Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement.The mean is the measure of central tendency most likely to be affected by an outlier.

The area of a regular hexagon inscribed in a circle is equal to two-thirds of the area of the circle.  [tex]$324\pi\div 2\div 3[/tex]= [tex]108\pi$  $108\pi \approx 339.292$[/tex] square units  The answer in simplest radical form is[tex]$\sqrt{339.292}$[/tex]  square units.  

it is important to first understand the concept of a regular hexagon inscribed in a circle. A regular hexagon inscribed in a circle is a six-sided polygon whose interior angles are all equal and whose sides are all of equal lengths. This means that the hexagon will have six equal-length sides and six equal-sized angles.

The area of such a hexagon is equal to two-thirds of the area of the circle in which it is inscribed.   In this problem, the area of the circle is given as [tex]$324\pi$[/tex] square units. To determine the area of the regular hexagon inscribed in the circle, the area of the circle needs to be divided by two and then by three.

This yields a result of [tex]$108\pi$[/tex] square units, which is approximately equal to 339.292 square units. This result can be written in the simplest radical form as [tex]$\sqrt{339.292}$[/tex] square units, which is the answer to the problem.

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Answer:

f(x) = |x| g(x) = |3x - 7| f(x) = |-x + 9|

By square root, power and sign properties, the expression - 16 · y is the square root of 16 · y² for y < 0.

Let be n a real number, x is the square root of n if and only if n = x², that is:

x = √n

In addition, we find by sign properties the following two cases according to sign of variable y:

Now we proceed to find the square root of 16 · y² for y < 0. First, write the square root described in statement:

√(16 · y²)

Second, use square root and power properties:

√16 · √y², where y < 0.

- 16 · y

In conformity with square root, power and sign properties, the square root 16 · y² for y < 0 is the expression - 16 · y.

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The volume of the given solid is 464 cubic inches.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

From the given figure,

We know that, the volume of a cuboid is Length×Width×Height

Volume of two identical cuboid is

2(8×3×7)

= 336 cubic inches

Volume of small cuboid is

8×4×4

= 128 cubic inches

The volume of the solid =336+128

= 464 cubic inches

Therefore, the volume of the given solid is 464 cubic inches.

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x = 14000

y = 28000

z = 12000 units of each product were sold.

Solving this with the help of equation.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

Let, x, y and z are the three types of products.

In one year, the total revenue for the three products was $1,100,000, which corresponded to the sale of 54,000 units.

Thus, 30x + 20y + 10z = 1,100,000 ............ (i)

x + y + z = 54000 ............... (ii)

The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2

putting this in equation (i)

thus, 30x + 20 (2x) + 10z = 1,100,000

70x + 10z = 1100000 ......... (iii)

next putting the value of y = 2x in equation (ii) we get -

3x + z = 54000......... (iv)

Solve this two equation we get -

40x = 560000

or, x = 14000

now, y = 2x = 28000

z = 54000 - 3(14000)

z = 12000

Now, x = 14000

y = 28000

z = 12000 units of each product were sold.

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The units of each three types of product sold are 14000, 28000, and 12000 using equations.

Algebraic equations simply state the equivalence of two mathematical terms in a mathematical statement. For instance, the equation 6x + 5 = 11 has the two expressions 6x + 5 and 11 separated by the 'equal' sign.

The two forms of equations are identity equations and conditional equations. For just any value of both variables, equality remains true.

Let, x, y and z are the three types of products.

The three items generated a combined $1,100,000 in revenue in a calendar year, which is equal to the sale of 54,000 units.

30x + 20y + 10z = 1,100,000 ............ (i)

x + y + z = 54000 ............... (ii)

The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2

Putting this in equation (i)

Thus, 30x + 20 (2x) + 10z = 1,100,000

70x + 10z = 1100000 ......... (iii)

Next putting the value of y = 2x in equation (ii) we get -

3x + z = 54000......... (iv)

Solve these two equation we get -

40x = 560000

Or, x = 14000

Now, y = 2x

= 28000

z = 54000 - 3(14000)

z = 12000

Now, x = 14000

y = 28000

z = 12000

These units of each product were sold.

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The two positive numbers are 39 and 91 in the ratio 3:7

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x and y represent the two positive numbers. x represent the smaller while y is the larger

Two positive numbers are in the ratio 3:7, hence:

(3/10)(x + y) = x

3x + 3y = 10x

7x - 3y = 0   (1)

Their difference is 52, hence:

y - x = 52   (2)

From both equations:

x = 39, y = 91

The two numbers are 39 and 91

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The set of points in space whose coordinates satisfy a given combination of equations and inequalities can be described by a geometric shape or region in 3-dimensional space.

Enumerate the collection of spatial points whose coordinates fulfil the specified set of equations and inequalities.

The equations and inequalities will define the properties of the region, such as its shape, size, and location.

For example, if we have the equation x + y + z = 3 and the inequality x^2 + y^2 <= 1, the set of points that satisfy these conditions would be the points on or inside a sphere of radius 1 centered at the point (0,0,-1) in the x-y plane, and points on the plane x+y+z = 3.

Another example, if we have the equation x + y = 4 and the inequality y >= 2x-5, the set of points that satisfy these conditions would be the points on the line x+y = 4, above or on the line y = 2x-5.

It's important to note that the type of shape or region that is formed by the equations and inequalities will depend on the specific equations and inequalities being used and the number of variables in the problem.

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By using a trigonometric relation, we will see that the hypotenuse of the right triangle is:

x = 22

We want to find the value of x on the right triangle.

Notice, it is the hypotenuse of the right triangle.

We know one angle on the triangle, and also the adjacent cathetus, then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

We can replace the known values to get:

cos(30°) = 11*√3/x

(√3)/2 = 11*√3/x

Now we can solve this for x.

Dividing both sides by √3 we get:

1/2 = 11/x

x/2 = 11

x = 2*11

x = 22

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Answer:

2√(13)= 7.21

Step-by-step explanation:

The formula for Pythagoras' theorem is a² + b² = c². In this equation, c is the longest side of a right-angled triangle. This line is also known as the hypotenuse. A and b represent the other two sides of the triangle.

so h = √(6²+4²) = 2√(13)= 7.21 (approximately)

The equations can be framed as:

For Novelists

3 x 5 = 15

and, For Artists:

3 x 3 = 9 artists

A key part to understanding ratios is that it isn't part over whole. Ratios say that there are 5 novelists Per 3 poets.

This can be rephrased to say that there are 5 novelists per 8 TOTAL people.

From here, we can use fractions:

5/8 = x/24

where x is the number of novelists

Now,

Multiplying the left side by 3/3 yields 15/24

Therefore,

there are 15 novelists at the workshop.

We can use the same method for the poets :

3/8 = y/24

= 9/24

Complete Question:

A writing workshop enrolls novelists and poets in a ratio of 5:3.  There are 24 people at the workshop.  How many novelists are there?  How many poets are there?  Write a system of equations to model each situation.  Solve by any method.

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Answer:

108 degrees

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is given by the formula:

(n-2) x 180 degrees

Where n is the number of sides of the polygon. In the case of a pentagon, the number of sides is 5, so we can use the formula to find the sum of the measures of the interior angles of a pentagon:

(5-2) x 180 = 3 x 180 = 540

If we know that the pentagon is regular, meaning that all its angles have the same measure, we can use this information and the formula above to find the measure of each interior angle.

If we divide the sum of the measures of the interior angles by the number of sides, we get the measure of each interior angle of the regular pentagon.

540/5 = 108 degrees

So, the measure of each interior angle of a regular pentagon is 108 degrees

A function is a relation between sets where for each input, there is exactly one output.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

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Explanation:

The two interior angles 55 and 6x+8 add to the exterior angle 14x-1; this exterior angle is not adjacent to the interior angles mentioned.

Refer to the Remote Interior Angle Theorem for more information.

So,

55+(6x+8) = 14x-1

6x+63 = 14x-1

6x-14x = -1-63

-8x = -64

x = -64/(-8)

x = 8

Then we can determine angle T

angle T = 6x+8 = 6*8+8 = 56 degrees

The dimensions that will minimize the cost of 5920

Here is the process. Volume is the volume of a cylinder plus the volume of a sphere.

The surface area of a cylinder without the top and bottom plus twice the surface area of a spherical constitutes the cost of the material.

C = 2πrh + 2(4πr2)

Put what you discovered for h in this formula.

Consider Cost's derivative with regard to r. After that, zero out the derivative and find r.

Utilize the radius, r, value once you have it to solve for the height, h.

now,

V = πr2h + (4/3)πr3 = 5920

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Answer:

1 i think 2 if not

Step-by-step explanation:

Answer:

y = 6x

Step-by-step explanation:

In the table, for every x value, the y value is that number multiplied by 6.

For example:

x = 1

y = 6

And:

x = 8

y = 48

Answer:

Step-by-step explanation:

Look at the input and apply the rule. For example, if the rule is "Subtract 5" and the input is 9 then you subtract 5 from 9 to get 4, and 4 is the output. Let's take a look at some examples:

Probability is the branch of mathematics dealing with numerical descriptions of how likely a situation is to occur, or how likely it is that a proposition is true.

An expression for the probability of an event.

Probability of an event = Required number of event / Total number of possible events

Required number of events = 84

Total number of events = 320

Find the probability that both customers selected without replacement say service is poor.

customers say service is poor = 84 / 320

customer selected without saying service is poor= 83 / 319.

The final probability is: 84 ÷ 320 ×83 ÷ 319.

      = 6972 ÷ 201080

     = 1743 ÷ 25520

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Answer:

Gordon

Step-by-step explanation:

The domain is the x values and the range is the y values.  The y values are the not the same.  The y values for function A are all positive and the y values for function B are all negative.

The x values are the same for both functions, so the domain is the same for both functions.

Therefore, the supplied variable problem's solution is found to be quantitative.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Quantitative variables are numerical variables, whereas categorical/qualitative variables assign the people into a category.

Because the length is quantified by numbers, it is (a) quantitative (such as 200 ft).

So , by observing the following information we can conclude that it is quantitative.

As a result, it is quantitative.

Therefore, the supplied variable problem's solution is found to be quantitative.

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The complete question is " All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify and explain each variable as a) quantitative or qualitative; b) discrete or continuous; and c) by level of measurement. (10 points)

Route type (interstate, U.S., state, county, or city)

Length of maximum span (feet)

Number of vehicle lanes

Bypass or detour length (miles)

Condition of deck (good, fair, or poor)

Average daily traffic

Toll bridge (yes or no)"

On solving the provided question, we can say that 0.003 X 100 when we multiply with decimal it gets shifted to right side

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the

here,

for example

0.003 X 100

when we multiply with decimal it gets shifted to right side

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The correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.

For instance, any discrepancy between the average profits in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero.

So, the population proportion serves as the parameter.

The American Academy of Periodontology found that 27% of US individuals admit to lying to their dentist about how frequently they floss their teeth.

So, the following is the null hypothesis:

H0: p = 0.27

Dr. Garcia, a periodontist, thinks that the percentage should be higher than 27% since he feels it is too low.

Consequently, the competing theory is:

H0: p > 0.27

Therefore, the correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

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Complete question:

The American Academy of Periodontology released a survey, revealing that 27% of US adults admit they lie to their dentist about how often they floss their teeth. Periodontist Dr. Garcia believes that the percentage seems low, so he decides to conduct his own hypothesis test to determine the true proportion. What should he write as the null and alternative hypotheses for this situation?

Answer Options:

A: H0: p = 0.27; Ha: p > 0.27

B: H0: p = 0.27; Ha: p < 0.27

C: H0: p = 0.27; Ha: p ≠ 0.27

D: H0: μ = 0.27; Ha: μ > 0.27

E: H0: μ = 0.27; Ha: μ < 0.27

1. To get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Equation A is equivalent to Equation B

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Here, we have

1.  We are given the equation :

2x - 1 = 5x .............(A)

To get Equation B from A, we would subtract 2x from both sides of the equation.

2x - 2x - 1 = 5x - 2x

- 1 = 3x...... (B)

Hence, to get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Based on the previous answer,

2x - 1 = 5x  is equal to  -1 = 3x.

Hence, both Equation A and Equation B are equivalent expressions.

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The simplified form of the expression given is 17/11.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

To represent a mathematical expression in the simplest form possible is to simplify it. The expression is reduced to its most basic form when any redundant or redundant parts have been eliminated using the fundamental properties of numbers, exponents, algebraic rules, etc.

Consider, the given expression.

2/2 x 85/55

⇒  170 / 110

⇒ 17 / 11

Hence, the simplified form of the expression given is 17/11.

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A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length 2. So the area of this circle is 81π/32.

These are the specified parameters:

Sides of an isosceles triangle

a = 3

b = 3

c = 2

Find the height of an isosceles triangle

h² = a² - (c/2)²

    = 3² - 1²

    = 9 - 1

    = 8

h = √8

h = 2√2

Find the area of the triangle

A = 1/2 × c × h

  = 1/2 × 2 × 2√2

  = 2√2

Find the length of the radius of the circle

r = abc / (4 A)

 = (3 × 3 × 2) / (4 × 2√2)

 = 9/4√2

 = 9√2/8

Fnd the area of the circle

A = π × r²

  = π × (9√2/8)²

  = 81π/32

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There are 5 integer values of M that satisfy the given inequality.

An integer is a whole number, which means it is a number that can be written without a fractional or decimal component. Integers include positive numbers (e.g. 1, 2, 3), negative numbers (e.g. -1, -2, -3), and zero.

They are also often represented using the symbol "Z". Integers are a subset of the set of real numbers.

If M/20 is strictly between 1/3 and 3/5, then we have the following inequalities:

1/3 < M/20 < 3/5

To solve this, we can multiply both sides of the inequality by 20 to get rid of the denominator on the left side:

6 < M < 12

This tells us that M is an integer that lies strictly between 6 and 12 (i.e., 6 < M < 12), and the integers between 6 and 12 are 7, 8, 9, 10, and 11. Therefore there are 5 integer values of M that satisfy the inequality.

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The total monthly payment would be $17.36.

Option (d) is correct.

What is the annuity payment?

An annuity payment is a fixed, regular payment made to an individual or organization over a specific period of time. It is typically used in the context of financial transactions, such as loans, investments, and insurance.

To calculate the monthly payment Bianca will have to make to avoid interest capitalization, we can use the formula for the annuity payment:

PMT = (Loan Amount * Interest Rate / (1 - (1 + Interest Rate)^(-n))) / (Interest Rate / 12)

Where:

PMT is the monthly payment

Loan Amount is the amount of the loan, in this case, $2,600

Interest Rate is the annual interest rate, in this case, 6.2%

n is the total number of payments, in this case, 5 years * 12 months/year = 60 months

Plugging in the values, we get:

PMT = (2600 * 0.062 / (1 - (1 + 0.062)^(-60))) / (0.062 / 12)

PMT = $17.36

Hence, the total monthly payment would be $17.36

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Answer: C

Step-by-step explanation:Bianca took out a $2,600 unsubsidized Stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. The loan has an interest rate of 6.2%, compounded monthly. How much will she have to pay monthly to avoid interest capitalization?

a.

$12.40

b.

$19.29

c.

$13.43

d.

$17.36

Please select the best answer from the choices provided

The radius of the cone is , r = √(154 cm²/π) cm and the slant height is

L = √( 154 /π+ h²) cm.

To find the radius and slant height of the cone, we can use the formula for the total surface area of a cone, which is πr² + πrL, where r is the radius, L is the slant height, and π is pi.

Given that the curved surface area of the cone is 2/3 of its total surface area, we know that the total surface area of the cone is 462 cm², and the curved surface area is (2/3) * 462 cm² = 308 cm².

The formula for the curved surface area of a cone is πrL, where r is the radius, and L is the slant height.

So we know that:

πrL = 308 cm²

We also know that:

πr² + πrL = 462 cm²

Now we can solve for the radius and slant height of the cone by substituting the first equation into the second equation and solving the system of equations.

πrL = 308 cm²

πr² + πrL = 462 cm²

πr² = 462 cm² - 308 cm²

πr² = 154 cm²

r² = 154 cm²/π

Solving for r

r = √(154 cm²/π) cm

Now we can use the radius to find the slant height, by using the formula of slant height L = √(r² + h²) where h is the height of the cone.

Given that we do not have the height of the cone provided, we can't solve for the slant height.

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Step-by-step explanation:

the curved surface area is 2/3 of 462 cm².

462 × 2/3 = 308 cm²

that leaves 1/3 of 462 cm² for the base area, a circle.

462 × 1/3 = 154 cm²

the area of a circle is pi×r²

so, in our case

pi×r² = 154

r² = 154/pi

radius = r = sqrt(154/pi) = 7.001408606... cm

the slant height l

l = sqrt(r² + h²)

with h being the internal height.

to get l we have the total surface area A

A = pi×r(r + sqrt(h² + r²)) = pi×r(r + l)

A/(pi×r) = r + l

l = A/(pi×r) - r = 462/(pi×7.001408606...) - 7.001408606... =

= 14.00281721... cm

The coefficient of determination (R^2) tells you the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

It tells you how well the independent variable(s) are able to predict the dependent variable. An R^2 of 1 indicates a perfect fit, and an R^2 of 0 indicates that the model does not explain any of the variance in the dependent variable.

The residual plot is a graph that shows the residuals (the difference between the observed value of the dependent variable and the predicted value) on the vertical axis and the predicted value of the dependent variable on the horizontal axis.

The residual plot is used to check for patterns in the residuals, which can indicate a problem with the model. For example, if the residuals are not randomly dispersed around zero, it may indicate that the model is not a good fit for the data. The standard error of the estimate (s) is a measure of the average distance that the data points fall from the fitted line. It represents the average distance that the observed values deviate from the true values. Lower values of s indicate a better fit of the model to the data.

Overall, the R^2, residual plot and s are used to evaluate the goodness of fit of the model.

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