A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.

The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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Answer:

( 1, -6 )

Step-by-step explanation:

The solution to the graph is ( 1, -6 ) as that is the point where both equations cross. To double check you can also fill in the equations with the points given and they both should solve.

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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ANSWER

It is not symmetrical to the polar axis

EXPLANATION

To show that the curve

(a) No conditions. (b) The playlist must consist of exactly 3 songs from each artist. (c) The playlist must consist of at least 2 songs from each artist.

Working:

To build a playlist of 6 songs from 25 unique songs, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of songs and r is the number of songs we want to include in the playlist.

So the number of ways to build the playlist is:

25C6 = 25! / 6!(25-6)! = 177,100

Therefore, there are 177,100 ways to build the playlist without any conditions.

(b) The playlist must consist of exactly 3 songs from each artist.

To build a playlist of 6 songs with exactly 3 songs from each artist, we can use the formula for combinations again:

nCr = n! / r!(n-r)!

We need to choose 3 songs from artist A and 3 songs from artist B, so we can calculate the number of ways to do this separately:

Number of ways to choose 3 songs from artist A:

10C3 = 10! / 3!(10-3)! = 120

Number of ways to choose 3 songs from artist B:

15C3 = 15! / 3!(15-3)! = 455

To get the total number of ways to build the playlist, we can multiply these two numbers together:

120 * 455 = 54,600

Therefore, there are 54,600 ways to build the playlist with exactly 3 songs from each artist.

(c) The playlist must consist of at least 2 songs from each artist.

To build a playlist of 6 songs with at least 2 songs from each artist, we can break this down into cases:

Case 1: 2 songs from artist A and 4 songs from artist B

Number of ways to choose 2 songs from artist A:

10C2 = 10! / 2!(10-2)! = 45

Number of ways to choose 4 songs from artist B:

15C4 = 15! / 4!(15-4)! = 1,386

Total number of ways for case 1:

45 * 1,386 = 62,370

Case 2: 3 songs from artist A and 3 songs from artist B

We already calculated the number of ways for this case in part (b):

54,600

Case 3: 4 songs from artist A and 2 songs from artist B

Number of ways to choose 4 songs from artist A:

10C4 = 10! / 4!(10-4)! = 210

Number of ways to choose 2 songs from artist B:

15C2 = 15! / 2!(15-2)! = 105

Total number of ways for case 3:

210 * 105 = 22,050

Total number of ways to build the playlist with at least 2 songs from each artist:

62,370 + 54,600 + 22,050 = 139,020

Therefore, there are 139,020 ways to build the playlist with at least 2 songs from each artist.

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The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

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Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

Answer:

The difference of 16 and a number The quotient of 16 and a number A number divided by 16 Negative 16 divided by a number The quotient of a number and 16 Translating the algebraic expression 16/n: The quotient of –16 and a number; Negative 16 divided by a number.

Step-by-step explanation:

hope this helps..

The required whole number, is either -19/3 or 7 which satisfied the given conditions

let us consider the whole number be x .

we have given the following

the twice a certain whole number i.e x and subtracted it from 3 times the square of the number leaves 133. Mathematically ,

3x^2 - 2x = 133

=> 3x^2 - 2x - 133 = 0

Factorize the above formula we get

=> (3x + 19)(x - 7)= 0

=> 3x + 19 = 0

=> 3x = -19

=> x = -19/3

=> x - 7 = 0

=> x = 7

Hence, possible value of x a whole number is either equal -19/3 or 7.

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\(let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} \)

\( \gamma - p {}^{2} = 5p - p {}^{2} \)

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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Answer:

p=60

Step-by-step explanation:

p=4(15)

p=60

Answer:

2

Step-by-step explanation:

all steps are in the picture

The probability that the second card is a king given that the first card is not a king is 4/51.

This is because there are 4 kings in the deck and 51 cards left after the first card is drawn that are not kings.

To understand this problem, we need to use conditional probability. The event that the first card is not a king is our condition and we want to find the probability that the second card is a king given this condition. We know that there are 4 kings in the deck & 51 cards left after the first card is drawn that are not kings.. So the probability that the second card is a king given that the first card is not a king is 4/51.

The order in which the cards are drawn does not matter since we are not replacing the first card.

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Answer:

Hello There!!

Step-by-step explanation:

There are five components of physical fitness:

1. Body composition

2.Flexibility

3. Muscular strength

4. Muscular endurance

5. Cardiorespiratory endurance

I think he will have to develop Flexibility,Muscular Endurance and also Cardiorespiratory Endurance.

hope this helps,have a great day!!

~Pinky~

To determine which option is most appropriate in studying the product-process matrix describing layout strategies, we need to understand the purpose and characteristics of the product-process matrix and evaluate each option accordingly.

The product-process matrix is a tool used to analyze and determine the appropriate manufacturing layout strategy based on the volume and variety of products being produced. Here are the options to consider: Classifying products into four categories: This option is appropriate as it aligns with the fundamental concept of the product-process matrix. The matrix typically categorizes products into four types: project, job shop, batch, and continuous flow. This classification helps in understanding the production requirements and selecting the appropriate layout strategy.

Determining the optimal lot size for each product:

While determining the optimal lot size is an important consideration in production planning, it is not directly related to the product-process matrix or layout strategies. Lot sizing decisions involve factors such as demand, setup costs, and inventory management, but they do not specifically address the volume-variety trade-off.

Analyzing the supply chain network: While the supply chain network is essential for overall operations management, it is not directly related to the product-process matrix or layout strategies. The product-process matrix focuses on the internal layout of the manufacturing facility and the relationship between product variety and production volume.

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The probability that the balls are drawn from the first urn is 0.99.

The given problem provides information on two urns. In the first urn, 70% of the balls are red, and 30% are blue, while in the second urn, 70% of the balls are blue, and 30% are red. From one of the urns, 12 balls are randomly drawn, out of which 8 are red, and 4 are blue.

We need to determine the probability that the balls are drawn from the first urn.

Let A be the event that the balls are drawn from the first urn. The probability of selecting urn 1 is given by P(A). Out of the 12 balls drawn, 8 are red and 4 are blue. Hence, we can write P(RRBBRRRRRRRR) = P(A) x P(8 red balls and 4 blue balls are drawn | A).

The probability of selecting either urn 1 or urn 2 is 0.5, which is represented as P(A) = P(B). Therefore, P(RRBBRRRRRRRR) = 0.5 x (0.7)^8 x (0.3)^4 = 0.00424.

Let B be the event that the balls are drawn from the second urn. The probability of selecting urn 2 is given by P(B). Out of the 12 balls drawn, 4 are red and 8 are blue. Hence, we can write P(BBRRBBBBBBBB) = P(B) x P(4 red balls and 8 blue balls are drawn | B).

Therefore, P(BBRRBBBBBBBB) = 0.5 x (0.3)^4 x (0.7)^8 = 0.00043.

The probability that the balls are drawn from the first urn is given by P(A | RRBBRRRRRRRR) = P(A) x P(RRBBRRRRRRRR) / [P(A) x P(RRBBRRRRRRRR) + P(B) x P(BBRRBBBBBBBB)].

Substituting the values, we get P(A | RRBBRRRRRRRR) = 0.5 x 0.00424 / [0.5 x 0.00424 + 0.5 x 0.00043] = 0.989 which is approximately 0.99.

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1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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60 possible arrangements when a traveler can choose from three airlines, five hotels, and four rental car companies.

Number of airlines = 3

Number of hotels = 5

Number of rental car companies = 4

To calculate the total number of arrangements, we will multiply these numbers together

Total number of arrangements = Number of airlines × Number of hotels × Number of rental car companies

Total number of arrangements = 3 × 5 × 4

Total number of arrangements = 60

Therefore, there are 60 possible arrangements when a traveler can choose from three airlines, five hotels, and four rental car companies.

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Answer:

The answer is "25 ml".

Step-by-step explanation:

Dose\(= 500 \ mg\\\\\)

Solution \(= 100\ \frac{mg}{teaspoonful}\\\\\)

Calculating the Conversions:

Teaspoonful \(= 5 \ ml \ \text{(Ounce = 30 ml = 6 Tablespoonsful)}\)

\(\therefore\\\\Solution = \frac{100\ mg}{ 5\ ml} = 20\ \frac{mg}{ml}\\\\Dose \ volume = \frac{500\ mg}{ 20\ \frac{mg}{ml}} = 25\ ml\)

Answer:

Step-by-step explanation:

Jose is trying to calibrate his new fitness watch. The app that come with the watch asks the user to input their average stride. Jose measures this to be approximately 2.5 feet. Using 2.5 feet as his stride how many feet will Jose walk if he takes 6000 steps in a day?

The given proof that all horses are the same color is a fallacy of circular reasoning or proof by induction.                                

   Here’s why: There is a fallacy in the statement given in the proposition P(k) is true, so that all the horses in any set of k horses are the same color. The fallacy is that it assumes the truth of the proposition to be proven by circular reasoning. By saying that all horses in any set of k horses are the same color, it means that all horses in a set of 1 horse, which is the basis step, are the same color. But this is false because a horse, as a solitary individual, can be of any color.                                

So, the statement, "all horses in any set of k horses are the same color" assumes the conclusion to be proven. This flaw invalidates the entire proof by induction. Therefore, the "proof" that all horses are the same color is wrong.

What is induction?                                                                                                                                                                                                             Induction is the process of establishing a general statement or principle by looking at examples or instances. It involves a specific observation or case that leads to a general conclusion. It is useful in mathematical proofs, scientific inquiry, and problem-solving.
The issue with this "proof" that all horses are the same color lies in the inductive step. To clarify, let's go through the proof by induction process:

1. Basis Step: P(1) is true since there is only one horse, and it must be the same color as itself.
2. Inductive Step: Assume P(k) is true for some arbitrary k (all k horses have the same color).

Now, proof consider a set of k + 1 horses. You claimed that the first k horses have the same color and the last k horses have the same color. However, this argument fails when k = 1. In this case, you would have a set of 2 horses (k+1), and there is no overlap between the first horse and the second horse, so you cannot conclude that they have the same color based on the induction assumption.

Thus, the inductive step does not hold for all cases, and the proof that all horses are the same color is incorrect.

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Answer:

55

Step-by-step explanation:

hshshshhdhshshhshshsjjs

Answer:  need to buy 2 dozen muffins=24

need to buy 3 packs of orange juices=24

Step-by-step explanation:

To sketch the region enclosed by the given curves, which are y = sin(x), y = 3x, x = π/2, and x = b (where b is an unknown value), we can follow these steps:

Plot the graphs of y = sin(x) and y = 3x on the same coordinate system.

Identify the points of intersection between the two curves. These are the points where sin(x) = 3x.

Determine the x-values where sin(x) = 3x. This can be done numerically or graphically.

Sketch the region enclosed by the curves y = sin(x), y = 3x, x = π/2, and x = b, based on the information obtained in step 3.

Determine whether to integrate with respect to x or y. To make this decision, consider the orientation of the curves and the region enclosed. Based on the given curves, it is likely that integrating with respect to x would be more suitable in this case.

Draw a typical approximating rectangle within the enclosed region. The rectangle should have one side parallel to the x-axis (or y-axis, depending on the decision made in step 5) and have dimensions that represent the width and height of the region.

Note: The value of b is not provided, so the specific shape of the region and the size of the rectangle cannot be accurately determined without that information

Answer:

                 calories

Breakfast: 670  

Lunch:      555

Dinner:     910

Total = 2135 calories

Step-by-step explanation:

Let B, L and D, stand for the calories from Breakfast, Lunch, and Dinner

One day his calories from breakfast were 115 more, than his calories from​ lunch:  

B = L + 115

his calories from dinner were 200 less than twice his calories from lunch.:

D = 2L - 200

total caloric intake from meals was 2135:

B + L + D = 2135

------

We have B and D defined in terms of L from the first two equations, so use them in the third:

B + L + D = 2135

[L+115] + L + [2L-200] = 2135

4L - 85 = 2135

4L = 2220

L = 555 calories

B = L + 115

B = 555 + 115

B = 670 calories

D = 2L - 200

D = 2(555) - 200

D = 910 calories

================

CHECK

Does B + L + D = 2135 calories?

  670 + 555 + 910 = 2135?

 2135 = 2135?   YES

The prove to show that the area of the shaded portion is 18x  - 30 is as follows: 3x² + 13x - 30 - 3x² + 5x = 18x  - 30

The area of the shaded region can be represented as follows:

area of the shaded region = area of rectangle - area of triangle

Therefore,

area of the rectangle = (x + 6)(3x - 5)

area of the rectangle = 3x² - 5x + 18x - 30

area of the rectangle = 3x² + 13x - 30

area of triangle = 1 / 2 × 2x × 3x - 5

area of triangle = 3x² - 5x

Therefore,

area of the shaded portion =  3x² + 13x - 30 - 3x² + 5x

area of the shaded portion = 18x  - 30

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Answer:

I think it is 10

Step-by-step explanation:

hope this helps

Answer:

A. One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.

Hope this Helps!

Answer:

you answer is A

Step-by-step explanation:

i got it right on the quiz