The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:

1. The number shows the video game sold in 1986at $180.

2.  The function f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.

3.  The vertex of the given parabola is, (h, k) = (6.667, 46.667)

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.  The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 3x² - 40x +180

1. For f(0) put x= 0 we get

f(0) = 3(0)² - 40(0) +180

f(0) = 180

So, the number shows the video game sold in 1986 at $180.

2.  We know that the standard form of the parabola is y=ax²+bx+c.

Also we have  f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.

3.  Comparing the given equation with y = ax² + bx + c, we have

a = 3, b = -40, and c = 180.

So, x-coordinate is, h = -b/2a = - (-40)/ 2(3)

h= 40/6 = 6.667  

and, y-coordinate is, k = 3(6.667)² - 40(6.667) +180 = 46.667.

So, The vertex of the given parabola is, (h, k) = (6.667, 46.667)

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The radian measure of the central angle θ is 5.4 radians.

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To find the probability of selecting the letter "C" or the coin landing tails up, we need to calculate the probability of each event individually and then add the probabilities of the two events together.

The probability of selecting the letter "C" is:

1/5

This is because there are 5 letters in total, A, B, C, D, and E, and "C" is one of them, so the probability of selecting "C" is 1/5.

The probability of the coin landing tails up is:

1/2

This is because there are two possible outcomes when flipping a coin, heads or tails, and since the coin is fair, the probability of getting heads or tails is 1/2.

To find the combined probability of the two events we need to add them together using the rule of "or" in probability which is defined as:

P(A or B) = P(A) + P(B) - P(A and B)

However in this case A and B are mutually exclusive events, meaning they can't happen at the same time. There is no way to have "C" and coin landing tails up at the same time. Then we don't have to subtract P(A and B)

Therefore, the probability of selecting the letter "C" or the coin landing tails up is:

1/5 + 1/2 = 2/5 + 1/2 = 7/10

So the probability of selecting the letter "C" or the coin landing tails up is 7/10

Answer: Yes

Step-by-step explanation: 28/20 Simplified is 1 2/5

Answer:

Yes

Step-by-step explanation:

The scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The rectangle on right hand side is the scaled copy of the original rectangle. The scaled version of the rectangle is given as follows:

[tex]\frac{42}{63} \text{ and } \frac{15}{\frac{45}{2} } = \frac{30}{45}[/tex]

Rationalize the factors to find the scale factor.

Rationalize the factor [tex]\frac{42}{63}[/tex] by multiplying and dividing by 45.

[tex]\frac{(42)(45)}{(63)(45)}[/tex]

[tex]\frac{1890}{2835}[/tex]

Rationalize [tex]\frac{30}{45}[/tex] by multiplying and dividing by 63.

[tex]\frac{(30)(63)}{(45)(63)}[/tex]

[tex]\frac{1890}{2835}[/tex]

Scale factor = [tex]\frac{1890}{2835} = \frac{2}{3}[/tex]

Hence the scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].

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The equation of line segment AB, whose endpoints are A(x, y) = (2, 1) and B(x, y) = (1, - 1.5), is P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.

In this problem we need to determine the equation that described the line segment AB, whose endpoints are points within other two line segments. The location of a point can be found by means of the following formula:

P''(x, y) = P(x, y) + k · [P'(x, y) - P(x, y)], 0 ≤ k ≤ 1

Where:

First, determine the locations of endpoints A and B:

A(x, y) = (- 2, 3) + 0.5 · [(6, - 1) - (- 2, 3)]

A(x, y) = (- 2, 3) + 0.5 · (8, - 4)

A(x, y) = (- 2, 3) + (4, - 2)

A(x, y) = (2, 1)

B(x, y) = (4, 3) + 0.75 · [(0, - 3) - (4, 3)]

B(x, y) = (4, 3) + 0.75 · (- 4, - 6)

B(x, y) = (4, 3) + (- 3, - 4.5)

B(x, y) = (1, - 1.5)

Second, derive the equation of line segment AB:

P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)]

P(x, y) = (2, 1) + k · [(1, - 1.5) - (2, 1)]

P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.

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Answer: The interest rate is 0.16 or 16% ✅

Step-by-step explanation:

The interest rate is the percentage of the principal (the initial amount of money) that is paid as interest over a certain period of time. To find the interest rate in this scenario, we can use the formula:

Interest = Principal x Interest Rate x Time

In this case:

Interest = $12,800

Principal = $40,000

Time = 4 years

So we can set up the equation:

12800 = 40000 x Interest Rate x 4

To find the interest rate, we can divide both sides of the equation by 40000 x 4, which gives us:

12800 / (40000 x 4) = Interest Rate

We can simplify this fraction:

0.16 = Interest Rate

So the interest rate is 0.16 or 16%.

When Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years, the interest rate was 7.5%.

Simple interest is a formula for calculating the amount of interest that will be charged on a sum of money at a specific rate and during a specific time frame.

In contrast to compound interest, where the interest of one year's principal is added to the principal of the following year to calculate the interest, the principal sum in the case of simple interest stays the same.

Simple Interest = [tex]$ \frac{ \text P \times \text R \times \text T}{100}[/tex]

where,

P = Principal,

R = Rate of Interest in % per annum, and

T = Time, in years

Here given that,

Todd made $12,800 in interest, i.e. Simple Interest = 12,800

By placing $40,000 in a savings account, i.e. Principal = 40,000

with simple interest for 4 years, i.e. Time = 4 years

To find, interest rate

Substitute the data into the simple interest formula

[tex]$ \Rightarrow 12,800 = \frac{40,000 \times \text R \times 4}{100}[/tex]

[tex]$ \Rightarrow \text R = \frac{ 12,000 \times 100}{40,000 \times 4}[/tex]

[tex]$ \Rightarrow \text R = \frac{1,200,000}{160,000}[/tex]

⇒ R = 7.5%

Thus, the interest rate was 7.5%.

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The inequality using interval notation is given as 55 < x < 70

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Inequalities are used to show that an expression containing numbers and variables are not equal.

Interval notation involves using parentheses for opened ends and square brackets for closed ends.

Let x represent the allowed height to ride at an amusement park. A person has to be taller than 55 inches but shorter than 70 inches, hence:

55 < x < 70

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He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

A group of twelve is referred to as a dozen and is frequently abbreviated as doz or dz. Given that there are roughly twelve lunar cycles (or months) in each cycle of the sun (or year), the number twelve may be one of the earliest primitive integer groupings.

Twelve is useful because it has the greatest number of divisors among numbers up to its double, a property shared only by the numbers 1, 2, 6, 12, 60, 360, and 2520.

1 dozen = 12

3 dozen = 36

6 eggs costs 150 naira

36 eggs costs 150 naira = 36/6 × 150

                                         = 900 naira

Each egg costs 30 naira, then 36 eggs costs = 36 × 30

                                                                            = 1080 naira

Savings = 1080 - 900 = 180 naira

Thus, He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

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The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer: $180.02

Step-by-step explanation:

The total bill for the food will be $178.84 and then add the tip which is 18% to get the total.  One method of changing the 18% to money wise is 1.18 and then adding the two numbers together to get a total of $180.02.

Answer: Slower

Step-by-step explanation:

Speed is a measure of how quickly an object moves, and it is calculated as distance traveled divided by time. Since Jorge and Zahara's dad traveled the same amount of time but Jorge traveled a shorter distance, it can be inferred that Zahara's dad traveled at a faster speed.

Another way to understand this is that, if Jorge and Zahara's dad were driving at the same speed, they would have traveled the same distance in the same amount of time. However, since Jorge traveled a shorter distance than Zahara's dad, it can be inferred that Jorge was driving at a slower speed.

Answer:

Step-by-step explanation:

The number that represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level is 25.

When the hiker is at an altitude of 25 feet below sea level, he needs to go up 25 feet to reach sea level. This represents a change in altitude of 25 feet, regardless of the direction it is going.

So the number that represents the change in altitude to return to sea level is 25.

Therefore , the solution of the given problem of function comes out to be the correct options  are B, E and F

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is variable  a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function.

Here,

By observing the 1/4 placed ahead of the cubed root symbol, we can get the solution B. Every y value is reduced by a factor of 1/4, bringing it closer to the x axis.

By examining the 3 within the cube root symbol, we can determine solution E. The value is always moved left by that many spaces when we add a digit under the cube root symbol.

Finally, if we look at the 6 at the conclusion, we can locate F. Any integer used as a constant at the conclusion of an equation causes the graph to advance by that too many spaces.

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Both a ray and a line segment have two endpoints . A ray is bounded on one side , but a line segment is not bounded on either side.

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Answer:

456,754

Step-by-step explanation:

A ticker symbol is an abbreviation of one to four letters, which means it can be one letter, two letters, three letters or four letters. Each letter can be any of the 26 letters in the English alphabet, so there are 26 choices for each position.

For one letter ticker symbols:

26 (number of choices for the first letter) * 1 (number of positions) = 26 different possibilities.

For two letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) = 676 different possibilities.

For three letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) = 17,576 different possibilities.

For four letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) * 26 (number of choices for the fourth letter) = 456976 different possibilities.

So, the total number of different stock ticker symbols that are possible is 26 + 676 + 17,576 + 456976 = 456,754.

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

Given

A) f( x+ h ) = 4( x+ h ) - 6

B) f ( x+ h ) - f (x) = 4 (x+ h ) - 6 - 4 (x) - 6

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

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Answer: y=(-5/3)x+8

Step-by-step explanation: earrange 5x+3y=6 in slope intercept form

y=mx=b

5x+3y=6

     3y=6-5x

       y=2-(5x)/3

then slope for a line parallel is -5/3

Use point slope form y-y1=m(x-x1)

plug un values of (x,y) = (6,-2)

and m=-5/3

y-y1=m(x-x1)

y-(-2)=(-5/3)(x-6)

y+2=(-5/3)x+10

y=(-5/3)x+10-2

y=(-5/3)x+8 <-- solution

Answer:

x=-7/6, y=-8/3. (-7/6, -8/3).

Step-by-step explanation:

6x-3y=1

y=-2x-5

-------------

6x-3(-2x-5)=1

6x+6x+15=1

12x+15=1

12x=1-15

12x=-14

x=-14/12=-7/6

y=-2(-7/6)-5=7/3-5=7/3-15/3=-8/3

308 cubic yards of sand will be needed for 280 square yards of surface.

If 1.1 cubic yards of sand are needed for every 100 square yards of surface, we can find the amount of sand needed for 280 square yards of surface using the proportion:

1.1 cu yd / 100 sq yd = x cu yd / 280 sq yd

To find the value of x, we can cross-multiply and solve for x:

1.1 cu yd * 280 sq yd = x cu yd * 100 sq yd

x = 1.1 cu yd * 280 sq yd / 100 sq yd

x = 308 cu yd

So, 308 cubic yards of sand will be needed for 280 square yards of surface.

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Using Simple division, Number of sections that Niquelle create along the trail is 6 sections.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction. Simply write the first fraction, the division symbol (), and the second fraction to divide a fraction. For instance, your issue could be 3/4 5/8. Use horizontal rather than diagonal lines to conveniently divide each fraction's numerator (top number) and denominator (bottom number).

Partitive division and quotative division are the two types of division. In some circumstances, one form may be more beneficial than the other.

Length of the trail =  4 1/2 miles long = 9/2 miles

The signposts divide the trail into sections that are 3/4 mile long.

Number of sections that Niquelle create along the trail = 9/2 miles ÷ 3/4

⇒ 9/2 × 4/3

⇒ 6 sections

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The area of a rectangle is found by multiplying the length by the width.

To find the area of the base of Isabella's fort, we will use the following formula:

Area = length x width

We are given that the base of the fort is 78 inches wide and 92 inches long. So we can plug these values into the formula:

Area = 78 inches x 92 inches = 7176 square inches

Therefore, the area of the base of Isabella's fort is 7176 square inches.

Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.

In a graph, what exactly is a vertex?

The right response is, therefore, option B.

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Full Question-

What characteristics can you see in the graph of the quadratic function in the figure? Options for question 14: A: The vertex is at (-4,3), the y-intercept is at (5,0), the x-intercepts are at (0,1) and (0,5), and the symmetry axis is at (-4,3) B: The vertex is at (-3,-4), the y-intercept is at (0,5), the x-intercepts are at (1,0) and (5,0), and the symmetry axis is at (3); C: Vertex: (3, -4), y-intercepts: (1, 0), and (5, 0), x-intercept: (0, 5), axis of symmetry: (3 D) Axis of symmetry is at x = -3, vertex is at (-3,4), y-intercept is at (0,5), and x-intercepts are at (1,0) and (5,0).

The annual interest rate that yields $31 from $600 in 10 months is 6.2%

An interest is the amount earned by placing a sum of money in a savings account or in an investment.

The principal amount you put in the account, P = $600

The amount (interest) earned in 6 months, I = $31

The duration over which the interest of $31 is earned, T = 10 months

The annual interest rate is found as follows;

The annual interest rate is the interest rate per year

The number of months in a year = 12 months

The formula for the simple interest, I, is presented as follows;

I = P·R·T

Where;

I = The simple interest earned

P = The principal amount saved in the account

R = The annual interest rate

T = The time duration the amount was saved in years

12 months = 1 year

Therefore; 10 months = (1/12) × 10 year = (5/6) year

The time, T, of 10 months = (5/6) year

31 = 600 × R × (5/6)

R = 31/(600 × (5/6)) = 0.062

0.062 in percentage is 0.062 × 100 = 6.2%

The annual interest rate, R = 6.2%

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Therefore , the answer is the distance between P and R is 12,2m.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.

Here,

Using the sine rule, sin a/A = sin b/B in this instance, we can determine the distance between P and R.

Sin angle PQR/PR is equal to Sin angle QRP/PQ.

We are aware that the QRP angle is 45° because:

Since it is an alternative interior angle, angle NPR is 75°.

Since 75° – 60° = 15, the angle QPR would be 15°.

As a result, angle QRP would be 45° since 180° – 120° – 15° = 45°.

When we know the angle QRP, we can quickly calculate the PR by entering the values into a calculator.

Sin 120°/RP = Sin 45°/10

RP = sin(120,10) sin(45,45),

=root 6 × 5

= 12.2m(3s.f) (3s.f)

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540 yards should be purchased to enclose the deck and option B is correct.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides.

A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Pools dimension = 1:3

Length = 60 × 3

= 180

Breadth= 30 × 4

= 90

Perimeter of rectangle = 2(l+b) = 2(90+180)

P = 2(270) = 540 yards

Thus, 540 yards should be purchased to enclose the deck and option B is correct

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the area of the green parallelogram will be 15inch².

What is Area of Parallelogram?

The region in a two-dimensional plane that a parallelogram occupies is known as its area. A parallelogram is a form with four sides with two geometry dimensions. Because the opposing sides are equal and parallel, so it is a unique quadrilateral example. The space bounded by the four sides of a parallelogram is known as its area. A parallelogram's area is calculated as the sum of its length and height.

A blue parallelogram has a height of 6 inches and a base of 10 inches.

a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram.

So the height will be half and the base ill also be.

For the green parallelogram will be 3 inch and 5 inch.

The area will be 3*5 = 15inch²

Hence, the area of the green parallelogram will be 15inch².

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Answer:  15,24,plan A

Step-by-step explanation: you will need to use the 15 from 150 to see which one costs less because 24+ 15= 39 so its obvious that plan B costs less then plan A   the next step is pretty easy because they both  cost 24 at the same time but its obvious that plan A costs more  so your answer for each of them is

As a result, there are 1440 degrees total internal angles in a decagon.

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Answer:

30=(12-c)5

30=60-5c multiply 12 and c by 5

-30=-5c Subtract 60 from 30

-30 ÷ -5= c divide -30 by -5

c=6