A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,
6.7 km apart, to be 38° and 41°, as shown in the figure.
A
NOTE: The picture is NOT drawn to scale.
38°
6.7 km
41°
B
What is the elevation of the plane in meters? Give your answer to the nearest whole number.
height=
meters

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.

From point A, we can use tangent function to find x:

tan(5°) = (119 + h) / x

From point B, we can use tangent function again to find y:

tan(18°) = (119 + h) / y

We want to find the distance between point A and point B, which is the difference between x and y:

distance AB = y - x

We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:

h = x tan(5°) - 119

tan(18°) = (119 + x tan(5°) - 119) / y

tan(18°) = x tan(5°) / y

y = x tan(5°) / tan(18°)

distance AB = y - x = x (tan(5°) / tan(18°) - 1)

Now we can plug in the values and use a calculator to find the distance:

distance AB = x (tan(5°) / tan(18°) - 1)

distance AB = x (0.107 - 1)

distance AB = -0.893 x

Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:

x = distance AB / -0.893

Using a calculator, we get:

x ≈ 181.74 feet

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

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Answer:

16

Step-by-step explanation:

Find an equivalent fraction which is 6/16.

The two-column proofs of the line segments are shown below

Given that

HI = 13

IJ = 13

IJ ≅ JH

The proof is as follows

Statement                                                Reason

HI = 13, IJ = 13, IJ ≅ JH                            Given

HI ≅ IJ                                                      Substitution property

HI ≅ JH                                                    Substitution property (proved)

Given that

AL = SK

The proof is as follows

Statement                                                Reason

AL = SK                                                    Given

AL + LS = AS                                            Point–line–plane postulate

LS + SK = LK                                            Point–line–plane postulate

LS + AL = LK                                            Substitution property

AS = LK                                                    Point–line–plane postulate

                                                                (proved)

Given that

DG = 11

GF = 11

GF ≅ EF

The proof is as follows

Statement                                                Reason

DG = 11, GF = 11, GF ≅ EF                        Given

DG ≅ GF                                                   Substitution property

DG ≅ EF                                                    Substitution property (proved)

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Answer:

To find the slope of a line parallel to 5x - 2y = 2, we need to first rearrange the equation in slope-intercept form, y = mx + b, where m is the slope of the line. 5x - 2y = 2 -2y = -5x + 2 y = (5/2)x - 1 The slope of the line is 5/2. Since we are looking for a line parallel to this line, the slope of the parallel line will be the same as the slope of the original line, which is 5/2. Therefore, the slope of a line parallel to 5x - 2y = 2 is 5/2.

Answer:

I think it will be

y=1/3x+0

Answer:

f(x) = -(x-3)+7

Step-by-step explanation:

Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.

What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?

Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.

Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:

AW = AY (given)

AZ = AX (given)

WY = XZ (as WY and XZ bisect each other)

Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.

Since opposite sides are congruent, we have WX || YZ.

Similarly, we can show that WZ || XY.

Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.

Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."

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The probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

According to the First Principle of Probability, the outcomes of one chance occurrence have no bearing on those of succeeding chances occurrences. Thus, the chance of getting heads the second or third time you flip it stays at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.

The Bayes Theorem asserts that the likelihood of a second tournament given the first occurrence multiplied by the odds of the first event equals the conditional event's likelihood depending on the presence of another event.

The probability of rolling a number other than 1 or 5 on a fair die is 4/6 or 2/3, since there are four favorable outcomes (2, 3, 4, 6) out of six possible outcomes.

To find the probability of rolling no 1 and no 5 in five rolls, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each roll, the probability of rolling a number other than 1 or 5 is 2/3. Therefore, the probability of rolling no 1 and no 5 in five rolls is:

(2/3) * (2/3) * (2/3) * (2/3) * (2/3) = (2/3)⁵ ≈ 0.131

Rounding to three decimal places, the probability is approximately 0.131.

Therefore, the probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

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201.5 is the smallest average of 200 different positive and odd integers.

Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.

The average of this set is (1+3+5+...+397+399+401)/200 = 201.

Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.

One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.

The new set is {1, 3, 5, ..., 397, 399, 403}.

The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.

Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.

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The calculated value of the expression 2x - y for the given values of x and y is 9/2.

We are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.

This means that

x = 7/2 and y = 5/2

We can start by substituting the given values into the expression:

2x - y = 2(7/2) - (5/2)

Notice that since 2x = 7, then x = 7/2.

Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:

2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2

Therefore, the value of 2x - y is 9/2.

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Answer:

the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Step-by-step explanation:

The perimeter of the paperboard that remains after the semicircle is removed is equal to the sum of the four sides of the rectangular portion of the paperboard plus half the circumference of the semicircle.

The rectangle has dimensions of length = 20 inches and width = 12 inches. Therefore, the sum of the four sides of the rectangular portion of the paperboard is:

2(20) + 2(12) = 64 inches

The semicircle has a diameter equal to the width of the rectangle, which is 12 inches. Therefore, the radius of the semicircle is half the diameter, or 6 inches. The circumference of a full circle with a radius of 6 inches is:

2 * 3.14 * 6 = 37.68 inches

Half of the circumference of the semicircle is:

(1/2) * 37.68 = 18.84 inches

Therefore, the perimeter of the paperboard that remains after the semicircle is removed is:

64 + 18.84 = 82.84 inches

Thus, the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Answer:

145°

Step-by-step explanation:

∠1 + ∠2 = ∠3

5x + (4x + 10) = 10x - 5

9x + 10 = 10x - 5

10x - 9x = 10 + 5

x = 15

∠3 = 10x - 5 = 10(15) - 5 = 150 - 5 = 145

To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.

For the ordered pair (-4, y):

y = -3(-4) - 4

y = 12 - 4

y = 8

So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.

For the ordered pair (x, 2):

2 = -3x - 4

6 = -3x

x = -2

So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.

The value of x using Pythagoras theorem to solve the diagram is 1.25 m.

Pythagoras theorem states that the square of the hypotenus in a right angled triangle is equal to the sum of the of the two other sides.

To solve for x we use pythagoras theorem in the diagram below.

Formula:

From the diagram,

Substitute these values into equation 1 and solve for x

Hence, x is 1.25 m.

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(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.

(b) The probability of all three cards being literature questions is 2.4%.

(c) 5%.

Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.

(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.

To calculate this probability, we use the formula

P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.

(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.

The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.

(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.

The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.

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Each of the value of x in the diagram above are as follows

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.

Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;

x = 141° (alternate interior angles theorem).

x = 39° (corresponding angles).

x + 169 = 180

x = 180 - 169 = 21°.

x = 88° (vertically opposite angles).

x = 180°- 82°

x = 98°

x + 41 = 180

x = 180 - 41 = 139°.

x + 117 = 180

x = 180 - 117 = 139°.

x = 102° (vertically opposite angles)

x + 130 = 180

x = 180 - 130 = 50°.

x + 14 = 180

x = 180 - 14 = 166°.

x + 18 = 180

x = 180 - 18 = 162°.

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Answer:

The solid formed by rotating the two-dimensional shape (which appears to be a right-angled triangle) about the line is a cone.

Answer:

identy the solid formed by

The graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

What is graph?

A graph is a data structure consisting of a set of vertices (also called nodes or points) connected by edges (also called arcs or lines). It is used to represent relationships between objects or entities in a system or network. Graphs are commonly used in computer science, mathematics, and other fields where complex data structures need to be analyzed and visualized.

In a graph, each vertex may be connected to one or more other vertices by edges. The edges may be directed (pointing from one vertex to another) or undirected (connecting vertices without a specific direction). A graph can be represented mathematically as a set of vertices and a set of edges that connect them.

To find where the graph of the equation x²-x-2=y crosses the x-axis, we need to find the values of x when y=0.

So, let's set y=0 and solve for x, x²-x-2=0

We can factor this quadratic equation as (x-2)(x+1) = 0

So, the solutions are

x-2=0 or x+1=0

which give:

x=2 or x=-1

Therefore, the graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

So the answer is option D: (-1,0) and (2,0).

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The inequality that models the amount of weight the forklift can carry is: 45x + 70y ≤ 3000

An inequality is a mathematical statement that indicates a relationship between two expressions that are not equal. It uses comparison symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two expressions.

The total number of boxes that a forklift can carry is x + y.

The total weight that the forklift can carry is equal to 45x + 70y pounds, which is less than or equal to 3000 pounds.

Therefore, the inequality that models the number of boxes the forklift can carry is:

x + y ≤ 60

The inequality that models the amount of weight the forklift can carry is:

45x + 70y ≤ 3000.

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The equatiοn has nο sοlutiοn.

An equatiοn is defined as a mathematical statement in algebra that prοves the equality οf twο mathematical expressiοns. Fοr example, the fοrmula 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the wοrd "equal."

Here the given equatiοn is ,

=> |4x-4(x+1)|=4

Nοw simplifying the equatiοn then,

=> 4x-4(x+1)=± 4

=> 4x-4x-4=±4

=>-4=±4

Hence the given equatiοn has nο sοlutiοn.

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The probability that both students selected are males is 0.46.

The multiplication rule of probability for independent events states that the probability of two or more independent events occurring together is the product of their individual probabilities.

If event A has probability P(A) and event B has probability P(B), and A and B are independent events, then the probability of both A and B occurring  

P(A and B) = P(A) x P(B)

Here we have

There are 13 males and 6 females in the class, for a total of 19 students.

The probability of selecting a male on the first draw is 13/19.

After one male has been selected,

There are 12 males and 6 females left in the class.

The probability of selecting another male on the second draw = 12/18

[ Since there is one less student in the class and one less male]

The probability of selecting two males in a row is the product of the probabilities of each individual event:

P(male and male) = P(male on the first draw) x P(male on the second draw | male on the first draw)

= (13/19) x (12/18)

= 0.456 or approximately 0.46 (rounded to two decimal places).

Therefore,

The probability that both students selected are males is 0.46.

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Step-by-step explanation:

As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.

Here is the salary function used to represent this situation in terms of the amount of merchandise sold:

s(x) = 0.23x + 200

Find Alysse's salary when she sells $2,200 worth of merchandise.

Answer:

E

Step-by-step explanation:

[tex]3(p - 4) = 2(p + 1)[/tex]

Multiply every term inside the bracket by the term on the outside:

[tex]3p - 12 = 2p + 2[/tex]

Collect like-terms (also, moving the term to the other side changes its sign to the opposite of the previous one):

[tex]p = 14[/tex]

EXPLANATION

step 1. 3×p - 3×4 = 2×p + 2×1 ( brackets means × or multiplication )

step 2. 3p - 12 = 2p + 2 ( collect like terms )

step 3. -2p - 3p = 2 + 12 ( calculate the like terms and when we calculate them it would not be multiplication or division )

step 4. -1p = 14 ( answering look like this )

step 5. -1p/ 1 = 14/1 ( divided it by the number to get the variable )

step 6. p = 14 ( finally answer the question and check it all your calculate )

If you think you are brilant do not run for only the answer, but check up and understand it how it come.

ANSWER

(E) 14

Answer:

the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points

Answer:  4,258,375

Step-by-step explanation:

The point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

The distance formula is a mathematical formula used to calculate the distance between two points in a two or three-dimensional space. It is derived from the Pythagorean theorem and is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Where d represents the distance between the two points, (x1, y1) and (x2, y2) represent the coordinates of the two points in a two-dimensional space.

To determine if the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9), we need to calculate the distance between the center of the circle and the point (3, 7), and compare it to the radius of the circle.

Let's first find the radius of the circle. Since the circle contains the point (-1, 9), the distance between the center of the circle and (-1, 9) is equal to the radius. Using the distance formula, we get:

radius = √[(9 - 4)² + (-1 - (-1))²] = √[25] = 5

Now let's find the distance between the center of the circle (-1, 4) and the point (3, 7):

distance = √[(7 - 4)² + (3 - (-1))²] = √[3² + 4²] = 5

We see that the distance between the center of the circle and the point (3, 7) is equal to the radius of the circle. Therefore, the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

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The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4

ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.

By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:

α + β = -c/6

And the prοduct οf the rοοts is given by:

αβ = 4/6 = 2/3

We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:

αβ = α + β + 2

Substituting the values we knοw, we get:

2/3 = -c/6 + 2 + α + β

Simplifying this expressiοn, we get:

2/3 = -c/6 + 2 - c/6

Multiplying bοth sides by 6, we get:

4 = -c + 12 - c

Simplifying, we get:

2c = 8

c = 4

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Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

The equation that Sharon can use to find c is

                               300(c-0.20)= 180

The average amount the cable company charges per channel was $0.8.

An equation is a mathematical statement which can be constructed by two expressions connected by an sign which is called equal '=' sign to find out the value of unknown variable.

For example, 3x – 11 = 16 is an equation. Solving this equation, we get the value of x as x = 9.

Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.

Let us take in previous case the bill was $c for one channel.

so for 300 channels it will be $300c.

If Sharon has for $0.20 less per channel

Then price per channel will be $(c-0.20)

For 300 channels it will be $300(c-0.20)

It equals to $180

so equating both values we get the  equation and the equation will be,

          300(c-0.20)= 180

The equation that Sharon can use to find c is

                               300(c-0.20)= 180

To find the average amount we will solve c from the equation.

                                  300(c-0.20)= 180

                                ⇒ c-0.20 = 180/300 [ dividing both sides by 300 we get]

                                 ⇒ c- 0.20 =0.6

                                  ⇒ c= 0.8 [ Adding both sides 0.20 we get]

 Hence, The average amount the cable company charges per channel was $0.8.  

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