Solve the right triangle. If two sides are given, give angles in degrees and minutes.

B=68°35', b = 8 km
Round side lengths to one decimal place.

The probability that exactly 12 out of 22 pitches are strikes is approximately 0.18 (rounded to two decimal places).

To find the probability that exactly 12 out of 22 pitches are strikes, we can use the binomial probability formula. In this case, the probability of throwing a strike for each pitch is 0.431, and we want to calculate the probability of getting exactly 12 strikes out of 22 pitches.

Using the binomial probability formula, the probability of getting exactly 12 strikes out of 22 pitches is:

P(X = 12) = C(22, 12) * (0.431)^12 * (1 - 0.431)^(22 - 12)

where C(22, 12) represents the number of ways to choose 12 strikes out of 22 pitches.

Calculating this probability, we find:

P(X = 12) = 22! / (12! * (22 - 12)!) * (0.431)^12 * (1 - 0.431)^(22 - 12)

P(X = 12) ≈ 0.1832

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Therefore, the expected annual profit of Ruby Company is 2.703 billion dollars using probability.

Let X be the annual profit of the company. We know that X follows a normal distribution with variance equal to the cube of its mean, i.e., Var(X) = (E[X])^3.

To find the expected annual profit, we need to find the mean of X, denoted as E[X].

We are given that the probability of an annual loss is 5%. This means that the probability of making a profit is 1 - 0.05 = 0.95.

Let Z be a standard normal random variable, then we have:

P(X < 0) = P((X - E[X]) / sqrt(Var(X)) < (0 - E[X]) / sqrt(Var(X)))

= P(Z < -E[X] / (E[X])^(3/2))

Since P(X < 0) = 0.05, we have:

0.05 = P(Z < -E[X] / (E[X])^(3/2))

Using a standard normal table or calculator, we can find that P(Z < -1.645) = 0.05, where -1.645 is the 5th percentile of the standard normal distribution.

Thus, we have:

-E[X] / (E[X])^(3/2) = -1.645

this equation, we get:

E[X]^(1/2) = 1.645

Taking the square of both sides, we get:

E[X] = 2.703

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The small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

To determine the distance that the small submarine must travel to reach 180 feet below sea level, we need to use some basic math.
First, we need to determine the distance between the current position of the submarine (-1,320 feet) and its target depth (-180 feet below sea level). To do this, we subtract the target depth from the current depth:
-1,320 ft - (-180 ft) = -1,140 ft
This means that the submarine needs to travel 1,140 feet down in order to reach its target depth.
Next, we need to figure out how long it will take the submarine to travel that distance. We know that it has 60 minutes to do so, so we can use the formula:
distance = rate x time
We know the distance (1,140 feet), so we need to solve for rate. Rearranging the formula, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 1,140 ft / 60 min = 19 ft/min
So the small submarine needs to travel at a rate of 19 feet per minute in order to reach its target depth of 180 feet below sea level in 60 minutes.
In summary, the small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

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The general solution of the given system of differential equations is:

y = -37 × (1/2)x² + 5x + C, where C is the constant of integration.

The general solution of a system of derivative equations refers to a set of equations or formulas that represent all possible solutions of the given system. It includes an arbitrary constant or constants, which can take different values to yield different specific solutions.

The form of the general solution depends on the nature of the equations and the techniques used to solve them.

Here we have

dx/dt = 7x + y and dy/dt = -2x + 5y

To find the general solution of the given system of differential equations:

=> dx/dt = 7x + y  __ (1)

=> dy/dt = -2x + 5y  __(2)

Solve it using the method of simultaneous equations.

Solve Equation (1) for y:

y = dx/dt - 7x

Substitute the value of y in Equation (2):

dy/dt = -2x + 5(dx/dt - 7x)

Simplify the equation:

dy/dt = 5dx/dt - 2x - 35x

dy/dt = 5dx/dt - 37x

Rearrange the equation:

dy/dt - 5dx/dt = -37x

Multiply through by dt:

dy - 5dx = -37x dt

Integrate both sides of the equation:

∫(dy - 5dx) = ∫(-37x) dt

Integrate each term:

y - 5x = -37 * (1/2)x² + C

Simplify the equation:

y = -37 × (1/2)x² + 5x + C

Therefore,

The general solution of the given system of differential equations is:

y = -37 × (1/2)x² + 5x + C, where C is the constant of integration.

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The curved surface area of the cone is 148.19 square cm

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

Radius, r = 5 cm

Height, h = 8 cm

The slant  height l of the cone is calculated as

l² = 8² + 5²

So, we have

l² = 89

This gives

l = √89

The curved surface area of the cone is then calculaed as

Area = πrl

So, we have

Area = π * 5 * √89

Evaluate

Area = 148.19

Hence, the curved surface area of the cone is 148.19 square cm

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Answer:

We have congruent alternate interior angles.

39° + 96° + x° = 180°

135° + x° = 180°

x = 45

Answer:$15

Step-by-step explanation: Okay if the discount is of 3$ and a 20% is 100% if multiplied by 5 then you multiply 3 times 5 there EZ

A ratio is a relationship in which for every x units of one quantity there are y units of another quantity. Ratios are considered to be equivalent if they express the same x/y. A ratio compares 2 like or unlike quantities by division. Ratios can be shown visually using a graph or a ratio table.

The given statement is incomplete as the significance level is not mentioned. The chi-square value of 29.25 indicates that there is a statistically significant difference between the observed and expected frequencies of the categorical data.

The degrees of freedom in this case are three, which means that the data has been divided into four categories. The exact interpretation of the chi-square value depends on the significance level. If the significance level is 0.05, which is commonly used, then the calculated chi-square value is greater than the critical value of 7.815.

This means that the null hypothesis of no difference between the observed and expected frequencies can be rejected at the 0.05 level of significance. In other words, there is evidence to support the alternative hypothesis that there is a significant difference between the observed and expected frequencies.

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Para calcular la velocidad del joven, Podemos utilizar la fórmula de la velocidad promedio Por lo tanto, la posición del joven a las 9 h es 1100 km.

a) Para calcular la velocidad del joven, podemos utilizar la fórmula de la velocidad promedio:

velocidad = distancia / tiempo

La distancia recorrida por el joven es xf - xo = 500 km - 200 km = 300 km, y el tiempo transcurrido es 11 h - 8 h = 3 h. Entonces, la velocidad del joven es:

velocidad = 300 km / 3 h = 100 km/h

Por lo tanto, el joven se movió a una velocidad constante de 100 km/h.

b) La ecuación que determina la posición del joven en función del tiempo puede ser expresada como:

x = xo + velocidad × tiempo

donde x es la posición del joven en un momento dado, xo es la posición inicial (xo = 200 km), velocidad es la velocidad constante a la que se mueve el joven, y tiempo es el tiempo transcurrido desde la posición inicial.

Sustituyendo los valores conocidos, obtenemos:

x = 200 km + 100 km/h × t

donde t es el tiempo en horas.

c) Para calcular la posición del joven a las 9 h, podemos utilizar la ecuación que determina la posición del joven en función del tiempo:

x = 200 km + 100 km/h × t

Sustituyendo t = 9 h, obtenemos:

x = 200 km + 100 km/h × 9 h = 1100 km

Por lo tanto, la posición del joven a las 9 h es 1100 km.

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The best approximation of the volume of a sphere with a diameter of 12 units is approximately 904.78 cubic units.

The formula for the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r represents the radius.

Given the diameter of 12 units, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 units.

Now, we can substitute the radius into the volume formula:

V = (4/3)π(6^3)

 = (4/3)π(216)

 ≈ 904.78 cubic units

Using the approximation of π as 3.14, we can calculate the volume as follows:

V ≈ (4/3) * 3.14 * 216

 ≈ 904.78 cubic units

Therefore, the best approximation of the volume of the sphere with a diameter of 12 units is approximately 904.78 cubic units.

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The required area of the trapezoid PQRS is 144+72√3 square units. Option A is correct.

Area of trapezoid PQRS = [PQ+RS]/2 * QB

We are given PQ=18, QR = 24

The vertical line from Q to line SR is given as,
sin30 = V/24
V = 12
And horizontal measure over SR is given as,
cos30 = H/QR
H = 12√3

The length of QR is given as,
QR = 6 + 12√3

Area of trapezoid PQRS = [PQ+RS]/2 * QB
                                        = [18+6+12√3]/2*12
                                        = 144+72√3

Thus, the required area of the trapezoid PQRS is 144+72√3 square units.

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Here is a paragraph about the transformations I used to create my logo.

I started with a basic shape, a square. I then reflected the square across the horizontal axis, creating a mirror image. I then translated the reflected square up and to the right, creating a new shape. I then rotated the new shape 45 degrees, creating a third shape. The third shape is symmetric, meaning that it can be divided into two identical halves.

I then used these three shapes to create my logo. I used the first shape as the background, the second shape as the foreground, and the third shape as the logotype. I chose these shapes because they represent the three stages of transformation: the beginning, the middle, and the end.

The reflection represents the beginning of the transformation, when something is changed from its original state. The translation represents the middle of the transformation, when something is in the process of being changed. The rotation represents the end of the transformation, when something has been completely changed.

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It's important to note that without the actual data, I cannot provide a definitive assessment of the model's appropriateness. I recommend conducting the analysis with the provided dataset to draw accurate conclusions about the suitability of the linear regression model.

To develop an estimated regression equation and assess the appropriateness of a simple linear regression model, we need the specific data from the "productioncost" dataset. Since the data is not provided, I cannot perform the analysis or construct the standardized residual plot.

However, I can provide you with a general approach to determine the appropriateness of a simple linear regression model based on a standardized residual plot. After fitting the regression model, you can calculate the standardized residuals by dividing the residuals by their estimated standard deviation. Plotting these standardized residuals against the predicted values can help assess the model's appropriateness.

In a standardized residual plot, if the residuals exhibit random scatter around the horizontal line at zero, with no discernible patterns or trends, it suggests that the linear regression model is appropriate. On the other hand, if there are systematic patterns or trends in the residuals, such as a curved shape or unequal spread, it indicates that the linear regression model may not adequately capture the relationship between the variables.

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The distance between the center of the circle and the given point is 13 units.

The distance between the center of the circle (0, 0) and the given point (-5, 12) should be equal to the radius of the circle.

Using the distance formula,

d= √(-5-0)² + (12-0)²

d = √25 + 144

d = √169

d = 13 unit

Therefore, the distance between the center of the circle and the given point is 13 units.

Any point on the circle will have a distance of 13 units from the center.

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The best simulation to model the scenario of randomly selecting widgets and recording them as defective or working is a Bernoulli trial simulation.

A Bernoulli trial simulation is used when there are only two possible outcomes, such as success or failure. In this case, the two outcomes are defective or working widgets. The simulation involves randomly selecting a widget and recording whether it is defective or working. This process is repeated multiple times to generate a sample of widgets. The probability of success, or the proportion of defective widgets, is known and remains constant throughout the simulation. This type of simulation is appropriate for modeling the scenario because it allows for the calculation of the probability of selecting a defective widget and can be used to estimate the proportion of defective widgets in the factory's production.

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They would spend approximately 13.33 hours driving if they plan to cover a total distance of 800 miles at an average speed of 60mph.

To answer this question, we need to use the formula: time = distance/speed. In this case, the distance is 800 miles and the average speed is 60mph. Therefore, the time spent driving can be calculated as:
Time = 800 miles / 60 mph
Simplifying this equation, we get:
Time = 13.33 hours
So, the total time that they would spend driving is 13.33 hours. It's important to note that this is the average time it would take them if they maintained a constant speed of 60mph throughout their journey. However, if they encountered traffic, roadworks, or took any breaks during their trip, the actual time spent driving would be longer than this.
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Answer:

16y^2-13y+6

Step-by-step explanation:

(2y-3)(3y-2)

you have to expand the brackets

to do this you have to times each expression by the other bracket

2y×3y=6y^2

2y×-2=-4y

-3×3y=-9y

-3×-2=6

if you put these together u get:

6y^2-4y-9y+6

because there are two pairs containing y we can simplify this

-4y-9y=-13y

so the answer is

6y^2-13y+6

[tex]6y^{2}-13y+6[/tex]

[tex](2y-3)(3y-2)=\\2y(3y-2)-3(3y-2)[/tex]

[tex]6y^{2}-4y-3(3y-2)\\6y^{2} -4y-9y+6[/tex]

[tex]6y^{2} -4y-9y+6=\\6y^{2}-13y+6[/tex]

So the answer  [tex](2y-3)(3y-2)[/tex] is [tex]6y^{2}-13y+6[/tex]

I hope this helped, if it displeased tell me what I did wrong so I can possibly fix it ૮ ˶ᵔ ᵕ ᵔ˶ ა

Answer:

9.25 inches

Step-by-step explanation:

9.25 inches

Answer: b

Step-by-step explanation:

Check the picture below.

A graph representing the function g(x) = -1/2f(x + 2) is shown in the image below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 0)/(5 - 3)

Slope (m) = 4/2

Slope (m) = 2.

At data point (3, 0) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 2(x - 3)

y = f(x) = 2x - 6

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Answer:

36 π and 12 π respectively.

Step-by-step explanation:

To find the area of a circle, we do πr^2. For circumference, we do 2πr, where r is the radius. Since we know the diameter of this circle is 12, and we know the radius is half the diameter, then:

12/2 = 6 = r

knowing r, we can find out the area and the circumference. The area is:

πr^2 = π 6^2, so it is 36π for the area. The circumference is:
2πr = 2 π 6 = 12π.

The formula for the area of the shapes in:

8e). A = a[√(x² + a²)]

8f). A = a² - a[√[(2b)² - a²]]/4

Shape in 8e is a triangle and the height is derived using Pythagoras rule as;

triangle height = √(x² + a²)

Area of the triangle = 1/2 × 2a × √(x² + a²)

Area of the triangle = a[√(x² + a²)]

The shape in 8f is observed to be a triangle area cut out from a square area, thus;

Area of the square = a²

The triangle height = √[(b² - (a/2)²]

triangle height = √[(2b)² - a²]

Area of the triangle = 1/2 × a × √[(2b)² - a²]

Area of the triangle = a[√[(2b)² - a²]]/4

Area for the 8f shape = a² - a[√[(2b)² - a²]]/4

Therefore, the formula for the area of the shapes in:

8e). A = a[√(x² + a²)]

8f). A = a² - a[√[(2b)² - a²]]/4

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The equation of the circle in standard form is (x - 5)² + (y + 4)² = 36

The center of the circle is the midpoint of the diameter.

Using the midpoint formula, we can find the center as follows:

x-coordinate of center = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2)/2

= (-1 + 11)/2

= 5

y-coordinate of center = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2)/2

= (-4 - 4)/2

= -4

So the center of the circle is (5, -4) and the radius is half the length of the diameter:

radius = distance between endpoints of diameter/2

= √(11 - (-1))² + (-4 - (-4))²]/2

= 6

Therefore, the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36

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Let x be the number of one hour sessions that Mrs. B teaches and let y be the number of half hour sessions that she teaches per week. Then we can write the following system of inequalities to represent her goals:

60x + 40y > 800 (She hopes to make more than $800 tutoring)

x + y <= 12 (She can work a maximum of 12 hours per week)

To determine how many one hour sessions and half hour sessions she can teach, we need to graph these inequalities on a coordinate plane. The graph should show the shaded region that satisfies both inequalities.

To graph the inequality 60x + 40y > 800, we can first rewrite it as:

3x + 2y > 40

Then we can graph the line 3x + 2y = 40 by plotting the points (0,20) and (13.33,0) and drawing a line through them. Since we want to graph the inequality 3x + 2y > 40, we need to shade the region above the line.

To graph the inequality x + y <= 12, we can simply graph the line x + y = 12 by plotting the points (0,12) and (12,0) and drawing a line through them. Since we want to graph the inequality x + y <= 12, we need to shade the region below the line.

The shaded region that satisfies both inequalities is the region that is above the line 3x + 2y = 40 and below the line x + y = 12. This region is a triangle with vertices at (0,12), (8,4), and (13.33,0).

To determine if Mrs. B can teach 5 one hour sessions and 14 half hour sessions, we can plug these values into the inequalities and see if they are satisfied:

60(5) + 40(14) = 860 > 800 (This inequality is satisfied)

5 + 14 = 19 <= 12 (This inequality is not satisfied)

Since the second inequality is not satisfied, it is not possible for Mrs. B to teach 5 one hour sessions and 14 half hour sessions.

The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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The volume of the cylinder is 29.78 inches cube.

The volume of the cone is  9.93 inches cube.

The figure above is a sphere, cylinder and a cone. The volume of the figure can be represented as follows:

volume of a sphere = 4 / 3πr³

where

20 = 4 / 3 × π × r³

cross multiply

4r³π = 60

r³π = 15

r = ∛15 / π

r = ∛4.78

r = 1.68 inches

volume of a cylinder = πr²h

where

volume of a cone = 1 / 3 πr²h

where

Therefore, let's find the volume of the cylinder and cone with the following information.

Hence,

volume of the cylinder = π × (r)² × 2r

volume of the cylinder = 2(1.68)³π

volume of the cylinder = 29.78 inches cube

Therefore,

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × 3.14 × r² × 2r

volume of the cone = 1 / 3 × 3.14 × 2(1.68)³

volume of the cone = 29.77744896 / 3

volume of the cone = 9.93 inches cube

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The number of zeroes or x-intercepts of a polynomial function is related to its highest power, which is determined by the degree of the polynomial. Let's consider a polynomial of degree "n" where "n" is a positive integer.

The minimum number of zeroes or x-intercepts a polynomial can have is zero. This occurs when all the terms of the polynomial have non-zero coefficients and there are no factors that would cause the polynomial to equal zero. For example, a polynomial of degree 2, such as f(x) = x^2 + 1, has no zeroes.

The maximum number of zeroes or x-intercepts a polynomial of degree "n" can have is "n". This is known as the Fundamental Theorem of Algebra, which states that a polynomial of degree "n" can have at most "n" distinct zeroes.

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The correct expansion of (x + 4y)³ using the binomial theorem is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

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

(x + 4y)³

The binomial theorem of expansion states that

Given that an expression is (a + b)ⁿ, the current term is

ⁿCₓ * (a)ˣ * (b)ⁿ ⁻ ˣ

Using the above as a guide, we have the following:

(x + 4y)³ = ³C₀ (x)⁰(4y)³ +³C₁ (x)¹(4y)² + ³C₂ (x)²(4y)¹ + ³C₃ (x)³(4y)⁰

Rewrite as

(x + 4y)³ = [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

This means that the correct expansion is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

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