A chemistry student needs 25.0 ml of pentane for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that thedensity of pentane is 0.626 g.cm Calculate the mass of pentane the student should weigh out.Be sure your answer has the correct number of significant digits.

a. The circumference of the yellow circle is 43.96 ft.

b. The circumference of the purple circle is 28.26 ft.

A circle is a figure that is bounded by a curved path called circumference. Thus a circumference if the boundary of a given circle. It can be determined by;

circumference of a circle = 2πr

where r is the radius of the circle.

In the diagram given in the question, we have;

a. diameter of the purple circle = 9 ft, so that;

r = d/2

 = 9/2 = 4.5 ft

Circumference of the purple circle = 2πr

                         = 2*3.14*4.5

                         = 28.26

Circumference of the purple circle is 28.26 ft.

b. diameter of the yellow circle = 2.5 + 9 + 2.5

                                                    = 14

So that;

r = d/2

 = 14/2 = 7 ft

Circumference of the yellow circle = 2πr

                            = 2*3.14*7

                            = 43.96

The circumference of the yellow circle is 43.96 ft.

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

i think the answer is 18.15

Step-by-step explanation:

The first six terms of the Taylor series solution, centered at 0, of the given initial-value problem is y(x) = 1 + x + 1/2x² + 1/2x³ + 1/6x⁴ + 1/10x⁵+...

A function's Taylor series is an infinite sum of terms with each subsequent term having a bigger exponent, such as x, x2, x3, etc., and being stated in terms of the function's derivatives at any given point. In order to represent the Taylor series mathematically, the Taylor series formula is useful.

Using the derivatives of the function, the Taylor series formula aids in expanding a function around a value of the variable. s and be as ly,,,, texturs in a l

x a = f(x) = f(a) + f'(a)

y" = x + y²

y"' = 1 + 2yy'

y"" = 2(yy" + (y')²)

y""' = 2(yy"' + y'y" + 2y'y")

= 6y'y" + 2yy"

Now, y(0) = 1 and y'(0) = 1

y"(0) = 0 + y(0)² = 1

y"'(0) = 1 + 2y(0)y'(0) = 3

y"" = 2(y(0)y"(0) + (y'(0))²) = 4

y""' = 2(y(0)y"'(0) + y'(0)y"(0) + 2y'(0)y"(0)) = 12

Substitute these values in above equation :

so, first six terms of the Taylor's series

y(x) = 1 + x + 1/2x² + 1/6(3x³) + 1/4(24x⁴) + 1/120(12x⁵)+....

y(x) = 1 + x + 1/2x² + 1/2x³ + 1/6x⁴ + 1/10x⁵+.....

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Answer:

8.25

Step-by-step explanation:

55=100%

x=15%

100x=55*15

100x=825

x=8.25

or

15/100*55

0.15*55

8.25

The number of points gained overall by Julia playing the game is 30 point

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

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

Answer:  1/4

Step-by-step explanation:

If there are  6 black markers and they are a total combination of 24 difference colored markers.  

The  the fraction will be 6/24  which reduces to 1/4

Answer: 523.8 cubic inches

Step-by-step explanation:

Volume of the sphere, V = (4/3) * π * r^3

where r is the radius of the sphere.

Given, the diameter of the sphere (d) = 10 inches

Therefore, the radius of the sphere, r = d/2 =10/2 = 5 inches

Now, substituting the value of the radius to the volume formula,

V = (4/3) * π * (5^3)

= (4/3) * (22/7) * 125

≈ 523.8 cubic inches

Answer:

$5

Step-by-step explanation:

6:40 to 7:30 is 50 minutes

6 per hour

6÷6=1

1x5=5

hope this helps

Answer:

The answer would be 6/18 or 3/9

Step-by-step explanation:

Answer:

if dividing...0.3

if multiplying...0

Step-by-step explanation:

The intersection point is the solution of inequalities is (15, 7.5).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are 13x+37y≤481 -----(i) and 27x+21y≤567 -----(ii)

Here, x≥4 and y≥2

From the graph we can see that, inequalities are intersecting at (15, 7.5)

Therefore, the intersection point is the solution of inequalities is (15, 7.5).

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a. Given the 2nd order ODE

\(y''(x) = 4y(x) + 4\)

if we substitute \(z(x)=y'(x)+2y(x)\) and its derivative, \(z'(x)=y''(x)+2y'(x)\), we can eliminate \(y(x)\) and \(y''(x)\) to end up with the ODE

\(z'(x) - 2y'(x) = 4\left(\dfrac{z(x)-y'(x)}2\right) + 4\)

\(z'(x) - 2y'(x) = 2z(x) - 2y'(x) + 4\)

\(\boxed{z'(x) = 2z(x) + 4}\)

and since \(y(0)=y'(0)=1\), it follows that \(z(0)=y'(0)+2y(0)=3\).

b. I'll solve with an integrating factor.

\(z'(x) = 2z(x) + 4\)

\(z'(x) - 2z(x) = 4\)

\(e^{-2x} z'(x) - 2 e^{-2x} z(x) = 4e^{-2x}\)

\(\left(e^{-2x} z(x)\right)' = 4e^{-2x}\)

\(e^{-2x} z(x) = -2e^{-2x} + C\)

\(z(x) = -2 + Ce^{2x}\)

Since \(z(0)=3\), we find

\(3 = -2 + Ce^0 \implies C=5\)

so the particular solution for \(z(x)\) is

\(\boxed{z(x) = 5e^{-2x} - 2}\)

c. Knowing \(z(x)\), we recover a 1st order ODE for \(y(x)\),

\(z(x) = y'(x) + 2y(x) \implies y'(x) + 2y(x) = 5e^{-2x} - 2\)

Using an integrating factor again, we have

\(e^{2x} y'(x) + 2e^{2x} y(x) = 5 - 2e^{2x}\)

\(\left(e^{2x} y(x)\right)' = 5 - 2e^{2x}\)

\(e^{2x} y(x) = 5x - e^{2x} + C\)

\(y(x) = 5xe^{-2x} - 1 + Ce^{-2x}\)

Since \(y(0)=1\), we find

\(1 = 0 - 1 + Ce^0 \implies C=2\)

so that

\(\boxed{y(x) = (5x+2)e^{-2x} - 1}\)

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

6.b) The value of z(x) is \(z(x) = 5e^{2x} - 2\).

6.c) The value of y(x) is \(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\).

The given ordinary differential equation is y''(x) = 4y(x) + 4, y(0) = y'(0) = 1 ... (d).

We are also given a substitution function, z(x) = y'(x) + 2y(x) ... (z).

Putting x = 0, we get:

z(0) = y'(0) + 2y(0),

or, z(0) = 1 + 2*1 = 3.

Rearranging (z), we can write it as:

z(x) = y'(x) + 2y(x),

or, y'(x) = z(x) - 2y(x) ... (i).

Differentiating (z) with respect to x, we get:

z'(x) = y''(x) + 2y'(x),

or, y''(x) = z'(x) - 2y'(x) ... (ii).

Substituting the value of y''(x) from (ii) in (d) we get:

y''(x) = 4y(x) + 4,

or, z'(x) - 2y'(x) = 4y(x) + 4.

Substituting the value of y'(x) from (i) we get:

z'(x) - 2y'(x) = 4y(x) + 4,

or, z'(x) - 2(z(x) - 2y(x)) = 4y(x) + 4,

or, z'(x) - 2z(x) + 4y(x) = 4y(x) + 4,

or, z'(x) = 2z(x) + 4y(x) - 4y(x) + 4,

or, z'(x) = 2z(x) + 4.

The initial value of z(0) was calculated to be 3.

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

Transforming z(x) = dz/dx, and z = z(x), we get:

dz/dx = 2z + 4,

or, dz/(2z + 4) = dx.

Integrating both sides, we get:

∫dz/(2z + 4) = ∫dx,

or, {ln (z + 2)}/2 = x + C,

or, \(\sqrt{z+2} = e^{x + C}\),

or, \(z =Ce^{2x}-2\) ... (iii).

Substituting z = 3, and x = 0,  we get:

\(3 = Ce^{2*0} - 2\\\Rightarrow C - 2 = 3\\\Rightarrow C = 5.\)

Substituting C = 5, in (iii), we get:

\(z = 5e^{2x} - 2\).

6.b) The value of z(x) is \(z(x) = 5e^{2x} - 2\).

Substituting the value of z(x) in (z), we get:

z(x) = y'(x) + 2y(x),

or, 5e²ˣ - 2 = y'(x) + 2y(x),

which gives us:

\(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\) for the initial condition y(x) = 0.

6.c) The value of y(x) is \(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\).

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Answer:

1/2 x base x height our base being 140 and our height being 80 and the answer is 5600

Answer: d is your answer hope this helped

plz make brainly

Step-by-step explanation:

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

-3, 3, 0.54545455, 8, 3.14159265..., 0, 2.44948974, 6

these are the real numbers

Answer:

- 49/24

Step-by-step explanation:

Solving for x:

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Answer:

x = 20

Step-by-step explanation:

3x + 6x = 180, if you make them supplementary then they will be parallel

9x = 180

x = 20

Answer:

x=2×-1÷4

NOW

or,2x-1÷4

or,3÷4

or,0.75 answer

Answer:

2x+3y-3x-5y

2x-3x+3y-5y

-1x-2y

Answer:

what is the answers

Step-by-step explanation:

Given:

The point is:

Find-:

How many points lie on the x-axis

Explanation-:

At x-axis value of y is zero.

So, the point on the x-axis is:

So, the 2 points lie on the x-axis.

Answer:

A quadrilateral is a shape that has four straight sides and four angles.

A triangle is a shape that has three straight sides and three angles.

A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.

Steps to construct a regular hexagon inscribed in a circle are given by:

Step 1

Draw a circle with center A and a point on the circle B.

Step 2

Measure AB with a compass to get the distance of the radius.

Step 3

Place compass on point B and draw another circle with the same radius.

Step 4

Mark the new intersection points C and D. Move compass to point C with the same setting and draw another circle with the same radius.

Step 5

Continue drawing the circles this way until you have 6 points of intersection.

Step 6

Connect all intersection points to form the hexagon.

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

Guys the real answer is B C E

I really hope this helps :)

Answer:

The answer is B, C, E.

Step-by-step explanation:

B: t > 0

C: -4.3 < a

E: k less-than Negative StartFraction 5 Over 7 EndFraction

Answer:

T = 5c +5d,    where unit of the equation is $.

Step-by-step explanation:

Cost of 1 large cheese  pizza = $5

No. of large cheese pizza = c

therefore

cost of c  large cheese pizza = c*Cost of 1 large cheese  pizza = $5c

Cost of 1 large one topping  pizza = $6

No. of large one topping pizza = d

therefore

cost of d  large one topping pizza = d*Cost of 1 large one topping  pizza =             cost of d  large one topping pizza = $6d  

Total cost of  c  large cheese pizza and cost of d  large one topping pizza

= $5c +$6d

total cost is represented by T

thus, T = $5c +$5d  Answer

Answer: 4.125

Step-by-step explanation:

2+3/4= 2.75

2.75•1.5= 4.125

Answer:

5.59

Step-by-step explanation:

unit price = total price / total number of pairs

               = 33.54/6 = $ 5.59

Answer:

5.59 each pair of socks.

Step-by-step explanation:

33.54÷6=5.59