Cecilia has some chocolates. There are 24 pieces of white chocolate, 16 pieces of milk
chocolate and 8 pieces of dark chocolate. What is the ratio of dark chocolate to white
chocolate? SHOW WORK
a. 24:16
b. 24 to 8
c. 16/24
d. 16:8
e. 8 to 16
f. 8/24

The exact length of the curve y=ln[(e^x+1)/(e^x-1)], a ≤ x ≤ b, is equals to the ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

The exact length of curves implies the length of arc of curve. Arc length is the distance between two points along a section of a curve, formula

Arc length = ₕ∫ᵏ√( 1 + ( y')² dx , h≤x≤k

We have a curve , y = ln[ (eˣ + 1) /(eˣ - 1) ] , a≤x≤b , a> 0

firstly, determine the first derivative of y with respect to x ..

dy/dx = y' = [ 1/(eˣ +1) /(eˣ -1)] d/dx (( eˣ + 1) /(eˣ -1) )

( apply chain rule )

= (eˣ -1 )/(eˣ +1 )[{(eˣ -1) eˣ - ( eˣ +1)eˣ}/(eˣ - 1)²]

( using quotient rule)

= (eˣ -1 )/(eˣ +1 )[(e²ˣ - eˣ - e²ˣ - eˣ)/(eˣ - 1)²]

= (eˣ -1 )/(eˣ +1 )[(- 2eˣ)/(eˣ - 1)²]

= -2eˣ /(eˣ -1 )(eˣ +1 )

dy/dx = - 2eˣ /e²ˣ -1

so, (dy/dx)² = (- 2eˣ /(e²ˣ -1) )²

= 4e²ˣ /(e²ˣ -1 )²

and 1 + (dy/dx)² = 1 + {4e²ˣ /(e²ˣ -1 )² }

= {(e²ˣ -1 )² + 4e²ˣ}/(e²ˣ -1 )²

= (e⁴ˣ + 1 - 2e²ˣ + 4e²ˣ)/(e²ˣ -1 )²

= ( e⁴ˣ + 1 + 2e²ˣ )/(e²ˣ -1 )²

1 + (dy/dx)² = (e²ˣ + 1)²/(e²ˣ -1 )²

Now plugging the value in arc length formula,

Arc length = ₐ∫ᵇ √{1 + (dy/dx)²} dx

= ₐ∫ᵇ √{(e²ˣ + 1)²/(e²ˣ -1 )²} dx

= ₐ∫ᵇ√{(e²ˣ + 1)/(e²ˣ -1 )}² dx

= ₐ∫ᵇ {(e²ˣ + 1)/(e²ˣ -1 )} dx

= ₐ∫ᵇ[eˣ(eˣ + e⁻ˣ)/eˣ(eˣ - e⁻ˣ )] dx

= ₐ∫ᵇ[(eˣ + e⁻ˣ)/(eˣ - e⁻ˣ )] dx

Arc length= ₐ∫ᵇ(cosh x)/(sinh x)dx ( using hyperbolic functions formulas )

let sinh x = t => cosh xdx = dt

and when x = a => t = sinh a

when x = b => t = sinh b

so, arc length = ₛᵢₙₕ ₐ∫ˢᶦⁿʰ ᵇ (1/t) dt

= [ ln( sinh b ) - ln(sinh a) ]

= ln( sinh b/ sinh a)

Arc length= [( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)]

Hence, length of curve is ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

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Answer: not very sure but i think that may be 5

Step-by-step explanation:

Answer:

\(d = \sqrt{10}\)

Step-by-step explanation:

Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d = \sqrt{(-2-(-5))^2+(-1-0)^2}\)

\(d = \sqrt{(-2+5)^2+(-1)^2}\)

\(d = \sqrt{(3)^2+1}\)

\(d = \sqrt{9+1}\)

\(d = \sqrt{10}\)

Answer:

Step-by-step explanation: y=22.5

Answer:

14/27

Step-by-step explanation:

7/3 ÷ 9/2

7/3 x 2/9 = 14/27

Answer:

Step-by-step explanation:

10

Answer:

The side s has a length of 4 and side q has a length of 4\(\sqrt{3}\) ⇒ F

Step-by-step explanation:

In the 30°-60°-90° triangle, there is a ratio between its sides

side opp (30°) : side opp (60°) : hypotenuse

       1               :         \(\sqrt{3}\)            :        2

In the given triangle

∵ The side opposite to 30° is s

∵ The side opposite to 60° is q

∵ The hypotenuse is 8

→ Use the ratio above to find the lengths of s and q

side opp (30°) : side opp (60°) : hypotenuse

       1               :         \(\sqrt{3}\)            :        2

       s               :          q             :        8

→ By using cross multiplication

∵ s × 2 = 1 × 8

∴ 2s = 8

→ Divide both sides by 2

∴ s = 4

∴ The length of s is 4

∵ q × 2 = \(\sqrt{3}\) × 8

∴ 2q = 8\(\sqrt{3}\)

→ Divide both sides by 2

∴ q = 4\(\sqrt{3}\)

∴ The length of q is 4\(\sqrt{3}\)

Answer:

\(\huge\boxed{\sf{4c-8}}\)

Step-by-step explanation:

Hello.

Use the Distributive Property and distribute 4 in order to simplify the expression:

4(c-2)

4c-8 (we multiply c and -2 times 4)

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

Answer:

V =36000 pi cm^3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

We know the radius is 30

V = 4/3 pi (30)^3

V = 4/3 pi (27000)

V =36000 pi cm^3

Answer:

False

Step-by-step explanation:

\(2\sin x \cos x =\sin 2x \implies 4 \sin x \cos x=2\sin 2x \\ \\ \therefore \int 4\sin x \cos x dx=2\int \sin 2x dx \\ \\ 2\int \sin 2x dx=\frac{2}{2}(-\cos 2x)+C=-\cos 2x+C\)

Answer:

Step by Step Solution

More Icon

STEP

1

:

3

Simplify ——

x2

Equation at the end of step

1

:

3

((((2•(x2))-5x)-——)+2x)-3

x2

STEP

2

:

Equation at the end of step

2

:

3

(((2x2 - 5x) - ——) + 2x) - 3

x2

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x2 as the denominator :

2x2 - 5x (2x2 - 5x) • x2

2x2 - 5x = ———————— = ———————————————

1 x2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

2x2 - 5x = x • (2x - 5)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (2x-5) • x2 - (3) 2x4 - 5x3 - 3

————————————————————— = —————————————

x2 x2

Equation at the end of step

4

:

(2x4 - 5x3 - 3)

(——————————————— + 2x) - 3

x2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x2 as the denominator :

2x 2x • x2

2x = —— = ———————

1 x2

Polynomial Roots Calculator :

5.2 Find roots (zeroes) of : F(x) = 2x4 - 5x3 - 3

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The length of the wire of the same material whose resistance and diameter are 30 ohms and 1.25 mm, respectively is 100 meters.

We are given that the electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. So, we can write this relationship as:

\($$R \propto \frac{L}{d^2}$$\)

where R is the electrical resistance, L is the length of the wire and d is the diameter of the wire. We can replace the proportionality sign with an equal sign and add a constant of proportionality k to obtain the following equation:

\(R = k\frac{L}{d^2}\)

Now we can find the value of k by substituting the given values of R, L, and d in the above equation. So, we have:

\(25 = k\frac{30}{(0.75)^2}\)

\($$k = 25 \times \frac{(0.75)^2}{30}$$\)

k = 0.46875

Now we can use this value of k to find the length of the wire whose resistance and diameter are given as 30 ohms and 1.25 mm, respectively. So, we have:

\(30 = 0.46875\frac{L}{(1.25)^2}\)

\(L = 30 \times (1.25)^2 \times \frac{1}{0.46875}\)

\($$L = 100 \ \text{meters}$$\)

Therefore, the length of the wire of the same material whose resistance and diameter are 30 ohms and 1.25 mm, respectively is 100 meters.

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a) The selection probability you would assign to each of the package designs is equals to the 0.20.

b) No

c) The probability for assign to each package design ( selecting 1 to 5 packages) are 0.05, 0.15,0.30,0.40,0.10 respectively. Package 4 is the highest probability of selection by a customer.

We have a company that manufactures tooth paste is studying five different package designs.

a) We assume that one design is just as likely to be selected by a consumer as any other design so the selection probability you would assign to each of the package designs for all is same = 1/5 = 0.20

b) No, the data confirm does not belief that one design is just as likely to be selected as another.

c) However, according to the actual experiment total number of consumers

= 100

P(package 1 is selected ) = 5/100 = 1/20

= 0.05

P(package 2 is selected ) = 15/100 = 0.15

P(package 3 is selected ) = 30/100 = 0.30

P(package 4 is selected ) = 40/100 = 0.40

P(package 5 is selected ) = 10/100 = 0.10

clearly, we see that all the probabilities differ from one another according to the actual experiment of 100 samples. So, the data does not confirm the belief that one design is just as likely to be selected by a consumer as any other design. Hence, package 4 has highest probability of selection.

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Complete question:

a company that manufactures toothpaste is studying five different package designs.

a) assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs (to 2 decimals)?

b) In an actual experiment, 100 consumers were asked to pick the design they preferred. the following data were obtained. number of design times preferred 1 5 2 15 3 30 4 40 5 10

do the data confirm the belief that one design is just as likely to be selected as another? select

c) based on the actual experiment, what probability would you assign to each package design (to 2 decimals)? design probability 1 2 3 4 5 which package design has the highest probability of selection by a customer? select

Answer:

B

Step-by-step explanation:

there are 30 buildings...

78.4 ÷ 0.56 = 140

I just used an online calculator like you could do. But, here you go.

Answer:

222

Step-by-step explanation:

for sure 100%

gurantee at your own risk

An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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Answer: the height is 18 cm.

Step-by-step explanation:

The equation for the volume of a cone is the following: V = 1/3 × B × h, where B (base) = πr². Because we are given the radius of the base, but not the base’s area itself, we will use V = 1/3πr²h.

Here, we are trying to solve for h, the height, so first we can first rearrange the equation to solve for h:

1) V = 1/3πr²h

2) h = V ÷ 1/3πr² (divide both sides by 1/3πr²h)

Now, we just need to input the given values: V = 471, π = 3.14, r = 5

h = 471 ÷ 1/3(3.14)(5²)

= 471 ÷ 1/3(3.14)(25)

= 471 ÷ 1/3(78.5)

= 471 ÷ (78.5/3)

= 18 cm

Answer:

3/14

Step-by-step explanation:

1 1/4 can be written as 5/4

5 5/6 can be written as 35/6

so divide (5/4)/(35/6)

= (5/4)*(6/35)

=(1/4)*(6/7)

=6/28

simplified = 3/14

The equation of the circle is:

\((x + 4)^2 + (y + 2)^2 = 17^2\)

The general equation for a circle of radius R and center (a, b) is:

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

Here the center is (-4, -2), and it contains the point (4, -17), so the radius is:

\(R = \sqrt{(4 - (-4))^2 + (-2 + 17)^2} = 17\)

So the equation of the circle is:

\((x + 4)^2 + (y + 2)^2 = 17^2\)

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Answer:

Because it is terminating.

Step-by-step explanation:

0.71875 is rational because it is terminating (has a clear end). If it were a bunch of random numbers that never ended, then it would be irrational.

0.71875 is a rational number because it is a terminating and non-repeating decimal.

Rational numbers are numbers that can be written as the ratio of two integers. For example: 1/2, 3/4, are rational numbers

Irrational numbers, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of√2.

Now,the given number is 0.71875

Here we see that digits after decimal 71875 stops,

hence the given number can be convert into fraction of the form a/b

So,

0.71875 = 71875/100000

So 0.71875 can be expressed in the form of a/b

Therefore 0.71875 is rational because it is a terminating and non-repeating decimal.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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The expression that is equivalent to \(Cos(\frac{\pi }{2}+r )\) is \(-Sinr\).

Given trigonometric expression is:

\(Cos(\frac{\pi }{2}+r )\)

The value of \(Cos(\frac{\pi }{2}+\theta )\) is \(-Sin\theta\) because \(\frac{\pi }{2} +\theta\) lies in the second quadrant and the cosine function is negative in the second quadrant.

So, \(Cos(\frac{\pi }{2}+r )= -Sin r\)

The range of sine and cosine functions is the same i.e. [-1,1].

Both the functions are periodic functions with periods 2π.

Hence, the expression that is equivalent to \(Cos(\frac{\pi }{2}+r )\) is \(-Sinr\).

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Answer:

I'm getting $9.80

Step-by-step explanation:

$48.86 • 0.20= $9.772 and then I just rounded to the nearest tenth.

The length, width and height of the open rectangular box is 4.76, 4.76 and 2.38 respectively.

Open rectangular box, so there is no top

SA = 2lh + 2wh + lw

V = lwh = 54cm^3

h = 54/(wl)

SA = 2xl(54/(wl)) + 2w54/(wl) + lw

SA = 108/w + 108/l + lw

Find minimum SA: take partial derivatives to get critical point(s)

SAw = -108/w² + l

SAl = -108/l² + w

Both the partials have to be 0, so...

0 = -108/w² + l and 0 = -108/l² + w

108/w² = l

0 = -108/(108/w²)² + w (plug into second equation)

0 = -w⁴/108 + w

0 = w(1-w³/108)

1 = w³/108 or 0 = w (impossible answer)

108 = w³

4.76 = w

Plug w back into 108/w² = l

108/(4.76)² = l

4.76 = l

Plug w and l back into h = 54/(wl)

h = 54/(4.76x4.76)

h = 2.38

The Surface Area:2lh + 2wh + lw

SA = 2 x 4.76 x2.38 + 2x4.76 x2.38 + 4.76 x4.76

SA = 22.65 + 22.65 + 22.65

SA = 67.97

So the answer is length = 4.76cm, width = 4.76cm, and height = 2.38cm, with Surface Area of 67.97cm²

Therefore, the length of the edges of the open rectangular box is 4.76, 4.76 and 2.38 respectively.

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A bar chart is a graph that shows the differences in frequencies or percentages among categories of a nominal or an ordinal variable.

A bar chart is a commonly used graphical representation to display the distribution of data in different categories. It is particularly useful when working with nominal or ordinal variables, where the categories are distinct and unordered or have a specific order.

In a bar chart, each category is represented by a rectangular bar whose length corresponds to the frequency or percentage associated with that category. The height of the bar represents the magnitude or count of the variable in each category, allowing for easy visual comparison between the categories.

The bars in a bar chart can be arranged horizontally or vertically, depending on the preference or nature of the data. The chart may also include labels or annotations to indicate the category names or additional information.

By examining the lengths or heights of the bars in a bar chart, it becomes easy to identify the categories with the highest or lowest frequencies or percentages, as well as to compare the relative magnitudes among the different categories. This graphical representation aids in visualizing and interpreting the distribution of a nominal or an ordinal variable effectively.

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Answer:

X=20; the labeled angles are 80 and 100

Step-by-step explanation:

These angles are "consecutive interior angles" so they will add up to be 180.

180 = 5x + 4x

180 = 9x

180/9 = 9/x

20=x

Let a be the first, b be second and c be the third whole number.

Since the sum of these three numbers is 100.

So, \(a+b+c=100\) (equation 1)

Since, The first number is a multiple of 15

Therefore, \(a = 15n\)

And, the second number is ten times the third number.

\(b = 10c\)

Substituting the values of 'a' and 'b' in equation 1

So, \(15n+10c+c=100\)

\(15n+11c=100\)

\(11c=100-15n\)

\(c=\dfrac{100-15n}{11}\)

Therefore, \(100-15n\) should be exactly divisible by 11.

So, by taking \(n= 1\) and 2, \(100-15n\) is not divisible by 11

Let \(n =3\)

\(c=\dfrac{100-15\times3}{11}\)

\(c= 5\)

Now, second number (b) \(= 10c = 10\times5=50\)

As, \(a+b+c=100\)

\(a+50+5=100\)

\(a+55=100\)

\(a=45\)

Therefore, the three whole numbers are 45, 50, 5.