find the volume pls help asap

The Demand function D(x) = -0.00094x + 4.54

Step 1: To find the equation for D(x), we need to find the slope and the y-intercept of the demand function. The slope can be found using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Step 2: We can use the given information to find the slope. The first point is (1919, 2.74) and the second point is (3131, 1.60). Plugging these values into the formula, we get:

m = (1.60 - 2.74)/(3131 - 1919)
m = -1.14/1212
m = -0.00094

Step 3: Now we need to find the y-intercept, b. We can use the point-slope form of a line, y - y1 = m(x - x1), and plug in one of the points and the slope to find b.

y - 2.74 = -0.00094(x - 1919)
y = -0.00094x + 2.74 + 0.00094(1919)
y = -0.00094x + 4.54

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Ryan needs to make a  monthly deposit of $774.08 in order to have $30,000 for a down payment on a home.

To calculate the monthly deposit that Ryan needs to make in order to have $30,000 in 3 years, we can use the formula for the future value of an annuity:

FV = Pmt * [(1 + r)ⁿ - 1] / r

where FV is the future value (in this case, $30,000),

Pmt is the monthly deposit,

r is the monthly interest rate (5% / 12 = 0.00417), and

n is the number of compounding periods (36 months).

Substituting the values we have:

30,000 = Pmt * [(1 + 0.00417)³⁶ - 1] / 0.00417

38.75564454Pmt = 30,000

Pmt = 30,000/38.75564454

Pmt = $774.08

Therefore, Ryan needs to deposit approximately $774.08 each month in order to have $30,000 for a down payment on a home.

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The difference between the volume of the 2 rectangular prism containers is V = 70 inches³

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the difference between the volume of the rectangular prism be D

Now , the amount of sand poured into the container = 375 inches³

And , the dimensions of the first rectangular container = 5 inches x 7 inches x 9 inches

So , the volume of the first rectangular prism V₁ = 5 x 7 x 9 = 315 inches³

where amount of sand poured into the container > volume of the first rectangular prism

Therefore , the sand cannot be poured into the prism container

b)

The height of the second rectangular container = ( h + 2 ) inches = 11 inches

So , the volume of the second prism container V₂ = 5 x 7 x 11

The volume of the second prism container V₂ = 385 inches³

And , the difference in the volumes of the 2 containers V = V₂ - V₁

On simplifying , we get

The difference between the volume of the 2 rectangular prism containers is V = 385 - 315

The difference between the volume of the 2 rectangular prism containers is V = 70 inches³

c)

The dimensions of the container which contains 375 inches³ of sand is given by V₃ = 5 inches x 5 inches x 15 inches

Hence , the volume of the rectangular prism is solved

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The complete question is :

Jack has 375 in. of sand to pour into a rectangular prism. The base of the prism is 5 inches by 7 inches and the height is 9 inches.Part A

Will the sand fit in the container? Explain why or why not.

Part B

A second rectangular prism is 2 inches taller than the first.

What is the difference in the volumes of the 2 containers? Show your work.

Part C

What are the measurements of a rectangular prism that will hold exactly 375 in. of the sand? Justify your answer.

Answer:22 because thats what each chart says

Step-by-step explanation:

Answer:

19-21 inches.

Step-by-step explanation:

The average term infant's length at birth is between 19-21 inches. As would be expected, taller parents tend to produce longer neonates. At the end of their first month, most infants have increased their length by approximately 1 inch.

The output of the code will tell us whether the events are independent or not. If the events are independent, then the probability of one event occurring does not affect the probability of the other event occurring.

To determine whether the events "The rose blooms late" and "Getting a green rose" are independent, we can use the formula for conditional probability, P(A|B) = P(A and B)/P(B). If P(A|B) = P(A), then the events are independent. In this case, A is the event "The rose blooms late" and B is the event "Getting a green rose".

We can use R code to simulate the picking of a random rose and calculate the probabilities of the events.

```{r}
# Set the number of simulations
n <- 10000

# Create a data frame with the roses and their characteristics
roses <- data.frame(color = c(rep("blue", 8), rep("green", 11)),
                   bloom = c(rep("early", 3), rep("late", 5), rep("early", 5), rep("late", 6)))

# Simulate picking a random rose n times
sim <- sample(1:19, n, replace = TRUE)

# Calculate the probabilities of the events
P_A <- sum(roses$bloom[sim] == "late")/n
P_B <- sum(roses$color[sim] == "green")/n
P_A_and_B <- sum(roses$bloom[sim] == "late" & roses$color[sim] == "green")/n
P_A_given_B <- P_A_and_B/P_B

# Check if the events are independent
if (P_A_given_B == P_A) {
 print("The events are independent")
} else {
 print("The events are not independent")
}
```

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The we have shown that \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}\).

The given equation is \[\boldsymbol{x} \ast \boldsymbol{y}=\left(x_{1} y_{1}, \ldots, x_{n} y_{n}\right),\] where \(\boldsymbol{x} = (x_1, x_2, ..., x_n)\) and \(\boldsymbol{y} = (y_1, y_2, ..., y_n)\).In the above equation, the output of \(\boldsymbol{x} \ast \boldsymbol{y}\) will contain only 1s if the value of both the coordinates in \(\boldsymbol{x}\) and \(\boldsymbol{y}\) is 1 otherwise it will contain 0.The multiplication of vectors \(\boldsymbol{x}\) and \(\boldsymbol{y}\) is an example of bitwise multiplication. It is used to multiply each bit of two numbers. Here, the vectors \(\boldsymbol{x}\) and \(\boldsymbol{y}\) contain only 1's and 0's.We know that bitwise multiplication of two numbers is also known as logical multiplication. When we multiply two numbers bit by bit, then we get a new number.

The new number will have 1 at the same position where both numbers contain 1, otherwise 0 will be there.We have to show that if \(w\) is a subset of the n-element set \(\{1,2, \ldots, n\}\), then the formula holds: $$\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}.$$Let's break down the above expression into the following steps:First, calculate the product of coordinates of vector \(\boldsymbol{x}\) for every element in the set \(w\). This will give \(\prod_{i \in w} x_{i}\).Secondly, calculate the product of coordinates of vector \(\boldsymbol{y}\) for every element in the set \(w\). This will give \(\prod_{i \in w} y_{i}\).Multiply the result obtained in step 1 and step 2. This will give \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}\).Finally, calculate the product of the coordinates of vector \(\boldsymbol{x} \ast \boldsymbol{y}\) for every element in the set \(w\). This will give \(\prod_{i \in w} x_{i} y_{i}\).Therefore, we have shown that \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}\).

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The ranges overlap, it is possible for both measurements to be correct.

Since they show how precise and accurate the numbers being utilised are, significant figures are crucial in measurements and computations. In order to prevent mistakes and maintain the required degree of precision, it is crucial to maintain consistency in the number of significant figures throughout computations. This indicates the amount of uncertainty in a measurement.

Given that, Deondra measures an object as 2 3/4 inches and  Abdul measures 2 1/2 inches to the nearest half inch.

The actual length for Deondra is  between 2 5/8 inches and 2 7/8 inches.

For Abdul the actual length is between 2 inches and 3 inches.

Since the ranges overlap, it is possible for both measurements to be correct.

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The periods of the given trigonometric functions are (a) 2π (b) 2π (c) π (d) 2π (e) 2π and (f) π.

The period of a trigonometric function is the smallest positive value of x for which the function repeats its values. In other words, it is the length of one complete cycle of the function. The period of the basic trigonometric functions are as follows:

a) The period of f(x)=sin x is 2π.
b) The period of f(x)=cos x is 2π.
c) The period of f(x)=tan x is π.
d) The period of f(x)=sec x is 2π.
e) The period of f(x)=csc x is 2π.
f) The period of f(x)=cot x is π.

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The building's depression angle relative to the plane is found as  24.49°.

According to an aerial photographer who specializes in taking pictures of real estate properties.

The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.

Height h = 406 ft

Distance d =891 ft

The building's depression angle relative to the plane:

tan Ф = Height / Distance

tan Ф = 406 / 891

tan Ф = 0.455

Ф = 24.49°

Thus, the building's depression angle relative to the plane is found as  24.49°.

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The possible solutions from the triangle does not exist

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

B = 50 degrees

a = 102 units

b = 41 units

The angle A is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(A)/102 = sin(50)/41

This gives

sin(A) = 102 * sin(50)/41

Evaluate

sin(A) = 1.9057

Take the arc sin of both sides

A = DNE

This is so because the solution does not exist for the angle A

By extension, the values of angle C and side c cannot be calculated

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The equation that shows the relationship between the age of Danny and Terry is D = T - 6.

Let's represent Danny's age with the variable D and Terry's age with the variable T. We know that Danny is 22 years old, so we can write the equation D = 22.

We also know that Danny is 6 years younger than Terry, so we can write the equation D = T - 6. Now we can substitute the value of D from the first equation into the second equation to find the value of T.

D = T - 6

22 = T - 6

Add 6 to both sides of the equation:

22 + 6 = T

28 = T

So Terry is 28 years old.

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The theater sold 1875 regular tickets and 625 discount tickets.

Let x be the number of regular tickets sold and y be the number of discount tickets sold. We can symbolize the given information as a system of equations:
x + y = 2500 (total number of tickets sold)
28x + 20y = 65000 (total revenue)
To solve this system, we can use the substitution method. First, we can isolate one variable in one equation. Let's isolate x in the first equation:
x = 2500 - y
Now, we can substitute this expression for x into the second equation:
28(2500 - y) + 20y = 65000
Simplifying this equation gives:
70000 - 28y + 20y = 65000
-8y = -5000
y = 625
Now, we can substitute this value of y back into the first equation to find x:
x + 625 = 2500
x = 1875
So, the theater sold 1875 regular tickets and 625 discount tickets.

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Answer:

Power – A power is an expression that represents repeated multiplication of the same number or variable, such as a raised to the power of n, denoted by aⁿ.

Base – The base is the number or variable that is raised to a power or exponent in a power expression.

Exponent – The exponent is the number that indicates how many times the base is to be multiplied by itself in a power expression.

Coefficient – The coefficient is the numerical factor of a term that contains a variable in an algebraic expression.

Exponential Form – The exponential form is a way of writing a number using a base and an exponent, such as aⁿ, where a is the base and n is the exponent.

Expanded Form – The expanded form is a way of writing an expression as the sum or difference of its individual terms, such as (a+b)² = a² + 2ab + b².

Standard Form – The standard form is a way of writing a number using digits, such as 1234 or 1.234 x 10³.

Exponent Laws – The exponent laws are a set of rules that describe how exponents can be manipulated in algebraic expressions, including the product law, quotient law, power law, and negative exponent law. These laws help simplify and solve equations involving exponents.

After simplification, the solution of the expression is,

⇒ 0

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 2 (- 3) + 27 ÷ (- 3) + 3

Now,

We can simplify by the rule of BODMAS as;

⇒ - 2 (- 3) + 27 ÷ (- 3) + 3

⇒ - 2 (- 3) + (- 9) + 3

⇒ 6 - 9 + 3

⇒ 9 - 9

⇒ 0

Thus, After simplification, the solution of the expression is,

⇒ 0

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6x^3 + 6x - 6 = 0

The given equation is equivalent to a linear equation. To solve this, we will first factor out the denominators to create a common denominator.

The common denominator is (x+1)(x-1)(x^2-1). Then, multiply each side of the equation by the common denominator:

(3)(x+1)(x-1)(x^2-1) + (3)(x^2-1) = (4)(x+1)(x-1)(x^2-1)

Simplifying each side of the equation:

3x^3 + 3x^2 - 3x - 3 + 3x^2 - 3 = 4x^3 + 4x^2 - 4x

Finally, combine like terms on each side of the equation to get the linear equation:

6x^3 + 6x - 6 = 0

Therefore, the given equation is equivalent to the linear equation 6x^3 + 6x - 6 = 0.

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Using algebra, we can conclude that, if Jamie only works 10 hours during the week, he will not be able to meet his goal of earning at least $279, because the total pay he will earn, which is $232.50, is less than the amount he wants to earn.

The method to use to solve this problem would be algebra. We will use variables to represent the number of hours that Jamie works during the week and on the weekend, and we used equations to express the relationship between the total pay Jamie earns and the number of hours he works.

Let's first find out how many hours Jamie works during the week and on the weekend.

Let's say Jamie works x hours during the week. Then, he works 2x hours on the weekend.

The total amount of money Jamie earns is given by:

Total pay = Pay for week hours + Pay for weekend hours

Pay for week hours = $7.75 per hour * x hours

Pay for weekend hours = $7.75 per hour * 2x hours = $15.50 per hour * x hours

Total pay = $7.75x + $15.50x = $23.25x

Now let's substitute x = 10, since Jamie wants to work 10 hours during the week, to see if he can meet his goal of earning at least $279:

Total pay = $23.25 * 10 = $232.50

Since $232.50 is less than $279, Jamie will not meet his goal by working 10 hours during the week alone. He will need to work more hours during the week and/or on the weekend to reach his goal.

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The number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).

The total volume of the cubes in a container is 8^(7)  cubic centimetersand the volume of each individual cube is 8^(2) cubic centimeters. To find the number of cubes in the container, we need to divide the total volume by the volume of each individual cube.

This can be written as:

Number of cubes = 8^(7) / 8^(2)

Using the rule of exponents, when we divide two numbers with the same base, we can subtract their exponents. In this case, 7 - 2 = 5.

So the number of cubes in the container is:

Number of cubes = 8^(5)

Therefore, the correct answer is 8^(5).

The other option, 8^(7)*8^(-2), is also correct. This is because multiplying two numbers with the same base means we can add their exponents. In this case, 7 + (-2) = 5. So this also gives us the same answer, 8^(5).

In conclusion, the number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).

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A wheel of 28 cm diameter must rotate 400 times to go 352 m.

Let 'r' represents the radius, 'd' represents the diameter of the wheel.

Here, d = 28 cm

So, r = 14 cm

Let us assume that a wheel needs to rotate 'n' number of times.

We know that the formula for the circumference of circle is 2πr

Let 's' represents the circumference of wheel.

Using above formula,

s = 2 × π × r

s = 2 × 22/7 × 14

s = 44 × 2

s = 88 cm

Now we find the value of n.

First we convert the distance 352 m in centimeters.

352 m = 35200 cm

n = 35200 / s

n = 35200/88

n = 400

Therefore, a wheel must rotate 400 times.

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b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{kmh}{rate}&\stackrel{hrs}{time}\\ \cline{2-4}&\\ Upstream&60&b-c&5\\ Downstream&60&b+c&3 \end{array}\hspace{5em} \begin{cases} 60=(b-c)(5)\\\\ 60=(b+c)(3) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{60=(b-c)5}\implies \cfrac{60}{5}=bc\implies 12=b-c\implies 12+c=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{60=(b+c)3}\implies \cfrac{60}{3}=b+c\implies 20=b+c\implies \stackrel{\textit{substituting from above}}{20=(12+c)+c} \\\\\\ 20=12+2c\implies 8=2c\implies \cfrac{8}{2}=c\implies \boxed{4=c}~\hfill \stackrel{ 12~~ + ~~4 }{\boxed{b=16}}[/tex]

Among the answer choices provided, the closest percentage to the actual rate is 9.3%.

For instance, a study published in the Journal of American College Health found that only 11.1% of college students in the United States consumed the recommended five or more servings of fruits and vegetables per day. Similarly, a study published in the Journal of Nutrition Education and Behavior found that only 9.2% of college students in the United States met the daily recommendations for fruit and vegetable intake.

Based on these research studies, it is clear that the percentage of college students who consume the recommended amount of fruits and vegetables daily is quite low, with estimates ranging from 6.8% to 11.1%.

Therefore, among the answer choices provided, the closest percentage to the actual rate is 9.3%.

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Answer:

Inequality:

29.2x + 501.60 ≤ 560

Answer:

She may buy up to 2 reflectors.

Step-by-step explanation:

She can spend up to $560, so the total expense has to be less than or equal to $560.

total expense ≤ 560

All items she buys have a price and a number of items except for the outfits which have a price but an unknown number.

Let x = number of outfits.

total expense = $425.05 + 4 × $15.19 + $15.79 + x × $29.20

total expense = 29.2x + 501.60

Inequality:

29.2x + 501.60 ≤ 560

29.2x ≤ 58.4

x ≤ 2

She may buy up to 2 reflectors.

As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.

Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty. For instance, since there is a one in six possibility of rolling a six, the probability of rolling a six on a fair six-sided die is 1/6 or roughly 0.167. Another way to describe probability is as a percentage or as odds. A probability of 0.5, for example, corresponds to 50% or chances of 1:1. (meaning there is an equal chance of the event occurring or not occurring). Science, engineering, economics, and banking all use probability theory, a significant area of mathematics.

given

Assume Manuel has information on 100 aircraft with delays of no more than 25 minutes, of which 40 had delays of no more than 5 minutes.

The estimated likelihood that an arbitrarily chosen flight would arrive late by 5 minutes or less would then be:

P(late by 5 minutes or less) is equal to the number of planes that are 5 minutes or less late divided by the total number of flights that are 25 minutes or less late.

P(late by no more than 5 minutes) = 40/100

P(late by no more than 5 minutes) = 0.4

As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.

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The value of x from quadratic equation 8x²+15x=7x-4 is x=-1/2+i/2 and x=-1/2 - i/2

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is 8x²+15x=7x-4

Let us convert it to a quadratic equation.

8x²+15x-7x+4=0

Add the like terms

8x²+8x+4=0

x=-8±√8²-4.8.4/2.8

x=-8±√64-128/16

x=-1/2+i/2 and x=-1/2 - i/2

Hence, the value of x from quadratic equation  8x²+15x=7x-4 is x=-1/2+i/2 and x=-1/2 - i/2

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The volume of the sunglasses case is 292.5 cm^3 and the surface area is 324 cm^2.

The volume and surface area of the sunglasses case can be calculated using the following formulas:

[tex]Volume = Length * Width * Height[/tex]

[tex]Surface Area = 2(LW + LH + WH)[/tex]

Plugging in the given values:

[tex]Volume = 15 cm * 3.0 cm * 6.5 cm[/tex]

[tex]Volume = 292.5 cm^3[/tex]

[tex]Surface Area = 2(15 cm * 3.0 cm + 15 cm * 6.5 cm + 3.0 cm * 6.5 cm)[/tex]

[tex]Surface Area = 2(45 cm^2 + 97.5 cm^2 + 19.5 cm^2)[/tex]

[tex]Surface Area = 2(162 cm^2)[/tex]

[tex]Surface Area = 324 cm^2[/tex]

Therefore, the volume of the sunglasses case is 292.5 cm^3 and the surface area is 324 cm^2.

The volume of a cube is calculated by multiplying the three (3) sides of the figure, that is, height times length times width. This is given by the expression: [tex]V = a*b*h[/tex].

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1- The forecast for June using exponential smoothing with an alpha value of 0.2 and assuming the forecast for Jan is 34 is B. 36.1.

2- The MAD value for the two-month moving average is A. 2.67.

1- The forecast for June using exponential smoothing can be calculated as follows:
Ft = Ft-1 + α(At-1 - Ft-1)
Where Ft is the forecast for the current period, Ft-1 is the forecast for the previous period, At-1 is the actual sales for the previous period, and α is the smoothing constant.

Using the given data and an alpha value of 0.2, the forecast for June can be calculated as follows:

FJan = 34
FFeb = 34 + 0.2(34 - 34) = 34
FMar = 34 + 0.2(36 - 34) = 34.4
FApr = 34.4 + 0.2(39 - 34.4) = 35.32
FMay = 35.32 + 0.2(37 - 35.32) = 35.66
FJune = 35.66 + 0.2(38 - 35.66) = 35.87

Therefore, the forecast for June is 35.87, which is closest to option b. 36.1.

2- The MAD value for the two-month moving average can be calculated as follows:

MAD = (|34 - 35| + |36 - 34.5| + |39 - 35.5| + |37 - 37.5| + |38 - 38|) / 5 = 2.67

Therefore, the MAD value for the two-month moving average is 2.67, which is closest to option a. 2.67.

So the correct answers are B: 36.1 for the forecast for June and A: 2.67 for the MAD value for the two-month moving average.

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The measurement of the angle F in the given circle is 41°

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle, with secants FX and FB, we need to find the measurement of the angle F in the given circle

Using the property of circle,

∠ F = 1/2(arc XB - arc VW)

∠ F = 1/2(126°-44°)

∠ F = 1/2 x 82

∠ F = 41°

Hence, the measurement of the angle F in the given circle is 41°

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Answer:

4

Step-by-step explanation:

put number in order from smallest from largest.

4, 4, 4, 4, 5, 6

then take one away from each side until the middle is left.

it would be

4, 4, 4, 5

then

4, 4, 5

then

4

so the answer is 4

Height of the light house is 95.6 feet .

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

Given,

Shadow of the lighthouse = 22 feet

Angle of elevation α = 77°

Height of the light house = ?

tanα = Perpendicular/base

In this case

tanα = Height/Shadow

tan 77° = Height/22

4.33 = Height/22

Height = 22 × 4.33

Height = 95.26 ≈ 95.6 feet

Hence, 95.6 feet is height of the light house.

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a) Sin 2x = 2 tan x / 1 + tan^2 x is an identity.

b) Tan x + cot x = 2 csc 2x is an identity.

To verify that each equation is an identity, we will simplify both sides of the equation and show that they are equal.

For part a, we will use the double angle formula for sine and the Pythagorean identity.

sin 2x = 2 sin x cos x

2 tan x / 1 + tan^2 x = 2 sin x / cos x / 1 + sin^2 x / cos^2 x

= 2 sin x / cos x / cos^2 x / cos^2 x

= 2 sin x / cos x / 1 - sin^2 x

= 2 sin x / cos x / cos^2 x

= 2 sin x cos x

Therefore, sin 2x = 2 tan x / 1 + tan^2 x is an identity.

For part b, we will use the definitions of the trigonometric functions and the double angle formula for cosecant.

tan x + cot x = sin x / cos x + cos x / sin x

= (sin^2 x + cos^2 x) / (sin x cos x)

= 1 / (sin x cos x)

= 2 / (2 sin x cos x)

= 2 / sin 2x

= 2 csc 2x

Therefore, tan x + cot x = 2 csc 2x is an identity.

In conclusion, we have verified that both equations are identities.

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