Do imaginary numbers follow the rules of algebra?

The diagram that represent the distance and the journeys is added as an attachment

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

Using the above as a guide, we have the following:

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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The first mistake is in step 1, where the "15" should not  be in the denominator.

Therefore the correct solution of the given expression is 76

The steps are given as :

The original equation is something as shown:

1 + 45/3*5

Step 1:  1 + 45/15

Step 2:  1 + 3

Step 3:  4

Now, the original equation is:

"we divided by 45, divided by 3, times 5".

And in step 1 you take the product as it was in the denominator, which should have been determined from left to right.

1 + 45/3*5

1 + (45/3)*5

1 + 15*5

1 + 75  = 76

That should be the solution to the given expression.

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#complete question:

Find the mistake in this student's work. Identify the first step containing wrong information, then solve the problem correctly.

a. Which step is the FIRST step to contain incorrect information?

b. What should the correct answer actually be?

Step 1. 1/45/3x5

step 2 =1+45/15

Step 3 : 1+3 =4

Answer:

$37.5

Step-by-step explanation:

25% = 1/4

50/4 = 12.5

50 - 12.5 = 37.5

hope this helped (:

Answer:

37.5

Step-by-step explanation:

Convert the 25% to a decimal (0.25) and multiply by 50

Which is 12.5

Subtract 50 by 12.5

Answer is $37.5

You could also multiply 50 * .75

The total value of the income stream would be $187,500.

WE are given that integral of R(t) with respect to t ∫[0,5] R(t) dt = ∫[0,5] (30,000 + 3,000t) dt

To determine the total value of the income stream, we need to evaluate the definite integral of the function R(t) over the given interval. The integral of R(t) with respect to t is:

∫[0,5] R(t) dt = ∫[0,5] (30,000 + 3,000t) dt

Evaluating this integral gives:

∫[0,5] R(t) dt = (30,000t + 1,500t²) [0,5]

= (30,000(5) + 1,500(5²)) - (30,000(0) + 1,500(0²))

= 187,500

Therefore, the total value of the income stream is 187,500.

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Answer:

proportional<3

Step-by-step explanation:

Ex 8. the solution to the differential equation y'' + y = t² with initial condition y(0) = -2 and y'(0) = 0 is y(t) = t² - 2. Ex 9. the isolated form of Y(s) for the given differential equation and initial conditions is: Y(s) = (1/(s - 3) + 6/s⁴ + s² + 2s + 4) / (s³ + s)

a) To find the Laplace transform of the given differential equation y'' + y = t², we first take the Laplace transform of both sides of the equation. Let's denote the Laplace transform of y(t) as Y(s).

Applying the Laplace transform to the equation, we get:

s²Y(s) - sy(0) - y'(0) + Y(s) = 1/s³

Substituting the initial conditions y(0) = -2 and y'(0) = 0, we have:

s²Y(s) + 2s + Y(s) = 1/s³

Now, let's isolate Y(s):

s²Y(s) + Y(s) = 1/s³ - 2s

(Y(s))(s² + 1) = 1/s³ - 2s

Y(s) = (1/s³ - 2s) / (s² + 1)

b) To find y(t) from the Laplace transform Y(s), we can apply the inverse Laplace transform. In this case, we need to use partial fraction decomposition to simplify the expression.

Y(s) = (1/s³ - 2s) / (s² + 1)

Y(s) = (1/s³) / (s² + 1) - 2s / (s² + 1)

Y(s) = 1/s³ * 1/(s² + 1) - 2s / (s² + 1)

Using partial fraction decomposition, we can express 1/(s² + 1) as A/(s + i) + B/(s - i), where i represents the imaginary unit.

1/(s² + 1) = (A/(s + i)) + (B/(s - i))

Multiplying through by (s + i)(s - i), we get:

1 = A(s - i) + B(s + i)

Expanding and equating the coefficients of the corresponding powers of s, we have:

0s² + 0s + 1 = (A + B)s + (B - A)i

Equating the coefficients, we get:

A + B = 0 (coefficient of s)

B - A = 1 (constant term)

Solving these equations, we find A = -1/2 and B = 1/2.

Now, we can rewrite Y(s) as:

Y(s) = 1/s³ * (-1/2)/(s + i) + 1/s³ * (1/2)/(s - i) - 2s / (s² + 1)

Taking the inverse Laplace transform of each term using standard formulas, we find:

y(t) = (-1/2)e^(-it) + (1/2)e^(it) - 2sin(t)

Since e^(-it) and e^(it) represent complex conjugates, their sum simplifies to:

y(t) = -2sin(t)

EXERCISE 9:

To find the Laplace transform of y''' + y' = e^(3t) + t³ with initial conditions y(0) = 1, y'(0) = 2, y''(0) = 3, we can follow a similar process as before. However, without solving the equation, we can isolate Y(s) by applying the Laplace transform to both sides of the equation and using the initial conditions:

s³Y(s) - s²y(0) - sy'(0) - y''(0) + sY(s) - y(0) = 1/(s - 3) + 6/s⁴

Substituting the initial conditions, we have:

s³Y(s) - s² - 2s - 3 + sY(s) - 1 = 1/(s - 3) + 6/s⁴

Now, let's isolate Y(s):

s³Y(s) + sY(s) = 1/(s - 3) + 6/s⁴ + s² + 2s + 4

(Y(s))(s³ + s) = 1/(s - 3) + 6/s⁴ + s² + 2s + 4

Y(s) = (1/(s - 3) + 6/s⁴ + s² + 2s + 4) / (s³ + s)

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Answer:

-6

Step-by-step explanation:

\(b(x)=x+4\\\\b(-10)=(-10)+4\\\\b(-10)=-10+4\\\\b(-10)=-6\)

Answer:

The answer is 9 miles.

Step-by-step explanation:

14-5=9.

Answer:

9 miles

Step-by-step explanation:

So if you pay $5 for the cab ride then 1$ for every mile driven and you have to pay a total of $14 you go 14-5=9

Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.

We are given asked when the sample size is kept the same,

we know that the margin of error is nothing but a statistic which tells us how many percentage points our results will differ from the real population value.we know that when a greater error is allowed, the more will be the confidence(fundamental concept of confidence intervals)

Let Margin of Error be represented by E and the confidence level by C hence the relationship goes like this,

                                           E↑⇔C↑and E↓⇔C↓

Here we are asked when the sample size is kept the same, what will happen to the level of confidence if the margin of error decreases .

The answer is that Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down.

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Answer:

Becky

Step-by-step explanation:

Look at it.... i mean 21:35 is the greatest in fraction, decimal and percentage.

Answer:

it's answer is C 0.8

hope it helps you

Answer:

210 people

Step-by-step explanation:

so we know that the number of employees in 2005 is (50)3= 150

so taking 14/10* 150= we get 14*15= 210 people

Answer:

The ratio of the circumference of a circle to the diameter of that circle is the value pi (22/7)

Step-by-step explanation:

Mathematically,

the circumference of a circle is by the formula;

C = 2 * pi * r

Now, as we know, 2r is d where r is the radius of the circle and d is the diameter of the circle

that means;

C = pi * d

hence;

C/d = pi

So the ratio of the circumference of any circle to the diameter is the value called pi

The graph of constant of proportionality of y = 3.75x is attached

The constant of proportionality is a term that indicates a reciprocal relationship between two variables, in which the change of one affects the other similarly.

When x and y are directly linked in this way, the following equation can be used to calculate how they operate together:

y = kx,

where

k serves as the aforementioned constant.

In the problem k = 3.75

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Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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The measure of the angles of the cyclic quadrilateral are:

Arc PQ = 130

QR = 50°

Arc RS = 70°

∠PSQ = 65°

∠PSB = 65°

∠SBP = 80°

AQS = 30°

PS = 110°

From the figure, the arc PQ is subtended by the angle PAQ.

This means that:

PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

The measure of PSQ is then calculated using:

∠PSQ = 0.5 * Arc PQ ----- inscribed angle is half a subtended angle.

This gives: ∠PSQ = 0.5 * 130

∠PSQ = 65°

Hence, the measure of ∠PSQ is 65°

The measure of arc QR

A semicircle measures 180°

Thus:

QR + PQ = 180°

Thus, we get:

QR = 180° - PQ

Substitute 130° for PQ

QR = 180° - 130°

QR = 50°

Hence, the measure of QR is 50°

The measure of arc RS

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

So, we have:

35 = 0.5 * Arc RS

Multiply both sides by 2

Arc RS = 70°

The measure of angle AQS

In (a), we have:

∠PSQ = 65°

This means that:

∠PSQ = ∠PSB = 65°

So, we have:

∠PSB = 65°

Next, calculate SBP using:

∠SBP + ∠BPS + ∠PSB = 180° ---- sum of angles in a triangle.

So, we have:

∠SBP + 35 + 65 = 180°

∠SBP + 100 = 180

∠SBP = 80°

The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

AQS = 180 - (180 - 80) - (180 - 130)

AQS = 30°

The measure of arc PS

A semicircle measures 180°

This means that:

PS + RS = 180°

This gives

PS = 180 - RS

RS = 70

Thus:

PS = 180 - 70

PS = 110°

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This means we are 95% confident that the true population means completion time is between 6.1 and 7.5 hours.

The formula for the confidence interval is:

sample mean ± (t-value * standard error)

where the standard error is the sample standard deviation divided by the square root of the sample size:

standard error = sample standard deviation / √sample size

Plugging in our values, we get:

6.8 ± (2.009 * (1.5 / √50))

6.8 ± 0.7

Completion refers to the act of finishing or bringing something to a state of finality. It can apply to various areas of life, such as education, work, personal projects, or relationships. In education, completion often refers to successfully finishing a degree program or course of study. Work completion involves finishing a task, project, or assignment within the given time frame and meeting the required standards.

Completion in personal projects is about reaching a goal, such as finishing a book, completing a home renovation project, or achieving a fitness milestone. In relationships, completion can mean resolving conflicts or reaching a state of mutual understanding.

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The graphical representation that will be most appreciated for the data would be box plot, because the median can easily be determined from the large set of data. That is option A.

The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

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Answer: 25%

Step-by-step explanation:29 cash, 26 debit card, and 62 credit card.

\color{steelblue}{29}+26+62=

29+26+62=

\,\,\color{indianred}{117}

117

There were a toal of 117 customers. 29 paid with cash.

Probability the next customer will pay with cash:

\frac{\color{steelblue}{29}}{\color{indianred}{117}}=

117

29

​

=

\,\,0.247863...

0.247863...

0.247863...\times100\%\approx

0.247863...×100%≈

\,\,24.7863\%

24.7863%

Answer:

If the angle degree and size of triangle are similar or same, it is depicted as congruent.

Answer:

C and most likely A

Step-by-step explanation:

Answergood question

Step-by-step explanation:

The equation for the flowing rate of aamir will be as y = -12x  +360.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The slope-intercept form of the equation of a line, which is:

y   =  mx  +  c

So we just need to find to solve this problem.

This problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is;

Negative slope because Amir is descending.

So,

y   =  -   12x  +  b

Now, we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point.

Therefore, substituting this point into our equation;

y  =  -12x  +  b

0  =   -12(30)   +  b

b   =   360

Finally, The equation for the flowing rate of aamir will be as y = -12x  +360.

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Answer:

6$ each pair of pants

Step-by-step explanation:

6 times 3 = 18

Answer:

n= -1.2

Step-by-step explanation:

I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.

The point estimate of the difference between the two population proportions is 0.024.

The point estimate of the difference between two population proportions can be calculated using the following formula:

\(\hat{p}1 - \hat{p}2 = (x1/n1) - (x2/n2)\)

where \(\hat{p1}\) and \(\hat{p2 }\) are the sample proportions, x1 and x2 are the number of failures in each sample, and n1 and n2 are the sample sizes.

Using the given data:

\(\hat{p1}\)  = 53/400 = 0.1325

\(\hat{p2 }\) = 51/470 = 0.1085

n1 = 400

n2 = 470

Substituting these values into the formula, we get:

\(\hat{p1}-\hat{p2}\)  = (0.1325) - (0.1085) = 0.024.

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The correlation coefficient measures the proportion of the dependent variable's overall fluctuation that the independent variable adequately captures.

The relationship between two parametric variables is represented by the correlation coefficient. It ranges from -1 to +-1. It means there is no correlation between the two variables when it is 0. When it is 1 or 1, there is a significant correlation between the variables.

Determinant coefficient: It shows how much of the variance in the dependent variable can be accounted for by the independent variable. It ranges from 0 to 1 and is represented by the symbol R2.

As a result: b) The coefficient of determination is the proportion of the dependent variable's variation that can be attributed to the independent variable.

Answers that are incorrect:

a) A linear regression is one that employs a regression formula with the form y=ax=b.

c) Correlation is a metric for determining how two variables are related.

d) The statistical technique of regression is used to build mathematical models that link two or more variables.

Option B is the proper response, thus.

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