A forest ranger looking out from a ranger's station can see a forest fire at a 35 degree angle of depression. The ranger's position is 100 feet above the ground. How far is it from the ranger's station to the fire? Round your answer to the nearest tenth of a foot.

Answer: 300000000000000000

Step-by-step explanation:

50000x6000000000000 can be written as 3 times 10^17

So the answer is 300000000000000000

The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.

Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.

We are given

x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]

we need to find its derivative only then we can comment on its increasing decreasing nature

x'(t) = [tex]4t^3 -48t\\\\[/tex]

we will check where derivative is zero

[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]

hence increasing for all x E R except interval (0,4)

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Answer:

a. 88

b. I disagree with Kris

Step-by-step explanation:

88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.

The cost of the pyramid shape sign is $240.

A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.

We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.

∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,

= (1/3)×6×3×5 cubic feet.

= 30 cubic feet.

Given, The aluminum costs $8 per cubic foot.

∴ The total cost of the pyramid is = (30×8) = $240.

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Answer:

d = 5m

Step-by-step explanation:

Look at point (1, 5).

When the number of months is 1, the amount in dollars is 5.

The amount in dollars is always 5 times the number of months.

d = 5m

Answer:

Parallel: Y= -7/3x - 37/3

Perpendicular: Y=3/7x + 7

Step-by-step explanation:

Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.

Remember when the slope is parallel it's always the same slope in this case -7/3

When perpendicular flip it and change the sign 3/7

Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9

The definition of reciprocal in mathematics is the inverse of a value or a number.

If n is a real number, then 1/n will be n's reciprocal.

Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.

The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.

Similarly,  36 / 5 = 8 / a

the reciprocal is 5 / 36 = a / 8

cross multiplying

5 * 8 = 36 * a

36a = 40

a = 40 / 36

a = 10/9

The value of a is 10/9

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If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.

A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant,  cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.

How to solve?

In quadrant I, cos x = 2/3 and sin x > 0.

sin(2x) = 2sin x cos x

sin(2x) = 2 * 2/3 * (sin x)

sin(2x) = (4/3)sin x

If sin x > 0, then sin(2x) = (4/3)sin x > 0.

The exact value of sin(2x) is (4/3)sin x

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Answer:  [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

===============================================

Work Shown:

[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

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

Explanation:

The process to find the inverse involves this outline.

This process is followed in the "work shown" portion above.

To confirm the answer, let g(x) be the inverse of f(x).

If they were inverses of each other, then these two properties would hold true:

Here's the verification for the first part.

[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]

I'll let you do the other confirmation.

0.954 represents population of the town increases by 0.954 each year.

Two or more expressions with an Equal sign is called as Equation.

Given,

The population of a heard of buffalo after t

years is represented by the function

[tex]f(x)=2186(0.954)^{t}[/tex]

We need to find the what does the value 0.954 represent in this

situation.

In the given function 2186 represent the initial population.

t represents the time in years

and 0.954 represents population of the town increases by 0.954 each year.

Hence, 0.954 represents population of the town increases by 0.954 each year.

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The correct statement regarding the exponential functions g(x) and h(x) is given as follows:

B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients of the function are described as follows:

Function h(x) is defined as follows:

h(x) = 3^x - 2.

For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:

a = 4.

When x = 1, y = 5, hence the rate of change of the function is obtained as follows:

b = 5/4.

b = 1.25.

Then function g(x) is given as follows:

g(x) = 4(1.25)^x.

Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.

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The values obtained after solving the given equation is x  = 6 and y = 10.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equations are,

-5x + 3y = 0   (i)

7x - 4y = 2    (ii)

Multiply equation (i) by -7 and equation (ii) by 5.

35x - 21y = 0       (iii)

35x - 20y = 10       (iv)  

Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.

-y = -10

y = 10

Substitute y = 10 in equation (i)

-5x + 3(10) = 0

-5x = -30

x = 30/6

x = 5

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The length is 28.75 inch and width is 11.25 inch.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Perimeter= 80 inches

let the width be x.

length= 3x- 5

Now, perimeter of a rectangle = 2( l+ w)

80= 2( x+ 3x- 5)

40 = 4x -5

45 = 4x

x= 11.25

and, length = 3(11.25)- 5 = 28.75

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$150 is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer.

RAM is a type of volatile memory, which means that data is only stored there while the chip is powered and is completely erased when the computer is turned off. In gigabytes, RAM memory is measured (GB).

Random access memory is referred to as RAM. Because the data may be swiftly read and updated in any sequence, it is termed random access. Compared to previous storage devices like CD-RWs, which access data in a slower, predetermined order, this is faster.

There are much more methods through which we can improve computer performance but by spending the least amount of money we can do it by upgrading  your RAM. We can upgrade the RAM of the system to 8 GB and 16 GB. If we want to upgrade the RAM to 8 GB then it can be done for around $75 and If we want to upgrade the RAM to 16 GB then it can be done for around $150.

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The complete question is as follows:

What is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer?

Answer:

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

[tex] slope=\frac{8-1}{7-1} [/tex]

[tex] slope=\frac{7}{6} [/tex]

slope = 7/6

From the given ratio, there is a total of 100,000 vending machines in Osaka.

What is the ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.

Given, the ratio of vending machines to people is 1 to 24

That means, for every vending machine, there are 24 people.

In the city of Osaka, there are about 2,400,000 people.

So, the number of  vending machines = 2400000/24 = 100000

Hence, there is a total of 100,000 vending machines in Osaka.

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The total Volume of tank = 35 liters

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the

According to the Given information

Volume of each marble = 0.04 liters

Number of marbles to be put in the water tank = 50 marbles

Volume of 50 marbles = 0.04 × 50 = 2 liters

Volume of water added to the tank = 33 liters

Total Volume of tank = 2 liters + 33 liters

                                    =     35 liters

SO,

The total Volume of tank = 35 liters

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The average number of customers waiting in the queue is 20

In this question, we have been given that the customers arrive at the rate of two per minute.

On average a customer waits 10 minutes in a queue.

We need to find the number of customers waiting in the queue on average.

Assume that the average number of customers waiting in the queue is N.

We have the average Rate of Arrival = 2 customers per minute

So, by the formula for average waiting time under the Single-Server Queue Model,

10 = N/2

N = 10 * 2

N = 20

The average number of customers waiting according to the single-server queue model given the above conditions is 20

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The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Answer:

This would not form a triangle

Step-by-step explanation:

due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.

hope this helps! :3

Answer:

a.) x=6 b.) y=-7 c.) a=0.25

Step-by-step explanation:

a.) 2(3x+2)=2x+28

6x+4=2x+28

subtract 4 on both sides

6x=2x+24

subtract 2x on both sides

4x=24

divide both sides by 4

x=6

b.) 5y+13=-43-3y

add 43 on both sides

5y+56=3y

subtract 5y on both sides

56=-8y

divide both sides by 8

-7=y or y=-7

c.) 4(2a+2)=8(2-3a)

8a+8=16-24a

add 24a on both sides

32a+8=16

subtract 8 on both sides

32a=8

divide both sides by 32

a=0.25

(hope you understood how I solved for each equation..)

Part a: y = -6x + 5 is : Not proportional.

Part b: y = 7/8x proportional:  proportionality constant = 7/8.

For the stated question;

Part a: y = -6x + 5

To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.

The ratio = y/x must be same.

For x = 1, y = -1

y/x = -1

And, for x = 2, y = 7

y/x = 7/2

Thus, ratio is not equal, Not proportional.

Part b:  y = 7/8x

For x = 1, y = 7/8

y/x = 7/8

Now, For x = 2, y = 14/8

y/x = 7/8, both ratios are equal.

Thus,  y = 7/8x proportional:  proportionality constant = 7/8.

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Answer:

l

v

Step-by-step explanation:

80, 5, 30, 7, and 3,

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

What is the coordinates?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.

Here given coordinates are

[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]

Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become

[tex]A(x,y)=A(x+a,y+b)[/tex]

As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.

So, [tex]a=4,b=-3[/tex] and the coordinates are

[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]

Then,

[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

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Answer: 1/3

Step-by-step explanation:

Answer:

top right

Step-by-step explanation:

6x3=18

The slope of the given function is 0.25. The function that has  the same slope is y = 0.25x + 5. Option B is the correct option.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given table is

x         0          1            2             3

y      -0.5       -0.25      0           0.25

The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25

The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25

Now compare the equation y = -0.25x - 2 with y = mx + c

m =  -0.25

The slope of the function is -0.25.

Now compare the equation y = 0.25x + 5 with y = mx + c

m =  0.25

The slope of the function is 0.25.

Now compare the equation y = 4x - 5 with y = mx + c

m =  4

The slope of the function is 4.

Now compare the equation y = -4x + 34 with y = mx + c

m =  -4

The slope of the function is -4.

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The solutions of the quadratic equation are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

For a general quadratic:

a*x^2 + b*x + c = 0

The solutions are given by the quadratic formula

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic equation:

2x^2 + x + 3 = 0

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]

So we will have two complex solutions, these are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

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Answer:

Step-by-step explanation:

1. Lin, Tyler, and Jada's information is missing.

2. 9 1/8 = 73/8

1 2/8 = 10/8

73/8 - 10/8 = 63/8.

His shoe length was 63/8 inches.