\(4 \frac{1}{9} + 1 \frac{1}{2} \)
\(4 \frac{1}{2} \div \frac{3}{5} \)
need help please​

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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There are 3,276,000 possible license plates in the given country if no repetitions of letters or digits are allowed.

Assuming that there are 26 letters in the alphabet and 10 digits (0-9) available for use:

There are 26 choices for the first letter and 25 choices for the second letter (because we can't repeat the first letter), giving us a total of 26 x 25 = 650 possible letter combinations.

Similarly, there are 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit (because we can't repeat any of the previous digits), giving us a total of 10 x 9 x 8 x 7 = 5,040 possible digit combinations.

To calculate the total number of possible license plates, we can multiply the number of letter combinations by the number of digit combinations:

650 x 5,040 = 3,276,000

Therefore, there are 3,276,000 possible license plates in the given country if no repetitions of letters or digits are allowed.

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A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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So, the power series for the function f(x) is given by the formula f(x) = 1 + x + 4x2 + 3x3 + 0x4 + 0x5 +...,, and we can use this formula to evaluate f(x) for any value of x or to find the general formula for the coefficients of the power series.

The given power series for the function f is f(x) = 1 + (x+1) + (x+1)^2. To evaluate this function for a specific value of x, we need to substitute that value into the expression for f(x). For example, if we want to find f(0), we substitute x=0 into the expression for f(x) as follows:

f(0) = 1 + (0+1) + (0+1)^2
    = 1 + 1 + 1^2
    = 3
Therefore, f(0) = 3.

If we want to find the general formula for the coefficients of the power series for f(x), we can expand the expression (x+1)^2 using the binomial theorem as follows:

f(x) = 1 + (x+1) + (x+1)^2
    = 1 + (x+1) + (x^2 + 2x + 1)
    = x^2 + 3x + 3

Therefore, the coefficients of the power series for f(x) are 1, 1, 1, 0, 0, ... , where the kth coefficient is given by the formula (k=0,1,2,...)

[a_k] = [x^k] f(x) = [x^k] (1 + (x+1) + (x+1)^2)
     = [x^k] (x^2 + 3x + 3)
     = [k=2] 1 + [k=1] 3 + [k=0] 3
     = {1 if k=2, 3 if k=1, 3 if k=0, 0 otherwise}

In other words, the coefficient of x^k in the power series for f(x) is 1 if k=2, 3 if k=1, 3 if k=0, and 0 for all other values of k. This gives us the general formula for the power series for f(x):

f(x) = 1 + (x+1) + (x+1)^2
    = 1 + (x+1) + 3x + 3x^2 + 0x^3 + 0x^4 + ...
    = 1 + x + 4x^2 + 3x^3 + 0x^4 + 0x^5 + ...

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Answer:

y = 18 - 6x / 2 OR y = 9 - 3x

Step-by-step explanation:

Make y the subject of formula.

The mean, Margin of error at 99% confidence level and 99% confidence interval for the given data is 66.75 inches, 2.73 inches and [64.02, 69.48] respectively.

Mean is the arithmetic average of all the observations.

Mean = Sum of all the observation/ Total no.ofobservation

= 66 + 65 + 74 + 66 + 63 + 69 + 63 + 68 / 8

= 534 / 8 = 66.75 inches

Standard error = Standard deviation / √n

= 3 /√8 = 1.06 inches

Margin of error = Z * Standard error

Where Z, is the critical value (corresponding to the desired confidence level)

Using standard normal distribution we get Zvalue roughly around 2.576.

= 2.576 * 1.06 = 2.73 inches

Confidence Interval = ( Mean - Margin of error), (Mean + Margin of error)

= 66.75 - 2.73, 66.75 + 2.73

= [64.02, 69.48]

Therefore, the mean height is 66.75 inches, the margin of error at 99% confidence level is 2.73 inches, and the 99% confidence interval is  [64.02, 69.48].

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The complete question is:

Suppose the mean height in inches of all 9th grade students at one high school estimated. The population standard deviation is 3 inches. The heights of 8 randomly selected students are 66,65, 74, 66, 63, 69,63 and 68.

Find Mean

Margin of error at 99% confidence level

99% confidence interval

Answer:

A =576 pi in ^2

Step-by-step explanation:

Circumference  is given by

C = 2 * pi *r

48 pi = 2 * pi *r

divide by 2 pi

48 pi /2 pi = 2 * pi * r / 2 pi

24 = r

We can find the area by

A = pi r^2

A = pi (24)^2

A =576 pi in ^2

Answer:

576π in^2

Step-by-step explanation:

Circumference of circle (C) = 2πr = 48π in

2πr = 48 π

r = 48π/2π = 24 in

Area of circle (A) = πr^2

r (radius of circle) = 24 in

A = π(24 in)^2 = 576π in^2

Answer: The non solutions of the inequality are A and D.

Step-by-step explanation:

Caroline bought chips and an 8-pack of juice bottles. To find the cost of each juice bottle (xx), we'll use an equation that represents the total cost before tax. This will us an answer of 1.88.

Caroline bought a bag of chips for $2.39 and an 8-pack of juice bottles. Let's represent the cost of each juice bottle with the variable xx. We know that the total cost before tax was $17.43.

To find the cost of each juice bottle, we need to create an equation that represents the total cost before tax. We'll add the cost of the chips to the total cost of the 8-pack of juice bottles, which is 8 times the cost of each bottle (8 * xx).

The equation that represents this context is:

2.39 + 8 * xx = 17.43

Now, we can use this equation to solve for xx, which will give us the cost of each juice bottle.
xx = 1.88

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Answer:

its 4.55 because 4.5 is simple 4.50, so, 4.55 is 0.05 bigger than 4.5

A boat can travel approximately distance 116 miles on 39 number of gallons of gasoline.

To calculate the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

174 miles ÷ 58 gallons x 39 gallons = 116.37 miles

Therefore, a boat can travel approximately 116 miles on 39 gallons of gasoline.

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Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

<95141404393>

Answer:

3

Step-by-step explanation:3x2=6

Answer:

31cm

Step-by-step explanation:

14 + 8 + 9 = 31

Make sure to add the cm on the end!

The perimeter of the triangle is 31cm.

The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.

In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.

In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.

For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.

In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.

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The best way to compare exam score to the number of hours of sleep is by

Histogram, you can easily determine the score using the bars on the histogram at every hours of sleep.

Scatter

Answer:

y+6 = -5/4(x-8)

Step-by-step explanation:

The point slope form of the equation of a line is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y --6 = -5/4 ( x - 8)

y+6 = -5/4(x-8)

Answer:

-1/6f

Step-by-step explanation:

-f+1/6uA=4=

So the sum of the geometric series is 1/17.

To determine whether the geometric series is convergent or divergent, we need to check the absolute value of the common ratio:

|-8/9| = 8/9 < 1

Since the absolute value of the common ratio is less than 1, the series is convergent.

To find the sum of the series, we use the formula for the sum of an infinite geometric series:

sum = a / (1 - r)

where a is the first term and r is the common ratio.

In this case, a = (-8)^0/9^1 = 1/9 and r = -8/9.

Therefore,

sum = (1/9) / (1 - (-8/9)) = (1/9) / (17/9) = 1/17

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Answer:

To determine the missing parts of the triangle, we can use the law of cosines, which states that for a triangle with sides of lengths a, b, and c and angles opposite those sides of A, B, and C, respectively:

c^2 = a^2 + b^2 - 2ab cos(C)

b^2 = a^2 + c^2 - 2ac cos(B)

a^2 = b^2 + c^2 - 2bc cos(A)

Using the given values of a, b, and c, we can solve for the angles A, B, and C.

a = 8.1 in

b = 13.3 in

c = 16.2 in

c^2 = a^2 + b^2 - 2ab cos(C)

cos(C) = (a^2 + b^2 - c^2) / (2ab)

cos(C) = (8.1^2 + 13.3^2 - 16.2^2) / (2 * 8.1 * 13.3)

cos(C) = 0.421

C = cos^-1(0.421)

C ≈ 97.3°

b^2 = a^2 + c^2 - 2ac cos(B)

cos(B) = (a^2 + c^2 - b^2) / (2ac)

cos(B) = (8.1^2 + 16.2^2 - 13.3^2) / (2 * 8.1 * 16.2)

cos(B) = 0.268

B = cos^-1(0.268)

B ≈ 54.8°

We can find angle A by using the fact that the sum of the angles in a triangle is 180°:

A = 180° - B - C

A = 180° - 54.8° - 97.3°

A ≈ 27.9°

Therefore, the missing parts of the triangle are:

A ≈ 27.9°

B ≈ 54.8°

C ≈ 97.3°

So, the answer is option 1.

Answer: B

Solution: Because the line is a dotted line. so print (-3, -1) and (3, 3) , (0, 0) are not the solution, so , answer is (0, 5) choice B.

Answer:

C

Step-by-step explanation:

first way: (easier way)

Plot the points out, points in the blue region are solutions. points on the dotted line are not solutions since it is a dashed line.

(0,5 is in the blue region)

second way:

find the equation of the in-equality:

the line that divides solutions and non-solutions passes through 3,3 and -3,-1

y=mx+b

m=change in y/change in x = (-1-3)/(-3-3) = 2/3

y=2/3x+b

plug x=3, y=3 (from the point "3,3")

3=2/3*3+b

3=2+b

b=1

y=2/3x+1 is the solution of the line.

the in-equality is

y(?)2/3x+1

plug in -5,5, which is a solution (looking at the graph)

5>-7/3

so use >, and not <

y>2/3x+1 is the equation of the in-equality, now just plug the answer choices in to see that

x=0,y=5 is a solution

Answer:

Step-by-step explanation:

One of the Answers is C

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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If a series an is defined by the equations a1 = 2 an+1 = 3 + cos(n) / √n · an, then  Σan is absolutely convergent. Therefore, the answer is: a) absolutely convergent.

To determine whether Σan is absolutely convergent, conditionally convergent, or divergent, we need to analyze the behavior of the series as n approaches infinity.

First, let's look at the absolute value of the terms in the series:

|an| = |2 × (3 + cos(n) / √n · an-1)|
    = |6 + 2cos(n) / √n · an-1|

Next, we can use the Comparison Test by comparing the series to a known convergent or divergent series. Let's compare the series to the p-series:

∑1/n^p

where p = 3/2. This series is known to converge by the p-test.

Now, we can rewrite the absolute value of an in terms of the p-series:

|an| = |6 + 2cos(n) / √n · an-1|
     ≤ |6 + 2 / √n · an-1|          (since cos(n) ≤ 1)
     ≤ 6 + 2 / √n · |an-1|           (using the triangle inequality)

Therefore, we have:

|an| ≤ 6 + 2 / √n · |an-1|

If we take the limit of both sides as n approaches infinity, we get:

lim n→∞ (6 + 2 / √n · |an-1|) / |an-1|
= lim n→∞ (6 / |an-1|) + (2 / (√n · |an-1|))
= 6 / lim n→∞ |an-1| + 0

Since lim n→∞ |an-1| exists (as an is a well-defined series), we can conclude that the limit is a finite number. Therefore, by the Comparison Test, Σ|an| converges.

Finally, we can use the Ratio Test to determine whether Σan converges absolutely or conditionally:

lim n→∞ |an+1 / an|
= lim n→∞ |(3 + cos(n+1) / √(n+1) · an) / an|
= lim n→∞ |(3 + cos(n+1)) / (√(n+1) · an)|

Using L'Hopital's Rule, we can show that the limit of the cosine term is 0, and the limit of the denominator is infinity. Therefore, the limit of the ratio is 0.

Since the limit of the ratio is less than 1, we can conclude that Σan converges absolutely.

Therefore, the answer is: a) absolutely convergent.

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Answer:

so first you would subtract the 10x from the one side so the equation now looks like

2y = -10x + 40

y = −5x + 20

im not sure if this is what you mean but this is how i interpreted it.

if right pls brainly

Answer:

The answer is 11 300.06

\((4 \times 1000) + (3 \times 100) + (6 \times \frac{1}{100}) + (7 \times 1000) \)

\( = 4000 + 300 + \frac{6}{100} + 7000\)

\( = 11 \: 300 + 0.06\)

\( = 11 \: 300.06\)

if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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The probability of a goal given that Wayne took the shot would depend on various factors,

To determine the probability of a goal given that Wayne took the shot, we would need to know the success rate of Wayne's shots.

If we have that information, we can use it to calculate the conditional probability of a goal.

For example,

If we know that Wayne has a 20% success rate on his shots, then the probability of a goal given that Wayne took the shot would be 0.2 (or 20%).

The probability of a goal given that Wayne took the shot would depend on various factors, such as Wayne's skill level, the position he took the shot from, the opposition team's defense, the weather conditions, and many other factors.

If you have more information about these factors or any other relevant details, please provide them, and I will try my best to help you with the calculation.

However,

If we don't have any information on Wayne's success rate, it would be difficult to calculate the probability accurately.

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Answer: The common ratio is 5 because each time, you multiply the previous number by 5 to get the next number.

Step-by-step explanation:

Answer:

52, 61 and 70

Step-by-step explanation:

Given

\(Divisor = 9\)

\(Remainder = 7\)

Required

Determine first 3 possible dividends

The relationship between the \(dividend,\ divisor,\ quotient\ and\ remainder\) is:

\(Dividend = Divisor * Quotient + Remainder\)

Substitute: \(Divisor = 9\) and \(Remainder = 7\)

\(Dividend = 9* Quotient + 7\)

Since the Dividends must be greater than 50, then the values of the quotient will be 5, 6 and 7

So, we have:

\(Dividend = 9* 5 + 7 = 45 + 7 = 52\)

\(Dividend = 9* 6 + 7 = 54 + 7 = 61\)

\(Dividend = 9* 7 + 7 = 63 + 7 = 70\)

Hence, the three numbers are: 52, 61 and 70

The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

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