What is 2 multipled by 6 ?

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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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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Answer:

Step-by-step explanation

33

The density of unknown liquid is 7.447 kg/m³

According to the question,

Density of a solid aluminum cylinder : d = 2700 kg/m³

Weight of cylinder in the air = 0.66N

Weight of cylinder when immersed in an unknown liquid = 0.26N

The volume of the cylinder : v = m /d

where , m is mass of cylinder and d is density

Mass of cylinder : m = g/W

Where , g is acceleration due to gravity = 9.8m/s²

And w is weight of cylinder in air = 0.66N

Substituting the values of g and w

Therefore , m = 9.8 / 0.66

=> m = 14.8 kg

So, Volume of cylinder = 14.8 / 2700

=> V = 5.481 ×  10⁻³m³

To calculate the density of liquid ,

Density of liquid  = Upthrust / (volume of object × acceleration due to gravity)

Upthrust of the liquid = 0.66 - 0.26

=> 4 × 10⁻¹N

Volume of cylinder = 5.481 ×  10⁻³m³

Acceleration due to gravity  = 9.8m/s²

Therefore , The density of unknown liquid = 4 × 10⁻¹N / (5.481 ×  10⁻³m³ × 9.8m/s²)

=> 4 × 10⁻¹N / 53.71×  10⁻³

=> 0.4 / 0.05371

Hence , the density of liquid is 7.447 kg/m³

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The total area of all four walls is 150sq.m

What do you mean by surface area?

A solid object's surface area is a measurement of the total area that the surface of the object takes up. In mathematics, the area of a plane region or plane area refers to the area of a shape or planar lamina, whereas the area of a surface or the boundary of a three-dimensional object is referred to as the surface area.

Solution Explained:

Given in question,

Base floor area = 25sq.ft

Height = 6ft

So, the total area of all four walls is,

= Area of base X Height

= 25 X 6

= 150 sq.m

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The equation of the line in slope-intercept form is: y = 1/4x + 5.

To write the equation of a line in slope-intercept form, first, find the slope of the line using two points on the graph.

Slope (m) = change in y / change in x = 1/4

m = 1/4.

The y-intercept is the point where the line intercepts the y-axis, which is at 5. Therefore, the y-intercept is b = 5.

To write the equation of the line in slope-intercept form, substitute m = 1/4 and b = 5 into y = mx + b:

y = 1/4x + 5.

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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 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 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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You're correct answer would be $14.

[tex]35/20 = 1.75[/tex]

[tex]8x1.75=14[/tex]

Answer:

14

Given:

[tex]20 books= 35[/tex]

Step-by-step explanation:

[tex]35/20=1.75[/tex]

[tex]8*1.75= 14[/tex]

The sample size of the given question is 83  and the t-test value is -0.6578.

Hypotheses:

H0 : Ha:  ц < 7.

Sample mean = 6.5

SD = 1.1

n = 83

ц =7

Null hypothesis:   ц >= 7

Alternative hypothesis:    ц < 7

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by

t = (mean - ц )/ ц \sqrt{n}

t-test is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value.    

t =  -0.5 / 0.76

  = -0.6578

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The maximum rate of change of f at the given point is 0.3678

Rate of change

Rate of change defined as the percentage change in value over a defined period of time, and it represents the momentum of a variable.

Given,

Here we the function  f(x, y) = [tex]xe^{-y}[/tex], (1, 0)

Now, we need to find the the maximum rate of change of f at the given point.

We know that, the average rate of change of f(x) on the interval [a, b] is written as,

=> f(x) = (fb) - f(a)/ b - a

Here the value of a = 1 and b = 0.

So, apply the values on the function to solve it,

f(1,1) = 1e⁻¹

f(1,1) = 1 x 0.3678

f(1,1) = 0.3678

Similarly, the value of f(0,0) is,

=> f(0,0) = 0e⁰

=> f(0,0) = 0 x 1

=> f(0,0) = 0

So, the rate of change is,

=> R = 0 - 0.3687/0-1

=> R = 0.3678.

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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:

The answer to the second question is B

Step-by-step explanation:

Cosine is a trigonometric function that is the ratio between the side next to an acute angle in a right triangle and the hypotenuse.

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 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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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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Jean-Auguste-Dominque Ingres believed history was the best subject for art, a preference that can be seen in his work Jupiter and Thetis

Jean Auguste Dominique Ingres was an early 19th-century painter with a long French name and a very famous teacher. Ingres was taught the art of painting by the great French master Jacques-Louis David. David epitomized the Neoclassical movement in art, which reinvigorated Greek and Roman forms, often in the styles of the Italian Renaissance, an earlier culture to venerate classical civilization.

Jupiter and Thetis is an 1811 painting by  Jean-Auguste-Dominique Ingres, in the Musée Granet, Aix-en-Provence, France. Painted when the artist was yet 31, the work severely and pointedly contrasts the grandeur and might of a cloud-born Olympian male deity against that of a diminutive and half-bare nymph. Ingres' subject matter is borrowed from an episode in Homer's Iliad when the sea nymph Thetis begs Jupiter to intervene and guide the fate of her son Achilles; who was at the time embroiled in the Trojan War, this show how he believed history was the best subject for art.

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The cheetah traveled 15.334 miles approximately.

SOLUTION:

Given, Suppose the cheetah sprinted at maximum speed for 8 minutes

Then, slowed to 40mph the next 8 minutes  

We have to find how far would the cheetah have traveled

Now, we know that, maximum speed of cheetah is 68 – 75 mph, as we want maximum we are taking 75 which greater than 68.

So, cheetah sprinted at 75 mph for 8 minutes and then sprinted at 40 mph for next 8 minutes.

First let us convert 8 minutes into hours,

Total distance traveled = distance traveled with 75 mph speed + distance traveled with 40 mph speed

Hence, the cheetah traveled 15.334 miles approximately

Answer:

Step-by-step explanation:

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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The value of this golden ratio = 1/2 (1 + √5) = 1.618

Ratio:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

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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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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:

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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Triangle ABC is congruent to ADC.

Two triangles are congruent if all of their corresponding parts are congruent. This means that congruent triangles will have three pairs of congruent sides and three pairs of congruent angles.

Given information,

AB = AD

BC = CD

and

AB = AD

CB = CD

also

AC = AC (common sides)

Hence triangles ABC and ADC are congruent to each other.

Congruence in two or more triangles depends on the measurements of their sodes and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.  

Given question is incomplete.

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The value of m + n is 12 where , m is 4 and n is 8

Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots. It was discovered by Francois Vieta. The simplest application of Vieta’s formula is quadratics and are used specifically in algebra.

Rearranging the log

[tex]\frac{8}{\log n \log m}(\log x)^2 - \left(\frac{7}{\log n}+\frac{6}{\log m}\right)\log x - 2013 = 0[/tex]

Using the Vieta's Theorem,

The sum of the possible values of log x is [tex]\frac{\frac{7}{\log n}+\frac{6}{\log m}}{\frac{8}{\log n \log m}} = \frac{7\log m + 6 \log n}{8} = \log \sqrt[8]{m^7n^6}[/tex]

But the sum of the possible values of log x is the logarithm of the product of the possible values of x. Thus the product of the possible values of x is equal to [tex]\sqrt[8]{m^7n^6}[/tex]

It remains to minimize the integer value of [tex]\sqrt[8]{m^7n^6}[/tex].

   Since m, n>1 , we can check that m = 2² and n = 2³.

Hence , m = 4 and n = 8

m + n = 4 + 8

=> 12

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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.