The light from the Cape Florida Lighthouse in Key Biscayne is visible for a distance of 15 mi. If the beam of light sweeps in an arc of 270°, what is the area covered by the beam?

Answer:

(1.2075)

Step-by-step explanation:

Lets assume we are increasing a price on a $100 item to help visualize the steps.

The two steps of 5% and then 15% can each be expressed as:

5%:  (1+0.05)  [The 1 represents the fact that the final cost is full price (1) plus 5%(0.05)]

15%  (1+0.15)   [Same explanation, but now with 0.15 for 15%]

We can apply these factors individually:

Assume a base of $100:

5% increase would make it $105  [$100*(1.05)=$105]

15% increase:  On top of the 5%, we would go to:  $105*(1.15) = $120.75

Or we can use a single multiplier.

If we look at the steps from above, we see that the algebra consisted of taking the origianl price ($100) and multiplying it twice:  once with (1+0.05) and once with (1+1.15).  Write this in the form of an equation:

  ($100)*(1+0.05)*(1+0.15) = $120.75

Let's multiply (1+0.05)*(1+0.15)

                       = (1.2075)

We can use this single factor (multiplier) to find the correct/same value as before:

              (1.2075)($100) = $120.75

Answer:

E

Step-by-step explanation:

My answer

[tex] \frac{2}{5} [/tex]

Option B is the correct answer.

The correct answer to the given question is Option B, which is "I would replace the missing values with the average value of that specific variable."What are Data Preparation activities?Data preparation activities consist of operations that change the quality, consistency, or completeness of data. These are performed to improve the data's accuracy and, as a result, the resulting insights.When it comes to numerical data, there are certain techniques you can use to deal with missing data. There are many ways to deal with missing numerical data, but one of the simplest is to use the mean or median value of the dataset to replace the missing values. This method is also known as mean imputation.Therefore, if during the data preparation activities, you have identified a small amount of missing numerical data, you should replace the missing values with the average value of that specific variable. Therefore, Option B is the correct answer. The other options such as excluding all observations with missing data, excluding all variables with missing data, and none of the above is true are not accurate.

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Answer: 9

Step-by-step explanation: sorry if it is wrong

Answer:

0

Step-by-step explanation:

2p - (p + 3) + 3

2(6) - (6 + 3) + 3

12 - (9) + 3

12 - 12 = 0

The correct response, based on the facts provided, is 625.

What does a math power mean?

When a base number is raised to an exponent in mathematics, the exponent represents how many times the base number has been multiplied, and the base amount is the factor that is multiplied by itself.

What do you call 5 to the power of?

In mathematics and mathematics, the fifth power, or subsolid, of a number, n, is obtained by multiplying five occurrences of n around each other:[tex]n⁵ = n × n × n × n × n.[/tex]The fourth power of a number or the squares of a number of times its cube can also be used to create fifth powers.

5 to the fourth power (also written as 5⁴) is:

[tex]5 × 5 × 5 × 5 = 625[/tex]

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√3/2  and √3x / x.

The value of sin (cos-1 (1/2)) and tan (sec-1 (x/3)) are:Sin (cos-1 (1/2)):In the trigonometry section, the cosine inverse (or arccosine) is used to find the angle whose cosine value is equal to a given number.The cosine inverse (or arccosine) of a number is the angle whose cosine is equal to that number (cos-1). Therefore, cos-1 (1/2) represents the angle that has a cosine of 1/2.The sine is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.Sin (cos-1 (1/2)) = sqrt (1 - cos2 (cos-1 (1/2)))Since cos (cos-1 (1/2)) = 1/2, we can substitute it.Sin (cos-1 (1/2)) = sqrt (1 - (1/2)2) = sqrt (3/4) = √3/2Tan (sec-1 (x/3)):The secant inverse (or arcsecant) is used to find the angle whose secant value is equal to a given number.The secant inverse (or arcsecant) of a number is the angle whose secant is equal to that number (sec-1). Therefore, sec-1 (x/3) represents the angle that has a secant of x/3.The tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.Tan (sec-1 (x/3)) = sqrt (sec2 (sec-1 (x/3)))Since sec (sec-1 (x/3)) = 3/x, we can substitute it.Tan (sec-1 (x/3)) = sqrt (3/x) = √3 /√x = (√3 /√x) × (√x /√x) = √3x / xTherefore, sin (cos-1 (1/2)) = √3/2 and tan (sec-1 (x/3)) = √3x / x.

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The value of the stock needs to go up by 42.86% to be equal to what the investor first paid for it.

Let's say the investor initially paid $100 for the stock. A 30% decrease in the value of the stock would mean it is now worth $70. To bring the value of the stock back up to $100, it needs to increase by $30, which is 42.86% of the current value ($30/$70).

Therefore, the value of the stock needs to go up by 42.86% from its current value for the investor to break even.

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Add "Spade" to the Card column, with branches to "Even" and "Odd" in the Die column. Thus, option 3 is correct.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο cοmplete the tree diagram, we need tο add the missing branch fοr the spades suit in the card cοlumn.

Here is the cοmpleted tree diagram:

We have added the missing branch fοr the spades suit, which alsο branches intο even and οdd fοr the die rοll. We have alsο filled in the οutcοmes fοr each branch οf the tree, which include the pοssible values fοr the card (2, 3, 4, 5, 6, οr 1 fοr Ace) and the die rοll (even οr οdd).

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The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.

The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.

The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.

To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.

So the function f(w) representing the remaining area, in square meters, is:

f(w) = 2w² - (w² + 6w)

f(w) = 2w² - w² - 6w

f(w) = w² - 6w

Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.

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Complete question:

A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.

1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.

2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.

Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?

The value of z can be determined by solving the equation 7z-94 = 2z+76, which yields z=35.

To determine the value of z in the given equation, it is necessary to solve the equation 7z-94 = 2z+76. Begin by subtracting 2z from both sides of the equation, which yields 7z-2z-94 = 76. Simplifying this yields 5z-94 = 76. To solve for z, add 94 to both sides of the equation, which yields 5z = 170. Dividing both sides by 5 yields z = 34. Since the equation is not asking for an exact value, it can be rounded to the nearest whole number, which is 35. Therefore, the value of z is 35.

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The probability that exactly 5 of the invoices will be paid within ten working days is 19.34% or 0.1934.

This is a binomial distribution problem, with n = 12 (the sample size) and p = 0.5 (the probability of success, which is an invoice being paid within ten working days). We want to find the probability that exactly 5 of the invoices will be paid within ten working days.

Using the binomial probability formula, the probability of exactly 5 invoices being paid within ten working days is:

P(X = 5) = (12 choose 5) * (0.5)^5 * (1-0.5)^(12-5) = 0.1934

Where (12 choose 5) is the binomial coefficient, which represents the number of ways to choose 5 invoices from a sample of 12.

Therefore, the correct answer is 0.1934 rounded to four decimal places.

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Answer:

14

Step-by-step explanation:

6/9 = x+2/24

Cross multiply to expand

9( x + 2) = 24x 6

9x + 18 = 144

Subract 18 from both sides

9x = 126 Divide both sides by 9

X = 14

10/ 2x-9 = 20/9

Cross multiply

20( 2x - 9) = 10 x 9

40x - 180 = 90

Add 180 to both sides

40x = 270

Divide both sides by 40

X = 6.75

Scale question

Convert 240miles to inches

240 x 63, 660 = 15,206,400

Ratio is 3:15,206,400

Reduce to lowest term by divide both sides by 3

Scale is 1: 5068800

The amount in the account after 5 years would be $137.

Continuous compound interest is a method of calculating the interest earned on a principal amount that is continuously reinvested

We can use the formula for continuous compound interest:

A = Pe^(rt)

where:

A = final amount

P = principal amount

e = Euler's number (approximately 2.71828)

r = annual interest rate (as a decimal)

t = time in years

In this case, we have:

P = $110

r = 0.041 (4.1% expressed as a decimal)

t = 5 years

Substituting these values into the formula, we get:

A = 110e^(0.0415)

A ≈ $136.69

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The population density of seals is 0.0111 seals/m³.

To calculate the number of meters of tiles needed to purchase, we must first calculate the area of the pool. This can be done by multiplying the length by the width:

9m x 4m = 36m²

We then multiply this area by the depth of the pool to get the total volume:

36m² x 2.5m = 90m³

Now, to calculate the number of meters of tiles needed, we must divide the total cost of the tiles, including installation, by the cost of the tiles per meter:

90 pesos + 50 pesos = 140 pesos

140 pesos ÷ 90 pesos = 1.55 meters

Therefore, 1.55 meters of tiles must be purchased to cover the pool.

To calculate the volume of water for two seals, we must first calculate the volume of the pool, which can be done by multiplying the length by the width and then by the depth:

9m x 4m x 2.5m = 90m³

We then multiply this volume by the number of seals to get the total volume of water needed:

90m³ x 2 seals = 180m³

Therefore, 180m³ of water is needed for two seals to live in the pool.

To calculate the population density of seals, we must divide the total population of seals by the total volume of water needed:

2 seals ÷ 180m³ = 0.0111 seals/m³

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The expression of the dimensions are 3w - 2 by w

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

The length of a rectangle is 2 less than 3 times as long as the width

Using the following variable definitions, we have

Based on the given information, we can express the length (l) in terms of the width (w):

l = 3w - 2

Hence, the dimensions are 3w - 2 by w

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The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.

To determine which one is correct, you would need to know the radius or diameter of the circle.

Use the formula for the area of a circle, which is

A = πr²,

where A is the area and

r is the radius.

If you have the radius, plug it into the formula and calculate the area.

Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)

to determine which one is closest to the area of Circle B.

Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the

options given.

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Answer:

4+3=7

4/7*72/1=288/7=41.1

3/7*72/1=216/7=30.9

41.1:30.9=4:3

The perimeter of the triangle present in above figure is 42 dm. Then the value of x is equals to the 9 dm and all three sides of triangle are 9 dm, 11 dm and 22 dm.

We have a triangle present in above figure. The perimeter is the length of the boundaries of a shape. A triangle is a type of polygon with three sides. In other words, it is a closed two dimensional shape having three straight sides. So, perimeter of a triangle = sum of all three sides. Here, perimeter of triangle = 42 dm

Now, first side length of triangle= (3x - 5 ) dm

Second side length = (x + 2) dm

Third side length = x dm

Now, using perimeter formula for triangle,

=> 3x - 5 + x + x + 2 = 42

=> 5x = 42 + 5 - 2 = 45

=> x = 45/5 = 9

3x - 5 = 22 dm

x + 2 = 11 dm

So, sides of triangle are 9 dm, 11 dm and 22 dm.

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Complete question :

The perimeter of the triangle is 42 dm. By determining the measure of its sides, he obtains that the value of x is _? see the above figure

The length of MN is equal to: 32.2 ft.

In Mathematics, Pythagorean's theorem is modeled by the following mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the length of sides of a right-angled triangle.

In order to determine the length of MN in right-angled triangle LNM, we would have to apply Pythagorean's theorem.

LN² + MN² = LM²

16² + MN² = 36²

256 + MN² = 1,296

MN² = 1,296 - 256

MN² = 1,040

MN = √1,040

MN = 32.2 ft.

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Each visit, Olivia ordered a sandwich and left a $2. 25 tip. She spent a total of $39. Therefore, an equation that represents this situation, if c represents the cost of a salad is  4(x+2.25) = 39.

Equation:

An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages ​​may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.

According to the Question:

Let the cost of each salad = c

Therefore we can write

    4(x+2.25) = 39

or, x+ 2.5 = 39

or, x = 39 − 2.5

or, x = 39 − 2.5

or, x = 26.5

Therefore, The equation that represents this situation, if c represents the cost of a salad is 4(x+2.25) = 39.

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It is not possible to determine the relationship between the two variables based on this scatterplot.

The scatterplot below does not show a good candidate for linear regression because the points do not follow a clear pattern. There is no consistent trend that shows a correlation between the X and Y variables. Therefore, it is not possible to determine the relationship between the two variables based on this scatterplot.The linear regression is a statistical technique that enables the analysis of relationships between two or more continuous variables. The method attempts to find the line of best fit, which represents the overall relationship between the two variables. A scatterplot, which is a graphical display of a dataset, can be used to determine whether two variables are good candidates for linear regression.In order for two variables to be a good candidate for linear regression, they must have a strong positive or negative correlation. In other words, the points on the scatterplot must follow a clear pattern that shows a linear relationship between the X and Y variables. If there is no clear pattern or the points are randomly scattered, then it is not possible to determine the relationship between the two variables based on a linear regression model.

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Answer:

Option C) is the correct answer.

The domain of the given function H (t) is 0 ≤ t ≤ 40.

What is the domain of a function?

The collection of all the values for which a function is defined is known as the domain of that function.

We are given that the height of a model rocket, H (t) is a function of time since it was launched, t.

From the graph, we can see that the value of t is represented on the x- axis is ranging from 0 to 40.

Hence, the domain of the given function H (t) is 0 ≤ t ≤ 40.

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For the standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.

The amount of cardboard needed to make a banner depends on the size of the banner. If we know the dimensions of the banner, we can calculate the area of cardboard needed.

Assuming that the banner is a rectangle, let's say its width is w inches and its height is h inches.

Then, the area of the banner can be calculated as:

Area = width x height

Area = w x h

To find out how many square inches of cardboard are needed, we need to add a margin to the dimensions of the banner to account for the thickness of the cardboard. Let's say the margin is m inches.

Then, the width of the cardboard needed is (w + 2m) inches, and the height of the cardboard needed is (h + 2m) inches.

The area of the cardboard needed can be calculated as:

Area of cardboard = (width of cardboard) x (height of cardboard)

Area of cardboard = (w + 2m) x (h + 2m)

So, the total area of cardboard needed for one banner is:

Total area of cardboard = Area of cardboard + Area of margin

Total area of cardboard = (w + 2m) x (h + 2m) + 4m(w + h + 2m)

if we assume that the banner is 2 feet wide (24 inches) and 4 feet long (48 inches), and we add a margin of 1 inch on each side, then we can calculate the total area of cardboard needed as follows:

Total area of cardboard = (24 + 2) x (48 + 2) + 4(1)(24 + 48 + 2)

Total area of cardboard = 26 x 50 + 4(74)

Total area of cardboard = 1300 + 296

Total area of cardboard = 1596 square inches

So, for this standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.

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The current flows through the element with resistance of an electric stove burner element is 11 ohms when it runs off a 220 volt line is equals to the 20 Ampere.

The resistance of an electric stove burner element is, R = 11 ohms.

The magnitude or amount of potential

difference in a line that is voltage V

= 220 V.

We have to determine the value current flows through this element.

According to ohm's law : If all physical conditions and temperature remain constant, the voltage across a conductor is proportional to the current flowing through it. The expression is, V = I x R

here, I-> the amount of current

V--> potential difference

R--> resistance

The current value flowing through the element is written by I = V/R

=> I = 220 V/11 ohms

=> I = 20 A

Hence, the required current value is 20 A.

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the value of a is -7/4.

Simply change x in the original equation to -1/4 to determine the value of a:

y = 4x² - 7x - 2

y = 4(-1/4)² - 7(-1/4) - 2

y = 1 - (-7/4) - 2

y = 1/4 - 2

y = -7/4

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

from the question:

We must discover a solution for x before we can find the solutions to the equation y = 4x2 - 7x - 2. By calculating the quadratic equation while putting y equal to zero, we can achieve this:

4x² - 7x - 2 = 0

(4x + 1)(x - 2) = 0

This quadratic equation has two solutions:

4x + 1 = 0 or x - 2 = 0

4x = -1 or x = 2

x = -1/4 or x = 2

As a result, the equation has solutions a = -1/4 and b = 2, where a b.

Simply change x in the original equation to -1/4 to determine the value of a:

y = 4x² - 7x - 2

y = 4(-1/4)² - 7(-1/4) - 2

y = 1 - (-7/4) - 2

y = 1/4 - 2

y = -7/4

Therefore, the value of a is -7/4.

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An item is regularly priced at 70. Shen bought it on sale for 20% off the regular price. Shen paid 56 for the item on sale.

To determine how much Shen paid for the item on sale, follow these steps:

Find the discount amount

Subtract the discount amount from the regular price.

Calculate the discount amount.

Discount amount = Regular price × Discount percentage

Discount amount = 70 × 20%

Discount amount = 70 × 0.20

Discount amount = 14

Calculate the sale price.

Sale price = Regular price - Discount amount

Sale price = 70 - 14

Sale price = 56

Shen paid 56 for the item on sale.

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