Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.

Answer:

[tex]\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

[tex]\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}[/tex]

[tex]x=\cos \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]x=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The base of one of the right triangles can be found by using the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

[tex]\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}[/tex]

[tex]y=\sin \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]y=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

[tex]\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}[/tex]

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}[/tex]

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

[tex]\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

Answer:

The correct answer is option C. (-4,2) lies in the Quadrant II .

It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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Note that in  Circle Q, m∠1  = 66° (Option A)

Note that inthe circle above, the angle which creates the arc 114° lies ont he same line with ∠1. Since sum of angles on a Straight line sum up to 180°.

∠1 = 180 -114 = 66°

A circle is defined as a form made up of points in a two-dimensional plane that are equidistant from a particular location. A circle is defined as a closed curve with no corners or vertices. Circles define several circular forms in our everyday lives.

Circular shapes include:

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There are 10 possible results when Dan spins the wheel of destiny with the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 20.

Every possible result is represented by a different number, and Dan has an equal probability of choosing any of them.

The wheel serves as a tool for randomization, adding a degree of ambiguity and unpredictability to the experiment. There are 20 possible outcomes total, with increments of 2 between the lowest and highest numbers.

Thus, these results stand in for various values that Dan might get from spinning the wheel. We may analyse the likelihood and probable range of results for this particular experiment by taking into account all the conceivable possibilities.

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The Triangle is Equilateral and Equiangular.

We will use theses property of Equilateral Triangle as

We have a Triangle.

The Triangle all three angles measured 60 degree each.

and, We know the equilateral Triangle all angles measures 60 degree.

Now, from the figure all the three sides of triangle are equal.

and, we know Equilateral triangle have the three sides equal

Thus, the Triangle is Equilateral and Equiangular.

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Answer:

Median, because Sunny Town is symmetric.

[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]

14 inches taller by the tallest player than the shortest player on the basketball team. The correct option is A .

To determine how much taller the tallest player is than the shortest player on the basketball team, we need to examine the given line plot and calculate the difference between their heights.

To find the height difference, we need to identify the tallest and shortest players on the team. The line plot should display the heights of each player, allowing us to determine these values.

Once we have these heights, we can subtract the height of the shortest player from the height of the tallest player to calculate the difference.

Based on the options provided, we can consider each possibility:

A. If the height difference is 14 inches, then the tallest player is 14 inches taller than the shortest player. B. If the height difference is 10 inches, then the tallest player is 10 inches taller than the shortest player.

C. If the height difference is 13 inches, then the tallest player is 13 inches taller than the shortest player. D. If the height difference is 12.5 inches, then the tallest player is 12.5 inches taller than the shortest player.

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Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.  

For Design 1:

Dimensions: 3 m x 3 m x 30 cm

We find the total area:

Two faces measures 3 m x 3 m = 9 m² each for the bottom and top

Two faces measures 3 m x 30 cm = 0.9 m² each for back and front

Two faces measures 3 m x 30 cm = 0.9 m² each

Therefore the total area of materials needed for Design 1 is found as

= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²

Design 2:

Dimensions: 3.25 m x 3.25 m x 25 cm

In the same way, we find  the area of materials needed for Design 2:

Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²

Design 1 volume is :

Volume = Length x Width x Height

Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³

Design 2 volume is :

Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³

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The interest Pedro will have to pay is $5200

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

Principal = $32.500

Rate = 4% simple interest

Time = 4 years

The formula of simple iinterest is

I = Principal * Rate * Time

substitute the known values in the above equation, so, we have the following representation

I = 32500 * 4% * 4

Evaluate

I = 5200

Hence, Pedro have to pay $5200 as interest

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The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.

Recall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.

In this case

∠1 ≅ ∠2 - Given

hence they is bisected by AX

Also ∠5 ≅ ∠6. This means that they are bisected by CX

Since AX and CX form AC, and

AC = CA (Reflexive Property)
Also

BD = DB  (Reflexive Property)

Then it means that AC ⊥ BC (QED)

Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.

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The given image is a parallelogram, because the two lines are Parallel to each other implying that they will never cross each other

Based on the question above,  the coordinates of the figure are:

O = (0,0)

P = (a, b)

S = (a + c, b)

T = (c,0)

Note that the vertices O and T and they can be seen on the same horizontal level, due to the fact that they have the same y-coordinate and can be used also for vertices P and S

The length of the sides by distance formula will be:

PS = c

OT = c

So this implies that the opposite sides are parallel and congruent. Therefore, the image is a parallelogram

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Answer:

Step-by-step explanation:

4x/3 + x/6 =6

get a common denominator first

8x/6 + x/6 =6

then add

9x/6 = 6

multiply by six

9x = 36

divide by 9

x= 4

Given that a randomly selected applicant has more than 10 years of experience, the likelihood that they have a graduate degree is roughly 0.4016.

To find the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience, we need to use conditional probability. We can use the formula:

P(grad degree | over 10 years of experience) = P(grad degree and over 10 years of experience) / P(over 10 years of experience)

From the given information, we know that:

P(grad degree and over 10 years of experience) = 51 (number of applicants with over 10 years of experience and a graduate degree)

P(over 10 years of experience) = 127 (number of applicants with over 10 years of experience)

So, plugging in these values:

P(grad degree | over 10 years of experience) = 51 / 127

Using a calculator, we get:

P(grad degree | over 10 years of experience) ≈ 0.4016

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience, is approximately 0.4016.

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Answer: 15/38 or 0.39473684210526315789473684210526

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

Answer:

Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.

Step-by-step explanation:

Answer: Thats a Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

Scale drawings are valuable tools in various fields such as architecture, engineering, and design, allowing professionals to visualize and communicate ideas accurately. By employing scale factors and maintaining proportions, these drawings provide a reliable representation of real-world objects and spaces.

A scale drawing is a representation of an object or space that is proportional to the actual size or dimensions of the original. It involves using a scale factor, which is a ratio that compares the measurements on the drawing to the measurements of the real object or space. The scale factor determines how much the drawing is enlarged or reduced in relation to the actual size.

When creating a scale drawing, it is important to maintain the same proportion as the original object. Proportion refers to the relationship between the different parts of an object or space, ensuring that the relative sizes are accurate. This ensures that the scaled drawing provides an accurate representation of the original, even if it is smaller or larger in size.

The scale factor is typically expressed as a ratio or a fraction, such as 1:100 or 1/4. This ratio indicates how many times larger or smaller the drawing is compared to the actual object. For example, if the scale factor is 1:10, every unit on the drawing would represent ten units in reality. This allows for accurate measurements of length, as well as area.

Length is an essential aspect of scale drawings. By using the scale factor, the length of lines or dimensions on the drawing can be determined to reflect the corresponding measurements in the real object. For instance, if a line on the scale drawing represents 5 centimeters, and the scale factor is 1:10, the actual length of the line would be 50 centimeters.

In addition to length, scale drawings can also accurately represent areas. The scale factor can be used to determine the relationship between the areas on the drawing and the actual areas of the object or space. By applying the scale factor to the dimensions, the areas can be scaled up or down accordingly, maintaining the proportionality of the original.

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The calculated value of the period of the function is 6

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

The equation, f(x) = 2cos(2π/6(x + 4)) +3

A sinusoidal function is represented as

f(x) = acos(2π/b(x + c)) + d

Where the period is B

When the equations are compared, we have

2π/b = 2π/6

This gives

b = 6

Hence, the period of the function is 6

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Complete question

Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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After considering the given data we conclude that the value generated after performing divison of the given expression is 18x, under the condition that we follow the principles of divison.

Let us proceed by evaluating the given expression by applying division
4x(3+6) divided by 2
= 4x9/2
= 36x/2
= 18x
Division is considered one of the four basic mathematical operations, then the other three are addition, subtraction, and multiplication.
In short , division is referring to the breaking down of a given bigger number or expression into simpler yet smaller forms to meet the criteria of performing a function.
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Answer:

? ≈ 9.09

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a, b , c are the sides opposite angles A , B , C

we require the third angle in the triangle

third angle = 180° - (51 + 109)° = 180° - 160° = 20°

then with

a = 4 , ∠ A = 20°

b = ? , ∠ B = 51°

[tex]\frac{4}{sin20}[/tex] = [tex]\frac{?}{sin51}[/tex] ( cross- multiply )

? × sin20° = 4 × sin51° ( divide both sides by sin20° )

? = [tex]\frac{4sin51}{sin20}[/tex] ≈ 9.09 ( to the nearest hundredth )

Answer:

2a+15b+11

Step-by-step explanation:

2*a + 2*4b + 5 + 7b + 6

2a + 8b + 5 + 7b + 6

2a + 8b + 7b + 5 + 6

2a + 15b + 11

Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.

To find the direction angle of a vector, we can use the formula:

θ = arctan(y/x)

In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.

Plugging the values into the formula, we get:

θ = arctan(8/0)

However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.

When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.

In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.

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There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Using the equation y=−x+9.6, we can calculate the predicted values for y as follows:

When x = 1: y = -(1) + 9.6 = 8.6

When x = 2: y = -(2) + 9.6 = 7.6

When x = 3: y = -(3) + 9.6 = 6.6

When x = 4: y = -(4) + 9.6 = 5.6

When x = 5: y = -(5) + 9.6 = 4.6

When x = 6: y = -(6) + 9.6 = 3.6

We can then calculate the residuals by subtracting the predicted values from the actual values of y:

When x = 1: residual = 5.8 - 8.6 = -2.8

When x = 2: residual = 8.7 - 7.6 = 1.1

When x = 3: residual = 2.9 - 6.6 = -3.7

When x = 4: residual = 0.8 - 5.6 = -4.8

When x = 5: residual = 5.1 - 4.6 = 0.5

When x = 6: residual = 1.7 - 3.6 = -1.9

There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Therefore, we can say that the equation y=−x+9.6 is not a good fit for this data.

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The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc TV = 2(m∠TUV)

54x - 2 = 2(80)

54x - 2 = 160

54x = 160 + 2 {collect like terms}

54x = 162

x = 162/54 {divide through by 3}

x = 3

Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.

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Answer:

D=2, 3, 5, 6, 7, 8, 9,

Step-by-step explanation:

btw can i js get 1  brainly?

{2,3,5,6,7,8,9}

The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.

To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.

Do you have this information available?