After making several scale drawings Joseph decides on the best placement for a new grillon deck He uses a scale of 2 cm for every 5 in What is the actual area of the space for Joseph's new square inches ? ​

The expression for the area under the graph is \(A = \lim_{n \to \infty} \left(\frac{2}{n}\right)\Sigma_{i=1}^{n} \left(4+\frac{2\cdot i}{n} \right)^{2} + \lim_{n \to \infty} \left(\frac{2}{n} \right)\Sigma_{i = 1}^{n}\sqrt{1+2\cdot \left(4+\frac{2\cdot i}{n} \right)}\).

In this case, we must assume that the area below the curve is equivalent to the sum of infinite rectangles, that is to say:

\(A = \lim_{n \to \infty} \left(\frac{b-a}{n}\right) \Sigma_{i=1}^{n} f\left[a + i\cdot \left(\frac{b-a}{n} \right)\right]\) (1)

If we know that \(a = 4\), \(b =6\) and \(f(x) = x^{2}+\sqrt{1+2\cdot x}\), then we have the following expression:

\(A = \lim_{n \to \infty} \left(\frac{2}{n} \right)\Sigma_{i=1}^{n} f\left(4+\frac{2\cdot i}{n} \right)\)

\(A = \lim_{n \to \infty} \left(\frac{2}{n} \right)\Sigma_{i=1}^{n}\left[\left(4+\frac{2\cdot i}{n} \right)^{2}+\sqrt{1+2\cdot \left(4+\frac{2\cdot i}{n} \right)}\right]\)

\(A = \lim_{n \to \infty} \left(\frac{2}{n}\right)\Sigma_{i=1}^{n} \left(4+\frac{2\cdot i}{n} \right)^{2} + \lim_{n \to \infty} \left(\frac{2}{n} \right)\Sigma_{i = 1}^{n}\sqrt{1+2\cdot \left(4+\frac{2\cdot i}{n} \right)}\)

The expression for the area under the graph is \(A = \lim_{n \to \infty} \left(\frac{2}{n}\right)\Sigma_{i=1}^{n} \left(4+\frac{2\cdot i}{n} \right)^{2} + \lim_{n \to \infty} \left(\frac{2}{n} \right)\Sigma_{i = 1}^{n}\sqrt{1+2\cdot \left(4+\frac{2\cdot i}{n} \right)}\).

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Nota - The statement has some typing errors. Corrected statement is presented below:

Use the definition to find an expression for the area under the graph of \(f\) as a limit. Do not evaluate the limit: \(f(x) = x^{2}+\sqrt{1+2\cdot x}\), \(4\le x \le 6\).

The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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Answer:

Step-by-step explanation:

1. M is the midpoint of CD; CM = 3x - 10; MD = 6x - 22;        GIVEN

2.  CM = MD                                                                       Definition of Midpoint

3.  3x - 10 = 6x - 22                                                            Substitution Property

4.  -3x - 10 = - 22                                                      Subtraction Prop of Equality

5.  -3x =-12                                                               Addition Prop of Equality

6.  x = 4                                                                    Division Prop of Equality

The missing reasons in the two-column proof are:

1. Given

2. Definition of a midpoint

3. Addition property of equality

To apply the addition property of equality, both sides of an equation is added with equal quantity to make it balanced.

In the two-column proof given, the missing reasons are:

1. Given (the information was stated already)

2. Definition of a midpoint (CM = MD)

3. Addition property of equality (10 was added to both sides of the equation).

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The equation for the remaining work is given by the equation  25 - (x+y)

let x be the number of pizza made by Mario and y be the number of pizza made by luigi

let z be the pizza that still need to be made

so x+y+z=25

=> z = 25 - ( x + y )

so the total remaining pizza is given by 25 - (x+y) ---(i)

given that Mario had made 11 pizza so x = 11

and Luigi had made 3 pizza so  y = 3

so total remaining work is found using equation (i)

so z = 25 - ( 11 + 3)

=> 11

so remaining work is 11

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Step-by-step explanation:

Let use have a interger,n

Thus three consectice intergers can be represented by

\(n\)

\(n + 1\)

\(n + 2\)

Multiply, and we get

\(n(n + 1)(n + 2)\)

\(n( {n}^{2} + 3n + 2)\)

\(n {}^{3} + 3 {n}^{2} + 2n\)

Then add the middle number, n+1.

\( {n}^{3} + 3n {}^{2} + 3n + 1\)

We must prove that the middle number cubed = the equation.

Using the binomial theroem,

\((n + 1) {}^{3} = {n}^{3} + 3( {n}^{2} 1 {}^{1} ) + 3n( {1}^{2} ) + 1 {}^{3} \)

\((n + 1 ){}^{3} = {n}^{3} + 3 {n}^{2} + 3n + 1\)

So this is indeed true.

You can do the subsitue variables for n to prove it.

Answer:

-1

Step-by-step explanation:

so -x-6 and x-4 are both = to y so that means they are both = to each

other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1

Answer:

Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.

Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.

If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.

The system with impulse response g(t, t) = e^(-2|t|^-|t|) is not BIBO stable, while the system with impulse response g(t, t) = sin(t)e^(-(-t^2)) is BIBO stable.

To determine if a system is BIBO (Bounded-Input Bounded-Output) stable, we need to analyze the impulse response of the system.

For the first system with impulse response g(t, t) = e^(-2|t|^-|t|), let's examine its behavior. The function e^(-2|t|^-|t|) decays rapidly as |t| increases. However, it does not decay fast enough to satisfy the condition for BIBO stability, which requires the integral of |g(t, t)| over the entire time axis to be finite. Since the integral of e^(-2|t|^-|t|) diverges, the first system is not BIBO stable.

For the second system with impulse response g(t, t) = sin(t)e^(-(-t^2)), the term e^(-(-t^2)) represents a Gaussian function that decays exponentially. The sinusoidal term sin(t) can oscillate, but it is bounded between -1 and 1. As the exponential decay ensures that the impulse response is bounded, the second system is BIBO stable.

In summary, the system with impulse response g(t, t) = e^(-2|t|^-|t|) is not BIBO stable, while the system with impulse response g(t, t) = sin(t)e^(-(-t^2)) is BIBO stable.

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Answer:

-1

Step-by-step explanation:

I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)

Answer:

$31.56

Step-by-step explanation:

We know

Skateboard cost: $37.50

20% off, so 80% left = 0.8

5.2 tax + 100% = 105.2% = 1.052

So, we have the equation

37.50 (0.8) (1.052) = $31.56

So, Petra will pay $31.56 for the skateboard deck in all!

The cost of one calzone given the information in the table is $8.75 (first option).

The first step is to form a system of equation to represent the information in the question:

16p + 12c = 269 equation 1

20p + 8c = 275 equation 2

Where:

p =cost of pizzas bought

c = cost of calzones bought

The elimination method would be used to determine the cost of one calzone.

Multiply equation 1 by 5 and equation 2 by 4

80p + 60c = 1345 equation 3

80p + 32c = 1100 equation 4

Subtract equation 4 from equation 3

28c = 245

Divide both sides of the equation by 28

c = 245 / 28

c = $8.75

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Answer:

co-ordinates are (-3,7) and (5,7)

or

(-3,-5) and (5,-5)

length of diagonal=10 units

Step-by-step explanation:

\(length=\sqrt{(5+3)^2+(1-1)^2} =\sqrt{64} =8\\slope ~of~length=\frac{1-1}{5+3} =0\\\\length ~of~rectangle~is~parallel~to~x-axis\\ width~ is~ parallel ~to~y- axis~and~is~6~units~away~from~length.\\other co-ordinates ~of~rectangle are~(-3,1+6)~and ~(5,1+6)~or~(-3,7)~and~(5,7)\\and~other~co-ordinates~are~(-3,1-6)~and~(5,1-6)~or~(-3,-5)~and~(5,-5)\)

length of diagonal

d=\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10 ~units\\or\\d=\sqrt{(5+3)^2+(1-7)^2} =\sqrt{64+36} =\sqrt{100} =10~units.

Answer:

associative property

commutative property

Step-by-step explanation:

Line 1 to line 2:

change of grouping is associative property of multiplication

Line 2 to line 3:

change of order is commutative property of multiplication

Answer:

\(y = 42( { \frac{1}{2}) }^{x} \)

Answer:

c-2x+3+x

Step-by-step explanation:

Answer:

Choice B: \(2x+3=18\)

Step-by-step explanation:

First of all we know that the x will represent the number of pencils that Miguel has. So if it mentioned that Imani has 3 more than twice of Miguel's pencils, that can be made into this expression \(2x+3\). Then it said that both of their pencils added together is 18. So we take the expression and add an equal sign with the 18. So once we put it together it makes Choice B \(2x+3=18\).

Answer:

x=15

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

If 2 tables seat 16 students, then 1 table seats 8 students. Using this information, we can complete the table as follows:

Tables Students

2 16

14 112

18 144

We are given that 2 tables seat 16 students, which means that each table seats 8 students. To find out how many students can be seated at 14 tables or 18 tables, we can simply multiply the number of tables by the number of students per table. So, 14 tables times 8 students per table give us a total of 112 students that can be seated.

Similarly, 18 tables times 8 students per table give us a total of 144 students that can be seated. Therefore, the completed table shows that 14 tables can seat 112 students, and 18 tables can seat 144 students.

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The possibility that something will occur, prior measures, and conventional objective measurements all influence the likelihood that something will occur.

What is probability and what types are there in total?

The study of probability is a field of mathematics that determines the probability of an event occurring, which is represented by a number between 1 and 0. When an event has a probability of 1, it can be said to be a certainty. For instance, if the coin lands flat, the likelihood that it will come up  "heads or  tails" is 1. There are no other possible outcomes. A probability of .5 indicates that there is an equal chance that an event will occur or not.

Probability can be quantitatively represented in the simplest form as follows: the total number of possible outcomes multiplied by the ratio of the number of occurrences of a targeted event divided by the sum of the occurrences and failures of occurrences:

P(a) = P(a)/[P(a) + P(b)]

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\($$\begin{aligned}&\text { (1) } \int \sqrt[8]{x^9} d x=\int x^{9 / 8} \cdot d x=\frac{(x)^{\frac{9}{8}+1}}{\frac{9}{8}+1}+c=\frac{8 x^{17 / 8}}{17}+c\\\\&\Rightarrow \int \sqrt[8]{x^9} d x=\frac{8}{17} \sqrt[8]{x^{17}}+c,(c \text { is constant })\\\)

In the previous two chapters, we were given a function and asked to determine its derivative. We are now going to reverse the situation, beginning with this part. We now want to know what function we discriminated in order to obtain the function. This previous example has two implications. The initial goal was to encourage you to start considering solutions to these difficulties. First, it's crucial to keep in mind that we are only asking what we differentiated to obtain the specified function. The second thing to keep in mind is that we could potentially employ an endless number of different functions, and they would all be different by a constant.

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Answer:

$275/mont 2.

Step-by-step explanation:

aaaaaaaaaaaaaaaaaaaaaaaa

Solution: B. 1/2

Analysis

We are transforming triangle ABC to DFE. If we see the graph, we can see the measures of each side of the triangle, decrease by half. According to that, it would be 1/2 of the original measure.

Answer:

13 students

Step-by-step explanation:

4 plus 9 = 13

Answer:

ist it 13 students (・o・)

We can use trigonometry to solve this problem. Let h be the height of the radio tower. Then we have:

tan(69°) = h/60

Multiplying both sides by 60, we get:

h = 60 tan(69°)

Using a calculator, we find that:

h ≈ 178.37 feet

Therefore, the height of the radio tower is approximately 178.37 feet.

According to the Question, the value of Buli's investment after 27 days is approximately $153.57 (rounded to 2 decimal places).

We must solve the above differential equation to determine the value of Buli's investment after 27 days.

The differential equation is:

\(\frac{(dI)}{dt} =0.002I+5\)

To solve this equation, we can separate the variables and integrate both sides concerning t

\(\int\frac{1}{(0.002I+5)} dI=\int dt\)

To evaluate the integral on the left side, we can use the substitution u = 0.002I + 5, which gives us du = 0.002dI. Substituting these values, the integral becomes:

\(\int\frac{1}{u} =\int dt\)

This simplifies to:

\(ln|u|=t+C\)

Where C is the constant of integration

Now, substituting back u = 0.002I + 5 and solving for I, we have:

ln∣0.002I + 5∣ = t + C

Exponentiating both sides:

\(0.002I + 5=e ^{t+C}\)

Since \(e^C\) just another constant, we can rewrite the equation as

\(0.002I+5=Ce^ t\)

Now, let's solve for C. We know that when t = 0, I = 60 (the initial principal). Substituting these values, we get:

\(0.002(60)+5=Ce^0\\0.12+5=C\\C=5.12\)

So the equation becomes:

\(0.002I+5=5.12e^t\\\)

We can now use t = 27 to calculate the amount of I after 27 days.

\(0.002I+5=5.12e^{27}\\\\0.002I=5.12e^{27}-5\\\\I=\frac{(5.12e^{27}-5)}{0.002}\)

Calculating this value using a calculator or computer software, we find that I ≈ 153.57.

Therefore, the value of Buli's investment after 27 days is approximately $153.57 (rounded to 2 decimal places).

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The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

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Answer:

A

Step-by-step explanation:

It's the only one that passes the vertical line test

The seasonalized sales for this period when the deseasonalized sales are 2,889.00 units and the seasonal index for this period is 1.70 is 4911.30.

There are two types of sales numbers: seasonalized sales and deseasonalized sales. Deseasonalized sales are the revenues of a business that have been adjusted for seasonal fluctuations. The value of seasonalized sales is then adjusted by the seasonality factor to determine the seasonalized sales for the period.

This adjustment enables businesses to compare their performance in different periods of the year without being influenced by seasonal fluctuations. This makes it easier to compare performance over time.

Therefore, the formula to calculate the seasonalized sales is;

Seasonalized sales = Deseasonalized sales * Seasonal index= 2889 * 1.70= 4911.30

Therefore, the seasonalized sales for this period when the deseasonalized sales are 2,889.00 units and the seasonal index for this period is 1.70 is 4911.30.

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Answer:

The function g(x) that outputs a y value to satisfy the equation -4·x - 6 = -5·y + 2 is g(x) = y = 4/5·x + 8/5

Step-by-step explanation:

The y value of the equation that the required function g(x) outputs = -4·x - 6 = -5·y + 2

Therefore, we have;

-4·x - 6 = -5·y + 2

-5·y + 2 = -4·x - 6

-5·y = -4·x - 6 - 2 = -4·x - 8

Therefore, y = (-4·x - 8)/(-5) = 4/5·x + 8/5

y = 4/5·x + 8/5

Which gives;

g(x) = y = 4/5·x + 8/5

Therefore;

The function g(x) that outputs a y value to satisfy the equation -4·x - 6 = -5·y + 2 is g(x) = y = 4/5·x + 8/5

The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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First find the critical points by equating the two terms

Then test out the intervals between critical points.

Therefore the solution is x < 5, and x > -5.