What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?

The sample space will be 243, 743, 1243, 1743, 2243, 2743, 3243, 3743, 4243, and 4743.

A sample space is the collection of all potential results of a random experiment or process in probability theory. It's represented by the symbol (the uppercase Greek letter omega).

For instance, if we flip a fair coin, the sample space is H, T, where H stands for the outcome of a heads result and T stands for a tails result. The sample space on a normal six-sided dice is 1, 2, 3, 4, 5, and 6.

No matter how likely they are, all outcomes are included in the sample area. In order to accurately estimate the probability of an event, the sample space must be defined.

Now,

To choose a systematic sample of size n = 10 from a town with 5000 people, we will use a systematic sampling technique. Here are the steps to follow:

Determine the sampling interval: The sampling interval is the number of people in the population divided by the desired sample size. In this case, the sampling interval is 5000/10 = 500.

Select a random starting point: To ensure the sample is representative of the population, we need to select a random starting point between 1 and 500.

We can use a random number generator to choose a starting point. Suppose we choose the number 243 as our starting point.

Select every nth person: Starting from the chosen starting point, we will select every 500th person until we reach a sample size of 10.

So, we will select people with the following index numbers: 243, 743, 1243, 1743, 2243, 2743, 3243, 3743, 4243, and 4743.

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The length of the diagonals will be WZ = XZ = 11 units.

A diagonal in geometry is a line segment that connects two polygonal or polyhedral vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.

The length of the two diagonals of the rectangle is equal. The value of x will be calculated as,

6x - 7 = 3x + 2

3x = 9

x = 3

WZ = 6x - 7

WZ = 6 x 3 - 7

WZ = 18 - 7

WZ = 11

XZ = 3x + 2

XZ = 3 x 3 + 2

XZ = 11

Therefore, the length of the diagonals will be WZ = XZ = 11 units.

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Answer:

120 because 20 x 6 = 120 when u take of sunday it will be 6 days

Step-by-step explanation:

The mathematical expression for 21 fewer stars than three times a number h is : 3h - 21

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtract, multiplication, division, exponents, and other as-yet-unlearned operations and functions.

The given statement is-

21 fewer stars than three times a number h

so,

mathematical expression is:

3h - 21

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Answer:

x = 20

Step-by-step explanation:

x² − 1 = 399

x² = 400

x = 20

According to the given composite function the correct answer is , (g o h)[tex](n/2) = 8n^2 + 42n + 35.[/tex]

What is a composite function?

A composite function is a function that is formed by combining two or more functions. It is obtained by taking the output of one function and using it as the input of another function.

Suppose we have two functions, f(x) and g(x). The composite function of f and g, denoted by f o g, is defined as:

(f o g)(x) = f(g(x))

In words, this means that we apply the function g to the input x, and then we apply the function f to the output of g. The result is a new function that combines the effects of both f and g.

For example, if we have [tex]f(x) = x^2[/tex] and g(x) = 2x + 1, then the composite function f o g is:

[tex](f o g)(x) = f(g(x)) = f(2x + 1) = (2x + 1)^2 = 4x^2 + 4x + 1[/tex]

The composite function f o g takes an input x, applies g to it to get 2x + 1, and then applies f to that to get [tex]4x^2 + 4x + 1[/tex] as the final output.

To compute (g o h)(n/2), we need to first evaluate h(n/2) and then substitute the result into g(n) in place of n.

So, first we evaluate h(n/2):

h(n/2) = 4(n/2) + 5 = 2n + 5

Now we substitute this expression into g(n):

[tex]g(h(n/2)) = 2(h(n/2))^2 + h(n/2)[/tex]

[tex]= 2(2n + 5)^2 + (2n + 5)[/tex]

[tex]= 2(4n^2 + 20n + 25) + 2n + 5[/tex]

[tex]= 8n^2 + 42n + 35[/tex]

Therefore, [tex](g o h)(n/2) = 8n^2 + 42n + 35.[/tex]

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Answer:

the correct option is: L′(-1, 11).

Step-by-step explanation:

To translate the preimage 9 units up, we need to add 9 to the y-coordinate of each vertex of the polygon. Thus, the image of polygon JKLM after the translation will have vertices J′(−2, 4), K′(−4, 9), L′(−1, 11), M′(0, 8). Therefore, the image coordinates of L′ are (-1, 11).

After translation the image coordinates of L' is (-1, 11). Therefore, option B is the correct answer.

Given that, Polygon JKLM is drawn with vertices J(-2, -5), K(-4, 0), L(-1, 2), M (0, -1).

When the shape is moved up by k units, then replace y with y + k.

The translation is as follows:

Here, J(-2, -5) → (-2, -5+9) → J'(-2, 4)

K(-4, 0) → (-4, 0+9) → K'(-4, 9)

L(-1, 2) → (-1, 2+9) → (-1, 11)

M(0, -1) → (0, -1+9) → (0, 8)

Therefore, option B is the correct answer.

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The probability of getting tens depends on the context. If you are referring to a regular deck of cards, there are four tens out of 52 cards, so the probability is 4/52 or 1/13. If you are referring to rolling a regular six-sided die, there is only one ten, so the probability is 1/6.

The probability of getting tens depends on the context. If you are referring to a regular deck of cards, there are four tens (10 of hearts, diamonds, clubs, and spades) out of a total of 52 cards. So the probability of drawing a ten is 4/52 or 1/13. If you are referring to rolling a regular six-sided die, there is only one ten (the number 10 itself) out of a total of six possible outcomes. So the probability of rolling a ten is 1/6.

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By answering the above question, we may state that Find any dots that expressions are distant from the other dots to identify outliers. They might be anomalies and need more research.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. .  

You should check for the following data when interpreting a dot plot:

Determine the dot plot's lowest and maximum values by using the range concept.

Shape: Search for any patterns or groups of dots that could point to a certain data distribution.

Central Tendency: Locate the dot plot's centre to ascertain the typical value of the dataset. Finding the data's median or mean can be used to achieve this.

Find any dots that are distant from the other dots to identify outliers. They might be anomalies and need more research.

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The requried (a) median for the chocolate candy and nonchocolate candy sales are $3040 and $1566.5 respectively. (b) The range for the chocolate candy sales, the range is ($1941, $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

A histogram is a graphical representation of the distribution of a set of numerical data. It consists of a set of rectangles, where the area of each rectangle is proportional to the frequency (or count) of the observations falling within a particular interval, called a bin.

Here,
A. The interval for the median for each data set can be found by arranging the data in ascending order and finding the middle value. For the chocolate candy sales, the median falls in the interval of 2800-3,099 dollars. While for the Nonchocolate candy, it falls under 1300 -1599

The median for the chocolate candy sales  = $3040
The median for the Nonchocolate candy sales  = $1566.5

B. The range for each data set can be found by subtracting the minimum value from the maximum value. For the chocolate candy sales, the range is ($1941, to $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

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Survey is a method used to collect the information from the group by asking  relevant questions.

It is simply how  likely the event can be occurred or in other words it is a likelihood of an event occurring

Let the events be:

A----Cooked food P(A)=10

B----washed dishes P(B)=13

C----- operated the cash register.

P(C)=25

P(A∩B)=5

(cooked + washed dishes)

P(A∩C)=5

(cooked & operated the cash register)

P(B∩C)=8

(washed dishes and operated the cash register)

P(A∩B∩C)=3 did All three jobs

P(A∩B∩C)'=3 did none of these jobs

P(AUBUC) = P(A) + P(B) + P(C) - P(A∩B)-P(A∩C)-P(B∩C) + P(A∩B∩C).

A.) How many employees were surveyed?

=P(A) + P(B) + P(C) - P(A∩B)-P(B∩C)-P(C∩A) + P(A∩B∩C)

=(10+13+25)-(5-5-8)+3

=48-(-8)+3

= 48 + 8 + 3

= 59

= 59+ 3 (members who did none of the jobs)

=62

62 employees were surveyed

x=A∩B∩C

=3

ab= A∩B-x

=5-3

=2

bc=B∩C-x

=8-3

=5

ca=A∩C-x

5-3

=2

b) only cooked food:

=A-(ab+x+ca)

= 10-(2+3+2)

=10-7

=3

3 employees only cooked food

c)only operated the cash register:

=C-(bc+x+ca)

=25-(5+3+2)

=25-10

=15

15 employees only operated the cash register

d) employees cooked food or operated the cash register:

P(A or C)=P(A)+P(C)

=10+25

=35

e) washed dishes or operated the cash register

P(B or C)= P(B)+P(C)

=13+25

=38

f)only washed dishes:

=B - P(bc+x+ab)

=13-(5+3+2)

=13-10

=3

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this question is incomplete

The complete question is:

In a survey of employees at a fast food​ restaurant, it was determined that 10 cooked​ food, 13 washed​ dishes, 25 operated the cash​ register, 5 cooked food and washed​ dishes, 5 cooked food and operated the cash​ register, 8 washed dishes and operated the cash​ register, 3 did all three​ jobs, and 3 did none of these jobs. Complete parts A) through F) below,

A.) How many employees were surveyed?

B.) How many of the employees only cooked food?

C.) How many of the employees only operated the cash register?

D.) How many of the employees washed dishes or operated the cash register?

E.) How many of the employees washed dishes or operated the cash register ?

F.) How many of the employees only washed dishes?

The value if x in the inequality is x > -2 2/13

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

greater than is represented by >

less than is represented by <

greater than or equal to is represented by ≥

less than or equal to is represented by ≤

-5/7(21x+35)<1/3(9-6x)

-15x -25 < 3-2x

collect like terms

-25-3 < 15x -2x

-28 < 13x

-28/13 < x

therefore x > -28/13

x> - 2 2/13

therefore the value of x in the inequality is x > -2 2/13

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The selling price is the cost a customer pays for a good or service.

(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .

(4) Profit = Rs.9712 . (5) Loss % =  7.5% .

The amount a buyer pays for a good or service is known as the selling price.

It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.

The cost price of an item is the sum paid for it or the cost at which it was produced. C.P. stands for "cost price." Selling Price: The selling price of a good is the price at which it is sold.

So, the table would be:

(1)

CP = Rs.8000 , SP = Rs.10000

if SP > CP, we have profit.

Profit = SP - CP = 10000 - 8000 = Rs.2000 .

Profit % = (Profit * 100) / CP = (2000 * 100) / 8000 = 25% .

(2)

SP = Rs.6890 , Profit = Rs.390 .

CP = SP - Profit = 6890 - 390 = Rs.6500 .

Profit % = (Profit * 100) / CP = (390 * 100) / 6500 = 6% .

(3)

CP = Rs.25000 , Loss = Rs.1000 .

SP = CP - Loss = 25000 - 1000 = Rs.24000 .

Loss % = (Loss * 100) / CP = (1000 * 100) / 25000 = 4% .

(4)

CP = Rs.48560 , Profit = 20% .

SP = CP * (100 + Profit%) / 100 = (48560 * 120) / 100 = Rs.58272 .

Profit = SP - CP = 58272 - 48560 = Rs.9712 .

(5)

CP = Rs.28320 , SP = Rs.26196 .

CP > SP, we have a Loss.

Loss = CP - SP = 28320 - 26196 = Rs.2124 .

Loss % = (Loss * 100) / CP = (2124 * 100) / 28320 = 7.5% .

Therefore, the selling price is the cost a customer pays for a good or service.

(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .

(4) Profit = Rs.9712 . (5) Loss % =  7.5% .

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Complete question:

Find the profit or loss and complete the table.

Cost Price Selling Price Profit () Loss

Profit Loss

Percentage Percentage

6000

1000

6000

(a) 5000

(b) 6200

(c) 2400

(d) 1900

400

300

1590

190​

The area of the triangle is approximately 1.987 square units.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Using sin rule of a triangle,

[tex]\frac{Sin A}{a} = \frac{Sin C}{c} = \frac{Sin B}{b}[/tex]

In our case,

[tex]\frac{Sin 18}{1.6} = \frac{Sin Q}{4.2} = \frac{Sin P}{QR}[/tex]

From equation 1

[tex]\frac{Sin 18}{1.6} = \frac{Sin Q}{4.2} \\\frac{(Sin 18)*4.2}{1.6} = {Sin Q}\\Sin \ Q =21/8* sin\ 18\\[/tex]

Thus,

∠Q = 125.79 degrees

since sum of all angles is 180 degrees

so,

∠P = 180-125.79-18

∠P = 36.21

So From the equation 1

[tex]\frac{Sin 18}{1.6} = \frac{Sin P}{QR}\\\frac{Sin 18}{1.6} = \frac{Sin 36.2}{QR}\\QR = \frac{Sin 36.2}{\frac{Sin 18}{1.6}}[/tex]

QR = 3.06 cm

To find the area of the triangle, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the side lengths and s is the semi perimeter:

s = (a + b + c)/2

Plugging in the values we get:

s = (4.2 + 1.6 + 3.052)/2

s ≈ 4.426

Now we can use Heron's formula:

Area = √(4.426(4.426-4.2)(4.426-1.6)(4.426-3.052))

Using a calculator, we find:

Area ≈ 1.987 square units

Therefore, the area of the triangle is approximately 1.987 square units.

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Complete question:

The diagram shows triangle PQR, PR =  4.2 cm, PQ = 1.6 cm Given that angle PQR is obtuse triangle, work out the area of triangle PQR Give your answer correct to 3 significant figures. Angle PRQ = 18° Diagram NOT accurately drawn​

The required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.

Rate of change is defined as the change in value with rest to another value is called rate of change.

Here,
In Frank's city,
y = 0.3x + 2

The rate per mile is represented by the slope of the linear equation.
So,
m = $0.3 per mile

For Seattle

The rate per mile is given by the slope of the relation shown in the graph. So,
m = 3.2 - 2.4 / 6 - 2
m = $0.2 per mile

Similarly,
For Orlando, m = $0.25 per miles
For Miami, m = $0.4 per mile
For Honolulu m = $0.75 per mile

Thus, the required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.

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Answer:

Step-by-step explanation:

i think so

On using unit conversion the value for 31.5 inches is obtained as 80.01 centimeters.

What is unit conversion?

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.

To convert inches to centimeters, we can multiply the number of inches by 2.54.

So to convert a 31.5 inch board to centimeters, use the arithmetic operation of multiplication.

We can multiply 31.5 by 2.54 -

31.5 inches × 2.54 centimeters/inch = 80.01 centimeters

Therefore, the board is 80.01 centimeters long.

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The answer to this question is as follows Hence, the appropriate expressions response would be: Sort the company's revenue gain from least to biggest percent: D, C, A, B

In mathematics, you can multiply, divide, add, or subtract. This is how an expression is put together: Expression, numerical value, and math operator Numbers, parameters, and operations make up a mathematical expression. It is feasible to use contrasting words and phrases. Any mathematical statement containing variables, numbers, and a mathematical action between them is referred to as an expression, often known as an algebraic expression. For instance, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Based on the information in the graph, the firms are ranked from having the least % growth in revenue to having the largest:

With a 5% rise in revenue, Company D

A 10% rise in revenue for Company C

A 15% rise in revenue for Company A

A 20% rise in revenue for Company B

Hence, the appropriate response would be:

Sort the company's revenue gain from least to biggest percent: D, C, A, B

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Answer:

Two monomials with the quotient 24a2b5 are:

12a b³

48a³ b²

Step-by-step explanation:

Answer: -7

Step-by-step explanation:

-2x+5=19

-5 |-5

-2x=14

-2x/-2 = 14/-2

x = -7

We get abοut 4 minutes if we rοund tο the clοsest minute. The sοlutiοn is thus A. 4 minutes οr sο.

A mathematical nοtiοn knοwn as prοpοrtiοnality describes the relatiοnship between twο quantities that cοnsistently change tοgether. When twο quantities are prοpοrtiοnal, their relatiοnship stays cοnsistent οver time. Tο put it anοther way, if twο variables, A and B, are prοpοrtiοnal, then the ratiο οf A tο B must be cοnstant and can be written as fοllοws:

A/B = k

where k is a ratiο cοnstant. This means that tο keep the ratiο cοnsistent, if οne οf the quantities is multiplied by a certain factοr, the οther quantity must alsο be multiplied by the same factοr.

given

dT/dt = -k (T - Ts)

where T is the οbject's temperature, Ts is the envirοnment's temperature, and k is a prοpοrtiοnality factοr. dT/dt stands fοr the rate οf change οf temperature.

In this instance, the rοοm is currently 70°F and the pοt οf water is οriginally 200°F. We thus have:

dT/dt = -k (200 - 70) = -k(130) (130)

The water's temperature has decreased tο 164°F after 5 minutes. Therefοre, we are aware that t = 5 at T = 164:

[tex]164 = 200e^{(-k*5)[/tex]

calculating k:

[tex]e^{(-5k)} = 164/200 = 0.82[/tex]

-5k = ln(0.82) (0.82)

k = -ln(0.82)/5

We can nοw calculate the time it takes fοr the water tο cοοl tο 150°F using this number οf k:

[tex]150 = 200e^{(-k*t)[/tex]

[tex]e^{(-k*t)}= 150/200 = 0.75-k*t = ln(0.75) (0.75)[/tex]

t = -ln(0.75)/k

By changing the amοunt οf k, we οbtain:

t = -ln(0.75)/(-ln(0.82)/5) ≈ 3.8

We get abοut 4 minutes if we rοund tο the clοsest minute. The sοlutiοn is thus A. 4 minutes οr sο.

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27 ÷ 5 = 5.4

∴ 5.4 feet of ribbon goes to each bracelet.

The general form of the equation for the given circle centered at O(0, 0) is B. x² + y² - 41 = 0.

A circle is a round, two-dimensional shape with all points on its boundary equidistant from its center.

Since the center of the circle is O(0,0), the equation of the circle will have the form x² + y² + ax + by + c = 0. To find the values of a, b, and c, we can use the fact that point B(4, 5) lies on the circle. Substituting the coordinates of B into the equation and simplifying, we get:

4² + 5² + a4 + b5 + c = 0

16 + 25 + 4a + 5b + c = 0

41 + 4a + 5b + c = 0

We now have one equation with three variables, so we need more information. Since the center of the circle is (0,0), we know that the distance from the center to any point on the circumference is equal to the radius of the circle. The distance between points (0,0) and (4,5) is the length of the line segment joining them, which can be found using the distance formula:

[tex]\sqrt{(4-0)\² + (5-0)\²} = \sqrt{(16+25) }= \sqrt{41}[/tex]

Therefore, the radius of the circle is √(41). We can use this fact to eliminate one of the variables in the equation we derived earlier. Since point (0,0) lies on the circle, we can substitute its coordinates into the equation to get:

41 + 0a + 0b + c = 0

c = -41

Now we can substitute this value of c back into the equation we derived earlier to get:

41 + 4a + 5b - 41 = 0

4a + 5b = 0

Finally, we have two equations with two variables, which we can solve to get:

a = -5/4

b = 4/5

Substituting these values into the equation of the circle, we get:

x² + y² - 5x/4 + 4y/5 - 41 = 0

Multiplying by 20 to eliminate fractions, we get:

20x² + 20y² - 25x + 16y - 820 = 0

Simplifying, we get:

x² + y² - 25/4x + 4/5y - 41 = 0

Which is equivalent to:

x² + y² - 41 = 0

So the answer is B. x²+ y² - 41 = 0.

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Answer:

5 apples

Step-by-step explanation:

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

[tex]4x^2+5xy+y^4=370[/tex]

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

[tex]\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370[/tex]

Differentiate the terms in x only (and constant terms):

[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0[/tex]

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

Use the product rule to differentiate terms in both x and y.

[tex]\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}[/tex]

[tex]\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

[tex]\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

[tex]\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}[/tex]

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}[/tex]

Therefore, slope of the tangent line to the curve at the given point is -11/7.

The table that shows proportional relationship is x = 1,3,4,5 and y = 50, 150, 200,250 ( table 1).

The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

To determine the proportionality the ratio of x toby must be thesame Ina table

in table 1

x/y = 1/50 = 3/150 = 4/200 = 5/250 = 1/50

table 1 show proportional relationship

in table 2

3/1.5 is not equal to 7/3 , therefore table 2 does not show proportional relationship

in table 3

1/1.5 is not equal to 3/6 , therefore table 3 does not show proportional relationship

therefore the table that show proportional relationship is table 1

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The numeric values of the composite functions are given as follows:

The composite function of f(x) and g(x) is given by the equation with rile presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which for this example is g(x), serves as the input of the outer function, which for this example is f(x).

Hence the functions are given as follows:

At x = 3, the numeric values are given as follows:

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The distance between points D(1,3) and H(9,8) found using the distance formula is 9.43 units.

To find the distance between two points, the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is sometimes used to calculate the distance between two places. The length of the line segment bridging two points on a plane is known as the distance between the points.

d=√((x2 - x1)² + (y2 - y1)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

Assuming the question is the one given below.

The points given are:

D = (1,3) = (x1,y1)

H = (9,8) = (x2,y2)

The distance D between these two points can be found using the distance formula.

D = [tex]\sqrt{{(x_2-x_1)}^2 + {(y_2-y_1)}^2 } = \sqrt{{(9-1)}^2 + {(8-3)}^2 }[/tex] = √89 = 9.43 units

Therefore the distance between points D(1,3) and H(9,8) found using the distance formula is 9.43 units.

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The percent abundance of the medium nails in the sample is given as follows:

27.07%.

The percent abundance is obtained applying the proportions in the context of the problem.

The total length of nails is given as follows:

67 x 2.5 + 18 x 5 + 10 x 7.5 = 332.5 cm.

The length relative to medium nails is given as follows:

18 x 5 = 90 cm.

Meaning that the percent abundance is given as follows:

90/332.5 x 100% = 27.07%.

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Answer:

The answer that you are looking for is 70º

Step-by-step explanation:

Usually, in three-sided figures, there is a total of 3 angles all adding up to 180º.

So in turn, since most quadrilaterals are made up of 2 triangles all the sides have to equal to 360º.

We can use the equation 360 = 110×2+q2

To find the value of q.

The First step to do is to simplify all terms with 110×2 being equal to 220 and q2 staying the same.

We then use the opposite symbol to remove 220 leaving q2 by itself while 360 is subtracted by 220 and turned into 140.

The only thing left to do is to do the opposite operation of multiplying, which is dividing and dividing both sides by 2 leaving q = 70.

You can find the equation below:
360 =  110×2+q2
360 =  220 + q2
-220 = -220 + q2
 140 = q2
  ÷2 = ÷2
  70 = q

I hope this was helpful!