The measures of the exterior angles of a hexagon are x, 2x, 4x, 5x, 8x, and
10x.

The approximate side length of the largest square envelope that can be placed into the mailbox without bending it is 0.71x.

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each. It is a two-dimensional shape that can be represented by a closed polygon with four straight sides and four right angles.

First, we need to measure the size of the mailbox. Let's say that the length of each side of the mailbox opening is "x" inches. We can then set up an inequality to find the maximum size of the side of the square envelope that can fit into the mailbox. The inequality is:

side length of square envelope ≤ x

This inequality tells us that the side length of the square envelope must be less than or equal to the size of the mailbox opening. We want to find the largest possible side length of the square envelope, so we'll use the "less than or equal to" symbol.

To find the largest possible side length of the square envelope, we'll use the value of "x" to set up an equation. We know that the diagonal of the square envelope will be equal to the length of the side of the square envelope multiplied by the square root of 2. Therefore, we can set up the following equation:

diagonal of square envelope = side length of square envelope × √2

We want to find the maximum side length of the square envelope, so we'll use the maximum value of the diagonal of the envelope. We know that the diagonal of the envelope must be less than or equal to the length of the mailbox opening (which is "x"), so we can set up the inequality:

side length of square envelope × √2 ≤ x

We can solve for the side length of the square envelope by dividing both sides of the inequality by the square root of 2:

side length of square envelope ≤ x/√2

To get the largest possible side length of the square envelope, we'll use the maximum value of "x". Therefore, the largest possible side length of the square envelope that can fit into the mailbox without bending is:

side length of square envelope ≤ x/√2 ≈ 0.71x

We can round this value to two decimal places, which gives us:

side length of square envelope ≈ 0.71x

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Answer:

48 residents

Step-by-step explanation:

Let's assume that there are 100 residents in the neighboring house. 64% of the residents subscribe to "Our Football" magazine, so there are 64 residents who subscribe to it. 84% of the residents subscribe to "Top Gear" magazine, so there are 84 residents who subscribe to it. The number of residents who subscribe to both magazines can be calculated by finding the intersection of the two sets, which is equal to the number of residents who belong to both sets. This can be found using the formula:

Number of residents subscribing to both magazines = 100 - (100 - 64) - (100 - 84)

= 100 - 36 - 16

= 48

Therefore, 48 residents of the neighboring house subscribe to both magazines.

An equivalent expression for 18c+144 is 18(c+8), by factoring out the greatest common factor of the terms 18 and 144.

In the original expression 18c + 144, we have two terms that do not have any common factors other than 1. However, we can see that both terms are multiples of 18, with 18 as the greatest common factor. So, we can factor out the 18 to simplify the expression.

To factor out 18, we divide each term by 18, which gives us:

18c/18 + 144/18

The first term simplifies to c, and the second term simplifies to 8, so we have:

c + 8

This expression represents the sum of c and 8, and it is equivalent to 18c + 144. However, we can still simplify this expression further by factoring out the common factor of c + 8, which gives us:

c + 8 = 18(c + 8)

So, we have the equivalent expression 18(c + 8), which is the original expression 18c + 144 after factoring out the greatest common factor of 18.

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The graph that best models the exponential function is given as follows:

Graph A.

An exponential function is defined as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

y = 200000(1.06)^x.

The value of the home after 5 years is given as follows:

y = 200000(1.06)^5

y = $267,645.

Which is best approximated by the Graph A.

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There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.

2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60

60 possible arrangements for the 4 grade levels

60 * 6 (the number of ways to arrange 6 people) = 360

360 * 6 (the number of ways to arrange 6 people) = 2160

2160 * 6 (the number of ways to arrange 6 people) = 12,960

12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720

6,720 possible arrangements for the school dance committee.

The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.

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Another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

If the relationship between the number of hours worked and total earnings for Reece at Fries n More is given by y = 8.25x, where y is total earnings and x is the number of hours worked, then Reece earns $8.25 per hour worked.

To compare Reece's earnings per hour to another person, we would need to know the hourly wage of the other person. For example, if another person named John earns $9.00 per hour, then John earns more per hour than Reece. Conversely, if another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

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The area of the composite figure is equal to 99 mm² square milimetresmetres.

The composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the bigger horizontal rectangle = 11 mm × 3 mm

area of the bigger horizontal rectangle = 33 mm²

area of the smaller horizontal rectangle = 5 mm × 2 mm

area of the smaller horizontal rectangle = 10 mm

area of the vertical rectangle = 14 mm × 4 mm

area of the vertical rectangle = 56 mm²

total area of the composite figure = 33 mm² + 10 mm² + 56 mm²

total area of the composite figure = 99 mm²

Therefore, the area of the composite figure is equal to 99 mm² square milimetres.

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The absolute value function on the graph is:

f(x) = |x + 2| + 3

We know that for an absolute value function with a vertex at (a, b), then the absolute value function is:

f(x) = |x - a| + b

Here we can see that the vertex is at the point (-2, 3)

Then:

a = 2

b = 3

The function will be:

f(x) = |x + 2| + 3

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Answer: 77

Step-by-step explanation: to find the radius divide the circumference by 2.

The function V(r) is representing the volume of basketball when the radius is r.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, the function V(r) =  4/3 πr³, can be used to find the volume of air inside a basketball given its radius (r).

We are asked to find that what does V(r) represents,

Here, V(r) is the function's output is r is the input, the only variable in the formula is r, that means the volume totally depends on the radius of the basket ball. & volume is changes with the radius.

Thus, this function represents the volume of the basketball when radius is r.

Hence, the function V(r) is representing the volume of basketball when the radius is r.

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Check the picture below.

so the figure is really just a semi-circle, a rectangle and three triangles, let's simply get their area and sum them all up.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ semicircle }{\cfrac{1}{2}\pi (2)^2}~~ + ~~\stackrel{ rectangle }{(4)(5)}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{2})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{1})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{2})}} \\\\\\ 2\pi ~~ + ~~20~~ + ~~3~~ + ~~2~~ + ~~4 ~~ \approx ~~ \text{\LARGE 35.28}[/tex]

Answer:

If a = -8 and b = -1 there is exactly one solution to the equation

Step-by-step explanation:

I was unable to find the other one...

Are you sure there are two possible solutions, or did you forget to include one of the options...?

Answer:

Step-by-step explanation:

Difference means subtract or minus (-)

So we always switch 29 and x into x and 29

Can't really explain that much more but it's the correct answer though, trust me! :)

The length of the radius of the circle is 7.5 inches.

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

Given that the diameter of the circle is 15 inches.

The radius of the circle is half the measure of the diameter.

That is,

R = d/2

R = 15/2

R = 7.5 inches

Hence, the length of the radius of the circle is 7.5 inches.

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The given statement is True.

What is developing logarithms?

The emergence of logarithms was predicted by comparing arithmetic and geometric series.

True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.

Together, they created the logarithmic tables that became a powerful tool in mathematics and science.

Therefore, The given statement is True.

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Option A. TRUE. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.

The Intermediate Value Theorem is a fundamental theorem in mathematics that states that, for any given continuous function on an interval, every value between the minimum and maximum values of the function on the interval must be taken by the function at some point within the interval. This theorem states that, given a function f defined on an interval [a, b], if f(a) and f(b) have different signs (i.e. one is positive and the other is negative), then there exists at least one c in the interval (a, b) such that f(c) = 0. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.

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Volume of solid generated by revolving the plane region about the y-axis is [tex]\pi \left(\frac{1392}{7}\right)[/tex]

The shell method formula is used to find the volume of a solid of revolution, formed by rotating a region about a line that is parallel to one of its sides.

The formula for the shell method is V = 2π* ∫r(x)h(x) dx where V is the volume of the solid, r(x) is the distance between the axis of revolution and the curve being rotated and h(x) is the height of the shell at x.

The shell method can be used when the region is more easily described by an equation in one variable. In contrast, the disk/washer method is used when the region is more easily described by an equation in two variables.

It is a powerful tool for solving many types of problems in calculus, physics and engineering. The shell method formula helps to determine the volume of a solid of revolution, which is an important concept in various fields of study.

Given:

y = [tex]x^\frac{3}{2}[/tex]

y = 27

x = 0

Shell method:

V = [tex]2\pi \int\limits_c^d p(y)h(y) dy[/tex]

Then the volume of a solid is

V = [tex]2\pi \int\limits_0^4x(27 - x^\frac{3}{2})dx[/tex]

= [tex]2\pi \left[ \int\limits_0^4 27x dx - \int\limits_0^4 x^\frac{5}{2}dx\right][/tex]

[tex]= 34\pi \left[\frac{x^2}{2} \right]_0^4 - \frac{4}{7} \pi \left[ x^\frac{7}{2} \right]_0^4[/tex]

[tex]= 34\pi \left(\frac{4^2}{2} \right) - \frac{4\pi}{7}(4)^\frac{7}{2}[/tex]

[tex]= 4\pi \left( \frac{68}{7} - \frac{2^7}{7} \right)[/tex]

[tex]= 4\pi \left( \frac{476 - 128}{7} \right)[/tex]

[tex]4\pi \left( \frac{348}{7} \right)[/tex]

[tex]= \pi \left( \frac{1392}{7} \right)[/tex]

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The mentioned characteristics of quadrilateral are the properties of the Rhombus. So option C is correct.

Given that,

A quadrilateral  TUVW,

UV || WT,  

TU || VW

TV = UW  (Diagonals )

TV ⊥ UW (Diagonals are perpendicular)

Hence, the given characteristics are of the rhombus.

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The magazine will have 33320 subscribers at the end of 10 years.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given that, a publishing industry report predicts that magazine

subscriptions will drop by 10% each year.

The problem thus represents an exponential decay problem.

The exponential decay is given as:

[tex]F = P (1 - r)^t[/tex]

Here, F is the future value.

P is the present amount = 98000.

r is the rate of decrease = 10% = 0.1

t is the time = 10 years.

Substituting the values we have:

[tex]F = 98000(1 - 0.1)^{10}\\[/tex]

F = 33320

Hence, the magazine will have 33320 subscribers at the end of 10 years.

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The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' be the number of weeks and 'y' be the total test. Then the equations are given as,

y = 4 + 3x           ...1

y = 8 + x            ...2

From equations 1 and 2, then we have

4 + 3x = 8 + x

3x - x = 8 - 4

2x = 4

x = 2

The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

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Answer:

r = 55

Step-by-step explanation:

Sum means addition

r + 18 = 73   Subtract 18 from both sides

r = 55

Answer:

The equation is:

r + 18 = 73

and the result is:

r = 55

Step-by-step explanation:

The  sum of r and 18 is 73, in equation is:

r + 18 = 73

Solve:

r + 18 - 18 = 73 - 18

r + 0 = 55

r = 55

Check:

55 + 18 = 73

Answer: 19

Step-by-step explanation: 15 x 19 = 285ft^2

List of perfect squares smaller than 10 are: {1, 4, 9}

Subtract 1 from each value to get a new list of {0, 3, 8}

None of these new values are a factor of 12.

The possible answers are: 0, 3, and 8

Using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

What is Pythagoras' Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean Theorem. According to this statement, the square of the side of a triangle known as hypotenuse is equal to the sum of squares of the other two sides of the triangle.

The complete question is given below in the image.

It is given that a triangle is formed by the cue ball, eight ball and pocket as shown below.

The ∠y is greater than 90°.

The two sides of the triangle are 8 in. and 6in.

Two find the minimum distance between the cue ball and the pocket, we assume that the minimum angle formed by the paths of the cue ball and eight ball is 90°.

That is ∠y = 90°.

Then the triangle becomes a right-angle triangle.

So the distance x becomes the hypotenuse.

Using the Pythagoras theorem, we can find the hypotenuse of the triangle.

x² = 8² + 6²

x² = 100

x = 10 inches.

This is the minimum distance between the cue ball and pocket when y = 90°.

Therefore using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

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Based on the conversion factors, the equivalent values are as follows:

1 Tbsp. = 1/16 c

1/4 c. = 4 Tbsp

1 c. = 16 Tbsp

1 c. = 1/2 pint

1/3 c. = 80 mL

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

The conversion factor for Tbsp to c is 1/4, which means that 1 Tbsp. is equal to 1/4 c.

The conversion factor for c to mL is 236.6, which means that 1 c. is equal to 236.6 mL (rounded to one decimal place).

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The cost of red grapes per pound is $2.8.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.

Let the cost of red grapes be x.

So, the total cost = 7.71+2.4x

Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.

The total cost = 9.95+1.6x

Person and his brother spent same amount of money.

So, 7.71+2.4x=9.95+1.6x

2.4x-1.6x=9.95-7.71

0.8x=2.24

x=2.24/0.8

x=$2.8

Therefore, the grapes cost per pound is $2.8.

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Brand₂ has the highest impact on the price of a smartphone, increasing the price by $80 for each unit increase in that variable.

Regression analysis is a statistical method that helps us understand the relationship between two or more variables.

Based on the regression equation, we can determine which brand increases the price of a smartphone the most. The regression equation is as follows:

Price = 1100 + 50 (Brand₁) + 80 (Brand₂) + 30 (Brand₃) + 20 (Battery Life) + 10 (Camera Resolution)

In this equation, the intercept (1100) represents the average price of a smartphone with all other variables set to zero. The coefficients for each variable represent the change in the price of a smartphone for a one-unit increase in that variable, holding all other variables constant.

Brand₁ and Brand₂ have a lower impact on the price, increasing it by $50 and $30, respectively, for each unit increase in those variables. Battery life and camera resolution have the smallest impact on the price, increasing it by $20 and $10, respectively, for each unit increase in those variables.

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Complete Question:

Can brand, battery life, and camera resolution affect a smartphone's price? Use α= o.05 to perform a regression analysis for the Smartphones01BC dataset and answer the following questions. Solve this problem using Excel and Mega Stat, and write your complete answers in the Response Box so I know that you can interpret the output.

Based on your regression equation, which brand increases the price of a smartphone the most? Use the statistics from your output to explain your answer.

The speed of each boy is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, the parameters are given as follows:

Hence the functions are given as follows:

They meet at 1 pm, which is three hours after 10 am, hence the velocity of the faster boy is obtained as follows:

3v = 68 - 3(v - 3)

3v = 68 - 3v + 9

6v = 77

v = 77/6

v = 12.83 miles per hour.

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Answer: 46ft

Step-by-step explanation:

Alright so for this you must reference the pythagorean theorem which is:

a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.

You can therefore set this up like this:

a^2+20^2=50^2 (where a is the side you are looking for- listed as x)

Solve:

a^2=50^2-20^2

a^2=2500-400

a^2=2100

sqrt(a^2)=sqrt(2100)

a= 45.8257569496

Round: a (or x)=46