write an algebraic equation for the cost of 21 liters of gasoline ,if x pesos per liter is 2,092

Answers

Answer 1

the algebraic equation for the cost of 21 liters of gasoline at x pesos per liter is: Cost of 21 liters of gasoline = x pesos/liter x 21 liters

why it is and what is an algebraic equation?

Assuming that the cost of gasoline is directly proportional to the number of liters purchased, we can write:

Cost of gasoline = Cost per liter x Number of liters

Let's substitute the given values:

Cost of 21 liters of gasoline = 2,092 pesos/liter x 21 liters

Simplifying the equation, we get:

Cost of 21 liters of gasoline = 43,932 pesos

Therefore, the algebraic equation for the cost of 21 liters of gasoline at x pesos per liter is:

Cost of 21 liters of gasoline = x pesos/liter x 21 liters

An algebraic equation is a mathematical statement that expresses the equality of two algebraic expressions, with one or more variables involved.

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Related Questions

consider the multistep reaction. what is the best rate law for the overall reaction? a) rate = k₁[a][b][c] b) rate = k₂[c] c) rate = k₁[a]²[b] d) rate = (k₁[a][b])/(k₂[c]) e) rate = k₁k₂[a]²[b]

Answers

For the first step, rate = k₁[a][b], and for the second step, rate = k₂[c]. By combining these two rate laws, we get rate = (k₁[a][b])/(k₂[c]). This rate law takes into account all of the relevant information and is thus the best rate law for the overall reaction.

The best rate law for the overall reaction is rate = (k₁[a][b])/(k₂[c]), where k₁ and k₂ are the rate constants for the individual steps of the reaction, and [a], [b], and [c] are the concentrations of the reactants. This rate law takes into account the fact that the overall reaction is the sum of two steps, and therefore the rate of the overall reaction is dependent on both the rate constants and the concentrations of each reactant. This can be demonstrated by considering the rate law for each of the individual steps and then combining them to get the overall rate law. For the first step, rate = k₁[a][b], and for the second step, rate = k₂[c]. By combining these two rate laws, we get rate = (k₁[a][b])/(k₂[c]). This rate law takes into account all of the relevant information and is thus the best rate law for the overall reaction.

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Help me please... I have a lot more things to do and I wanna get this done.

Help me please... I have a lot more things to do and I wanna get this done.

Answers

Answer:

-6

Step-by-step explanation:

count

Answer:

-6

Step-by-step explanation:

each dash on the line changed by one. So i you go down, you subtract 1, and if you go up, you add 1.

Help will be appreciated?

Help will be appreciated?

Answers

The answer is yes, you plug in 0 for x and y in the equation and then solve like normal, if the equation is correct then it is a solution

8 5/6 rounded to the nearest whole number

Answers

Answer:

9

Step-by-step explanation:

5/6>0.5

"Suppose we are using the CPM with three time estimates
(PERT) to schedule a project. What is the variance of the
length of the critical path if the standard deviation is 2.4?
A. 5.76
B. 2.34
C. 2.96
D. 3.19
E. 4.46

Answers

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

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A, B, and C are midpoints of ∆XYZ. What is the length of ? YZ

A, B, and C are midpoints of XYZ. What is the length of ? YZ

Answers

Answer:

\(YZ = 48\)

Step-by-step explanation:

Given

\(AB = 24\)

\(XZ = 60\)

Required

Find YZ

From the attachment, AB is parallel and equal to YC;

This implies that

\(AB = YC = 24\)

Given that C is the midpoint of YZ;

This implies that

\(YC = CZ = 24\) and \(YZ = YC + CZ\)

Substitute values for YC and CZ

\(YZ = 24 + 24\)

\(YZ = 48\)

Answer:

48

Step-by-step explanation:

the students of 3 sections of a class have to stand in rows each row has an equal number of students if there are 24 , 36 , and 60 students in 3 sections find the maximum number of students in each row​

Answers

The maximum Number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

To find the maximum number of  scholars in each row, we need to determine the  topmost common divisor( GCD) of the total number of  scholars in each section. The GCD represents the largest number that divides all the given  figures unevenly.  

Given that there are 24, 36, and 60  scholars in the three sections, we can calculate the GCD as follows    Step 1 List the  high factors of each number  24 =  23 * 31  36 =  22 * 32  60 =  22 * 31 * 51    

Step 2 Identify the common  high factors among the three  figures  Common  high factors 22 * 31    Step 3 Multiply the common  high factors to find the GCD  GCD =  22 * 31 =  4 * 3 =  12  

 thus, the maximum number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

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5.2. lognormal stock prices. consider the special case of example 5.4 in which xi d ei where i d normal. ; 2/. for what values of and is mn d m

Answers

We need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

In Example 5.4, we have the following:

The stock price at time t, St, is modeled as a geometric Brownian motion with constant drift and volatility, such that dSt = μSt dt + σSt dWt, where μ is the drift rate, σ is the volatility, and dWt is a Wiener process increment.

Taking the natural logarithm of both sides, we get d ln(St) = (μ - 0.5σ^2)dt + σdWt.

Letting Xt = ln(St), we have dXt = (μ - 0.5σ^2)dt + σdWt.

From the problem statement, we have that Xi = ei, where ei ~ N(0,1) for i = 1, 2, ..., n, where n is the number of time steps.

We want to find values of μ and σ such that Mn = exp(1/n Σi=1^n Xi) = exp(1/n Σi=1^n ei) = exp(1/n En) is a martingale, where En is the average of the N(0,1) random variables.

Using the fact that exp(a+b) = exp(a)exp(b), we have:

Mn+1 = exp(1/(n+1) Σi=1^(n+1) Xi) = exp(1/(n+1) Σi=1^n Xi)exp(Xn+1)

For Mn+1 to be a martingale, we need:

E[Mn+1 | Fn] = Mn

where Fn is the filtration up to time n. Since Xi are independent and identically distributed, we have:

E[Mn+1 | Fn] = E[exp(1/(n+1) En+1 + 1/(n+1) Σi=1^n ei) | Fn] = Mn exp(1/(n+1) E[en+1])

where en+1 ~ N(0,1). Note that E[en+1] = 0 and Var[en+1] = 1.

Thus, we need:

Mn exp(1/(n+1) E[en+1]) = Mn

or equivalently:

exp(1/(n+1) E[en+1]) = 1

Taking the logarithm of both sides, we get:

1/(n+1) E[en+1] = 0

or:

E[en+1] = 0

Therefore, we need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

This is the same condition as in Example 5.4, which ensures that the lognormal stock prices follow a martingale.

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Find the equation of the line.
Use exact numbers PLEASEEE

y = ___ x+ ___

Find the equation of the line.Use exact numbers PLEASEEEy = ___ x+ ___

Answers

Step-by-step explanation:

\(y = \frac{3}{4} x - 2\)

is the required equation

I hope it helped you

Answer:

y = \(\frac{3}{4} x-2\)

Step-by-step explanation:

y = mx + c

m = gradient= \(\frac{-5-(-2)}{-4-0}\)= \(\frac{3}{4}\)

c = y-intercept = -2

an incomplete table of values for an exponential function is shown. the exponential function is of the form y=a*b^x, where a is a real number such as a does not equal 0 and b is a positive number not equal to 1. complete the table with possible values for the exponential function

Answers

The table showing the exponential function is completed and presented below  

x      y

0    96

1    192

2   384

3   768

How to complete the table

The expression for the table is given as

y = a * b^x,

Point (0, 96) is on the table.

a = 96,

when b = 2, we have that

for x = 1

y = 96 x 2^x = 96 x 2^1 = 192

for x = 2

y = 96 x 2^x = 96 x 2^2 = 384

for x = 3

y = 96 x 2^x = 96 x 2^3 = 768

Therefore, The required exponential function will be  

x      y

0    96

1    192

2   384

3   768

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an incomplete table of values for an exponential function is shown. the exponential function is of the

please help!!!!!!!!!!!!!!!!!! 2+3

Answers

Answer:

5 ...

Step-by-step explanation:

add 3 more to 2

Answer:

It’s 5

Step-by-step explanation:

60 passengers have boarding passes for a plane with 60 seats. The first k (k < 10) passengers lose their boarding passes, and are instructed to just sit anywhere, so they randomly pick seats on the plane. The remaining passengers board the plane one at a time, each one sitting in his or her assigned seat if it is unoccupied, otherwise randomly choosing an empty seat. For each of the last five passengers P56, P57, P58, P59, and P60, determine the probability that he or she will end up in his or her assigned seat. Partial Answer: P56 = 5/(k + 5).

Answers

The partial answer provided is correct:

P56 = 5/(k+5) if we substitute k+1 = 5, we get P56 = 1/(k+1) = 1/(5+1) = 1/6 = 5/30 = 5/(k+5).

To determine the probability that each of the last five passengers (P56, P57, P58, P59, and P60) will end up in their assigned seat, we need to consider the seating arrangements based on the actions of the first k passengers.

For P56, there are k possibilities for the first passenger who lost their boarding pass to end up in P56's assigned seat. In that case, P56 will be forced to sit randomly somewhere else on the plane, and there will be no effect on the remaining passengers. Therefore, the probability that P56 will end up in their assigned seat is given by the fraction 1/(k+1), where k+1 represents the total number of available seats including P56's assigned seat. However, since it is given that k < 10, we know that k+1 is less than or equal to 11.

For P57, if the first passenger who lost their boarding pass took P57's assigned seat, then P57 will be forced to sit randomly somewhere else on the plane. In this case, P57 has k-1 possible seats to choose from. Alternatively, if the first passenger took another seat, P57's assigned seat will still be available, and P57 will sit in it. Therefore, the probability that P57 will end up in their assigned seat is given by the fraction (1 + k-1)/(k+1) = (k)/(k+1).

Similarly, for P58, the probability is (2 + k-2)/(k+1) = (k)/(k+1).

For P59, the probability is (3 + k-3)/(k+1) = (k)/(k+1).

For P60, the probability is (4 + k-4)/(k+1) = (k)/(k+1).

Hence, the probability for each of the last five passengers to end up in their assigned seats is as follows:

P56 = 1/(k+1) = 1/(k+1)

P57 = k/(k+1)

P58 = k/(k+1)

P59 = k/(k+1)

P60 = k/(k+1)

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The ratio of the interior angle measures of a triangle is 2:3:5. What are the angle measures? In order from least to greatest, the angle measures are

Answers

Answer:

36, 54, 90

Step-by-step explanation:

angle ratio = total internal angles

2x + 3x +5x = 180

10x = 180

x = 18

2×18:3×18:5×18

36, 54, 90

What are the properties of the circumcenter of a triangle quizlet?

Answers

For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

What do you mean by a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

What do you mean by circumcenter of triangle?

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle. Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.

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Suppose James randomly draws a card from a standard deck of 5252 cards. He then places it back into the deck and draws a second card. A standard deck of cards contains four suits: clubs, diamonds, hearts, and spades. There are 1313 cards in each suit, which includes three face cards: jack, queen, and king. What is the probability that James draws a queen card as the first card and a diamond card as the second card

Answers

The probability that James draws a queen card as the first card and a diamond card as the second card is 1/52 or approximately 0.0192, which is about 1.92%.

To find the probability that James draws a queen card as the first card and a diamond card as the second card, we need to calculate the probability of these two independent events occurring in sequence.

First, let's consider the probability of drawing a queen card as the first card. In a standard deck of 52 cards, there are 4 queens (one in each suit), so the probability of drawing a queen as the first card is 4/52 or 1/13.

Next, we move on to the second card. After replacing the first card back into the deck, the deck is restored to its original composition. So, for the second card, the probability of drawing a diamond is 13/52 since there are 13 diamonds in the deck.

To find the probability of both events happening in sequence, we multiply the individual probabilities:

(1/13) * (13/52) = 1/52.

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The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from.

Answers

The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .

The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.

The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.

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WHAT IS THE CONFIDENCE LEVEL FOR THE FOLLOWING NUMBERS
Confidence Interval Question: What is the Confidence Interval for the following numbers: a random sample of 53 with sample proportion \( 0.88 \) and confidence of \( 0.94 \) ? Level of difficulty \( =

Answers

The confidence interval for the given numbers, with a sample proportion of 0.88 and a confidence level of 0.94, is approximately (0.798, 0.962) when rounded to two decimal places.

To calculate the confidence interval for a random sample with a sample proportion of 0.88 and a confidence level of 0.94, we can use the formula:

\[ \text{Confidence Interval} = \text{Sample Proportion} \pm \text{Margin of Error} \]

The margin of error can be calculated using the formula:

\[ \text{Margin of Error} = \text{Critical Value} \times \text{Standard Error} \]

The critical value can be obtained from the Z-table or calculated using the inverse cumulative distribution function for the standard normal distribution.

Since the level of difficulty is set to 2, we can assume a two-tailed test. The critical value for a 94% confidence level with a two-tailed test is approximately 1.99.

The standard error can be calculated using the formula:

\[ \text{Standard Error} = \sqrt{\frac{\text{Sample Proportion} \times (1 - \text{Sample Proportion})}{\text{Sample Size}}} \]

Plugging in the values:

Sample Proportion (\( p \)): 0.88

Sample Size (\( n \)): 53

Confidence Level: 0.94

Critical Value (\( z \)): 1.99

We can calculate the standard error:

\[ \text{Standard Error} = \sqrt{\frac{0.88 \times (1 - 0.88)}{53}} \]

Now, we can calculate the margin of error:

\[ \text{Margin of Error} = 1.99 \times \text{Standard Error} \]

Finally, we can calculate the confidence interval:

\[ \text{Confidence Interval} = 0.88 \pm \text{Margin of Error} \]

Calculating the values:

Standard Error ≈ 0.041

Margin of Error ≈ 0.082

Confidence Interval ≈ (0.798, 0.962)

Therefore, the confidence interval for the given numbers, with a sample proportion of 0.88 and a confidence level of 0.94, is approximately (0.798, 0.962) when rounded to two decimal places.

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hector received three a's and one b in his college courses. what is his grade point average?assume each course is three credits. a

Answers

The grade point average received by hector is 3.75.

What is GPA?

Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades. A perfect score, or an A, is a 4.0.

The unit value for each course in which a student obtains one of the grades mentioned above is multiplied by the grade point total for that grade to determine the GPA. Then, divide the sum of these products by the sum of the units. The cumulative GPA is calculated by dividing the total grade points by the total number of units.

3 a and one is B received by Hector.

The A = 4.0, B = 3.0, C = 2.0, D = 1.0 is given by college

We have GPA= A+A+A+B/4

GPA=4+4+4+3/4

GPA= 15/4

GPA=3.75

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Complete question

Hector Ramirez received three A's and one B in his college courses. What is his grade point average? Assume each course is three credits. A = 4.0, B = 3.0, C = 2.0, D = 1.0

I need help on the last two finding the function notation

I need help on the last two finding the function notation

Answers

\(f(x)=3x+5\)\(\begin{gathered} f(f)=3(3x+5)+5 \\ f(f)=(3\cdot3x)+(3\cdot5)+5 \\ f(f)=9x+15+5 \\ f(f)=9x+20 \end{gathered}\)

For the second before last f(f), you have to replace x with the function f(x).

For the last one you have to replace x with the function g(x)

\(g(x)=2x^2+1\)\(\begin{gathered} f(g)=3(2x^2+1)+5 \\ f(g)=(3\cdot2x^2)+(3\cdot1)+5 \\ f(g)=6x^2+3+1 \\ f(g)=6x^2+4 \end{gathered}\)

de.there is a spinner with 10 equal areas, numbered 1 through 10. if the spinner is spun one time, what is the probability that the result is a multiple of 2 and a multiple of 5?/app/student

Answers

For a spinner with 10 equal areas, numbered 1 through 10, the probability that the result is a multiple of 2 and a multiple of 5 is equals to 0.1.

Probability is calculated by dividing the favourable outcomes to the total possible number of outcomes. There is a spinner with 10 equal areas. It can be numbered from 1 to 10. Spinner is spin one time. We have to determine the probability that the result is a multiple of 2 and a multiple of 5. Let us consider an event E : results multiple of 2 and a multiple of 5

Now, Total possible outcomes = 10

= { 1,2,3,4,5,6 ,7,8,9,10}

Multiples of numbers 2 and 5 in 1 to 10 numbers = 1 = {10}

So, number of favourable outcomes = 1

Probability that result is a multiple of 2 and a multiple of 5 = \(\frac{1}{10} = 0.1\)

Hence, required probability is 0.1.

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4
Carson decides to buy a new phone. He pays
$255 up front, and then will pay a set amount
each month for 15 months. The total cost of
the phone is $600. How much will Carson pay
each month?
o 23
1
Leave

Answers

Answer:

675

Step-by-step explanation:

4 +3+653=675

The optimal amount of x1, x2, P1, P2 and income are given by the
following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I
=4189 The new price of P1 is the foll

Answers

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

a circular diaphragm 58.06 cm in diameter oscillates at a frequency of 15.69 khz as an underwater source of sound used for submarine detection. far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. take the speed of sound in water to be 1450. m/s, and find the angle (in degrees) between the normal to the diaphragm and a line from the diaphragm to the first minimum.

Answers

The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees

To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:

sin(θ) = λ / (diameter)

where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.

First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:

wavelength = speed of sound / frequency

wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)

wavelength = 0.09257 meters (rounded to five decimal places)

Next, we can substitute the values into the formula to find the angle:

θ = \(sin^{(-1)}\) (0.09257 meters / 0.5806 meters)

θ ≈ 9.43 degrees (rounded to two decimal places)

Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.

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Astronauts brought back 500 lb of rock samples from the moon.how many kilograms did they bring back?1 kg = 2.20 lb227 kg227 kg498 kg498 kg500 kg500 kg1,100 kg

Answers

Astronauts brought back 500 lbs rock samples from the moon they brought back 227 kilograms of sample. The correct option is D.

Who, in brief, is an astronaut?

A space traveler is referred to as an astronaut. The term "astronaut" is currently used to designate to anyone traveling on a spaceship, including civilians, whereas it was previously reserved for military-trained experts.

As the astronaut brought 550 lbs sample,

2.20lbs = 1 kg.

1 lbs = 1/2.20

1 lbs = 0.45

so, 500 lbs nearly implies 227kgs.

Thus, the correct option is D.

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5. Find the Fourier coefficients of the periodic ( -5 to 5) function y(t) = -3 when -5

Answers

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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) On January 2, 2019, Helmkamp Company purchased a $30,000 machine. It had an estimated useful life of 5 years and a residual value of $3,000. What is the amount of depreciation expense for 2020, the second year of the asset's life, using the double declining-balance method? (Round intermediary calculations to two decimal places and your final answer to the nearest dollar. )

Answers

The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.


Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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min 8x₁ + 6x₂ subject to
a. 4x₁ + 2x₂ ≥ 20
b. −6x₁ + 4x₂ ≤ 12
c. x₁ + x₂ ≥ 6
d. x₁ + x₂ ≥ 0

Answers

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Find the simplified difference quotient for the given function. [ f(x)=m x^{2}+b x+k ] The simplified difference quotient is
Find the simplified difference quotient. [ f(x)=sqrt{2 x+2} ] The simplified difference quotient is
"

Answers

The simplified difference quotient for the function f(x) = √(2x + 2) is 2 / (√(2(x + h) + 2) + √(2x + 2)).

To find the simplified difference quotient for the function f(x) = mx^2 + bx + k, we need to evaluate the expression (f(x + h) - f(x)) / h and simplify it.

(f(x + h) - f(x)) / h = ((m(x + h)^2 + b(x + h) + k) - (mx^2 + bx + k)) / h

= (mx^2 + 2mxh + mh^2 + bx + bh - mx^2 - bx - k) / h

= (2mxh + mh^2 + bh) / h

= 2mx + mh + b

Therefore, the simplified difference quotient for the function f(x) = mx^2 + bx + k is 2mx + mh + b.

For the function f(x) = √(2x + 2), the difference quotient would be:

(f(x + h) - f(x)) / h = (√(2(x + h) + 2) - √(2x + 2)) / h

To simplify this expression further, we can multiply the numerator and denominator by the conjugate of the numerator to eliminate the square root:

(f(x + h) - f(x)) / h = [(√(2(x + h) + 2) - √(2x + 2)) / h] * [(√(2(x + h) + 2) + √(2x + 2)) / (√(2(x + h) + 2) + √(2x + 2))]

Simplifying the numerator using the difference of squares formula, we get:

(f(x + h) - f(x)) / h = [((2(x + h) + 2) - (2x + 2)) / h] / (√(2(x + h) + 2) + √(2x + 2))

= [(2x + 2h + 2 - 2x - 2) / h] / (√(2(x + h) + 2) + √(2x + 2))

= [2h / h] / (√(2(x + h) + 2) + √(2x + 2))

= 2 / (√(2(x + h) + 2) + √(2x + 2))

Therefore, the simplified difference quotient for the function f(x) = √(2x + 2) is 2 / (√(2(x + h) + 2) + √(2x + 2)).

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A rectangular wing with an aspect ratio of 6 is to generate 3,000lbf of lift when it flies at a speed of 250ft/s at sea level. Determine the length of the wing if its lift coefficient is 1.0. How fast does the plane need to fly to generate the same lift at an altitude of 35,000ft ?

Answers

a. The length of the rectangular wing is 14.16 ft.

b.  The plane needs to fly at a speed of 462 ft/s at an altitude of 35,000 ft to generate the same lift as at sea level.

Determining the air speed

The lift generated by a wing can be calculated using the formula below

L = 1/2 * ρ *\(V^2\) * S * CL

where

L is the lift,

ρ is the density of air,

V is the airspeed,

S is the wing area, and

CL is the lift coefficient.

Given that the lift generated is 3,000 lbf, the airspeed is 250 ft/s, and the lift coefficient is 1.0

3000 lbf = \(1/2 * 0.002378 slugs/ft^3 * (250 ft/s)^2 * S * 1.0\)

\(S = 28.14 ft^2\)

The aspect ratio of the wing is defined as the ratio of the wing span (b) to the wing chord (c). For a rectangular wing

b = AR * c

where AR is the aspect ratio.

Substitute the given aspect ratio of 6 and the wing area calculated above

\(b * c = 28.14 ft^2\\6c^2 = 28.14 ft^2\)

c = 2.36 ft

Therefore, the length of the wing is b = AR * c = 6 * 2.36 ft = 14.16 ft

To find the airspeed required to generate the same lift at an altitude of 35,000 ft

solve for the airspeed required at 35,000 ft:

3000 lbf = \(1/2 * 0.00052 slugs/ft^3 * V^2 * 28.14 ft^2 * 1.0\)

V = 462 ft/s

Hence, the plane needs to fly at a speed of 462 ft/s at an altitude of 35,000 ft to generate the same lift as at sea level.

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draw the graph of the function y= 2x+2​

Answers

Answer:

here is a table sorry i know it is not a graph

Step-by-step explanation:

to put on a graph simply, for example, move 1 right then go 4 up to complete 1,4

x y

1 4

2 6

3 8

4 10

5 12

Hope this helps <3

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