There is a linear relationship between the number of stuffed animals and the number of action figures displayed at the prize booth at a fair.

When 20 stuffed animals are displayed, 15 action figures are also displayed.

When 60 stuffed animals are displayed, 45 action figures are also displayed.

Graph the linear relationship between the number of stuffed animals, x, and the number of action figures, y. Then, use the point tool to indicate whether the relationship is proportional or not.

Answer:

Step-by-step explanation:

The number of partitions possible for a set A with n elements is given by the Bell number, denoted as Bn.

For a set A = {a, s, i, m, o, v} with 6 elements, the number of partitions possible is given by the 6th Bell number, which can be computed as follows:

B6 = ∑k=1 to 6 {6 choose k} * Sk

where Sk is the Stirling number of the second kind, which counts the number of ways to partition a set of n elements into k non-empty subsets.

Using this formula, we can compute the Bell number for n = 6 as follows:

B6 = {6 choose 1} * S1 + {6 choose 2} * S2 + {6 choose 3} * S3 + {6 choose 4} * S4 + {6 choose 5} * S5 + {6 choose 6} * S6

S1 = 1, S2 = 15, S3 = 25, S4 = 10, S5 = 1, S6 = 0 (using a table of Stirling numbers)

B6 = (6 choose 1) * 1 + (6 choose 2) * 15 + (6 choose 3) * 25 + (6 choose 4) * 10 + (6 choose 5) * 1 + (6 choose 6) * 0

= 1 + 90 + 200 + 150 + 6 + 1

= 448

Therefore, there are 448 possible partitions of the set A = {a, s, i, m, o, v}.

The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70

To calculate the cost of gasoline for the old truck, we can use the following formula:

Cost of gasoline = Price per gallon × Number of gallons used

Given that

Price per gallon = 3.74

Number of gallons used = 5 gallons

We have

Cost of gasoline = $3.74/gallon × 5 gallons

Evaluate

Cost = $18.70

Hence, the cost is $18.70

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Complete question

An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon

Answer:

Step-by-step explanation:

To find the equilibrium quantity and equilibrium price for the demand and supply functions, we need to find the point where the quantity demanded and the quantity supplied are equal. This point is known as the equilibrium point and is represented by the intersection of the demand and supply curves.

The demand function is given by p = -0.1q²-0.2q+9, and the supply function is given by p = 0.2q²+0.4q+1.8.

To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied:

-0.1q²-0.2q+9 = 0.2q²+0.4q+1.8

Simplifying and rearranging the terms, we get:

0.3q² + 0.6q - 7.2 = 0

Using the quadratic formula, we can solve for q:

q = (-0.6 ± √(0.6² - 4(0.3)(-7.2))) / (2(0.3))

q = (-0.6 ± √(0.6² + 8.64)) / 0.6

q = (-0.6 ± √9.36) / 0.6

q = (-0.6 ± 3.06) / 0.6

q = 4.6, -5.0

Since the quantity cannot be negative, the equilibrium quantity is q = 4.6.

To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply function:

p = 0.2q²+0.4q+1.8

p = 0.2(4.6)²+0.4(4.6)+1.8

p = 7.82

Therefore, the equilibrium quantity is 4.6 units and the equilibrium price is $7.82.

Since the graph is constant, the function is not changing within any interval. Therefore, there are no intervals where the function is changing.

In mathematics, a graph is a visual representation of a set of objects and the relationships between them. Graphs are widely used in many areas, including mathematics, computer science, engineering, social sciences, and more.

A graph consists of two main components: vertices (also known as nodes) and edges. The vertices represent the objects, and the edges represent the connections or relationships between them. The edges can be directed or undirected, meaning they can be one-way or two-way relationships.

There are many types of graphs, including:

Undirected graphs: Graphs in which edges have no direction.

Directed graphs: Graphs in which edges have a direction, often represented by arrows.

Weighted graphs: Graphs in which edges have weights or values, representing some kind of numerical data.

Bipartite graphs: Graphs in which the vertices can be divided into two distinct sets, with edges only connecting vertices in different sets.

Complete graphs: Graphs in which every vertex is connected to every other vertex by an edge.

Graphs are used to model and analyze various kinds of data, such as social networks, transportation systems, financial transactions, and more. They are also used in algorithms and data structures, such as shortest path algorithms and tree data structures. In addition, graphs are often visualized using software tools to help people better understand complex relationships and patterns in data.

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The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The length of the rectangle is 0.9 cm.

The width of the rectangle is 0.4 cm.

The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.

The area of the rectangle is:

A = (l)(b)

Substituting the values:

A = (0.9)(0.4)

A = 0.36 sq. cm.

The area of the circle is:

A = πr²

A = (3.14)(0.2)²

A = 0.1256 sq. cm.

The area of the shaded portion is:

Area of shaded portion = area of rectangle - area of circle

Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm

Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

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The amount paid with discount for the laptop is $ 660.

Discount is the amount of money removed from the price of an object being sold.

Amount paid is the total cost of an item.

Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.

First, we need to know how much discount is given.

Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150

Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60

So, the total amount paid is T =  price - discount + tax

= $ 750 - $ 150 + $ 60

=  $ 660

So, the amount paid is $ 660.

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All of the solutions of the given system of linear inequalities above include the following:

A. (0, 3).

C. (6, 2)

E. (0, -1)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear inequalities.

In this scenario, we can reasonably infer and logically deduce that the solution to the given system of linear inequalities is the shaded region and it lies in both quadrant I and quadrant IV with the following ordered pairs:

Ordered pair = 0, 3).

Ordered pair = (6, 2)

Ordered pair = (0, -1)

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Answer:

Step-by-step explanation:

(2x + 3)(3x - 2) + (3 - 4x)(2x + 3) - 4x² + 9     FOIL the first and second set of parentheses.

6x² - 4x + 9x - 6 + 6x + 9 - 8x² - 12x - 4x² + 9   Combine like terms

-6x² - x + 12     Factor.

(-3x + 4)(2x + 3)

1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

∠LMN = ∠BMN + ∠LMB (linear angles)

59x + 3 = 160 + (-1 + 7x)

59x - 7x = 160 - 1 - 3

52x = 156

x = 156/52 = 3

The discounted price per yard for ribbons and for fabrics is A. Ribbon costs $ 1. 50 per yard and fabric costs $ 5. 75 per yard.

You can find the discounted price by using the options and then multiplying the prices given, by the purchases of Gwen and Penelope to find out which price is right.

If the discounted price of ribbons were $ 1.50 per yard and the fabric was $ 5. 75 per yard, then the cost to Gwen would be:

= ( 1. 50 x 6 ) + ( 10 x 5. 75 )

= $ 66. 50

For Penelope :

= ( 1. 50 x 5 ) + ( 8 x 5. 75 )

= $ 53. 50

These are the amounts spent so these are the discounted prices.

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Note that where you have a square with a side of 20dm is inscribed in a circle, the area of the shaded region is At = [tex]\approx[/tex] 257.08dm²

A square is a geometrical shape with four equal sides and four equal angles, each measuring 90 degrees.

In the figure we will determine the area of the shade:

The formula is given as follows:

1/2(Area of the Square) + ∡AB + ∡DC

Note that the above equation subsists because:

i)  the shaded region comprises of two congruent or similar triangles since the diagonals of a Square will bisect each other equally creating 4 congruent triangles.

ii) A square in a circle will always create 4 equal Chords.

Thus, imputing the figures we have:
(20dm)²/2 + [π ((20√2)/2)² - (20dm)²]/4

= 200 + [200π -400]/4
= 200 + (50π -100)
= 100 + 50π

= 257.079632679

[tex]\approx[/tex] 257.08dm²

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Full Question:

A square with a side of 20 dm is inscribed in a circle. Determine the shaded area shown in the figure.

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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Therefore, the rational function whose graph has an x-intercept at x=2.

In mathematics, a function is a rule that assigns to each input value from a set (called the domain) exactly one output value from another set (called the range). In other words, a function is a relationship between two sets of numbers, such that for each input value there is a unique output value. Functions are commonly denoted by an equation that defines the relationship between the input and output variables. For example, the equation y = f(x) defines a function f, where x is the input variable and y is the output variable.

Here,

To identify the rational function whose graph is given below, we need to determine its equation. We know that the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.

We also know that the function is a rational function, which means it can be written as a ratio of two polynomials. The general form of a rational function is:

f(x) = p(x)/q(x)

where p(x) and q(x) are polynomials, and q(x) cannot be zero.

To find the specific equation of the function whose graph is shown, we can use the information about the intercepts to write down two points that are on the graph. We can use these points to set up a system of equations that we can solve for the coefficients of the polynomials p(x) and q(x).

Using the x-intercept, we know that the point (2,0) is on the graph. Using the y-intercept, we know that the point (0,-2/3) is on the graph. So we can set up the following system of equations:

p(2)/q(2) = 0

p(0)/q(0) = -2/3

Since the denominator of a rational function cannot be zero, we know that q(2) and q(0) cannot be zero. This allows us to set up a third equation:

q(x) ≠ 0

Now we can use algebra to solve for the coefficients of p(x) and q(x). We can start by writing the rational function in general form:

f(x) = p(x)/q(x)

and then multiplying both sides by q(x):

f(x)q(x) = p(x)

We can now substitute x=2 and x=0 to get two equations:

f(2)q(2) = p(2) = 0

f(0)q(0) = p(0) = -2/3

We also have the equation q(x) ≠ 0. This means that the denominator cannot have any factors that would make it equal to zero, so we can assume that q(x) has a linear factor of (x - 2), since we know that the graph has an x-intercept at x=2. We can then write:

q(x) = a(x - 2)

where a is some constant.

Now we can substitute this expression for q(x) into the equation f(x)q(x) = p(x) and simplify:

f(x)q(x) = p(x)

f(x)a(x - 2) = p(x)

We can now substitute x=0 and use the equation we found for p(0):

f(0)a(-2) = -2/3

f(0) = 1/3a

Next, we can substitute x=2 and use the equation we found for p(2):

f(2)a(0) = 0

f(2) = 0

Finally, we can substitute these values for f(0) and f(2) into the general form of the rational function and simplify:

f(x) = p(x)/q(x)

f(x) = p(x)/(a(x - 2))

We know that p(x) = f(x)q(x) from the equation we derived earlier, so we can substitute this into the equation above:

f(x) = f(x)(x - 2)/a(x - 2)

We can now cancel the f(x) terms from both sides and simplify:

1 = (x - 2)/a

a = x - 2

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The number of coins Mark have is 48.

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. Therefore, the number of coins Mark have can be calculated as follows:

Let's write the equation for the word problem before solving.

Hence,

let

x = number of coins Mark has

Therefore,

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore,

number of coins Mark have = 48 coins

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The height of the tower is 17.32 meters

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Ical is 10 meters away from a tower [since angle is not given let the angle of the top of the tower be 60°], we need to find the height of the tower, [see the figure attached]

The whole scene is making a right triangle, so using the concept of trigonometric ratios,

We get,

Tan 60° = height of the tower / distance of Ical from the tower

Tan 60° = height of the tower / 10

Height of the tower = 10 × Tan 60°

Height of the tower = 10 × √3

Height of the tower = 10√3

Height of the tower = 10 × 1.73

Height of the tower = 17.32

Hence, the height of the tower is 17.32 meters

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Answer:

f = 648

Step-by-step explanation:

[tex]\frac{f}{24} =27[/tex]

Multiply both sides by 24

[tex]f=648[/tex]

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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The triangle whose sides are √13, 6, and 7, is a right triangle.

What is the right triangle?

A right triangle is defined as a triangle with one right angle or two perpendicular sides. The longest side of a right triangle is called the hypotenuse.

Pythagorean Theorem :

The square on the hypotenuse is equal to the total of the squares on the legs of a right triangle.

Mathematically, let r be the length of the hypotenuse of a right triangle. Again let p, q be the lengths of other sides of this triangle. By the Pythagorean Theorem,

r² = p² + q².

How to solve this problem?

We just check which triangle's sides follow the above theorem.

Option A (Triangle with sides √13, 6, and 7 ):

13 + 36 = 49

i.e. (√13)² + 6² = 7²

This triangle's sides follow the Pythagorean Theorem.

So, the triangle with sides √13, 6, and 7 is a right triangle.

Option B (Triangle with sides 7, 8, and 13 ):

49 + 64 ≠ 169

i.e. 7² + 8² ≠ 13²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 7, 8, and 13 is not a right triangle.

Option C (Triangle with sides 10, 11, and 12 ):

100 + 121 ≠ 144

i.e. 10² + 11² ≠ 12²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 10, 11, and 12 is not a right triangle.

Option D (Triangle with sides √10, 9, and 8 ):

10 + 64 ≠ 81

i.e. (√10)² + 8² ≠ 9²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides √10, 9, and 8 is not a right triangle.

Therefore the triangle whose sides are √13, 6, and 7, is a right triangle. So, option A is correct.

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The value of the indicated trigonometric ratio cosβ is equal to 11/12.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

In order to determine the magnitude of cosβ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Therefore, we have the following cosine trigonometric function:

cosβ = 22/24

cosβ = 11/12

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Answer:

Δ JKE

Step-by-step explanation:

the figure is a triangle and is named using its vertices.

the vertices are J, K, E

to name the triangle start with any vertex , then in clockwise/ anticlockwise order the other 2 vertices. in this case starting with J , then clockwise for K and E.

in this case then the figure is Δ JKE

Step-by-step explanation:

8/8 in decimal form is equal to 1. To simplify 8/8 to a decimal, you divide the numerator (8) by the denominator (8). This is equal to 1. Therefore, 8/8 simplified into a decimal is 1.

Answer:

When using the number line, you represent subtraction of a negative number with an arrow going to the right. The direction of the arrow indicates the movement of the number line towards the positive side, which is the opposite of the direction of a negative number. Subtraction of a negative number is equivalent to addition of a positive number, so the arrow going to the right represents the addition of the absolute value of the negative number. For example, if you are subtracting -5 from 10, you can represent this on a number line by starting at 10 and drawing an arrow to the right that goes 5 units, ending at 15.

Answer:

When using the number line to represent subtraction of a negative number, you would represent it with an arrow going to the right (or in the positive direction).

For example, let's say you want to represent the following subtraction on a number line:

5 - (-3)

You can start at 5 on the number line and then move to the left by 3 units, since you are subtracting a negative number. However, instead of leaving the arrow pointing to the left to represent the subtraction, you can turn it around and point it to the right, which is the positive direction. This means that you end up at a point that is 8 units to the right of 0 on the number line, which represents the answer of 8.

So, the arrow would go to the right to show the subtraction of a negative number on the number line.

Answer:

slope = 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 24 ) and (x₂, y₂ ) = (0, 0 )

m = [tex]\frac{0-24}{0-6}[/tex] = [tex]\frac{-24}{-6}[/tex] = 4

The t-test statistic of the data is -1.23

To test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3 with a significance level of 0.05, we can use a one-tailed t-test since the sample size is small and the population standard deviation is unknown.

The formula for the t-test statistic is:

t = (x(bar) - μ) / (s / √n)

Where:

x(bar) = sample mean

μ = population mean (null hypothesis)

s = sample standard deviation

n = sample size

Given the sample of six measurements: 2, 3, -1.5, 1.2

First, we need to calculate the sample mean, sample standard deviation, and t-test statistic.

Sample mean (x(bar)) = (2 + 3 - 1.5 + 1.2) / 4 = 1.93

Sample standard deviation (s) = √[(∑(x - x(bar))^2) / (n - 1)]

= √[((2 - 1.93)^2 + (3 - 1.93)^2 + (-1.5 - 1.93)^2 + (1.2 - 1.93)^2 +  / (4 - 1)]

= 1.92

t-test statistic = (x(bar) - μ) / (s / √n)

= (1.93 - 3) / (1.92 / √5)

= -1.23 (rounded to two decimal places)

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Answer:

To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:

g(x) = cos((1/6)x)

To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:

g(x) = cos((1/6)x) - 5

So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.

The solution is, the total surface area is 92 sq. inches.

Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.

here, we have,

Total paper required = total surface area

Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],

Where 'l' is the length, 'b' is the breadth and 'h' is the height

For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]

=2[24 + 6 + 16]

=2[46]

= 92 sq. inches

Hence, The solution is, the total surface area is 92 sq. inches.

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Let's call the position of the plane "P", and the positions of clearing A and clearing B "A" and "B", respectively. We want to find the distance from the plane to clearing A.

First, draw a diagram. The angle of depression to clearing A means that the line from the plane to clearing A makes a 32 degree angle with the horizontal. Similarly, the angle of depression to clearing B means that the line from the plane to clearing B makes a 56 degree angle with the horizontal. We know that the distance between clearings A and B is 5.7 km.

Now, we can use trigonometry to find the distance from the plane to clearing A. Let's call this distance "d". We can set up the following equation:

tan(32) = d/x

where x is the horizontal distance from the plane to clearing A. We can rearrange this equation to solve for d:

d = x tan(32)

Similarly, we can set up an equation for the distance from the plane to clearing B:

tan(56) = (x + 5.7) / d

We can rearrange this equation to solve for d:

d = (x + 5.7) / tan(56)

Now we can set the two expressions for d equal to each other and solve for x:

x tan(32) = (x + 5.7) / tan(56)

x tan(32) tan(56) = x + 5.7

x (0.6561) = x + 5.7

0.6561 x = x + 5.7

-0.3439 x = 5.7

x = -5.7 / 0.3439

x ≈ -16.57

Since the distance from the plane to clearing A is a positive distance, we can ignore the negative solution. Therefore, the distance from the plane to clearing A is approximately:

d = x tan(32) ≈ (-16.57) tan(32) ≈ 9.18 km

Rounding this to the nearest hundredth of a kilometer gives:

d ≈ 9.18 km

Therefore, the distance from the plane to clearing A is approximately 9.18 km.

:)?

Answer:

C

Step-by-step explanation:

If you start by picking a point to plug in you can check easily to see what works.

Lets start with x=pi. If we plug that into all the answer choices,

A. sec(pi/2)+2 = does not exist

B. 1/2sec(2pi) = 1/2

C. 2sec(pi/2) = does not exist

D. 2csc(pi/2) = 1

So, since at pi there is a vertical asymptote it should not exist. So, A or C.

Then pick x = 0, y must be 2.

A. sec(0) +2 = 1+2 = 3

C. 2sec(0) = 2

So, C must be the answer.