

x = -50 * p + b

you want a linear relationship between x and p

that would be a straight line equation with the general form of y = mx + b

m is the slope

b is the y-intercept

since you x in terms of p, then:

let y = x

let x = p

the equation of y = mx + b is the same as the equation of x = mp + b after you replace y with x and x with p.

in the equation of x = mp + b, you have coordinate points in the form of (p,x)

since y = x and x = p, this is the same as the form of (x,y), which is the standard form of the linear equation coordinate points.

we'll work with x = mp + b and then later translate to y = mx + b for graphing purposes.

your standard form is x = mp + b with coordinate points of (p,x).

you have two coordinate points they are (3.5,25) and (3,50)

m is equal to slope which is equal to (y2-y1)/(x2-x1) which is then translated to (x2-x1)/p2-p1 when you replace y with x and x with p.

  assign (3.3,25) to (p1,x1) and assign (3,50) to (p2,x2) and the slope       equation becomes (50-25)/(3-3.5) which becomes 25/-0.5 = -50

your slope is -50 and your equation of x = mp + b becomes

x = -50 * p + b

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The Yield to Maturity (YTM) of the Bond is 8.27%

Given data,

A bond has a $1,000 par value, 12 years to maturity, and an 8% annual coupon and sells for $980,

Par Value = $1,000

Annual Coupon Amount = $80 [$1,000 * 8%]

Bond Price = $980

Maturity Years = 12 Years

To find its yield to maturity (YTM),

Therefore, Yield to Maturity

[YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [ (Par Value + Bond Price) / 2 ]

          = [$80 + {($1,000 – $980) / 12 Years)] / [($1,000 + $980) / 2]

          = [($80 + $1.67) / $990]

          = [$81.67 / $980]

          = 0.0827

          = 8.27%

Hence, the Yield to Maturity (YTM) of the Bond is 8.27%

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The standard error of the distribution of sample proportion is 0.0490.

What is the standard error of the distribution?

The standard error of a statistic's sampling distribution, denoted as x, describes how much the computed statistics should differ from one another when calculated from a sample of similar size and drawn from similar population models.

We have,

Population parameter (P) = 0.4,

n = 100,

The standard error (S.E.) =?

The formula of standard error (S.E.) =  [tex]\sqrt{\frac{P(1 - P)}{n} }[/tex]

By using the formula:

S.E. = √0.4(1 - 0.4)/100

S.E. = √0.0024

S.E. = 0.0489

S.E. = 0.0490

Hence, the standard error of the distribution of sample proportion is 0.0490.

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The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t) using the eigen value method.

The coefficients of a set of linear equations are represented by coefficient matrices. These matrices are frequently used to streamline the process of calculating equations  by arranging the coefficients in a standardized manner. The coefficient matrix is frequently designated as A, with the dimensions matching to the number of equations and variables in the system. A system of three equations with three variables, for inspection , would have a 3x3 coefficient matrix. The elements in the matrix reflect the coefficients of each variable in each equation and may be used to solve the problem using various approaches such as Gaussian elimination or matrix inversion.

How to solve?

x1' = -3x1 + 2x2

x2' = -3x1 - 2x2

The characteristic equation is (-3-λ)(-3+λ)+4=0, which simplifies to λ^2-9+4=0, or λ^2-5=0. This has solutions λ = +-sqrt(5).

For λ = +sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 + 2sqrt(5)x2

x2 = -(3/2)x1 + (1/sqrt(5))x2

eigenvector x2 = (1/sqrt(5))x1.

For λ = -sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 - 2sqrt(5)x2

x2 = -(3/2)x1 - (1/sqrt(5))x2

Dividing both sides by (1+3/2sqrt(5)), we get the eigenvector x2 = (-1/sqrt(5))x1.

The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t).

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