Express the area of the shaded region in the room shown algebraically

Answer:

A = 44º

[tex]b \approx 28.99[/tex]

[tex]c \approx 40.31[/tex]

Step-by-step explanation:

In this problem we are tasked with "solving the triangle," which means we need to solve for each of the triangle's non-given dimensions.

We can first solve for angle A, since we are given the other two interior angles of the triangle (90º and 46º), and we know that the measures of the interior angles of a triangle add to 180º.

A + 90º + 46º = 180º

A = 180º - 90º - 46º

A = 44º

Now that we have angle A, we can use the Law of Sines to solve for side length b.

[tex]\dfrac{a}{\sin(A)} = \dfrac{b}{\sin(B)}[/tex]

[tex]\dfrac{28}{\sin(44\textdegree)} = \dfrac{b}{\sin(46\textdegree)}[/tex]

[tex]b = \dfrac{28\sin(46\textdegree)}{\sin(44\textdegree)}[/tex]

[tex]b \approx 28.99[/tex]

Finally, we can solve for c using the Pythagorean Theorem.

a² + b² = c²

28² + 28.99² ≈ c²

[tex]c \approx \sqrt{1624.70}[/tex]

[tex]c \approx 40.31[/tex]

Answer:

[tex]x \approx 31.6\textdegree[/tex]

Step-by-step explanation:

Apply the Law of Sines.

[tex]\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b}[/tex]

↓ plug in given side lengths and angle measures

[tex]\dfrac{\sin(74\textdegree)}{22} = \dfrac{\sin(x)}{12}[/tex]

↓ multiply both sides by 12

[tex]\dfrac{12\sin(74\textdegree)}{22} = \sin(x)[/tex]

↓ take the inverse sine of both sides

[tex]\sin^{-1}\left(\dfrac{6\sin(74\textdegree)}{11}\right) = x[/tex]

↓ evaluate using a calculator and round to tenths place

[tex]x \approx 31.6\textdegree[/tex]

Series: 1 + 3 + 5 + 7 + 9 + ...

Proof by PMI:

P: The series starts with 1 and increases by 2 for each consecutive term.

M: The nth term of the series is 2n - 1.

I: The series is an arithmetic series with a common difference of 2.

Operations of functions:

Addition: (f + g)(x) = f(x) + g(x)

Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f + g)(x) = (2x + 1) + (3x - 2) = 5x - 1

Multiplication: (f * g)(x) = f(x) * g(x)

Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f * g)(x) = (2x + 1) * (3x - 2) = 6x^2 - 2x + 3x - 2 = 6x^2 + x - 2

GE4 is a mathematical modeling course, in which I have learned how to use mathematical methods and models to analyze and solve real-world problems. I learned how to use statistical analysis, optimization, and simulation to make predictions and decisions. I also learned how to use various tools and software to create and analyze models. I learned to use mathematical tools to solve problems in different fields such as finance, engineering, and science.

Y is 1/3x +5 an equation of the line that passes through point P.

The slope of the new line will be equal to (1/3) = 1/3because perpendicular lines have slopes that are the negative reciprocals of one another.

X and Y are represented by X and Y, (x,y) is the pair of coordinates for the point, and m is the slope in this equation, which reads: Y - y = m(X-x).

Y-4 = 1/3(X-1), which leads to Y = 1/3X +1 +4 and Y = 1/3X +5.

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The range of the function shown on the graph is, y ≥ 2.

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)

We have to given that;

The graph of function is shown in figure.

Now, We know that;

The range is the set of possible outputs values, which are shown on the y - axis.

Hence, By the graph;

The range of function is,

⇒ y ≥ 2

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The probability of rolling two trick number cubes with the numbers 5, 10, and 15 on them can be calculated using the formula P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.

In this case, the total number of possible outcomes is 6, since there are six possible combinations of two number cubes. The number of favorable outcomes for a sum of 10 is 2, since there are two possible combinations (5 and 5, and 10 and 15). Therefore, the probability of rolling a sum of 10 is 2/6, or one-third. The probability of rolling a sum of 15 is also one-third, since there is only one possible combination (10 and 5). The probability of rolling a sum of 20 is one-sixth, since there is only one possible combination (10 and 10). Therefore, the probability model for the sum of the two number cubes is a 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.

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Statistic is a measure that describes a characteristic of the whole population.

Estimate  is a measure that describes a sample.

A statistic is a measure of a characteristic of an entire population. This means that it is a measure that describes the entire population, such as the average age, number of people, etc.

An estimate is a measure of a characteristic of a sample. This means that it is a measure that describes a portion of the population, such as the average age of a group of people, number of people in a certain area, etc.

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According to mathematics, a regular hexagon's area A is  288 sq units option -A is correct answer.

How to Locate a Hexagon's Area

A regular hexagon's side length can be determined in step 1.

Step 2: Calculate the area using the formula for the area of a hexagon (3√3 s²)/2, where s is the length of the hexagon's sides.

A regular hexagon whose side length is 8 in.

and the apothem is 12 in.

The equation for the area,

A=(3√3)/2 × a²

Therefore

A = 6×(0.5×8×12)

A = 288 sq units

In conclusion, a regular hexagon's surface area A is 288 square feet.

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Answer:

Your answer is A) [tex]288in^{2}[/tex]

Step-by-step explanation:

The number of games played is 6 and the number of rides is 2.

Here it is given that the number of games played was 3 times the number of rides. So, by this, we get the value of both is the ratio.

That is $15,

number of games played: number of rides = 3: 1

Let x be the common ratio. So, we have

Number of games played = 3x, and number of rides = x

It is given that the cost of each game is $1.50 and cost of each ride is $3 and the total cost is $15.

By this, we get an equation,

1.50 × 3x + 3 × x = 15

4.5x + 3x = 15

7.5x = 15

x = 2

Therefore the number of games= 3x = 3×2 = 6 and the number of rides = x = 2.

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Answer:

44

Step-by-step explanation:

Because of similar triangles we have

VN/UN = VL/UM

11/8 = VL/24

Cross multiply.

8VL = 11 × 24

VL = 11 × 3

VL = 33

LN = VL + VN

LN = 33 + 11

LN = 44

Answer:

the answer is   d t d T ​ = c ( T + T 0 ​ )

Step-by-step explanation:

Answer:

how if there are no numbers or anything to find

Step-by-step explanation:

4000 donuts will Pamela need to sell in order to reach her goal.

What is the profit?

Profit is when the selling price is more than the cost price or revenue is more than the cost while loss is the opposite of profit.

To calculate the number of donuts Pamela needs to sell to reach her goal, you need to divide her desired profit by the profit per donut.

If the cost of ingredients for each donut is $0.67 and she plans to sell each donut for $2.99, the profit per donut would be $2.99 - $0.67 = $2.32.

To reach her goal of making at least 4000, she needs to make a profit of $2.32 x 4000 = $9280.

So she needs to sell $9280/$2.32 = 4000 donuts.

Hence,  4000 donuts will Pamela need to sell in order to reach her goal.

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The carrying capacity K for this equation be 33.33.

To determine how many people an ecosystem can support, carrying capacity is crucial. Without significant setbacks from environmental degradation, this is essential for sustainable growth.

The greatest population that may be supported in a given environment under a variety of restrictions is known as the carrying capacity. In the population vs. time graph, it is at the value K that the graph asymptotically approaches the graph y=K.

The population growth model is given by [tex]$\frac{d P}{d t}=0.01 P-0.0003 P^2$[/tex]

The population model can be re-written as:

[tex]$$\begin{aligned}\frac{d P}{d t} & =0.01 P-0.0003 P^2 \\& =0.01 P(1-0.03 P) \\& =\frac{1}{100} P\left(1-\frac{3 P}{100}\right)\end{aligned}$$[/tex]

Carrying capacity of the equation be

[tex]$$\begin{aligned}K & =\frac{P}{1-\frac{1}{r P} \frac{d P}{d t}} \\& =\frac{P}{1-\frac{100}{P} \cdot \frac{P}{100}\left(1-\frac{3 P}{100}\right)} \\& =\frac{P}{\frac{3 P}{100}} \\& =\frac{100}{3}=33.33\end{aligned}$$[/tex]

The complete question is:

Suppose that a population of bacteria grows according to the logistic differential equation [tex]$\mathrm{dP} / \mathrm{dt}=0.01 \mathrm{P}-0.0003 \mathrm{P}^2$[/tex] where P is the population measured in thousands and t is time measured in days.

a) Calculate the carrying capacity K for this equation? (You must justify your answer by showing how you derived K.)

b) What does the carrying capacity represent?

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The linear equation for the given situation is y= cx + 2.50.

What is a linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.

We are given that a car service charges $2.50 to pick us up and charges c cents for each mile of our trip.

So, the equation that represent the cost of a car based on the number of miles driven is given by:

y= cx + 2.50

Hence, the linear equation for the given situation is y= cx + 2.50.

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Answer:

32

Step-by-step explanation:

0.8 x

Answer:

32

Step-by-step explanation:

Answer:

Answer in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note that t(u) is different from t·u, t(u) is multiplying vectors together, while t·u is the dot product of 2 vectors.

Answer: g = 3 sqrt n/ n

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

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

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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Answer:

5.8%

Step-by-step explanation:

To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.

First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.

So the amount invested in mutual funds is 40/100 * $100 = $40

The amount invested in real estate is 40/100 * $100 = $40

The amount invested in stocks is 20/100 * $100 = $20

Then we can calculate the growth of each investment using the percentages provided:

The growth of mutual funds is 2/100 * $40 = $0.80

The growth of real estate is 7/100 * $40 = $2.80

The growth of stocks is 11/100 * $20 = $2.20

Now we can add up the growth of each investment and divide it by the total investment to find the average growth:

($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%

So the average growth on Alexandra's total investment is 5.8%.

Answer:

15

Step-by-step explanation:

35/k=7/3

7k=35*3

7k=105

k=15

Answer: five and six hundred-twenty-five

Step-by-step explanation:

the decimal point represents the and, and all you need to do is write out the numbers, then you are good to go

The distance traveled is 1190 m. We can evaluate using the speed and time formula.

Given Speed = 30mph

Time = 3.5 hr

We know that

Speed = Distance / Time

340 = distance /3.5

Distance = 1190m

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the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).

Initial value problem:

y'' + 4y' + 4y = 0, y(0)=1, y'(0)=2

The longest interval in which the initial value problem is certain to have a unique twice differentiable solution is the interval (-∞, ∞).

The given initial value problem is a second order linear homogeneous differential equation. This type of equation is known to have a unique twice differentiable solution on the interval (-∞, ∞). Therefore, the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).

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The value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

Let us solve this problem step by step.

For the given equation: y' + 2y = e^{-x}

We have the solution as: y = ce^{-2x} + e^{-x}

We have to find the value of c for which the solution satisfies the initial condition y(2)= 9.

Substituting x = 2 in the above equation, we get:

9 = c + e^{-2}.

Therefore, we can solve for c as:

c = 9 - e^{-2}

Hence, the value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

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Answer:

x=3

Step-by-step explanation:

-4(x-2)=2-2x

-4x+8=2-2x

-4x+8=-2x+2

-4x=-2x+2-8

-4x=2x-6

-2x=-6

x=3

Let's solve your equation step-by-step.

-4(x-2)=2-2x

Step 1: Simplify both sides of the

equation.

-4(x-2)=2-2x

Simplify:

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

(Distribute)

-4x+8=2+ -2x

-4x+8=-2x+2

Step 2: Add 2x to both sides.

-4x+8 + 2x = -2x+2+2x

-2x+8=2

Step 3: Subtract 8 from both sides.

-2x+8-82-8

-2x=-6

Step 4: Divide both sides by -2.

-2x -6 = -2 -2

x=3

Option (a) is the correct answer i.e. the graph that shows a line that passes through negative 5 comma 0 and 0 comma 2.5, there is a second line that passes through 0 comma 10 and 5 comma 0 and the lines intersect at 3 comma 4, represents the system of given equations.

What is a system of equations?

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.

Given equations : 2x + y = 10 .......equation 1

                             −x + 2y = 5 ......equation 2

Let's take the equation : 2x + y = 10

when x=0, y = 10 and when y=0, x=5

So, the first line passes through (0,10) and (5,0).

Now, If we look at second equation :   −x + 2y = 5

when x=0, y = 2.5 and when y=0, x= -5

So, the second line passes through (0,2.5) and (-5,0).

Now, we've −x + 2y = 5

we'll use substitution method to find out the intersection point.

multiplying it by 2, we get -2x + 4y = 10 ......equation 3

Adding equation 1 and 3,

we get, 5y = 20

             y = 4

Putting y = 4 in equation 3,

we get, x= 3.

Hence, The intersection point is (3,4).

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Answer: The quotient of 2 and 9 is 0.2222 (approximately) or 2/9

Step-by-step explanation:

Quotient is a mathematical term that refers to the result of dividing one number by another. In this case, the quotient of 2 and 9 is found by dividing 2 by 9, which results in 0.2222 (approximately) or 2/9.

It's important to note that the quotient is a decimal number because 9 doesn't divide into 2 exactly, so there is a remainder of 0.2222. The quotient represents the number of times 9 can be divided into 2, which is a fraction of a time. In this case, 9 can be divided into 2 only 0.2222 times.

I hope this helps :)

The quotient of 2 and 9 is the result of the division of 2 by 9 which is approximately 0.2222.

The question is asking for the quotient of 2 and 9. The quotient is the result of division. So, to find the quotient of 2 and 9, you need to divide two by nine.

The calculation is as follows: 2 ÷ 9 = 0.2222 (rounded to the fourth decimal place).

So, the quotient of 2 and 9 is approximately 0.2222.

Always remember, that when the divider (the number we divide by) is larger than the dividend (the number to be divided), we get a quotient less than one.

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Expression represents the probability of the given number of attempts and the success rate is given by option E. B( 60 , 45 , 30 ).

As given in the question,

In the given situation,

Let us consider 'n' represents the number of trials attempt by the weightlifter.

'p' represents the probability of success in his number of trials.

And 'r' represents the number of success out of his total number of attempts.

Here n = 60

p = 45%

r = 30

Using binomial distribution method we can represents the expression of the probability for the given condition  :

B( n , p , r )

Substitute the values we get,

= B( 60, 45, 30 )

Therefore, for the given total number of lifts , success rate the expression represents the probability is given by option E . B ( 60, 45 , 30 ).

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