A 12-foot ladder is leaned against the side of a building. If the bottom of the ladder
rests 3 feet from the wall, determine the height at which the top of the ladder rests
on the wall. Let h represent the height. Show all the steps. Don’t forget the units!!!

Draw the diagram and label it. Solve:
Therefore statement:

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 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 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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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 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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Answer: Semi-Conservative, and old.

Step-by-step explanation:

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 area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.

The surface area of the triangular prism will be given as,

Surface area = 5 x 12 + (5 + 12 + 13) x 6

Surface area = 60 + 180

Surface area = 240 square feet

The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

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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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The graph can be used to determine the median, quartiles, and other statistical measures.

(a). Class width = (maximum value - minimum value)/ number of classes = (109 - 45)/6 = 9

(b).

Class Limits  Class Boundaries Midpoints  Frequencies  Relative Frequencies  Cumulative Frequencies

45 - 54  44.5 - 54.5  49.5  2  0.0741  2

55 - 64  54.5 - 64.5  59.5  7  0.2593  9

65 - 74  64.5 - 74.5  69.5  17  0.6207  26

75 - 84  74.5 - 84.5  79.5  20  0.7407  46

85 - 94  84.5 - 94.5  89.5  14  0.5185  60

95 - 104  94.5 - 104.5  99.5  7  0.2593  67

(c). Histogram

(d). Relative-Frequency Histogram

(e). The basic distribution shape is right-skewed.

(f). Ogive

The ogive graph is a cumulative frequency plot that shows the number of data values that lie at or below each given value on the x-axis. It is constructed by plotting the cumulative frequencies of each data value on the y-axis against the corresponding data values on the x-axis. The points are then connected using closed line segments to form the ogive graph. The graph can be used to determine the median, quartiles, and other statistical measures.

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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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If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

Given data:

Mean = 122

Standard deviation = 5

Sample size = 200

Now let find the the standard deviation of the sampling distribution of the mean sample using this formula

Distribution of sample mean = Standard deviation/√Sample size

Let plug in the formula

Distribution of sample mean = 5 /√ 200

Distribution of sample mean = 5/14.14

Distribution of sample mean = 0.35

Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

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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.

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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∑[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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Answer: 6 2/5

Step-by-step explanation:

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

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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Answer:

2 is the scale of dilation

Commence at the beginning. The x-coordinate is Negative 3 and 12 units, thus move 3 and 12 units to the right. The difference between 3 and 4 is negative three-half.

A point's exact location on a two-dimensional plane is determined by a pair of numbers called its coordinates. The x and y axes, which are two axes that are at right angles to one another, are known as the coordinate plane's axes. How far along each axis a specific point is located is indicated by its coordinates.

Ordered pairs are a way of describing locations on the coordinate plane. A point's location is revealed by an ordered pair by linking the point's positions along the x-axis (the ordered pair's first value) and the y-axis (the second value of the ordered pair).

To locate points, one uses the numbers on a coordinate grid. Using an ordered pair of numbers, each point may be located.

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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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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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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:

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 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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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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The correct person regarding the classification of quadrilaterals is given as follows:

B. Jamie.

The slopes of each segment are given as follows:

-3 and 1/3.

The multiplication of these slopes is given as follows:

-3 x 1/3 = -1.

As the multiplication of the slopes is of -1, the adjacent sides meet at an angle of 90º, meaning that they are perpendicular, and hence the quadrilateral is classified as a square.

This means that Jamie is correct.

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Answer:

x=16

Step-by-step explanation:

x/2=5+3

x/2=8

x=8×2

x=16

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

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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