compare the two rates. has faulting taken place at a constant rate, or has the rate increased or decreased over time? explain in as much detail as possible.

$18021 is value of the principal investment

percentage, a relative value indicating hundredth parts of any quantity.

Given that after 16 years in an account with a 4.8% annual interest rate compounded continuously an investment is worth a total of $38,744.77

We have to find the value of the principal investment

[tex]A=Pe^{rt}[/tex]

Where P is the principal amount, r is rate of interest and A is total amount.

[tex]38744.77=Pe^{0.048(16)}[/tex]

[tex]38744.77=Pe^{0.768}[/tex]

38744.77=2.15P

Divide both sides by 2.15

18021=P

Hence, $18021 is value of the principal investment

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Answer:

its the 1st option

Step-by-step explanation:

i jus took the test

The simplified form of the expression is y - 1.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex]

The numerator of the expression can be written as below using the cross multiplication process.

1 - [tex]\frac{1}{y}[/tex] = (y - 1) / y

The whole expression becomes,

(1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex] = [(y - 1) / y] / [tex]\frac{1}{y}[/tex]

              = (y - 1) / 1

              = y - 1

Hence the simplified form is y - 1.

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The graph that represents the compound inequality –3 < n < 1 is option C.

The two sides of a mathematical equation having an inequality must be equal. We compare two values via inequality rather than equations. The equal sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.

The straight line from -3 to 1 with a hollow circle at the -3 point and the 1 point serves as the graph for the compound inequality -3 n 1. This is because n can only have values larger than -3, excluding -3, and less than -1, excluding -1, according to the symbol.

Therefore, the graph that represents the compound inequality –3 < n < 1 is option C.

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The area of the triangular prism is calculated as; 170 cm²

The given triangular prism when broken down is made up of;

2 triangles (top and bottom)

2 side rectangles

1 back rectangle

Formula for area of triangle = ¹/₂ * base * height

Formula for area of rectangle = length * width

Thus;

Area of trapezoid = 2(¹/₂ * 5 * 4) + 3(10 * 5)

Area = 20 + 150

Area = 170 cm²

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Check the picture below.

[tex]\begin{cases} ~\hfill 10x+(16y+6)=180\\\\ (4+18y)+(10x-6)=180 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{10x+(16y+6)=180}\implies 10x+16y=174\implies 10x=174-16y \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{(4+18y)+(10x-6)=180}\implies 18y+10x-2=180 \\\\\\ 18y+(\underset{10x}{174-16y})-2=180\implies 2y+172=180\implies 2y=8 \\\\\\ y=\cfrac{8}{2}\implies \boxed{y=4} \\\\\\ \stackrel{\textit{since we know that}}{10x=174-16y}\implies 10x=174-16(4)\implies 10x=110 \\\\\\ x=\cfrac{110}{10}\implies \boxed{x=11}[/tex]

A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.

We shall therefore have:

PVγ = 2.5P(0.5V)γ

We'll condense this to:

(1/0.5)γ = 2.5

γ = In2.5/In2

γ = 1.32

The volume temperature relation is written as follows if the volume expands in an adiabatic process:

T1V1∧γ-1 = T2V2∧γ-1

T1V1∧1.32-1 = T2(0.5V1)∧1.32-1

Condensing this results in:

T₁ = 1.24T₂

Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

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For the markov chain will end up in state 2, the probability that when the process moves into state 2, it does so from state 1 will be calculated as:

Let,

[tex]\tau = \min\{n: X_{n+1}= 2\}[/tex]

Now,

[tex]p_{i,j} = P(X_{\tau}=i|X_{0}=j)[/tex]

We can observe that,

[tex]p_{0,0} = P(X_{\tau}=0|X_{0}=0) = \sum_{k=0}^{2}{P(X_{\tau}=0,X_{1}=k|X_{0}=0)} [/tex]

[tex]=\sum_{k=0}^{2}{P(X_{1}=k|X_{0}=0)P(X_{\tau}=0|X_{1}=k,X_{0}=0)}[/tex]

A Markov chain or Markov process is a stochastic model that depicts a series of potential events where each event's likelihood is solely determined by the state it reached in the previous event. This can be thought of colloquially as, "What happens next depends only on the situation right now. Discrete-time Markov chains (DTMC) are produced by a countably infinite sequence where the chain changes state at distinct time steps. A continuous-time Markov chain (CTMC) is a continuous-time process. It bears the name Andrey Markov after the Russian mathematician. As statistical representations of processes in the real world, Markov chains have numerous uses.

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The height of the streetlight is 30 feet.

Let's call the height of the streetlight "h".

When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.

When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.

Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.

Solving for h, we get:

96 / h > 3.2 * h

96 > 3.2h

30 > h

So, the height of the streetlight is less than 30 feet.

To determine the exact height of the streetlight, we can use the equation:

96 / h = 3.2 * h

96 = 3.2h

30 = h

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Answer:

4th

Step-by-step explanation:

first is over y-axis and the linear translation: 6 horizontal and -5 vertical

C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

Two or more expressions with an Equal sign is called as Equation.

Given that Deion pays a cost of $50 per phone produced for materials and labor.

Deon also must pay a daily fixed cost of $200 to rent the building and equipment.

C = 200 + 50p

The above equation represents the total cost, in dollars, of producing p phones in a given day.

Number of phones (p) Total cost (C)

0                                   200

1                                   250

2                                  300

3                                   350

Hence, C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

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Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches[/tex]

In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).

This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.

Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.

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Solving for a in the triangle gives a = 6

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The figure is a triangle. Since the sum of angles in a triangle is 180°. We can write:

106.2° + (3.8a + 29.7)° + (2.4a + 6.9)° = 180°

106.2 + 3.8a + 29.7 + 2.4a + 6.9 = 180

142.8 + 6.2a = 180

6.2a = 180 - 142.8

6.2a = 37.2

a = 37.2/6.2

a = 6

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The ceiling for this problem is given as follows:

450 m.

The three trigonometric ratios are defined as follows:

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

tan(71.5º) = x/150

x = 150 x tangent of 71.5 degrees

x = 448.3 m.

Adding 1.7 m, the ceiling is obtained as follows:

448.3 + 1.7 = 450 m.

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From the given graph solution of lines is (32, 5).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

In the give graph two lines intersect at (32, 6).

Here, 32 represents the number of kites and 6 represents the total cost.

Therefore, from the given graph solution of lines is (32, 5).

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Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,

Given :

=>height = 11cm

=> radius = 6cm

Volume of cone :

=> 1/3πr²h

=> 1/3*π * 36 * 11

=> 132π cm³

Thus , volume of cone is  132π cm³

Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

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According to the information, it can be inferred that the percentages are from left to right and from top to bottom the following: 27, 21, 49, 37, 14, 51, 64, 36, 100.

Based on the information in the upper box, we must find the percentage to which each of the values in the lower box is equivalent. To find these percentages we must perform the following mathematical procedure:

1. We must make the rule of three in which the total equals 100%, then we must multiply each of the values in the upper box by one hundred and then divide it by 70.

With the previous procedure we will have the possibility of finding all the values as shown in the table below.

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Answer:

15 weeks

Step-by-step explanation:

1 write an equation fore each

you                    sister

y=25+3x            y=40+2x    

y is total money and x is weeks

we want to find when they have the same amount of  total money we set them equal to echother

25+3x=40+2x

-2x             -2x

25+x=40

-25      -25

x=15

you will have the same amount as yore sister in 15 weeks

Answer:

see below

Step-by-step explanation:

you: 25 +$3 /week * x weeks

sis: 40 + 2/week * x weeks

they have to equal to each other

so 25 + 3x = 40 +2x

move x around & simplify

so x = 15

total 25+3*15 = 25+45 = 70

The percent of adult American males could enter this contest is 2.23%

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

We solve using z score formula

z = (x-μ)/σ,

where, x is the raw score = < 64 inches

μ is the population mean = 69

σ is the population standard deviation = 2.5

Here Participants must be less than 64 inches tall.

For x < 64 inches

z = 64 - 69/2.5

z = -2

Probability value from Z-Table:

P(x<64) = 0.02275

Converting to percentage;

= 0.02275 × 100

= 2.275%

Approximately = 2.23%

The participants must be less than 64 inches tall to participate in this limbo contest, the percent of adult American males thag could enter this contest is 2.23%

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100 kernels are randomly selected from a population that is in Hardy-Weinberg equilibrium. 9 yellow kernels and 91 purple kernels are discovered. In this population, the yellow allele is 0.09 times more common.

Both citizens who are physically present in a country or who are temporarily away from it, as well as all foreigners who have permanently emigrated to that country, are included in the phrase "people." This indicator represents the population of a particular area. Growth rates are used to describe the differences in population that occur each year as a result of births, deaths, and net migration. In 2022, Russia had the highest population density in Europe—144.7 people per square mile. In terms of population size, Turkey came in second with 85 million people, followed by Germany with 83.4 million, the United Kingdom with 67.4 million, and France with 65.6 million. Vatican City has a population of just over 800, making it the world's least populous country. Vatican City is the smallest totally sovereign nation-state in the world.

The  frequency is 9/10 or 0.09

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The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.

The characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.

The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.

Your question is incomplete but most probably your full question was:

Which length and width are possible dimensions for the garden?

l = 20 ft; w = 5 ft

l = 20 ft; w = 10 ft

l = 60 ft; w = 20 ft

l = 55 ft; w = 30 ft

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The constant variation rate is given as follows:

62.5 miles per hour.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence we can solve for the constant as follows:

k = y/x.

In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:

k = 375/6

k = 62.5 miles per hour.

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Work done to pump the kerosene is equal to W = 126106 ft-lbs

"Information available from the question"

Height of the cylinder = 7 ft.

Diameter of cylinder = 8 ft.

Radius of the cylinder = 4 ft

Weight of the kerosene = 51.2 lb/ft³

Calculating the volume of cylinder for dy height

dV = π r² dy

dV = π 4² dy

dV = 16π dy

Force acting on the cylinder

dF = W x dV

dF = 51.2 x 16πdy...….(1)

We know

Work done = Force x displacement

Displacement = 7 - y

dW = 51.2 x 16πdy x (7 - y)

Now, integrating both side

[tex]\int\limits dW = \int\limits^7_0 {819.2\pi(7-y) } \, dy[/tex]

[tex]W = [819.2\pi (7-y)^2]^0_7[/tex]

By solving, we get

W = 126106 ft-lbs

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An illustrates the abuse of respondents in marketing research is :

Not providing the promised incentive for completing interviews or questionnaires.

The world organization body, the American Marketing Association (AMA), conveys the definition of marketing research is a function that connects customers, consumers, or the general public with marketers through information used to identify marketing problems and opportunities.

Meanwhile, Philip Kotler defines marketing research as the systematic design, collection, analysis, and reporting of data or findings that are relevant to a particular marketing situation faced by a company.

Simply put, marketing research is the identification, collection, analysis, and presentation of systematic and objective information to help companies make decisions related to problem solutions and find opportunities in the marketing process.

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The experimental probability of spinning a number less than 3 is 0.46 or 46%.

This can be defined as the likelihood an event occurs or does not occur. Most of the time, the probability is calculated based on the times a specific outcome is obtained versus the number of total outcomes.

To know the probability, let's use the formula getting less than a 3/ total times:

Times they got less than 3: 23 (8+6+9= 23)

Total times: 50

23/50 = 0.46 or 46% (0.46 x 100)

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The original polynomial is x^3 - x^2 + 8x + 26.

The division of a polynomial by a linear factor (x + 4) can be reversed by multiplication:

f(x) = (x^2 - x + 8) * (x + 4) + (-6)

Expanding the product on the right-hand side, we get:

f(x) = x^3 - x^2 + 8x + 32 - 6

f(x) = x^3 - x^2 + 8x + 26

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The correct option C. Rejecting a true null hypothesis, is the probability in  significance level in hypothesis testing.

By testing an experimental component against a no effect or even no relationship hypothesis based on a specific observation, NHST is a statistical inference technique.

Thus, the likelihood of rejecting a valid null hypothesis determines the significance level in hypothesis testing.

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The solution to the inequality is x < -4

From the question, we have the following parameters that can be used in our computation:

x+4/2x-1 < 0

Multiply both sides of the inequality

So, we have the following representation

x + 4 < 0

Subtract 4 from both sides of the expression

So, we have the following representation

x < -4

Hence, the solution is x < -4

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