If Emily throws the ball at an angle of 30 ∘ below the horizontal with a speed of 12 m/s , how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 8.0 m .
Express your answer with the appropriate units.

Answer: The formula for exponential decay is given by:

P(t) = P0 * e^(-rt)

where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.

In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).

First, we need to convert the rate of decrease from a percentage to a decimal:

r = 0.9% / 100 = 0.009

Now, we can plug in the values into the exponential decay formula:

P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)

We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.

Therefore, the profit in 2019 is:

P(5) = $9500 * 0.955 = $9027.25

So, the profit in 2019 would be $9027.25.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

f(2) = 10-4 = 6

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 5x - 4

We have to find,

→ The required value of f(2).

Now value of f(2) will be,

→ f(x) = 5x - 4

→ f(2) = 5(2) - 4

→ f(2) = 10 - 4

→ [ f(2) = 6 ]

Therefore, the answer is 6.

The solution is Option D.

The skate park should be build as the percentage of votes was 57.6 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage of votes be represented as A

Now , the skate park will be built if the percentage of votes is greater than 50 %

Now , the total number of voters = 125 voters

The number of voters who responded to building the park = 72 voters

Substituting the values in the equation , we get

A = ( number of voters who responded to building the park / total number of voters ) x 100

On simplifying the equation , we get

A = ( 72 / 125 ) x 100

A = 0.576 x 100

A = 57.6 %

And , A > 50 %

Therefore , they should plan for the skate park because the sample had about 57.6% people vote yes

Hence , the percentage of votes is 57.6 %

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Answer:

Step-by-step explanation:

6

The trait would be MOST useful for these farmers is to be considered as the fast growth rate.

The main goal of science that should create knowledge and understanding.

Since the plan for using the breeding to produce a new type for the wheat for farmers that lived in the northern areas.

The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

The annual average rate of change of the gross domestic product (GDP) at market prices based on constant local currency, for a given national economy, during a specified period of time.

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Using the fact that the figures are similar, we will find that MN = 12.4

We know that both figures are similar, then there is a scale factor that relates them.

We know the length of two correspondent sides, these are:

HI and LM

HI = 3

LM = 18.6

if k is the scale factor, then we can wite:

3*k = 18.6

k = 18.6/3 = 6.2

Now the length of MN will be 6.2 times the length of the correspondent side on the smaller figure:

MN = 6.2*2 = 12.4

That is the lenght.

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Step-by-step explanation:

Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.

A = L x W

For the large rectangle

A = 30 x 25 = 750

For the small rectangle

A = 26 x 21 = 546

Now to subtract these two

750 - 546 = 240

Answer:

Step-by-step explanation:

x/sin90=17.3/sin53

sin90=1

x=17.3/sin53

x=13.8

Answer:

Step-by-step explanation:

Range: the difference between the highest and lowest values

Heights:

130

142

142

143

144

145

147

147

149

150

151

153

154

154

158

161

162

Formula to find the range

R= H-L

R = range

H = highest value

L = lowest value

    R = 160 - 130.

The range is 30.

Answer: 150 Cubes.

Step-by-step explanation:

Volume of cuboid is l*b*h, Volume of cube is S^3.

= 75*50*40 = 1,50,000 CM, = 0.1m= 10cm^3= 1000

No of cubes in one cuboid= volume of cuboid/volume of cube

1,50,000/1000= 150 cubes.

1) The length of the missing side of the right triangle is 34.

2) The values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

What is Pythagorean Theorem?

Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).

Part 1

To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:

a² + b² = c²

Substituting the given values, we get:

16² + 30² = c²

Simplifying, we get:

256 + 900 = c²

1156 = c²

Taking the square root of both sides, we get:

c = sqrt(1156) = 34

Therefore, the length of the missing side of the right triangle is 34.

Part 2

To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:

sin A = a/c = 16/34 = 8/17

cos A = b/c = 30/34 = 15/17

tan A = a/b = 16/30 = 8/15

csc A = 1/sin A = 17/8

sec A = 1/cos A = 17/15

cot A = 1/tan A = 15/8

Therefore, the values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

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The length of the dotted line would be 7.922 ft.

A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.

The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.

When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.

We can solve this for q = 7.922

The dotted line would be 7.922 feet long as a result.

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We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four  operations are addition, subtraction, multiplication and division.

We are given two expressions as 3z - 4 and 2z + 5.

In order to add the expressions, we will add the like terms.

On adding the like terms, we get

⇒(3z - 4) + (2z + 5)

⇒3z + 2z - 4 + 5

⇒5z + 1

Hence, we get the expression as 5z + 1.

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Given the set of statements according to the questions are:

1) 28 ∈ A -  true.

2) 8 ∈ B -  true.
3) 31 ∉ A -  false.
4) 1 ∈ B  - false

What is a set?

In mathematics, a set is a collection of distinct objects or elements that are grouped together as a single entity. The objects in a set can be anything: numbers, people, animals, colors, or even other sets. The elements of a set are usually enclosed in braces, {}.

By using the given data:

A = {28, 29, 30, 31, 32, 33, 34, 35};

B = The set of even numbers greater than or equal to 6 and less than or equal to 12

B = {6, 8, 10, 12}

Now lets find the answer

1) 28 ∈ A - 28 is present in set A hence, this statement is true.

2) 8 ∈ B - 8 is present in set B, hence this statement is true.
3) 31 ∉ A - 31 is present in set A, hence this statement is false.
4) 1 ∈ B - 1 is not present in set B, hence this statement is false.

Hence,

1) 28 ∈ A -  true.

2) 8 ∈ B -  true.
3) 31 ∉ A -  false.
4) 1 ∈ B  - false

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The inverse of the given function is f(x) = 2x/(1 - x)

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is

f(x) = x/(2+x)

Assume that y = f(x) = x/(2+x)

Solve y = x/(2+x) for x:

y = x/(2+x)

Multiply (2+x) on both sides:

y(2+x) = x

2y + xy = x

Subtract xy from both sides:

2y = x - xy

2y = x(1 - y)

x = 2y/ (1 - y)

Now replace x with y and y with x:

y = 2x/(1 - x)

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Answer:

18x+9

Step-by-step explanation:

Answer: 18x + 9

Step-by-step explanation:

1) Combine like terms 23x -5x to get a new equation of 18x + 9.

Answer:

$2160

Step-by-step explanation:

Area of a rectangle = Length * Width

A = L * W

Divide both sides by width

W/(A = L * W)/w

[tex]\frac{A}{W} = L[/tex]

Plug in values

[tex]\frac{384}{24} =16[/tex]

Multiply Length and width to find perimeter

2W + 2L = P

plug in values

2(24) + 2(16) =  80

Multiply perimeter by cost per foot

1yd = 3ft

80yd * 3ft = 240ft

240ft * $9 = $2160

The required paragraphs regarding with given expression f(x) = x²-2x+1/4x+5 have been explained later in the section.

A rational expression is a fraction in which the numerator and denominator are polynomials.

Here,
a) To determine the values of x that make the rational function f(x) equal to 0, we need to solve the equation:

x² - 2x + 1 = 0

Next, we can factor the quadratic on the left-hand side of the equation:

(x - 1)(x - 1) = 0

The quadratic is a perfect square, and we can see that it is equal to 0 when x = 1. So, the value of x that makes the rational function 0 is x = 1.

b) To determine the values of x where the rational function f(x) is undefined, we need to look for values of x that would make the denominator, 4x+5, equal to 0. If the denominator is equal to 0, then we would be dividing by 0, which is undefined.

So, we set the denominator equal to 0,

4x + 5 = 0

4x = -5

x = -5/4

Therefore, the value of x where the rational function is undefined is x = -5/4.

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Answer: y > 8

Step-by-step explanation:

6 - 5y < -34

-5y < -40

y > 8

[tex]6-5y < -34[/tex]

Simplify:

[tex]-5y+6 < -34[/tex]

Subtract 6 from both sides:

[tex]-5y+6-6 < -34-6[/tex]

[tex]-5y < -40[/tex]

Since we are dividing by a negative number, the sign will reverse.

Divide both sides by -5:

[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]

[tex]\boxed{y > 8}[/tex]

Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.

To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.

Let us substitute cu for x in the equation Ax = 0, then we get:

A(cu) = A(c × u)

Using the distributive property, we can write:

A(c × u) = c × A(u)

Since u satisfies the equation Ax = 0, we have:

A(u) = 0

Substituting this into the above equation, we get:

c × A(u) = c × 0 = 0

Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

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The simplified value of the expression is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

From the question, we have the following parameters that can be used in our computation:

1/(b² - ab) - 1/(ab - a²)

Take the LCM of the expression

So, we have the following representation

[ab - a² - b² + ab]/[(b² - ab)(ab - a²)]

Evaluate the like terms

So, we have the following representation

[2ab - a² - b²]/[(b² - ab)(ab - a²)]

Open the bracket

[a² + b² - 2ab]/[2a²b² - ab³ - a³b]

Hence, the solution is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

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The value of x is 12. The solution has been obtained by using trigonometry.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.

We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.

Using trigonometry,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 11/x

Here, θ = 24°

So,

⇒cos 24° = 11/x

⇒x = 11/cos 24°

⇒x ≈ 12.04

⇒x ≈ 12

Hence, the  value of x is 12.

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a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.

A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).

b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:

Significantly reduced: - 2 = 18 - 2 2.12 13.76

Significantly greater: + 2 = 18 + 2 2.12 22.24

c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:

z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08

Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.

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Answer:

this hard

Step-by-step explanation:

Answer: C

Step-by-step explanation:

On solving the provided question we can say that the sets are as

U = {6, 7, 8, 9, 10, 11, 12}, and z(180) = (180-185)/4  = -1.25

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

the sets are as

U = {6, 7, 8, 9, 10, 11, 12},

A = {6, 7, 8, 9},

B = {6, 7, 10, 11},

C = {8, 10, 12}

1){8,10}

2)z(180) = (180-185)/4  = -1.25

P(x < 180) = P(z < -1.25)

3)28c5

4)-4

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Answer:

2 [tex]\frac{16}{17}[/tex] miles

Step-by-step explanation:

[tex]\frac{miles}{minutes}[/tex] = [tex]\frac{miles}{minutes}[/tex]

[tex]\frac{1 1/4}{8 1/2}[/tex] = [tex]\frac{x}{20}[/tex]

1 [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{4}{4}[/tex] + [tex]\frac{1}{4}[/tex]   (1 = [tex]\frac{4}{4}[/tex] )

8 [tex]\frac{1}{2}[/tex] is the same as [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{17}{2}[/tex]   (1 = [tex]\frac{2}{2}[/tex])

[tex]\frac{\frac{5}{4} }{\frac{17}{2} }[/tex] = [tex]\frac{x}{20}[/tex]

[tex]\frac{17}{2}[/tex] x = 20  multiply both sides by [tex]\frac{2}{17}[/tex]

[tex]\frac{2}{17}[/tex] [tex](\frac{17}{2})[/tex]x = [tex]\frac{2}{17}[/tex][tex](\frac{20}{1})[/tex]

x = [tex]\frac{40}{17}[/tex]

[tex]\frac{5}{4}[/tex] [tex](\frac{40}{17})[/tex] = x

[tex]\frac{50}{17}[/tex] or 2 [tex]\frac{16}{17}[/tex]

Answer:

he division story will be that there are 16 boys who want to share 4 oranges. What fraction will each person get?

Number of boys = 16

Number of oranges = 4

Fraction that each person will get will be:

= Number of oranges / Number of boys

= 4/16

= 1/4

Each boy gets 1/4.

Step-by-step explanation:

The ration will be sinA =[tex]\frac{P}{H}[/tex] =[tex]\frac{33}{65}[/tex] , cosA = [tex]\frac{B}{H}[/tex]=[tex]\frac{56}{65}[/tex]  & tanA = [tex]\frac{P}{B}[/tex]= [tex]\frac{33}{56}[/tex].

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use particular terminology to define the sides of right triangles. A right triangle's hypotenuse is always side opposite the right angle.

When one of a triangle's angles is exactly 90 degrees, the triangle is said to be right-angled. The remaining two angles together equal 90 degrees.. The sides that make up the right angle are perpendicular and the triangle's base. The third side, also referred to as the hypotenuse, is the longest of the three sides.

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Answer:

503.1222

rounded: 503.12

Answer: a) Calculate the probability of getting both contracts:

The probability of getting both contracts is given by P(Contract 1 and Contract 2) = P(Contract 1) * P(Contract 2|Contract 1) = 0.4 * 0.3 = 0.12

b) Calculate the probability of getting either contract:

The probability of getting either contract is given by P(Contract 1 or Contract 2) = P(Contract 1) + P(Contract 2) - P(Contract 1 and Contract 2) = 0.4 + 0.5 - 0.12 = 0.78

c) Calculate the probability of not getting either contract:

The probability of not getting either contract is given by P(Neither Contract) = 1 - P(Contract 1 or Contract 2) = 1 - 0.78 = 0.22.

So, there is a 22% chance that the construction firm will not get either contract.

Step-by-step explanation: