6-4 RectanglesQuadrilateral ABCDis a rectangle.1.IfAC= 2x+ 13 andDB= 4xâ 1, findDB.DB: 72.IfAC=x+ 3 andDB= 3xâ 19, findAC.AC= 143.IfAE= 3x+ 3 andEC= 5xâ 15, findAC.AC=604.IfDE= 6xâ 7 andAE= 4x+ 9, findDB.Db=825.Ifmâ DAC= 2x+ 4 andmâ BAC= 3x+ 1, findmâ BAC.6.Ifmâ BDC= 7x+ 1 andmâ ADB= 9xâ 7, findmâ BDC.7.Ifmâ ABD= 7xâ 31 andmâ CDB= 4x+ 5, findmâ ABD.8.Ifmâ BAC=x+ 3 andmâ CAD=x+ 15, findmâ BAC:39

The mean of the sample is the random variable in the given problem.

The mean of any given data set can be defined as summarizing a given group of data. It is done in order to make data sets and their values easier to understand. It can be obtained by first adding all the given values and then dividing the total sum by the number of data entries.

A random variable is any quantity that depends on random events. Here, we know that the mean of the given sample depends on all of the random events or we can say random values present in the table. Hence, we can conclude that the random variable is the mean of the sample.

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The linear function containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). is given as follows:

y = -1.67x + 6.5.

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

y = mx + b.

In which:

The median of the trapezoid is composed by these two points:

The coordinates of the midpoint of RS are given as follows:

The coordinates of the midpoint of TU are given as follows:

Hence the points of the function are:

(0, 6.5) and (4.5, -1).

When x = 0, y = 6.5, hence the intercept b is given as follows:

b = 6.5.

When x increases by 4.5, y decays by 7.5, hence the slope m is given as follows:

m = -7.5/4.5

m = -1.67.

Hence the function is:

y = -1.67x + 6.5.

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The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.

Option D is correct.

A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.

The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.

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A. An expression for the perimeter of the fountain is 8x + 12 ft.

B. The perimeter when x=2 ft. is 28 ft

The area of the fountain is given as 4x^2 + 12x + 9 square feet. Since the fountain is a square, we know that the length and the width of the fountain are equal. This means that we can express the area of the fountain in the form of (cx + d)^2.

Expanding (cx + d)^2 gives:

(cx + d)^2 = cx^2 + 2cxd + d^2

We can equate this to the given area of the fountain:

cx^2 + 2cxd + d^2 = 4x^2 + 12x + 9

To find the expression for the perimeter of the fountain, we need to find the dimensions (length and width) of the fountain. This can be done by factoring the area expression:

4x^2 + 12x + 9 = (2x + 3)(2x + 3)

So the dimensions of the fountain are (2x + 3) ft

The perimeter of a square is the sum of all four sides, so we can find the perimeter of the fountain by multiplying the length of one side by 4:

Perimeter = 4(2x + 3) ft = 8x + 12 ft

When x = 2 ft, the perimeter of the fountain is:

8(2) + 12 = 28 ft

So when x = 2 ft, the perimeter of the fountain is 28 ft.

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Pie charts are used to compare parts of a whole, not the difference between groups. This misleads the viewer to think more than half the people in all three parties voted Yes on Issue #1, when less than half of Republicans and Independents actually voted Yes on Issue #1.

This is a type of graph that resembles a pie because it is a circle that shows the proportion of different groups.

Note: Here is the missing information

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Answer: 6 2/5

Step-by-step explanation:

32 divided by 5 equals 6 with a remainder of 2.

Answer:

(1.1)

1000g=1kg

500÷1000=0.5kg

(1.2)

1000m=1km

1000×1000= 1000000m

(1.3)

1000kg=1tonne

165×1000= 165,000kg

The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]

We have to find two functions f and g such that (fog) (x) = H(x).

Let f(x) = 7x

g(x) = [tex]\sqrt{x-3}[/tex]

The composition of these functions is,

(fog)(x) = f (g(x))

           = 7 . g(x)

           = 7 [tex]\sqrt{x-3}[/tex]

           = H(x)

Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

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The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.

In a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.

Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.

Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.

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The instrument used here is a protractor.

An instrument used to measure angles in degrees is a protractor. When measuring angles using a protractor, it's crucial to check that the vertex of the angle is in the protractor's centre and that the angle's base is lined up with the protractor's baseline.

Acute Angle: - An angle that is less than 90 degrees is considered to be acute. For instance, if the angle is 30 degrees, we would line up the vertex of the angle with the protractor's centre and one of its sides with the baseline. The measurement would be read off the protractor scale, which in this instance would be 30 degrees.

Right Angle: - A right angle is a triangle with a 90 degree angle on each side. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a right angle. The measurement would be read off the protractor scale, which in this instance would be 90 degrees.

Obtuse Angle: - An angle that is more acute than 90 degrees is referred to as an obtuse angle. When using a protractor to measure an obtuse angle, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline. The measurement would then be taken from the protractor scale and would be more than 90 degrees in this instance.

Straight Angle: - A straight angle is one that is 180 degrees in length. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a straight angle. The measurement would then be taken from the protractor scale, which would be 180 degrees in this instance.

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Answer:

[tex]\textsf{a)} \quad K(t)=1500(1.12)^t[/tex]

b)  44940

c)  57.4 days

Step-by-step explanation:

Exponential Growth Function

[tex]f(t)=a(1+r)^t[/tex]

where:

Given values:

To create a function K(t) that expresses the number of users t days after the start of the year, substitute the given values into the exponential growth formula:

[tex]\implies K(t)=1500(1+0.12)^t[/tex]

[tex]\implies K(t)=1500(1.12)^t[/tex]

To calculate how many users there are after 30 days, substitute t = 30 into the function K(t) from part a:

[tex]\implies K(30)=1500(1.12)^{30}[/tex]

[tex]\implies K(30)=44939.8831...[/tex]

[tex]\implies K(30)=44940\; \rm users[/tex]

To calculate after how many days it takes to reach one million users, substitute K(t) = 1,000,000 into the function and solve for t:

[tex]\implies 1000000=1500(1.12)^t[/tex]

[tex]\implies \dfrac{2000}{3}=1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=\ln 1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=t \ln 1.12[/tex]

[tex]\implies t=\dfrac{\ln \left(\frac{2000}{3}\right)}{\ln 1.12}[/tex]

[tex]\implies t=57.3755016...[/tex]

[tex]\implies t=57.4\; \rm days[/tex]

The required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
From the table,
Mean = ∑fx / ∑f
Mean = 16010 / 100
Mean = 160.10

Standard deviation,
σ = √∑fd²/∑f
σ = √14265/100
σ = 11.94

The required range of weights from one standard deviation, below the mean is given as
= 160.10 - 11.94 ≤ mean

Thus, the required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

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∑[tex](k^2)[/tex] for k = 1 to 6 is the sum in sigma notation for this series of terms.

The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.

The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.

In the expression [tex]k^2[/tex]  which implies that we are adding up the square of the index of summation.

So, the sigma notation for this series of terms is ∑[tex](k^2)[/tex]  for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)

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The required constant of proportionality for the relationship is 1/2.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.

Let the relation between x and y is

y = kx

Where k is proportionality constant.

Using the given values of x ad y

1 = k(2)

k = 1/2

So, the constant of proportionality for the relationship is 1/2.

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The distance of IH is 1.089 meters.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given that,

Radius = 5.1 meters

EF = EI = 5.1

FG = 6.3 meters

HE is a perpendicular bisector of FG.

FH = HG = 6.3 / 2 = 3.15

Also, FH is the projection of EF in the vertical axis.

FH = EF sin (θ), where θ is the angle FEH.

3.15 = 5.1 sin (θ)

sin (θ) = 0.6176

θ = sin⁻¹ (0.6176)

θ = 38.14°

IH = EI - EH

We have,  EH is the projection of EF into the horizontal axis.

EH = EF cos (θ)

Substituting,

IH = 5.1 -  EF cos (θ)

IH = 5.1 - 5.1 cos (38.14)

IH = 5.1 ( 1 - cos (38.14))

IH = 1.089 meters

Hence the length of the line segment IH is 1.089 meters.

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The size of the payments that need to be made today and in six months are both $ 6, 961.69.

To find the payment that Caitlin needs to make today and in six months, assume this amount of x.

The payment in 6 months would be:

= (13, 000 - x) ( 1 + 2.4 / 100)⁶

The payment today would be x.

Equate them to find the payment:

x = (13, 000 - x) ( 1 + 2.4 / 100)⁶

x = 14, 988 - 1.1529x

x = 14, 987.979 / 2.1529

= $ 6, 961.69

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Answer:

a)  Growth rate of 2.737% (3 d.p.) per year

b)  117,897

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$f(t)=ae^{rt}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $r$ is the continuous growth/decay rate.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given exponential function:

[tex]P(t) = 90000\cdot e^{0.027t}[/tex]

As r > 0 the function is an exponential growth function.

The annual growth rate is:

[tex]\begin{aligned}\textsf{Annual growth rate}& = e^{0.027}-1\\&=1.02736780...-1\\&=0.0273678027...\\&=2.73678027...\%\\&=2.737\%\; \sf (3\;d.p.)\end{aligned}[/tex]

To calculate how many residents the model predicts will live in Asheville, NC in 2030, substitute t = 10 into the given function:

[tex]\begin{aligned}\implies P(10) &= 90000\cdot e^{0.027 \cdot 10}\\&= 90000\cdot e^{0.27}\\ &= 90000\cdot 1.30996445...\\&=117896.800...\\&=117897\; \sf (nearest\;whole\;number)\\\end{aligned}[/tex]

Therefore, the model predicts that there will be a population of approximately 117,897 living in Asheville, NC in 2030.

It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.

According to the commutative property, a mathematical principle, the product will not be affected by the order in which we multiply the integers. The commutative property of addition states that the sum is unaffected by the order of the addends.

Only addition and multiplication processes can use the commutative property. So, when adding or multiplying any two integers, we can swap the numbers around or modify their order. This is one of the fundamental characteristics of integers.

Adjective. involving, pertaining to, or involving commutation, exchange, substitution, or interchange. Mathematics. Commutative law for multiplication makes reference to the binary operation's property that one term working on another is equal to another term operating on the first, as in a + b = b a.

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a. The solutions to the system of equations f(x) = g(x) are given as follows: x = 0 and x = 1.

b. The explanation is that they have the same numeric value at these values of x.

A system of equations is composed by multiple equations.

The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.

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Answer:

see below

Step-by-step explanation:

1-1-2017

H 26K

W 24K

Net income 30K

H salary 12K

W salary 10K

remain: 8K shared EQUALLY so each gets 4K extra

Distribution:

30K - H gets12+4 =16K, and W gets 10+4 = 14K

The maximum possible number of points where two polygons can intersect is [tex]$n = 4$[/tex]. This is achieved when the two polygons are tangent to each other at four points.

There are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:

This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.

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Answer:

50 m

Step-by-step explanation:

The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high

My student ID is 21444367.

The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.

This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.

For my student ID, 21444367, the calculation would be:

0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.

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0.1920 mL of the anesthetic should be given to the patient.

First, we need to convert the patient's weight from kilograms to pounds:

58 kg x 2.20462 lb/kg = 128.01 lbs

Next, we can calculate the total amount of anesthetic to be given to the patient:

15 mg/10 lbs x 128.01 lbs = 19.20 mg

Finally, we can divide the total amount of anesthetic by the concentration of the anesthetic in each mL:

19.20 mg / 100 mg/mL = 0.1920 mL

So, 0.1920 mL of the anesthetic should be given to the patient.

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Answer:

$17.32

Step-by-step explanation:

44 hours

52.5 - 44 = 8.5 hours over time for 1.5x regular pay

assume regular pay is x

so 44x + 8.5 * 1.5x =983.15

44x + 12.75x = 983.15

56.75x=983.15

x=17.324

check to see if it's correct

44*17.324 + 12.75*17.324 = 983.14

The flagpole is visible to the student from 18 feet away and at a 22-degree inclination to the ground. The flagpole is 40.3 feet tall and 50 feet away from the structure.

At an elevation of 22 degrees, the student is looking out of a second-story school window. The building is 50 feet from the flagpole's base, and the window is 18 feet above the ground. We may compute the angle of the triangle formed by the window, the ground, and the top of the flagpole using the tangent ratio to determine its height. The opposing side (the flagpole) divided by the neighboring side equals the tangent of 22 degrees (the window to the ground). Consequently, the flagpole is 40.3 feet tall (50 divided by 1.224). This indicates that the student is 18 feet above the ground and is looking down at the flagpole.

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A. The percent error is 25%

B. Another estimate that gives the same percent error is the Theoretical value.

A. To find the percent error, we use the following formula:

percent error = (|experimental value - theoretical value| / theoretical value) x 100

In this case, the experimental value is 4000 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:

percent error = (|4000 - 3200| / 3200) x 100 = (800 / 3200) x 100 = 25%

B. To find an estimate that gives the same percent error, we can use the formula:

Theoretical value = experimental value / (1 + percent error / 100)

If we use the same percent error (25%) and experimental value (4000 years) as before:

Theoretical value = 4000 / (1 + 25/100) = 4000 / 1.25 = 3200

So, an estimate of 3200 years would give the same 25% percent error as the researcher's original estimate.

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Answer:

x = 15

Step-by-step explanation:

The sum of the four angles of a quadrilateral add up top 360°

Given:

m∠A = (5x+14)°  

m∠b = 109°        

m∠C = (3x+8)°    

m∠D = 109°°

Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°

The sum of the remaining two angles which are expressions in x should be:

360 - 218 = 142°

This is the sum of m∠A an m∠C

Substituting the terms for the two angle measures we get

(5x+14)  + (3x+8) = 142

5x+14  + 3x+8 = 142

Grouping like terms:

5x + 3x + 14 + 8 = 142

8x + 22 = 142

8x = 142- 22

8x = 120

x = 120/4

x = 15