A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 13^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

The composite figure consists of two rectangular pyramids, volume is 45 unit³.

Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at its base. If the base of a pyramid is rectangular, then it is called a rectangular pyramid.

Given,

Total height of two rectangular pyramids = 10 units

height of each pyramid is 5 unit.

Base lengths are 9units and 1.5 units.

Both are connected at their bases.

Dimensions are same of both pyramids

Composite figure consists of two rectangular pyramids.

Volume of the composite figure

= 2(length × width × height)/3

= 2(9×1.5×5)/3

= 2(13.5×5)/3

= 2(67.5)/3

= 135/3

= 45 unit³

Hence, 45 unit³ is volume of composite figure, that consists of two rectangular pyramids.

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Answer:A D

Step-by-step explanation:

The total revenue function is 60x.

The total cost function is 35x + 450.

The profit function is 25x - 450.

Since we have a constant selling price of GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item.

Let x be the number of items

Total revenue function =  constant selling price * x

Total revenue function = 60x

Total Cost Function = Variable cost + Fixed cost

Total Cost Function = 35x + 450

Profit function = Total revenue function - Cost function

Profit function = 60x - (35x + 450)

Profit function = 60x - 35x - 450

Profit function = 25x - 450

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The possible set of inequalities are;

x = -3,

x = -1,

x = 1,

x = 3,

x = 5.

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

The critical points of a rational inequality are the x-values at which the inequality changes direction (from "<" to ">" or vice versa). In this case, the critical points are -1, 3, and 4.

To find the complete solution to the inequality, we need to test points on either side of the critical points. For example, if we test a value less than -1, such as -2, and find that it satisfies the inequality, then all values less than -1 also satisfy the inequality. On the other hand, if a value less than -1 does not satisfy the inequality, then no values less than -1 satisfy the inequality.

Therefore, a complete solution to the inequality can be found by testing values around each critical point. A common set of points to test for this purpose is the critical points themselves, and values just less than and just greater than each critical point.

So, a possible set of points to test to find the complete solution to the inequality is:

x = -3,

x = -1,

x = 1,

x = 3,

x = 5.

These points bracket the critical values and allow us to determine which intervals of values satisfy the inequality.

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Answer:

100

Step-by-step explanation:

1.) Plug in the values of x and y into the equation

10(20/2)

2.) Divide 20 by 2

10(10)

3.) Multiply 10 by 10

100

Answer: X axis , Y axis , y=-2

Step-by-step explanation:

The correct answers are: a reflection across the x-axis and a translation 1, unit right,  a rotation of 180° about the origin and a translation of 1 unit left.

To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.

For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.

For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.

Therefore, the correct answers are:

a reflection across the x-axis and a translation 1 unit right

a rotation of 180° about the origin and a translation of 1 unit left.

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Answer:

Step-by-step explanation:

1. measurement of length

2. measurement of area

3. measurement of volume

4. measurement of weight

5. measurement of length

6. measurement of weight

7.measurement of volume

8. measurement of area

Answer:

√2

Step-by-step explanation:

√3 x√2/√3 =√2

Answer:

 [tex]\sqrt{2}[/tex]

explanation:

[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex]

= [tex]\sqrt{2}[/tex]

(Decimal: 1.414214)

The diameter of the pie is approximately 9 inches

What is a diameter ?

Diameter can be defined as the double of the radius

To determine the diameter of the pie, we need to use the formula for the circumference of a circle:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, we are given that the circumference (circumstances) of the pie is 28.26 inches, so we can set up the equation:

28.26 = 2πr

To solve for the radius, we can divide both sides of the equation by 2π:

r = 28.26 / (2π)

r ≈ 4.5

So the radius of the pie is approximately 4.5 inches. To find the diameter, we just need to double the radius:

d = 2r

d ≈ 9

Therefore, the diameter of the pie is approximately 9 inches.

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Answer:

k = 23/7

Step-by-step explanation:

To solve the problem, we can use the fact that the product of the slopes of two perpendicular lines is -1. We can start by finding the slope of the line passing through the points (3, 5) and (k, 12).

slope = (12 - 5) / (k - 3)

We can simplify this expression by multiplying both numerator and denominator by -1:

slope = (-7) / (3 - k)

Now, let's find the slope of the line passing through the points (0, 7) and (2, 10):

slope = (10 - 7) / (2 - 0) = 3 / 2

Since the two lines are perpendicular, we can set the product of their slopes equal to -1:

(-7) / (3 - k) * (3 / 2) = -1

Simplifying this equation, we get:

(7/2) * (3 - k) = 1

Multiplying both sides by 2/7, we get:

3 - k = 2/7

Subtracting 3 from both sides, we get:

-k = 2/7 - 3 = -21/7 - 2/7 = -23/7

Finally, dividing by -1, we get:

k = 23/7

Therefore, the value of k that makes the statement true is k = 23/7.

Answer:

Step-by-step explanation:

m1=y2-y1/x2-x1=12-5/k-3=7/k-3

m2=10-7/2-0=3/2

two lines with slopes m1 and m2 are perpendicular if m1×m2 = -1.

(7/k-3) *3/2=-1

3(7)=-2(k-3)

21=-2k+6

-2k=15

k=-15/2

Suppose that, Au=0 and Av=0. Then, we already have A(u+v)=Au+Av. Now, A(u + v) = Au + Av = 0 + 0 = 0.

Now, let c and d be scalars. Using both parts of Theorem 5, A(cu + dv) = A(cu) + A(dv) = cAu + dAv = c0 + d0 = 0.

A matrix, also known as matrices, is a rectangular array or table with numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of that object. Matrix types are not all associated with linear algebra. In particular, this applies to incidence matrices and adjacency matrices in graph theory.

Unless otherwise stated, all matrices in this article, which focuses on matrices related to linear algebra, represent linear maps or can be viewed as such. The majority of mathematical and scientific disciplines use matrices, either directly or indirectly through the use of geometry and numerical analysis.

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Simplifying the equations will give 3x -1 = 4x, 3x + 18 = 4x + 7 and 7x = 1

Lets simplify each of the equations in order to match with the  equivalent equation from the second set

3x+6=4x+7

Collecting like terms

3x +6 - 7 = 4x

3x -1 = 4x

The second equation

3(x+6)=4x+7

expanding the bracket

3x + 18 = 4x + 7

The third equation

4x+3x=7-6

simplifying the equation

7x = 1

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the coach can form 4 teams of 9 boys and 9 girls each, and there will be 9 players left over who cannot form a complete team.

The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more integers without leaving a remainder.

For example, the GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.

Given by the question.

To form teams with an equal number of boys and girls, we need to find the greatest common divisor (GCD) of 36 and 45.

The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 45 is 3^2 x 5.

The common factors are 3^2 = 9. Therefore, the GCD of 36 and 45 is 9.

This means that the coach can form teams of 9 boys and 9 girls each.

To find out how many teams he can form, we need to divide the total number of boys and girls by the number of players on each team:

Number of teams = Total amount of players / Number of players per team

Number of teams = (36 + 45) / 18

Number of teams = 81 / 18

Number of teams = 4 with a remainder of 9

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Answer:

Step-by-step explanation:

a

Answer:

ITS A

Step-by-step explanation:

The reason why is because that dude up there said the same thing so yeah..

The discrete probability distribution is given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

There are 153 nests, hence the distribution in this problem is constructed dividing each of the amounts by 153, as follows:

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The required solutions of the given system of equation are  x = 1 and y = 1.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

To find the values of x and y that satisfy the system, we need to solve the equations simultaneously:

y = -2x + 3 ... (1)

y = 5x - 4 ... (2)

Setting the right-hand sides of (1) and (2) equal to each other, we get:

-2x + 3 = 5x - 4

Simplifying this equation, we get:

7x = 7

Dividing both sides by 7, we get:

x = 1

Substituting x = 1 into either equation (1) or (2), we get:

y = -2(1) + 3 = 1

Therefore, the only solution that satisfies both equations is x = 1 and y = 1.

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The accumulated amount will be ​$133.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A student invests ​$70 each month in an ordinary annuity with 3% interest compounded monthly.

We know that;

⇒ Simple interest = P × r × t

Where, P is principle amount , 'r' is rate and t is time.

Here, P = $70

r = 3%

n = 30 years

Substitute all the values, we get;

Hence, We get;

⇒ Interest = P × r × t

⇒ Interest = 70 × 0.03 × 30

⇒ Interest = $63

Hence, The accumulated amount will be ;

⇒ P + Interest

⇒ $70 + $63

⇒ $133

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Answer:

The average of all the data is calculated in statistics. 

However, statistics is a field that goes beyond average and is not a complete science of it. 

There are other additional statistical tools. 

which explains how statistics is an extension of mathematics.

The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is; MN/LK||MN.

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we are given that ΔLKN and ΔKNM share the angle at vertex K, and we know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, that means MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, the additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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Answer:

504

Step-by-step explanation:

3780÷7.5=504

504 mph because 504 x 7.5 = 3780

Please give good review. :)

The Taylor series expansion of f(h) = ln(3 - 2h) around h = 0 is given by:

f(h) = f(0) + f'(0)h + R(h)

where f(0) = ln(3), f'(0) = -2/3, and R(h) is the remainder term.

To find the remainder term, we need to take the higher-order derivatives of f(h) and evaluate them at h = 0. We have:

f''(h) = 4/(3(3 - 2h))^2, f'''(h) = -32/(3(3 - 2h))^3, and so on.

Evaluating these at h = 0, we get f''(0) = 4/9 and f'''(0) = -32/27.

Thus, the remainder term can be expressed as:

R(h) = (1/2)f''(xi)h^2 = (1/2)(4/9)(xi)^2h^2 = (2/9)(xi)^2h^2

where xi is some unknown constant between 0 and 4.

Therefore, the first two terms in the Taylor series expansion of f(h) are:

ln(3) - (2/3)h

and the remainder term involves the unknown constant xi, given by R(h) = (2/9)(xi)^2h^2.

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A system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

Let's learn more about math equations in this tutorial.

So, we know that nickels are double quarters.

And nickels are represented by n and quarters are represented by q.

Then, we can write as:
n = 2q

Then, the equation that represents the situation will be:

25q + 5n = 7

Therefore, a system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.

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Answer:

If the ratio of lemon disinfectant to water is 4 oz to one gallon, then we can say that for each gallon of water, we need 4 oz of lemon disinfectant. To find how much lemon disinfectant is needed for 6 gallons of water, we can multiply the amount needed for one gallon by the number of gallons:

4 oz/gallon * 6 gallons = 24 oz

Therefore, we need 24 oz of lemon disinfectant to be added to 6 gallons of water.

Step-by-step explanation:

Answer:

Given: x * 4 oz = 6 gallons.

First, multiply 4 oz and x:

4x = 6 gallons.

Then convert 6 gallons to oz:

4x = 768 oz.

Then divide both sides by 4:

x = 192.

Function to calculate amount of coffee in Dave's system after x hours

= y = 135(0.6)ˣ

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to.

Given,

Dave drinks 12-ounce cup of coffee each morning

One cup has 136 mg of caffeine

caffeine in his system decreases about 40% every hour
In x hours,

Amount of caffeine in his system

y = a(1 - 40/100)ˣ

or

y = 136(1-0.4)ˣ

y = 135(0.6)ˣ

Hence, y = 135(0.6)ˣ is the function to calculate amount of caffeine in system of Dave after x hours.

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First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.

At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

⇒ 9⁶

First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.

The value of the exponent numerical expression 9⁶ will be 531,441.

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The correct question is given below.

What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?

When one and seventy one hundredth is written in decimal form, it would be 1. 71

A single part of something that has been evenly divided into one hundred parts is referred to as a hundredth in mathematics. The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.

This means that when given the number one and seventy One Hundredths in words, then the number, " one " would be written before the decimal and the 71 would be 0. 71 as a hundredth figure.

When put together, this becomes:

= 1 + 0. 71

= 1. 71

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The function is decreasing on the interval (-∞, -2), has a local minimum at x = -2, is increasing on the interval (-2, 2), and is increasing on the interval (2, ∞). The function has a relative minimum at x = 3 (f(3) = -27) and no relative maximum.

Begin by finding the derivative of y.

y' = 3x^2 - 12

Find the critical numbers. (Enter your answers as a comma-separated list.)

To find the critical numbers, we need to solve y' = 0 for x:

3x^2 - 12 = 0

x^2 - 4 = 0

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

So the critical numbers are x = -2 and x = 2.

Test the intervals to determine the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

To test the intervals, we can use a sign chart:

Interval (-∞, -2) (-2, 2) (2, ∞)

y' (-)(-) (-)(+) (+)(+)

y Decreasing Local Min Increasing

So the function is decreasing on the interval (-∞, -2), has a local minimum at x = -2, is increasing on the interval (-2, 2), and is increasing on the interval (2, ∞).

f(x) = x^4 - 4x^3

To find the relative extrema, we need to find the critical numbers and then evaluate the function at those points.

Find the derivative of f(x).

f'(x) = 4x^3 - 12x^2

Find the critical numbers by solving f'(x) = 0 for x.

4x^3 - 12x^2 = 0

4x^2(x - 3) = 0

x = 0 or x = 3

So the critical numbers are x = 0 and x = 3.

Evaluate the function at the critical numbers and the endpoints of the interval to find the relative extrema.

f(-∞) = ∞

f(0) = 0

f(3) = -27

f(∞) = ∞

So the function has a relative minimum at x = 3 (f(3) = -27) and no relative maximum.

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____The given question is incomplete, the complete question is given below:

Find the critical numbers and the open intervals on which the function is increasing or decreasing. Use a graphing utility to verity your results.

y = x^3 − 12x + 2

Step 1: Begin by finding the derivative of y.

y'=

Step 2: Find the critical numbers. (Enter your answers as a comma-separated list.)

x=

Step 3: Test the intervals to determine the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Increasing (___)

Decreasing (____)

2) Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

f(x) = x4 − 4x3

relative max:(____)

relative min:(_____)

The probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, 3 and 5, and 3 or 5 is 33.3%, 6.6%, and 46.7%, respectively.

To find the probability of randomly selecting a number between 1 and 1000 (including both ends), we can count the number of the desired outcomes and divide it by the total number of possible outcomes.

a. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, we can count the number of multiples of 3 between 1 and 1000, and divide by the total number of possible outcomes.

The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 1000 is 999.

999/3 = 333

So there are 333 multiples of 3 between 1 and 1000.

probability = 333/1000 = 0.333 = 33.3%

b. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 and 5, we can count the number of multiples of 15 (the least common multiple of 3 and 5) between 1 and 1000, and divide by the total number of possible outcomes.

The first multiple of 15 is 15, and the last multiple of 15 that is less than or equal to 1000 is 990.

990/15 = 66

So there are 66 multiples of 15 between 1 and 1000.

probability = 66/1000 = 0.066 = 6.6%

c. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 or 5, we can count the number of multiples of 3 or 5 (or both) between 1 and 1000, and divide by the total number of possible outcomes.

To count the number of multiples of 3 or 5, we can add the number of multiples of 3 and the number of multiples of 5, and then subtract the number of multiples of 15 (to avoid double-counting).

The number of multiples of 3 between 1 and 1000 is 333, the number of multiples of 5 is 200, and the number of multiples of 15 is 66.

probability = (200 + 333 - 66)/1000 = 0.467 = 46.7%

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