A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign? $$

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the height of cylinder is h and radius of base is r.

The volume of cylinder will be : [tex]\pi r^2h[/tex]

The cone is of same height means h and same base means radius will be r.

The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]

It means the volume of cone is one third of the volume of cylinder.

The volume of cylinder is given as π.

So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex]   :   Answer

Hope it will help :)

Try this option:

[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]

answer: B

B)    3 cm

Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]

Vcone =

1

3

πr2h

36π =

1

3

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

Answer:

√3

Step-by-step explanation:

got 100%

You have the main rule: no vowel is isolated between two consonants.

The word FIXTURE consists of 4 consonants and 3 vowels.

There are such possible cases:

1. Formed word begins with three vowels and ends with 4 consonants.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

2.  Formed word begins with two vowels and ends with one vowel (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

4. Formed word begins with with 4 consonants and ends with 3 vowels.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

5. In total 144+144+144+144=576 different words.

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

Given :

The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]

Given tangent line is horizontal . Tangent line is horizontal when slope =0

Slope is nothing but the derivative.

So we find out x values where derivative =0

Lets take derivative for the given curve y

[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]

Now we set the derivative =0 and solve for

[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]

So , the slope =0 when x=1 and x=-2

Now we find out the points . Use the original function

[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

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Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24

The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.

Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that   (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.

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Answer:

A

Step-by-step explanation:

⎡−25 26 −33⎤

⎥  4   −4    5  ⎥

⎥  3   −3    4  ⎦

Answer:

A if you look close at the story you will learn alot! hope this helps!

The description relates to an isosceles right triangle.

An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.

In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.

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Answer:

The answer is A: Quadrant 1

Step-by-step explanation:

On Edge :)

While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.

The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.

The price of the gas is $3.96.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Gas prices in Cook-County are at $3.30 per gallon.

If a market scientist predicts a 20% increase in the price of gas in the coming month,

that means,

100 + 20% = 120% increase = 1.2 in decimals.

The price of gas,

= 3.30 + 3.30 x 1.2

= 3.96

Therefore, the new price is $3.96.

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The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.

We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).

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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).

If a company bought 28 tickets and x of these tickets were for adults, then:

a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.

b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.

c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).

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Answer:  The correct option is (B).  It is not possible to determine if the triangles are congruent.

Step-by-step explanation:  We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.

As shown in the figure,

In ∆ABD and ∆ACD, we have

∠ADB = ∠ADC = 90°,

AD is the common side.

So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.

That is, to prove that the two triangles are congruent, we need one of the following two conditions:

(i)  BD = CD

or

(ii) ∠BAD = ∠CAD.

Since none of these two are given, so we cannot determine the congruence of the two triangles.

Therefore, it is not possible to determine if the triangles are congruent.

Thus, option (B) is correct.

The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.

To find the expected number of books a customer will purchase,

use the formula for the expected value (also known as the mean) of a random variable:

Expected Value (μ) = Σ (x × P(x))

Where:

μ is the expected value.

x represents the possible values of the random variable (in this case, 0, 1, and 2).

P(x) is the probability associated with each value of x.

Probability of purchasing 0 books (P(0)) = 0.2

Probability of purchasing 1 book (P(1)) = 0.4

Probability of purchasing 2 books (P(2)) = 0.4

Now, calculate the expected value:

μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)

μ = 0 + 0.4 + 0.8

μ = 1.2

To find the standard deviation (σ) of the customer's book purchases,

use the formula for the standard deviation of a discrete random variable:

Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]

Where:

σ is the standard deviation.

x represents the possible values of the random variable.

μ is the expected value.

P(x) is the probability associated with each value of x.

In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).

Now, calculate the standard deviation:

σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]

σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]

σ = √[0.288 + 0.064 + 0.256]

σ = √0.608

σ ≈ 0.78

Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.

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The length of the cable is the number of units on it.

The cable is 35.26 feet long

The function is given as:

[tex]h(x) = 15\cos(x/15)[/tex]

For all the lengths, we have the following differential equation

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]

So, we have:

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]

Evaluate

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]

This gives

[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]

Evaluate the exponents

[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]

The above function is an even function.

So, we have:

[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]

Integrate

[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]

Simplify

[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]

Expand

[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]

Solve

[tex]Length = 35.26[/tex]

Hence, the length of the cable is 35.26 feet

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An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.

The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.

Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.

The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Given an integral expression:

[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

This can be written as:

[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

It is required to find the integral value.

Let u = 5 + (ln (x))²

Differentiate.

[tex]du=2ln(x)*\frac{1}{x} dx[/tex]

Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]

Substitute the values.

[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]

[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]

[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]

Substitute back the value of u.

[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]

Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

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Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller

AND OR

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

Explicit Formula: an = a1 · dn-1

a1 = 64, d = 0.5

an = 64 · 0.5n-1