A nursery owner buys 5 panes of glass to fix some damage to her greenhouse. The panes cost ​$13.25. ​Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2
panes of​ glass?

The two intersecting arcs were made by placing the compass' fixed point at points C and E,

Hector would perform the following actions with a compass and straightedge to create the bisector of angle CEB:

The two intersecting arcs were made by placing the compass' fixed point at points C and E, respectively.

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The three statements that represent a unit rate are:

a. Carrots cost $2 per pound

d. A recipe calls for 2 cups of sugar for every gallon of water.

e. A teacher divides her class so there are 11 students per group.

The formula for calculating the overall score is:

overall value = number of units x value per unit.

For example, Budi buys a dozen pencils. The price of one pencil is IDR 2000. What is the total value or purchase price to be paid by Budi?

One dozen equals 12 pieces.

So, the purchase price = 12 x 2000 = 24,000

So, the total purchase price is IDR 24,000.

"The overall value is obtained from the product of the number of units with the value per unit."

The formula for calculating the unit rate is:

value per unit = total value : number of units.

For example, Aan bought ten candies for Rp. 2,500. How much does one candy cost?

To calculate it, we must use the value per unit formula.

The price of one candy = 2,500 : 10 = 250.

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As x increases from x=1 to x=5, the value of h remains constant at 4 and the output of the function v(x) changes from v(1) = 5 to v(5) = 29, with a difference of 24.

A function is a mathematical rule that assigns a unique output for every input.

Given the function h = 4, we can see that the output is always 4, regardless of the input value.

Now, if we consider the function

=> v(x) = x² + h,

we can see that the output is dependent on the input x and the constant value of h. As x increases from x=1 to x=5, the output of v(x) will also change.

We can calculate the value of v(1) as

=> v(1) = 1² + 4 = 5.

And similarly, we can calculate the value of v(5) as

=> v(5) = 5² + 4 = 29.

The difference between v(5) and v(1) can be calculated as

=> v(5) - v(1) = 29 - 5 = 24.

This represents the change in the output of the function v(x) as x increases from x=1 to x=5.

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The simplest form of the sum of the mixed fraction  [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]

A fraction represented with its quotient and remainder is a mixed fraction.

Given is a sum of two mixed fractions, [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex]

Converting into the simplest forms,

[tex]3\frac{2}{6} + 9\frac{4}{10}\\\\= \frac{20}{6} + \frac{94}{10} \\\\= \frac{10}{3} + \frac{47}{5} \\\\= \frac{50+141}{15} \\\\= \frac{191}{15} \\\\= 12\frac{11}{15}[/tex]

Hence, the simplest form of the sum of the mixed fraction  [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]

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Using algebraic expression, She needs to sell 150 / 5 = 30 T-shirts.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). It represents a value that can be determined if the values of the variables are known. An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

Harper's fixed costs for starting the business are $150.

She earns $10 for each T-shirt sold, and she spends $5 on each T-shirt she buys.

So, her profit is $10 - $5 = $5 per T-shirt.

To break even, Harper needs to earn enough money from selling T-shirts to cover her fixed costs of $150.

Therefore, she needs to sell 150 / 5 = 30 T-shirts.

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the average rate of change of the total cost as the shirt production increases from 10 to 20 is 90.

Given the function in the question;

f(x) = 3x² + 2

And production increases from 10 to 20.

To find the average rate of change, we use the expression;

[ f(20) - f(10) ] / [ 20 - 10 ]

Now, if f(x) = 3x² + 2

f(20) = 3( 20 )² + 2 = 1202

f(10) =  3( 10 )² + 2 = 302

Plug in the values and simplify

[ f(20) - f(10) ] / [ 20 - 10 ]

[ 1202 - 302 ] / [ 20 - 10 ]

[ 900 ] / [ 10 ]

900/10

90

Therefore, the average rate of change is 90.

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The equation has been verified and the solution has been obtained by using trigonometric identities.

What are trigonometric identities?

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

We are given cotθ/1-tanθ + tanθ/1-cotθ = 1 + tanθ + cotθ

Solving the LHS, we get

⇒ [(cosθ/sinθ)/1-(sinθ/cosθ)] + [(sinθ/cosθ)/1-(cosθ/sinθ)]

⇒ [(cosθ/sinθ)/[(cosθ-sinθ)/cosθ]] + [(sinθ/cosθ)/[(sinθ-cosθ)/sinθ)]]

⇒ [cos²θ/(cosθ-sinθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]

⇒-[cos²θ/(sinθ-cosθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]

⇒[sin²θ/(sinθ-cosθ)cosθ] - [cos²θ/(sinθ-cosθ)sinθ]

⇒(sin³θ - cos³θ)/(sinθ-cosθ)sinθcosθ

⇒(sinθ - cosθ)(sin²θ + sinθcosθ + cos²θ)/(sinθ-cosθ)sinθcosθ

⇒(sin²θ + sinθcosθ + cos²θ)/sinθcosθ

⇒sin²θ/sinθcosθ + sinθcosθ/sinθcosθ + cos²θ/sinθcosθ

⇒tanθ + 1 + cotθ

⇒1 + tanθ + cotθ = RHS

Hence, the expression is verified.

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Answer:

2/1

Step-by-step explanation:

black is 24 and blue is 12 so it'd be 24/12 which simplifies to 2/1

The amount of interest earned in 6 years will be $15.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Ellie has $50 in a savings account that earns 5% annually.  The simple interest is calculated as:-

Simple interest = ( P x R x T ) / 100

Simple interest = ( 50 x 5 x 6 ) / 100

Simple interest = $15

Hence, the value of the simple interest after 15 years will be $15.

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The volume of the trapezoidal prism can be calculated using the formula V = (1/2)(h)(b1 + b2)h, where h is the height, b1 is the length of the top base, and b2 is the length of the bottom base.

In this case, the height is 7 cm, the length of the top base is 10 cm, and the length of the bottom base is 12 cm. Therefore, the volume of the trapezoidal prism is V = (1/2)(7)(10 + 12)7 = 630 cm3.

In addition to calculating the volume of a trapezoidal prism, you can also calculate the surface area of a trapezoidal prism using the formula A = 2h(b1 + b2) + 2(l1 + l2), where h is the height, b1 and b2 are the lengths of the top and bottom bases, and l1 and l2 are the lengths of the lateral faces. The surface area of a trapezoidal prism is the total area of all of the faces of the prism.

Additionally, the lateral surface area of a trapezoidal prism can be calculated by using the formula A = 2h(b1 + b2), where h is the height, b1 and b2 are the lengths of the top and bottom bases. The lateral surface area of a trapezoidal prism is the total area of all of the lateral faces of the prism.

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The initial population of city A is 175,000 while its growth rate is 10%. The function that models the population of city B is B(t) = 350,000(0.97)^t, which is a case of exponential decay.

Here since nothing else is mentioned we will assume the Initial population of city A to be that of 2018, which is 175,000.

The growth rate of any city will be the percentage increase in its population every year. Here it is mentioned that the population of city A increases by 10% every year. Hence, the growth rate of city A is 10%.

Here we are already given that the function of the population of city B in a year is B(t) = 350,000(0.97)^t.

In model B(t) with every successive increase in time, the value of (0,97)^t will keep on reducing. Due to this, the product of 350,000(0.97)^t will reduce. Hence this is a case of exponential decay.

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The most appropriate level of measurement for the Monthly Rainfall is (d) Ratio .

Ratio measurement is used for variables where the values have a meaningful order, the differences between them are meaningful, and there is a true zero point. For example, height, weight, or time.

In the case of monthly rainfall,

(i) the values have a meaningful order (more rainfall or less rainfall),

(ii) the differences between the values are meaningful (0.2 inches difference),  

(iii) there is true zero point  (month with 0 inches of rainfall).

Therefore, the most appropriate level of measurement is Ratio .

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.

Monthly rainfall: 3.4 in, 3.6 in, 3.8 in, 4 in, and 4.2 in

Choose the correct answer below.

(a) Nominal

(b) Ordinal

(c) Interval

(d) Ratio

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A linear function is used to depict a relationship between two variables where one variable influences the other.

Those with a straight-line graph are considered to be linear functions. This is the format of a linear function. y = f(x) = a+bx. The only independent and only dependent variables in a linear function are both independent.

In a relationship between two variables, where one variable affects the other, a linear function is used to represent the relationship. Generally speaking, x and y are the independent and dependent variables, respectively, in a linear function (x influences y).

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

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Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it so The value of x is 77.

Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.

The total of the inner angles is 180 degrees, or 180. (43-34). The outer angles measure 43 , 34, and 120 degrees, respectively, because they are an addition to the inside angles. The outer angles add up to a total of 360 degrees.

Calculate the outside angle's dimensions.

< u = 43 + 34 - 180 = 103.

so

The value of x = 180 - 103 = 77.

Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it so The value of x is 77.

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The rational, irrational and imaginary zeroes for function c(x) = 18x³ + 9x² - 2x -1 are:

To solve this proble, we will use Rational Root Theorem and Descartes Rules of Signs.

Based on Rational Root Theorem, we can find that the function c(x) has rational roots of:

c(x) = 18x³ + 9x² - 2x -1

possible roots = ± {factors of a₀} / {factors of aₙ}

From the given function, we can use the possible roots concept:

Possible roots = ± factors of 18

                              factors of 1

Possible roots = ± {1, 2, 3, 6, 9, 18}

                                     {1}

We can conculde some possible roots such as: {-18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18}

Next, we need to confirm which possible roots are the rational roots by subtitute the possible roots into the function c(x). The rational roots will produce the function equals to zero (0).

c(1) = 18(1)³ + 9(1)² - 2(1) -1

c(1) = 18 + 9 - 2 - 1 = 24 --> irrational roots

c(2) = 18(2)³ + 9(2)² - 2(2) -1

c(2) = 18(8) + 9(4) - 2(2) - 1

c(2) = 144 + 36 - 4 - 1 = 175 --> irrational roots

c(3) = 18(3)³ + 9(3)² - 2(3) -1

c(3) = 18(27) + 9(9) - 2(3) - 1 = 560 --> irrational roots

c(6) = 18(6)³ + 9(6)² - 2(6) -1

c(6) = 4.199 --> irrational roots

c(9) = 18(9)³ + 9(9)² - 2(9) -1

c(9) = 13,832 --> irrational roots

c(18) = 18(18)³ + 9(18)² - 2(18) -1

c(18) = 107,855 --> irrational roots

c(-1) = 18(-1)³ + 9(-1)² - 2(-1) -1

c(-1) = -18 - 9 + 2 - 1 = -8 --> irrational roots

c(-2) = 18(-2)³ + 9(-2)² - 2(-2) -1

c(-2) = -105 --> irrational roots

c(-3) = 18(-3)³ + 9(-3)² - 2(-3) -1

c(-3) = -400 --> irrational roots

c(-6) = 18(-6)³ + 9(-6)² - 2(-6) -1

c(-6) = -3,553 --> irrational roots

c(-9) = 18(-9)³ + 9(-9)² - 2(-9) -1

c(-9) = -12,376 --> irrational roots

c(-18) = 18(-18)³ + 9(-18)² - 2(-18) -1

c(-18) = -120,176 --> irrational roots

Next, we will try to use Descartes Rule of Signs:

c(x) = 18x³ + 9x² - 2x -1

c(x) = +18x³ + 9x² - 2x -1

The sign is changing once, then the function c(x) has 1 positive roots.

Next, we change the value of (x) into (-x) and put it into the function:

c(-x) = 18(-x)³ + 9(-x)² - 2(-x) -1

c(-x) = -18x³ + 9x² + 2x -1

The signs are changing twice on between the first and second coefficient and between third and fourth. Hence the funciton c(x) has 2 or zero negative roots.

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A budget is a regular summary of the anticipated earnings and spending for a specific time period.

The calculation of James' monthly salary is as follows:

income each month = $47,000 / 12 = 3916

The necessary James personal monthly budget is given as follows;

The monthly personal budget is determined by inputting the supplied numbers into a budget template as shown below based on the monthly expenses mentioned above;

fixed expenses

Income

$3,916.6

Rent \s$950

Insurance for tenants

$25

Health Insurance: $185 Retirement: 401(k)

$157

vehicle insurance

$120

Utilities

a $100 cell phone

$85

Credit card for $70 for cable

$150

Car loan $554

$2,396 in total fixed expenditures

variable costs

Clothing  $8

Groceries n $300

Entertainment $196

$576 in total variable costs

Savings                                $944.

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48 plastic bandages should a small kit have

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that the ratio of fabric bandages to plastic bandages in each kit is 3 to 9

A small kit has 16 fabric bandages then we have to find the number of plastic bags.

Let x be the number of plastic bags for 16 fabric bandages.

3/9=16/x

Apply cross multiplication

3x=16×9

3x=144

Divide both sides by 3

x=48.

Hence, 48 plastic bandages should a small kit have

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The value of SAT from the following enumerated data is 7 (option a)

Enumerated data;

A set of named values known as enumeration constants, which are integral constants, make up an enumeration, a data type. Because you must list (enumerate) every value before giving it a name, an enumeration is also known as an enumerated type.

Enumeration refers to the act of counting, reciting, or listing numbers. If he starts with a deep sigh, a waiter's long list of all the various salad dressings can sound a touch hostile. Enumeration occurs while you are reciting a list of items.

Here,

Option a 7 is the value of SAT

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(x + 2) ^2 + (y - 3) ^2 + (z - 1^2 = 1 is an equation for a sphere with a center of (-2,3,1) and a tangent to the xz plane.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers.

Here,

The equation of a sphere with center (x0, y0, z0) and radius r is given by:

(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2

In this case, the center of the sphere is (-2, 3, 1) and it is tangent to the xz plane, which has equation z = 0. Hence, the sphere must have a z-coordinate of 1, so the equation becomes:

(x + 2)^2 + (y - 3)^2 + (z - 1)^2 = r^2

We need to find the value of r such that the sphere is tangent to the xz plane. If a sphere is tangent to a plane, it means that the distance between the center of the sphere and the plane is equal to the radius of the sphere. The distance between a point (x0, y0, z0) and the plane z = k is given by |z0 - k|. Hence, the distance between the center of the sphere (-2, 3, 1) and the xz plane is given by:

|1 - 0| = 1

Therefore, the radius of the sphere is equal to 1, so the equation of the sphere is:

(x + 2)^2 + (y - 3)^2 + (z - 1)^2 = 1^2

Simplifying, we obtain the equation of the sphere:

(x + 2)^2 + (y - 3)^2 + (z - 1)^2 = 1 is an equation for the sphere with center (-2,3,1) that is tangent to the xz plane.

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The value of k is 90.

The other factor of g(x) is, (x + 5)(x - 3)(x + 3)

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given the function,

g(x) = x⁴ + 3x³ - 19x² - 27x + k

and  (x - 2) a factor of g(x)

so g(2) = 0

g(x) = x⁴ + 3x³ - 19x² - 27x + k

g(2) = 2⁴ + 3(2)³ - 19(2)² - 27(2) + k

2⁴ + 3(2)³ - 19(2)² - 27(2) + k = 0

16 + 24 - 76 - 54 + k = 0

k = 90

the function is g(x) = x⁴ + 3x³ - 19x² - 27x + 90

B: -5 is a zero of the function,

f(-5) = 0, or x = -5

so factor is (x + 5)

the two factors are (x + 5)(x - 2)

(x + 5)(x - 2) = x² + 5x - 2x -10

(x + 5)(x - 2) = x² + 3x - 10

to find the other two factors we need to divide the function by

x² + 3x - 10

=>  (x⁴ + 3x³ - 19x² - 27x + 90) ÷ (x² + 3x - 10)

quotient after division is

x² - 9 = (x - 3)(x + 3)

The factors of the function are (x - 2)(x + 5)(x - 3)(x + 3)

Hence k = 90, and

the three other factors of g(x) are (x + 5)(x - 3)(x + 3)

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Answer:

AG=38.84

Step-by-step explanation:

Follow the steps in the image

-Hope this helped

Step-by-step explanation:

I just answered this. how often did you post it ?

the "incenter" means that this is the center point of the inscribed circle that is completely inside the triangle and touches every side in exactly one point.

therefore, all right-angled connections from that point to a side are equally long (the radius is the inscribed circle).

therefore,

GB = GF = GD

we know GF = 22

so, GB = 22

and now we use Pythagoras to find AG in the right-angled triangle ABG :

AG² = AB² + GB² = 32² + 22² = 1024 + 484 = 1508

AG = sqrt(1508) = 38.83297568...

if you round to hundredths : 38.83

So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.

The quantifier ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is a statement in first-order logic that says "there exists x and there exists y such that x is not equal to y and for all z, z is equal to x or z is equal to y".

The domain for this quantifier is the set of all values for which the statement inside the quantifier is true.

In this case, the domain for the quantifier is the set of all non-empty sets, since for any non-empty set, we can find at least two distinct elements x and y, such that x is not equal to y and for any element z in the set, either z is equal to x or z is equal to y.

So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.

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So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.

The quantifier ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is a statement in first-order logic that says "there exists x and there exists y such that x is not equal to y and for all z, z is equal to x or z is equal to y".

The domain for this quantifier is the set of all values for which the statement inside the quantifier is true.

In this case, the domain for the quantifier is the set of all non-empty sets, since for any non-empty set, we can find at least two distinct elements x and y, such that x is not equal to y and for any element z in the set, either z is equal to x or z is equal to y.

So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.

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The statement is referring to a market economy, where supply and demand forces affect the production and consumption decisions and there is little to no government control in such a system.

In a market economy, individuals and businesses make the decisions regarding production and consumption, and prices are determined by the interaction of supply and demand. The market is seen as the most efficient allocation mechanism, as prices communicate information about relative scarcities and help to direct resources to their most valuable uses. However, market economies may result in income inequality and market failures, where the market fails to allocate resources efficiently. Government intervention in a market economy is limited to correcting market failures and ensuring a level playing field.

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the equation of the parabola will be y=3/4 (x²-1).

What is parabola ?

A parabola is a curve whose equation places a point on it at a same distance from both a fixed point and a fixed line. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. The fixed point does not lie on the fixed line, which is another crucial factor to remember. A parabola is a locus of any point that is equally distant from both the focus and directrix of two supplied points. The point where a parabola makes its sharpest turn is known as the vertex. If a parabolic function has the shape of a "," it has a maximum value; otherwise, it has a minimum value.

A parabola has a vertex at (0, -1)  

passes through point (2, 2). Which of the following is the equation of

this parabola in the form y = a(x-h)² +k.

The equation will be (2,2)

x=2, y=2

2=a(2²)-1

2=a(4)-1

3=a(4)

a = 3/4

the equation is

y=3/4 (x²-1)

Hence the equation of the parabola will be y=3/4 (x²-1).

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Right ascension (RA) and declination (Dec) are coordinates used in astronomy to precisely describe the location of an object in the sky is  total of 62.3358° for the Dec.

RA is measured eastward along the celestial equator from the vernal equinox, which is the point in the sky where the Sun crosses the celestial equator from south to north at the beginning of spring. Dec measures the angle of an object above or below the celestial equator.

In this example, the right ascension is 15 06 53.62 and the declination is 62 20 10.0. This is expressed in terms of hours, minutes, seconds for the RA and degrees, minutes, seconds for the Dec. The RA can be converted to a decimal value by taking the 15 hours and multiplying it by 15 (1 hour = 15°) to get 225°. Then add 6 minutes (6/60 of an hour) which is equal to 10°, and add 53.62 seconds (53.62/3600 of an hour) which is equal to 0.1489°. This gives us a total of 225.1489° for the RA. For the Dec, we take the 62° and add 20 minutes (20/60 of a degree) which is equal to 0.333°, and add 10 seconds (10/3600 of a degree) which is equal to 0.0028°. This gives us a total of 62.3358° for the Dec.

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The probability that exactly two couples are dancing together in a party of 5 male-female couples is 1/126, which is a very low probability.

The problem of finding the probability that exactly two couples are dancing together can be solved using the combination formula. The number of ways to choose two couples from the five available couples is given by the binomial coefficient "C(5,2) = 10". The number of ways to arrange the chosen two couples is given by 2! (two factorial), since the order of the couples doesn't matter. The total number of ways to randomly pair the males and females is given by 10!. To find the number of ways in which exactly two couples are dancing together, we need to find the number of arrangements where two couples are dancing together and the remaining three couples are not dancing together.

Therefore, the probability that exactly two couples are dancing together is given by:

(C(5,2) * 2!) / 10! = 1/126

This shows that it is unlikely that exactly two couples will be dancing together in a random pairing of the males and females.

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By reading values from the given graph of f, use five rectangles to L a lower estimate and an upper the area under the given graph of f from x = 0 to x = 10 are as follows :

Using the five rectangle method , for upper limit choose the area of vertically longer rectangle in each case and vice versa for lower limit.

Upper limit = 5x2+4x2+2x2+1x2+1x2 = 26

Lower limit = 3x2+1x2+0x2+0x2+0x2 = 8

(b) Use the same approach as in the case above, the new estimates using ten rectangles in each case.

Upper limit = 5x1+4x1+4x1+3x1+2x1+2x1+1x1+1x1+1x1+1x1 = 24

Lower limit = 4x1+3x1+2x1+1x1+1x1+0x1+0x1+0x1+0x1+0x1 = 11

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The statement that identifies the scale used in this map would be

1 inch equals 19 miles.

A map is a visual depiction of specific features of a location, typically created on a flat surface. Maps provide straightforward, visible information about the globe. They demonstrate the sizes and shapes of the world's nations, the locations of its characteristics, and the distances between regions to teach about it.

Given:

There are 4 towns which are separated by 3 inches apart.

The actual distance apart = 57 miles

So, the actual scale is

3 inches = 57 miles

1 inch = x miles

x miles = 57/3

x = 19 miles.

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In testing the equality of population proportions using chi-square, at least 3 categories or populations need to be able to perform this analysis

Now, According to the question:

A chi-square test for equality of two proportions is exactly the same thing as a z-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're basically just repeating the chi-squared test on a subset of the contingency table.

The chi-square test is used to compare more than two independent populations. The test is pretty similar to that of two population proportions except for the fact that the contingency table involved in the study includes 2 rows and c number of columns indicating the number of populations.

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