A spherical boulder is 28 feet in diameter and weighs almost 8 tons. Find the volume Use 3.14 for pi

1 Yes  the set of rational expressions is closed under subtraction

2. Yes  the set of rational expressions is closed under multiplication

3. No  the set of rational expressions is not closed under division

1. The subtraction of two rational expressions results in another rational expression.

=  p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))

this is also a rational expression.

2. The multiplication of two rational expressions results in another rational expression.

=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))

this is a rational expression.

3. Division of two rational expressions may result in an expression that is not a rational expression.

= (p(x)/q(x)) / (r(x)/s(x)))

= ((p(x)s(x)) / (q(x)r(x)))

this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero

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Answer:

Step-by-step explanation:

The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.

Let y be the length of the side of the small square.

Then, the area of the small square is y^2 cm^2.

According to the question, the area of the small square is 1/25 of the area of the large square.

Thus, the area of the large square is (25)(y^2) cm^2.

The length of a side of the large square is given by the formula s = √A.

Therefore, the length of a side of the large square is √(25y^2) = 5y cm.

Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.

Therefore, y = 40/5 = 8.

Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.

The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3

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

The right triangle

The hypotenuse of the right triangle is calculated as

h² = 2² + 3²

When evaluated, we have

h = √13

The values of the trigonometry functions are then evaluated as

sin(θ) = 3/√13

cos(θ) = 2/√13

tan(θ) = 3/2

csc(θ) = √13/3

sec(θ) = √13/2

cot(θ) = 2/3

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The data given is an example of a B. Quadratic regression.

The r-squared ( r ²) value is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

The r² values are highest for the quadratic model (r ² = 0. 997), meaning this model explains the most variance in your data compared to the linear (r² = 0. 808) and exponential models (r ² = 0. 813). Thus, the data are best modeled with a quadratic regression.

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The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

Option C is the correct answer.

We have,

Profit = Amount Paid - Cost of Supplies

Given that the cost of supplies for each room is $32.50, we can represent the profit for each room as:

Profit per room = Amount Paid per room - $32.50

Zack wants to make a profit of more than $300 for painting 4 identical rooms.

The total profit for the 4 rooms should be greater than $300.

We can write this inequality as:

4 x (Profit per room) > $300

Substituting the expression for profit per room, we have:

4 x (Amount Paid per room - $32.50) > $300

Now, let's solve the inequality to find the dollar amount that Zack must be paid for each room:

4 x (Amount Paid per room - $32.50) > $300

4 x Amount Paid per room - 4 x $32.50 > $300

4 x Amount Paid per room - $130 > $300

4 x Amount Paid per room > $300 + $130

4 x Amount Paid per room > $430

Amount Paid per room > $430 / 4

Amount Paid per room > $107.50

Therefore,

The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

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Answer:

The car is moving 15 degrees South of East. This means that it is moving in a direction that is 75 degrees from the positive x-axis.

The velocity vector of the car can be broken down into its components in the x and y directions as follows:

vx = v * cos(theta) = 68 * cos(75) = 17.3 mph

vy = v * sin(theta) = 68 * sin(75) = 66.3 mph

where

v = 68 mph (magnitude of velocity)

theta = 75 degrees (angle of velocity vector with respect to the positive x-axis)

Therefore, the car is moving 17.3 mph in the Eastern direction and 66.3 mph in the Southern direction.

Answer: p(x) = f(x+8)-6

Step-by-step explanation:

Answer:  C f(x+8)-6

Step-by-step explanation:

You went left 8 or -8 in x direction, take opposite sign for x

also down 6 or -6 in y direction, take sign as is.

f(x+8)-6

Answer:

Yes

Step-by-step explanation:

These are the rules regarding polynomial graphs and their real zeros (solutions)

In the above graph we see that the graph touches the x-axis at x = 3. This means (x - 3)ᵃ  is a factor of the polynomial where p is an even number (2, 4, 6 etc)

That means x = 3 is a repeated real solution. It appears that the multiplicity is 2 so one factor of the polynomial is (x - 3)²

More inf o(ignore if you want)

The other real roots are x = -1 and x = 5 because the graph crosses the x axis at these two values of x. So the multiplicity of both factors ( x + 1) and (x - 5) is odd. Since at the crossover point, the graph is almost linear, we can safely assume that the multiplicity of the graph is odd at these points and equal to 1

Therefore the polynomial can be factored as
(x + 1)(x - 5)(x -  3)²

The degree of the polynomial is the sum of the multiplicities and is equal to 1 + 1 + 2 = 4 so it is a quartic polynomial of the form ax⁴ + bx³ + cx² + dx + e

Probability that exactly 10 flights arrive on time is 53.33%.

Given that,

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.

Recently, Southwest Air had the best rate with 80% of its flights arriving on time.

Total number flights in sample = 15

Probability that exactly 10 flights arrive on time is,

P = 10/15 × 80%

  = 0.5333

  = 53.33%

Hence the required probability is 53.33%.

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The missing angles in the cyclic quadrilateral are as follows:

a = 101°

b = 67°

c = 84°

d = 80°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

Opposite angles of a cyclic quadrilateral is supplementary.

c = 180 - 96

c = 84 degrees

d = 180 - 100

d = 80 degrees

100 = 1 / 2 (a + 99)

100 = 0.5a + 49.5

0.5a = 50.5

divide both sides by 0.5

a = 50.5 / 0.5

a = 101 degrees

84 = 1 / 2 (101 + b)

84 = 50.5 + 0.5b

84  - 50.5 = 0.5b

0.5b = 33.5

b = 33.5 / 0.5

b = 67 degrees

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Angles in each quadrant with common reference angle as 311° are :

First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.

Given that,

Reference angle = 311°

We have to find an angle in each quadrant with this reference angle.

311° is in the fourth quadrant.

The equivalent angle on the first quadrant is,

360° - 311° = 49°

Equivalent angle on second quadrant is,

180° - 49° = 131°

Equivalent angle on third quadrant is,

360° - 131° = 229°

Hence the angles are found.

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Answer:

[tex]( - 2, 0 )\; and \; ( 4, - 6)[/tex]

Step-by-step explanation:

To find the ordered pairs set the right side expressions equal to each other and solve for x, then use those values for x to evaluate f(x) values

We get

x² - 3x - 10 = -x - 2

Moving -x - 2 to the left side gives

x² -3x - 10 + x + 2   = 0
(moving an expression from one side to another changes the signs of the terms)

Grouping like terms:
x² - 3x + x -10 +2 = 0

x² -2x -8 = 0

Expression on the left can be factored as (x + 2)(x-4)

This results in
(x + 2)(x - 4) = 0 giving

(x + 2) = 0 ==> x = -2 as one solution for x

(x - 4) =0 ==> x = 4 as the second solution

Plug in x = -2 into the second expression -x - 2 to get

f(-2) = -(-2) -2 = 2 - 2 = 0

So one ordered pair is (-2, 0)

Plug in x = 4 into -x - 2 to get
f(4) = - 4 -2 = -6

So (4, -6) is another ordered pair

The exact value of the side length of the square is √55 unit.

Given that the shaded square has an area of 55 square units.

We need to determine the exact value of the side length of the square,

To determine the exact value of the side length of the square, we can use the formula for the area of a square, which is given by the equation:

Area = side length²

In this case, the area is given as 55 square units. Therefore, we can set up the equation as follows:

55 = side length²

To solve for the side length, we need to find the square root of both sides of the equation:

√55 = √(side length)²

Simplifying further:

√55 = side length

Thus, the exact value of the side length of the square is √55 unit.

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When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.

To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.

Evaluating f(-2):

Substitute x = -2 into the function f(x):

f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16

Evaluating f(1):

Substitute x = 1 into the function f(x):

f(1) = (1/4)^-1 = 4^1 = 4

Evaluating f(2):

Substitute x = 2 into the function f(x):

f(2) = (1/4)^-2 = (1/4)^2 = 1/16

Therefore, the evaluations of f(-2), f(1), and f(2) are:

f(-2) = 1/16

f(1) = 4

f(2) = 1/16

In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.

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The probability that Julie will be a captain, given that she makes the team is 1/3.

Given,

Number of students trying out for a soccer team = 40

Case of probability,

P(A) = n(A)/n(S)

n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.

Given ,

18 of 40 students will make the soccer team.

⇒ n(S) = 18

Let event A: Julie will be a captain, given that she makes the team

⇒ n(A) = 3

So, the probability that Julie will be a captain, given that she makes the team,

= P(A) = n(A)/n(S)

= P(A) = 3/18

= P(A) = 1/6

Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.

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Answer:

wheres it at?

Step-by-step explanation:

#Everything4Zalo

Answer:

360

Step-by-step explanation:

80*5=400 and .25*400=100 so it costs 300 for five nights without tax, and adding on the tax raises the cost to 60 (300+(.2*300)=360)

Answer:

-------------------------

Given:

Convert the interest rate to a decimal:

Convert the time from months to years:

Now, we can calculate the simple interest using the formula:

Finally, add the interest to the principal to find the amount due:

Susan's amount due for the loan is $1047.50.

The simple interest amount of Susan for time of 8 months is A = $ 1047.50

Given data ,

To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.

Principal (P) = $1000

Time (t) = 8 months

Interest rate (r) = 7 1/8% per annum

First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:

r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)

Next, we can calculate the simple interest using the formula:

Simple Interest (I) = Prt

I = $1000 x 0.07125 x (8/12)

I = $1000 x 0.07125 x (2/3)

I = $47.50

Finally, to find the amount due, we add the principal amount to the simple interest:

Amount Due = Principal + Simple Interest

Amount Due = $1000 + $47.50

Amount Due = $ 1047.50

Hence , the amount is A = $ 1047.50

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The correct answer is 4,128 square inches.

To determine the amount of material needed to replace the felt cover on the pool table, we need to calculate the surface area of the table.

The pool table has dimensions of 86 inches in length and 48 inches in width.  

Surface area is the measure of the total area of the external or exposed surfaces of a three-dimensional object.

It represents the sum of the areas of all the faces or surfaces of an object, including its top, bottom, and sides.

Surface area is typically measured in square units such as square inches, square centimeters, or square meters.

To find the surface area, we multiply these two dimensions together:

Surface area = Length [tex]\times[/tex] Width

Surface area = 86 inches [tex]\times[/tex] 48 inches

Surface area = 4,128 square inches.

Therefore, the correct answer is 4,128 square inches.

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The value of the angle m<WXY is 69 degrees

We need to know that the shape given is a parallelogram.

The properties of a parallelogram are given as;

From the information given, we have that;

Angel WZY and Angle WXY are opposite angles of the parallelogram

Then,

m<WXY = 69 degrees

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Answer:

Step-by-step explanation:

The equation f(x) = 3x^2 + 4x + 3 is a quadratic function. Here are three ways this equation can be used in the real world:

In physics, this equation can be used to model the height of an object thrown into the air. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the height of the object at any given time x, where x is the time elapsed since the object was thrown. The coefficient 3 in the equation represents the acceleration due to gravity, and the other terms represent the initial height and velocity of the object.

In economics, this equation can be used to model the profit of a company. If x represents the number of units sold, then f(x) = 3x^2 + 4x + 3 can be used to calculate the profit made by the company at any level of sales. The coefficient 3 in the equation represents the fixed costs of the company, while the other terms represent the variable costs and revenue.

In engineering, this equation can be used to model the trajectory of a projectile. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the distance traveled by a projectile at any given time x, where x is the time elapsed since the projectile was launched. The coefficient 3 in the equation represents the initial velocity of the projectile, and the other terms represent the effects of air resistance and gravity.

A surveyor plays a crucial role in land surveying and mapping, using various tools and techniques to accurately measure and analyze land features.

Trigonometric functions are fundamental mathematical tools that surveyors rely on to solve problems involving angles, distances, and elevations. By employing trigonometry, surveyors can determine the precise locations of points, measure distances between objects, and calculate elevations with accuracy and efficiency. This essay will explore how surveyors utilize trigonometric functions in their work, highlighting key vocabulary words and providing three detailed examples.

One of the primary applications of trigonometry in surveying is angle measurement. Surveyors use the concept of trigonometric ratios, such as sine, cosine, and tangent, to determine angles between reference points. By measuring the lengths of sides in a triangle formed by the surveyor's position and the target point, trigonometric functions enable them to calculate the unknown angles. For instance, when surveying a land boundary, a surveyor may use the tangent function to determine the angle of deflection between two adjacent lines, helping establish accurate boundary lines.

Another crucial application of trigonometry in surveying is distance measurement. By utilizing trigonometric principles, surveyors can measure distances that are difficult or impractical to physically traverse. For instance, when faced with measuring the width of a river or the height of a tall structure, a surveyor can employ trigonometry along with the concept of similar triangles. By measuring the angles of elevation or depression from the surveyor's position to the target point and knowing the distance between two reference points, they can calculate the unknown distance using trigonometric functions like sine or tangent.

Elevation determination is yet another area where surveyors rely on trigonometric functions. By combining angle measurements and distance measurements, surveyors can determine the elevation of a specific point above a reference level. For example, when conducting a topographic survey to create a contour map, surveyors measure the angles of elevation or depression to various points on the terrain. By applying trigonometry, they can calculate the differences in elevations between these points and establish contour lines representing the shape and relief of the land.

In conclusion, trigonometric functions are indispensable tools for surveyors in their day-to-day work. Angle measurement, distance measurement, and elevation determination are just a few examples of how surveyors employ trigonometry to accomplish accurate and precise land surveying. By understanding trigonometric concepts and utilizing key vocabulary words such as sine, cosine, tangent, angles of deflection, and angles of elevation, surveyors can confidently carry out their tasks, ensuring reliable measurements and mapping of land features. Trigonometry empowers surveyors to overcome challenges in measuring angles, distances, and elevations, contributing to the accurate representation of the physical world and supporting various engineering and construction projects.

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Answer:

Step-by-step explanation:

( 8n - 5 ) - ( -2n - 3 )

( 8n - 5 ) + ( 2n + 3 )

8n - 5 + 2n + 3

10n - 2

Answer: C 1/6*√2n

Step-by-step explanation:

• Simplify √n/18 as (1/3)^2*n/2

• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2

• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2

• Multiply √2n/2 with 1/3 to make √2n/6

√2n/6 is equal to 1/6*√2n

The radical expression √n/18 when simplified is 1/3√n/2

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

√n/18

Express 18 as 9 * 2

So, we have the following representation

√n/18 = √n/(9 * 2)

Rewrite as

√n/18 = √n/(2 * 9)

Take the square root of 9

This gives

√n/18 = 1/3 * √n/2

Evaluate the products

√n/18 = 1/3√n/2

Hence, the expression when simplified is 1/3√n/2

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If triangles ΔXYZ is congruent to ΔJKL, then the segment which corresponds to KJ is YX.

Given that, two triangles ΔXYZ and ΔJKL are congruent to each other.

So the corresponding vertices are,

Vertex X of ΔXYZ corresponds to vertex J of ΔJKL

Vertex Y of ΔXYZ corresponds to vertex K of ΔJKL

Vertex Z of ΔXYZ corresponds to vertex L of ΔJKL

Now, the segment which corresponds to KJ in ΔXYZ will be the segment formed by joining the vertices that corresponds to K and J.

We already have,

K corresponds to Y and J corresponds to X.

So the equivalent segment is YX.

Hence the segment required is YX.

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The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

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Answer:

6 hours

Step-by-step explanation:

So therefore,

4 roofers= 1 hour

1 roofer= 9 * 4

= 36 hours

6 roofers= 36/6=6 hours

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

The chord in this circle is RS while the radius of the circle is QT. If the diameter of the circle is 28 cm, then the radius will be 14 cm.

The chord of a circle refers to the line that connects two parts of the circle. In the diagram provided, points RS represent the chord of the circle. Also, the diameter of a circle are the points that run between two segemnts of the circle's center.

In this circle these are points GP. The radius is gotten by dividing the diameter by 2, so the radius of the given diameter is 28/2 = 14.

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The solution of the equation will be; [tex]\dfrac{1}{3y} (\dfrac{x + 9xy + 9y}{x + 2} )[/tex]

Since we know that equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation that is a statement with two equal sides and an equal sign in between.

We are given the equation as;

[tex]3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3} (\dfrac{x}{xy + 2y} )[/tex]

Taking y common as;

[tex]3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3} (\dfrac{x}{xy + 2y} )\\\\\\3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3y} (\dfrac{x}{x + 2} )\\\\\\ \dfrac{1}{3y} (\dfrac{x + 9xy + 9y}{x + 2} )[/tex]

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