Tyreek is planning on driving to Outer Banks from Philadelphia. On the map, Tyreek is using, each inch represents 50 miles. If the distance on the map from Philadelphia to OBX is 7/34 inches, how far is it in actual miles? Show your work.

a. The exact value of tan(cos⁻¹(-16/19)) in simplified radical form is -3/16.

b. sin⁻¹(tan(2π/3)) is undefined and does not have an answer.

a. We know that cos(cos⁻¹(x)) = x and hence cos(cos⁻¹(-16/19)) = -16/19.

Let θ = cos⁻¹(-16/19), then we have

cos(θ) = -16/19 and

sin(θ) = √(1 - cos²(θ))

= √(1 - (16/19)²)

= 3/19 (using the Pythagorean identity).

Now, we can use the identity tan(θ) = sin(θ)/cos(θ) to find the value of tan(cos⁻¹(-16/19)):

tan(cos⁻¹(-16/19))

= sin(θ)/cos(θ)

= (3/19) / (-16/19)

= -3/16.

Therefore, the exact value of tan(cos⁻¹(-16/19)) is -3/16 in simplified radical form.

b. The range of the function tan(x) is (-∞, ∞), which means that it can take any value. However, the range of the function sin⁻¹(x) is [-π/2, π/2], which means that it can only take values between -π/2 and π/2. In particular, sin⁻¹(x) is not defined for |x| > 1, since there is no angle whose sine is greater than 1 or less than -1.

Let's consider sin⁻¹(tan(2π/3)). We know that tan(2π/3) is undefined, since the tangent function has vertical asymptotes at odd multiples of π/2 (including 2π/3).

Therefore, sin⁻¹(tan(2π/3)) is also undefined and does not have an answer.

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The maximum height of the ball from the maximum compression of the spring is 13.39 m

Maximum height is the highest displacement of the object.

Since a spring of spring constant 504 N/m is compressed 7.66 cm by a ball of mass 11.2 g. If the ball is shot straight into the air, we desire the maximum height of the ball.

Using the law of conservation of energy, the elastic potential energy lost by the spring, E equals the gravitational potential energy gained by the ball, E'

So, E = E'

1/2kx² = mgh where

Making h subject of the formula, we have that

h = kx²/2mg

So, substituting the values of the variables into the equation, we have that

h = kx²/2mg

h = 504 N/m × (0.0766 m)²/(2 × 0.0112 kg × 9.8 m/s²)

= 504 N/m × 0.00586756 m²/(2 × 0.0112 kg × 9.8 m/s²)

= 2.95725024 Nm/(0.21952 kgm/s²)

= 13.47 m

So, the maximum height from the springs compression is H = h - x = 13.47 - 0.0766 m

= 13.3934 m

≅ 13.39 m

So, the maximum height is 13.39 m

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Answer:

x ≈ 2.7 m

Step-by-step explanation:

since the 2 triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{1.6}[/tex] = [tex]\frac{4}{2.4}[/tex] ( cross- multiply )

2.4x = 4 × 1.6 = 6.4 ( divide both sides by 2.4 )

x = [tex]\frac{6.4}{2.4}[/tex] = 2.6666...

height of statue x ≈ 2.7 m ( to 1 decimal place )

The correct calculation of the average is given as 0.2546

The average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.

The calculation of the average would be gotten by the number of hits / by the total bats that he had

This is given as

151 / 593

= 0.2546

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a) The linear function is defined as follows: y = 1 - 0.2x.

b) The slope and the intercepts are interpreted as follows:

c) The battery power is at 75% after 1.25 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:

m = -1/5

m = -0.2.

Hence the function is:

y = -0.2x + 1.

The battery power is of 75% = 0.75 when y = 0.75, as follows:

0.75 = -0.2x + 1

0.2x = 0.25

x = 0.25/0.2

x = 1.25 hours.

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Answer:

17 numbers in this range.

Step-by-step explanation:

For this function, the domain consists of all positive three-digit integers. There are 900 such integers, from 100 to 999.

The range consists of all numbers between 2 and 18, inclusive, since the smallest possible sum is 1+0+0 = 1 and the largest possible sum is 9+9+1 = 19, but the function only takes the sum of the largest and smallest digits. There are 17 numbers in this range.

Answer:

Step-by-step explanation:

The domain of this function consists of all positive three-digit integers. There are 900 three-digit integers in total, from 100 to 999 inclusive.

The range of this function consists of all integers between 2 and 18 inclusive, since the smallest and largest digits of a three-digit integer can range from 1 to 9, and their sum can range from 2 (1 + 1) to 18 (9 + 9). So the range has 17 elements in total: {2, 3, 4, ..., 18}.

Answer:

Step-by-step explanation:

To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:

(-1)(x+4) = 2(x-5)

Expanding both sides and simplifying, we get:

-x - 4 = 2x - 10

Bringing all the x terms to one side and all the constant terms to the other, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:

(-1)/(2-5) = 2/(2+4)

Simplifying, we get:

1/3 = 1/3

Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.

Answer: x = 2

Step-by-step explanation:

    [tex]\boldsymbol{\sf{The\:exercise\:is \longmapsto \ \dfrac{-1}{x-5}=\dfrac{2}{x+4} }}[/tex]

We cross multiply.

     -(x + 4) = 2(x - 5)

We apply the multiplicative law of distribution.

       -x -4 = 2(x - 5)

       -x - 4 = 2x - 10

We rearrange the unknown terms to the left side of the equation.

       -x - 2x = -10 + 4  <===Combine as terms===> -3x = -10 + 4

We calculate -10 + 4 = -6.

       -3x = -6

We divide both sides of the equation by the coefficient of the variable.

       [tex]\boldsymbol{\sf{x=\dfrac{-6}{-3} \iff \ x=\dfrac{6}{3} }}[/tex]

      x = 2

The x and y values are x=5 and y= -2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=4x-22 ----(1)

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

Substitute (1) into (2)

=> 2x+3(4x-22)=4

=> 2x+12x-66 = 4

=> 14x = 4+66

=> 14x = 70

=> x=70/14 = 5

(1) => y=4*5-22 = 20 - 22 = -2

So, the x and y values are x=5 and y= -2

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the x-intercepts will be -π/2, -3π/2,  π/2, 3π/2.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The x-intercepts are locations on the coordinate plane where the y-value of the ordered pair is 0.

y = cos(x)

so the x-intercepts will be -π/2, -3π/2,  π/2, 3π/2.

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We kindly invite to see the image attached below to know the representation of the parabola according to its features.

A parabola is the graphic representation of any quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. An alternative presentation is the vertex form:

y - k = C · (x - h)²

Where:

The procedure to sketch the parabola according to its features is described below:

Step 1 - Determine the y-intercept:

y = 6 · 0² - 17 · 0 + 12

y = 12

Step 2 - Determine the x-intercepts.

6 · x² - 17 · x + 12 = 0

6 · [x² - (17 / 6) · x + 2] = 0

6 · (x - 3 / 2) · (x - 4 / 3) = 0

x = 3 / 2 or x = 4 / 3

Step 3 - Determine the coordinates of the vertex:

y = 6 · x² - 17 · x + 12

y = 6 · [x² - (17 / 6) · x + 2]

y + 6 · (1 / 144) = 6 · [x² - (17 / 6) · x + 2 + 1 / 144]

y + 1 / 24 = 6 · [x² - (17 / 6) · x + 289 / 144]

y + 1 / 24 = 6 · (x - 17 / 12)²

(h, k) = (17 / 12, - 1 / 24)

Steps 4 & 5 - Add the points on Cartesian plane and match the resulting curve.

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At the Culver City Trampoline Park, customers leave their shoes in cubbies shaped like rectangular prisms while they jump. Each cubby is 11 inches deep, 6 inches tall, and has a volume of 396 cubic inches. So, each cubby is 6 inch wide.

Three-dimensional space is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or American customary units. 

Every object in three dimensions takes up that space. The volume of that kind of area is the one being measured. The area covered by such an object's boundaries in three-dimensional space generally said to as the volume. Other term for it would be an object's capacity.

Given that,

Each cubby is 11 inches deep,

6 inches tall, and

has a volume of 396 cubic inches.

Volume of rectangular prism = L × W × h

or, 396 = 11 × W × 6

or, W = 396 / 66

or, W = 6 inch

Thus, each cubby is 6 inch wide.

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In the parallelogram ABCD the measure of ∠BEC is obtained as 113°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

It is given that ABCD is a parallelogram.

The measure of ∠EAD = 30°.

The measure of ∠EDA = 37°.

In the parallelogram ∠EBC = ∠EDA as they form alternate interior angles pair.

Similarly, ∠ECB = ∠EAD as they form alternate interior angles pair.

The measure of ∠ECB = 30°.

The measure of ∠EBC = 37°.

Since EBC forms a triangle, so the sum of the angles of a triangle is 180°.

The equation is -

∠ECB + ∠EBC + ∠BEC = 180°

Substitute the values into the equation -

30° + 37° + ∠BEC = 180°

67° + ∠BEC = 180°

∠BEC = 180° - 67°

∠BEC = 113°

Therefore, the measure of ∠BEC = 113°.

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Answer: 17:20pm

Step-by-step explanation: If you add 24 minutes to 14:46, that gives you 15:20pm. Add the 2 hours. So your answer is 17:20pm

Answer:

x= −1088

Step-by-step explanation:

Answer:

-1088

Step-by-step explanation:

-17      =    x/64

*64           *64

-1088 = x

Answer: 48%

Step-by-step explanation:

The probability of the event between two and five lines, inclusive, are in use is 0.85.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that,

x         0         1         2       3        4         5         6

p(x)   0.12    0.18   0.20  0.20  0.20   0.07   0.03

a) At most three lines are in use

Here we need to find the probability for x≤3.

P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

= 0.12+0.18+0.20+0.20

= 0.70

b) Fewer than three lines are in use

Here we need to find the probability for x<3.

P(x<3)=P(x=0)+P(x=1)+P(x=2)

= 0.12+0.18+0.20

= 0.50

c) At least three lines are in use

Here we need to find the probability for x≥3.

P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)

= 0.20+0.20+0.07+0.03

= 0.50

d) Between two and five lines, inclusive, are in use

Here we need to find the probability for 2≤x≤5.

P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)

= 0.18+0.20+0.20+0.20+0.07

= 0.85

Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.

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Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

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Answer:

27.5

Step-by-step explanation:

(x – 3)2 = 49

(x – 3) = 49/2

(x – 3) = 24.5

x = 27.5

Answer: 480

Step-by-step explanation:

20 times 24 is 480

The equation and solution to find the length of mis teak wood piece is x/3=8 and 24;

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas;

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely;

We are given:

The length of oak wood is 8inches

Teak wood/3= oak wood

So,

Let the length of teak wood be x;

Now,

x/3=8

x=3x8

x=24

Therefore, by algebra the length of teak wood will be 24;

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Answer:

graph linked

Step-by-step explanation:

A fraction of [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.

If there are 70 vegetables altogether, then there are 10 potatoes.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

Some of the values are missing here.

Given that,

Aziz grows vegetables in his garden.

Let the total number of vegetables be x.

Assuming [tex]\frac{1}{2}[/tex] of the vegetables grow underground.

Number of underground vegetables =  [tex]\frac{1}{2}[/tex] x

Assuming,  [tex]\frac{2}{7}[/tex] of these underground vegetables, are potatoes.

Number of potatoes = [tex]\frac{2}{7}[/tex] × ( [tex]\frac{1}{2}[/tex] x ) = [tex]\frac{1}{7}[/tex] x

So, [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.

If there are 70 vegetables altogether,

Number of potatoes = [tex]\frac{1}{7}[/tex] x =  [tex]\frac{1}{7}[/tex] × 70 = 10

Hence of the total vegetables of 70, 10 are potatoes.

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Yes, The y - intercept is zero because it cannot intercept at any point on y - axis.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of your model is,

⇒ y = 0.122x

Here, The y - intercept is zero.

Since, The slope intercept form of equation of line is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

By comparing with the given equation, We get;

The y - intercept is zero.

And, By graph it cannot intercept at any point on y - axis.

Hence, The y - intercept is zero because it cannot intercept at any point on y - axis.

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Answer:

7 degress celcius

Step-by-step explanation:

The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft

The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.

To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.

Therefore, the correct answer is B) 12 ft.

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Hence, the graph of g is upward than the graph of f.

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

The functions are

f(x) = 2^x

g(x) = f(x) + 6

so, g(x) = 2^x + 6

Draw the graphs of both the equation

The graph of the g is differ from f because in the graph of g it is upward than the graph of f .

Hence, the graph of g is upward than the graph of .

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Answer: To find the percent increase in population, I used the following formula:

percent increase = (new value - old value) / old value * 100

In this case, the old value was the population from a decade ago (4360), and the new value was the current population (6590). So plugging these values into the formula, we get:

percent increase = (6590 - 4360) / 4360 * 100

percent increase = 51.38%

So the population of Placerville increased by approximately 51.38% over the past decade. The population of Placerville has increased by (6590 - 4360) = 2230 people over the past decade.

Step-by-step explanation:

Answer:

Using the ratio given, we know that for every 5 colored pencils, there are 2 markers in each box.

Therefore:

The first blank represents the number of colored pencils in the box. Since the ratio of colored pencils to markers is 5 to 2, we can calculate that there are 5 colored pencils for every 2 markers. This means that for each box, there are 5/7 of the total number of items are colored pencils. So the missing value in the first row is 35.

The second row indicates that there are 20 items in the box. We know that the first row (colored pencils) has 35 items, and since the total number of items in the box is 20, the missing value in the second row (markers) is 20 - 35/7 = 15.

The third row represents the total number of colored pencils and markers in each box. We know that there are 35 colored pencils and 15 markers in each box, so the total number of items in each box is 50.

Therefore, the completed table would be:

Boxes for sale

||||||||||||||||||||||||||||||||||||||||||

Number of Colored | 35 | 20 | 35 |

Pencils | | | |

||||||||||||||||||||||||||||||||||||||||||

Number of Markers | 6 | 15 | 6 |

| | | |

Total Number of ||||||||||||||||||||||||||||||||||||||||||||

Colored Pencils and | 41 | 35 | 50 |

Markers in the Box |||||||||||||||||||||||||||||||||||||||||||||​