Bryan is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 100-yard warmup and then swim laps in a lane that is 39 yards long. If Bryan swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus a main set that consists of 37 yards per lap. If Bryan swims the correct number of laps, he can complete the same distance in either pool. How long will Bryan's workout be in total? How many laps will that take?

y=-1/2x-1 is equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.

The slope of given line is 2

The slope of perpendicular line is -1/2

Now let us find the y intercept

1=-1/2(-4)+b

1=2+b

b=-1

Now the equation is y=-1/2x-1

Hence,  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3 is y=-1/2x-1.

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Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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Pi/(180 degrees) equals 1 degree in radians.

Radians are a unit of measurement for angles, just like degrees. The radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

To visualize this, imagine taking a circle with a radius of r and drawing an arc on the circle that is the same length as the radius. The angle subtended by this arc at the center of the circle is one radian. Since the circumference of a circle is 2pir, there are always 2*pi b in a full circle.

(180 degrees)/pi is equivalent to the value of 180 degrees in radians. To convert from degrees to radians, we multiply the degree value by (pi/180). So:

(180 degrees)/pi = (180 degrees) * (pi/180) = pi radians

Therefore, (180 degrees)/pi equals pi in radians.

On the other hand, pi/(180 degrees) is equivalent to the value of 1 degree in radians. To convert from radians to degrees, we multiply the radian value by (180/pi). So:

pi/(180 degrees) = pi * (180/pi) = 180 degrees

Therefore, pi/(180 degrees) equals 1 degree in radians.

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The 30th partial sum of the sequence 5x-12 = 1965

To derive the 30th partial sum of the sequence 5x -12, we need to add up to the first 30 terms of the sequence.

Th e nth term of the sequence will be:

5 -12

the first 30th terms are:

5(1) -12 = -7

5(2) -12 = -2

5(3) -12 = -3

5(4)  -12 = -8

and so on

So to get the 30th partial sum, we write:
-7 + (-2) = 3+ 8 ...... + (5(30)-12

If simplified, this expression will given us:

S = (n/2) (a+l)

In this case,

s is the sum of the n terms
A is the first term and
L is the last term.

In this ase, a = -7 (the first term) and L= 5(30) -12 = 138 (the 30th term) So  for the partial sum we say:

S30 = (30/2) (-7 + 138) = 30(131)/2
S30 = 1965

Thus, the partial sum of the sequence 5x-12) is 1965

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Answer:

We can use the double angle formulas to find sin(2θ) and cos(2θ):

sin(2θ) = 2sin(θ)cos(θ)

cos(2θ) = cos^2(θ) - sin^2(θ)

Since sin(θ) = -4/5 and θ is in the third quadrant (π < θ < 3π/2), we can use the Pythagorean identity to find cos(θ):

sin^2(θ) + cos^2(θ) = 1

cos^2(θ) = 1 - sin^2(θ)

cos(θ) = -√(1 - sin^2(θ))

cos(θ) = -√(1 - (-4/5)^2) = -√(1 - 16/25) = -√(9/25) = -3/5

Now we can substitute these values into the double angle formulas:

sin(2θ) = 2sin(θ)cos(θ) = 2(-4/5)(-3/5) = 24/25

cos(2θ) = cos^2(θ) - sin^2(θ) = (-3/5)^2 - (-4/5)^2 = 9/25 - 16/25 = -7/25

Therefore, the exact values of sin(2θ) and cos(2θ) are sin(2θ) = 24/25 and cos(2θ) = -7/25, respectively.

Finally, we can find the value of sin^2(2θ)cos^2(2θ):

sin^2(2θ)cos^2(2θ) = (sin(2θ))^2(cos(2θ))^2

sin^2(2θ)cos^2(2θ) = (24/25)^2(-7/25)^2

sin^2(2θ)cos^2(2θ) = 24^2/25^2 * 7^2/25^2

sin^2(2θ)cos^2(2θ) = (24*7)^2/25^4

Therefore, the exact value of sin^2(2θ)cos^2(2θ) is (24*7)^2/25^4.

The volume of the cube is 1.82 in³

We know that the formula for the area of the cube, as a function of the volume, is:

A = 326*V^(2/3)

Solving that equation for V, we will get.

V = (A/326)^(3/2)

Then the volume of a cube whose surface area is A = 486 square inches is:

V = (486 in²/326)^(3/2)

V = 1.82 in³

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Answer: 59 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees so we subtract that by the values we already know the get the last angle.
180-31-90= 59 degrees

Answer: 33.375 feet

Step-by-step explanation:

To find the maximum height, we need to find the vertex of the parabolic function h = 16t² + 12t + 30.

The vertex of a parabola with equation y = ax^2 + bx + c is located at x = -b/2a and y = c - b^2/4a.

In this case, a = 16, b = 12, and c = 30.

So,

t = -b/2a = -12/(2*16) = -3/8

h = 16(-3/8)² + 12(-3/8) + 30 = 33.375

Therefore, the maximum height reached is 33.375 feet.

Answer:

12 square units

Step-by-step explanation:

interior angles of rectangles are right angles

Area of the triangle: 6 x 4 / 2

Use a calculator to solve this problem!

Answer:

Step-by-step explanation:

775625 is the correct answer

The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.

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The value of x for the angles of the quadrilateral is: x = -4

We know that the sum of angles in a quadrilateral is 360 degrees.

The angles are given as:

(11x + 140)°

(13x + 143)°

(4x + 98)°

(11x + 135)°

Thus:

(11x + 140)° + (13x + 143)° + (4x + 98)° + (11x + 135)° = 360°

Thus:

39x + 516 = 360

39x = 360 - 516

39x = -156

x = -156/39

x = -4

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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Answer:

The area of the regular hexagon is 166.3 square units (to the nearest tenth).

Step-by-step explanation:

The formula for the area of a regular polygon is:

[tex]\boxed{\textsf{Area}=\dfrac{r^2n\sin\left(\frac{360^{\circ}}{n}\right)}{2}}[/tex]

where:

From inspection of the given regular polygon:

Substitute the values into the formula and solve for area:

[tex]\begin{aligned}\textsf{Area}&=\dfrac{8^2\cdot 6 \cdot \sin\left(\frac{360^{\circ}}{6}\right)}{2}\\\\&=\dfrac{64\cdot 6 \cdot \sin\left(60^{\circ}\right)}{2}\\\\&=\dfrac{384 \cdot \frac{\sqrt{3}}{2}}{2}\\\\&=\dfrac{192\sqrt{3}}{2}\\\\&=96\sqrt{3}\\\\&=166.3\; \sf square\;units\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the area of the regular hexagon is 166.3 square units (to the nearest tenth).

Answer:

44

Step-by-step explanation:

there are 792 trees but one acre has 18,

so to find the number of acres divide 792 by 18,

which would give you 44.

According to the given condition, the answer is (b) 44. There are 44 acres in Orangeland.

Expressions can be simple or complex, and can be used in many different contexts depending on the specific programming language or mathematical system being used.

The problem asks us to find the number of acres in Orangeland given the population density of orange trees and the total number of trees. We can use the formula for population density, which relates the number of individuals (in this case, orange trees) to the area they occupy.

The formula for population density is:

Population density = number of individuals/area

We can rearrange this formula to solve for the area:

Area = number of individuals/population density

In this problem, we are given the population density of Orangeland, which is 18 orange trees per acre. We are also given the total number of orange trees, which is 792. To find the area of Orangeland, we can substitute these values into the formula:

Area = 792 / 18

Simplifying this expression, we get:

Area = 44

Therefore, According to the given condition, the answer is (b) 44. There are 44 acres in Orangeland.

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Answer:

Step-by-step explanation:

1.To arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 ways to arrange all 6 tables in a line.

2.To choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

C(6,4) = 6! / (4! x 2!) = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1) = 15

Therefore, there are 15 ways to choose 4 out of the 6 tables.

There are 720 ways to arrange all 6 tables in a line.

And, there are 15 ways to choose 4 out of the 6 tables.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom.

Now, After arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Hence, there are 720 ways to arrange all 6 tables in a line.

And, For choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

Thus, there are 15 ways to choose 4 out of the 6 tables.

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If a taxi company charges ​f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.

To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.

f(2.7) = 2.20 + 0.6[4(2.7)]

f(2.7) = 2.20 + 0.6[10.8]

f(2.7) = 2.20 + 6.48

f(2.7) = 8.68

The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.

The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.

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This is the formula for calculating the present value of a future payment, where P1 is the present value, P2 is the future payment, and R is the interest rate.

To use the formula, you need to know the value of P2, the future payment, and the interest rate, R. Then, you can solve for P1, the present value of that payment. The formula works by discounting the future payment to account for the time value of money, which means that money today is worth more than the same amount of money in the future.

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Answer:0.00000221

Step-by-step explanation:

Move the decimal place 6 times

yes very cool math problem

The equation for the axis of symmetry for the given parabolic graph is found as: x = 3.

A parabola is the graph of a quadratic function and features a vertical line passing through its vertex as its axis of symmetry.

The graph is also symmetric, with the axis of symmetry being a vertical line that passes through the vertex.

Thus, the equation for the axis of symmetry for the given parabolic graph is found as: x = 3.

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Answer:

First, we can multiply both sides of the equation by the absolute value of x plus 8, to get rid of the fraction:

52 = 4(|x| + 8)

Now we can solve for the absolute value of x:

| x | + 8 = 13

| x | = 5

This means that x could be either positive 5 or negative 5. Therefore, the possible values of x are {-5, 5}.

So the answer is option D: {-5, 5}.

A circle with center Q and equilateral triangle NOP, where points N and O lie on the circle

What is a circle?

A circle is a two-dimensional shape with a perfectly round boundary that has no corners or edges. It is defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the boundary of the circle is called the radius.

The circumference of a circle is the distance around the boundary of the circle, and it is calculated as 2π times the radius. Circles are found in many natural and man-made objects, such as wheels, planets, and coins, and they have a wide range of applications in mathematics, science, and engineering.

To construct a circle with center Q and equilateral triangle NOP where points N and O lie on the circle, follow these steps:

Draw line segment PQ as the base of the equilateral triangle NOP.

Draw a perpendicular bisector of PQ, which intersects PQ at its midpoint, say M. This bisector will be the axis of symmetry of the equilateral triangle NOP.

With M as the center and MP (or MQ) as the radius, draw a circle that intersects PQ at two points, say X and Y.

Using Q as the center and QX (or QY) as the radius, draw two arcs that intersect the circle drawn in step 3 at two points, say N and O.

Draw the lines NQ and OQ to complete the equilateral triangle NOP.

Now, you have a circle with center Q and equilateral triangle NOP, where points N and O lie on the circle.

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The volume of the cylinder below is 5595.48 in².

Volume is the space accuppied by a solid shape.

To calculate the volume of the cylinder, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The domain is all real numbers, and the range is all real numbers greater than or equal to -4. So, correct option is A.

The given function f(x) = (x + 2)(x + 6) is a quadratic function, and its graph is a parabola that opens upwards. We are given that the vertex of the parabola is at (-4, -4), and it passes through the points (-6, 0) and (-2, 0).

The domain of a function is the set of all possible input values for which the function is defined. Since this is a polynomial function, it is defined for all real numbers. Therefore, the domain of the function f(x) is all real numbers.

The range of a function is the set of all possible output values that the function can take. Since the parabola opens upwards and its vertex is at (-4, -4), the lowest point on the graph is at (-4, -4), and it extends infinitely upwards. Therefore, the range of the function f(x) is all real numbers greater than or equal to -4.

Hence, the correct option is A).

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Complete question is:

The graph of the function f(x) = (x +2)(x + 6) is shown below.

On a coordinate plane, a parabola opens up. It goes through (- 6, 0), has a vertex at (- 4, - 4), and goes through (- 2, 0).

What is true about the domain and range of the function?

A) The domain is all real numbers, and the range is all real numbers greater than or equal to –4.

B) The domain is all real numbers greater than or equal to

–4, and the range is all real numbers.

C) The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.

D) The domain is all real numbers greater than or equal to

–4, and the range is all real numbers such that –6 ≤ x ≤ –2.

The coordinates of triangle A'B'C' after a dilation centered at the origin with a scale factor of 2 are:

A' (-10, -14).

B' (12, -6).

C' (4, 14).

In Geometry, a dilation is a transformation that is typically used for changing the dimension (size) of a geometric figure, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 2 that is centered at the origin as follows:

Ordered pair A (-5, -7) → Ordered pair A' (-5 × 2, -7 × 2) = Ordered pair A' (-10, -14).

Ordered pair B (6, -3) → Ordered pair B' (6 × 2, -3 × 2) = Ordered pair B' (12, -6).

Ordered pair C (2, 7) → Ordered pair C' (2 × 2, 7 × 2) = Ordered pair C' (4, 14).

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The probability of passing the true/false test of 60 questions if the minimum passing grade is 60% and all responses are random guesses is approximately 0.9802 or 98.02%.

Assuming that all responses are random guesses, we may describe this issue using a binomial distribution, where the number of right responses follows a binomial distribution with [tex]n = 60[/tex] and [tex]p = 0.5.[/tex]

If X represents the total number of accurate responses, it will follow a binomial distribution with[tex]n = 60[/tex] and [tex]p = 0.5[/tex] as its parameters.

If the passing grade is [tex]60%[/tex], then there must be a minimum of [tex]36[/tex]accurate responses [tex](0.6 * 60 = 36).[/tex]

The normal-approximation can be used to calculate the likelihood of receiving at least [tex]36[/tex] correct responses. We must determine the mean and variance of the binomial distribution in order to utilise the normal approximation.

The variance of a binomial distribution is

[tex]2 = np(1-p)[/tex]

[tex]= 60 * 0.5 * 0.5[/tex]

[tex]= 15[/tex]

and the mean is

[tex]= np[/tex]

[tex]= 60 * 0.5[/tex]

[tex]= 30.[/tex]

To calculate the probability of passing, we can use the normal distribution with mean 30 and variance 15 to approximate the binomial distribution with continuity correction.

[tex]P(X \geq 36) = P(Z \geq (36 + 0.5 - 30) / \sqrt{15})[/tex]

where Z is a standard normal random variable.

[tex]P(Z \geq 2.08) = 1 - P(Z \leq 2.08)[/tex]

[tex]= 1 - 0.0198[/tex]

[tex]= 0.9802[/tex]

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