what is 57 feet in cm?

No, the probability that a continuous random variable equals a certain value is zero does not imply that the probability of finding even or odd values is also zero.

The reason for this is that even and odd values are not specific points in the continuous probability distribution, but rather sets of points. For example, if we consider a uniform distribution over the interval [0, 1], the probability of any particular point in the interval is zero, including both even and odd values. However, the probability of finding an even value in the interval is 1/2, since half of the values in the interval are even. Similarly, the probability of finding an odd value is also 1/2. Therefore, the fact that the probability of a continuous random variable taking a certain value is zero does not imply anything about the probability of finding even or odd values.

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The slope and the intercept are interpret as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The variables for this problem are given as follows:

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Answer:

61

Step-by-step explanation:

the slope and y-intercept of the line of the fit equation through (0, 61) and (6, 91), which is given as $y=5x+61$.The slope is the rate at which one variable changes with respect to another variable. Here, the slope of the equation of the line of fit is 5, which means that for every additional hour spent studying, the test score will increase by 5. Thus, the slope of 5 shows a positive correlation between the hours spent studying and the test scores. A higher number of hours spent studying will likely result in a higher test score. The Y-intercept is the value of y when x=0. Here, the y-intercept of the equation of the line of fit is 61, which means that a student who does not study at all can still expect to score 61 on the test.

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9 inches is equal to 22.86 centimeter

To convert 1 inches to cm, we can use the following formula:

1 inch = 2.54 cm

The conversion factor is 2.54

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in cm = conversion factor × The length in inches

Substitute the values in the equation

9 inches = 9 × 2.54 cm

Multiply the numbers

= 22.86 cm ( rounded to two decimal places )

Therefore, 9 inch is 22.86 cm

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To determine how many miles Theden needs to hike on the third day to finish the trail, we can subtract the distance he hiked on the first two days from the total trail distance:

Total trail distance = 40 miles

Distance hiked on first day = 12.8 miles

Distance hiked on second day = 16.9 miles

Total distance hiked on first two days = 12.8 + 16.9 = 29.7 miles

Distance left to hike on the third day = 40 - 29.7 = 10.3 miles

Therefore, Theden needs to hike 10.3 miles on the third day to finish the trail.

Your rate is 52.5 miles per hour, calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).

To calculate this, take the total distance traveled (415 miles) and subtract the distance from Seattle at the start of the journey (215 miles). This gives you the total distance traveled, which is then divided by the total time taken (8 hours), giving you a rate of 52.5 miles per hour.

To better understand this concept, imagine driving from Seattle to Los Angeles. You know that Los Angeles is 800 miles from Seattle, and if you drive for 16 hours, you will reach your destination. In this case, your rate would be

The same principle applies here, which is why you can use the same formula to calculate your rate.

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Answer and Step-by-step explanation:

To find "b" and write the equation in standard form, we need to use the given points and the general form of the function:

h(x) = (1/b(x - h))³ + k

First, we can use the point (-5, -5):

-5 = (1/b((-5) - h))³ + k

Next, we can use the point (1, -2):

-2 = (1/b((1) - h))³ + k

Finally, we can use the point (-2, -3):

-3 = (1/b((-2) - h))³ + k

We can use these three equations to solve for "b" and "h". One way to do this is to subtract the third equation from the first equation, which gives:

2 = (1/b(3 - h))³

Taking the cube root of both sides and multiplying by b gives:

b³ = 1/8

b = 1/2

Now that we have found "b", we can use the second equation to solve for "h":

-2 = (1/2(1 - h))³ + k

Simplifying this equation and using the fact that k is a constant, we get:

-8 = (1 - h)³ + 8k

-1 = (1 - h)³ + k

We can use this equation along with the point (-5, -5) to solve for "h":

-5 = (1/2((-5) - h))³ + k

-5 = (1/2(-5 - h))³ + k

-5 = (1/2(-5 - h))³ + (-1/8)

-40 = (-5 - h)³

Taking the cube root of both sides and multiplying by -1 gives:

h = 5 - ∛(-40)

h = 5 + 2∛10

Now we have found "b" and "h", and we can use them to write the equation in standard form. First, we substitute the value of "b" into the general form of the function:

h(x) = (1/(1/2(x - (5 + 2∛10))))³ + k

Simplifying this expression and using the fact that k is a constant, we get:

h(x) = 8(x - (5 + 2∛10))³ + k

This is the equation in standard form. We could expand and simplify the expression further, but this is the final answer.

Answer:

Step-by-step explanation:

To solve the problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the principal amount (the initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

We can use this formula for each of the two years and then add the results to find the final amount.

For the first year, we know that the principal (P) is £12000, the time (t) is 1 year, and the final amount (A) is £12336. We do not know the interest rate (r) or the compounding frequency (n), but we can solve for them using the given information.

Using the formula, we have:

£12336 = £12000(1 + r/n)^(n*1)

Dividing both sides by £12000, we get:

1.028 = (1 + r/n)^n

Taking the natural logarithm of both sides, we get:

ln(1.028) = n*ln(1 + r/n)

Solving for n, we get:

n = ln(1.028) / ln(1 + r/n)

For the second year, we know that the principal (P) is £12336 (the final amount from the first year), the time (t) is 1 year, the interest rate (r) is x/2%, and the compounding frequency (n) is the value we just calculated.

Using the formula, we have:

A = £12336(1 + (x/2)/n)^(n*1)

Substituting the value we calculated for n, we get:

A = £12336(1 + (x/2)/ln(1.028))^(ln(1.028)*1)

Simplifying, we get:

A = £12336(1 + (x/2)/ln(1.028))^ln(1.028)

So the value of Jean's investment at the end of 2 years is the result of compounding the interest earned in the first year and second year, which is:

Final amount = £12336(1 + (x/2)/ln(1.028))^ln(1.028) * (1 + x/200)

Note that we use the annual interest rate of x/2% in the second year, but we need to express it as a decimal by dividing by 100. Similarly, we use x/200 instead of x/100 to express the interest rate over the 2-year period.

Answer:

£12 508.70

Step-by-step explanation:

Jean invests £12 000 in an account paying compound interest for 2 years.

In the first year the rate of interest is x%.

At the end of the first year the value of Jean’s investment is £12 336.

​In the second year the rate of interest is: x/2 %

​What is the value of Jean’s investment at the end of 2 years?

First, we find the interest rate for the first year.

Amount at beginning: £12 000

Amount after accruing interest for 1 year: £12 336

Amount of accrued interest in 1 year: £12 336 - £12 000 = £336

Interest rate:

£336 is what percent of £12 000?

percent = part/whole × 100%

percent = £336/£12 000 × 100%

percent = 2.8%

The interest rate of the first year was 2.8%.

The interest rate of the second year is 1/2 × 2.8% = 1.4%.

100% + 1.4% = 101.4% = 0.0104

Value after the second year, which is starting at £12 336 and earning 1.4% for 1 year:

1.0104 × £12 336 = £12 508.70

16 + 7.86 = 23.86cm

The perimeter of an object is the distance around the object or figure.

we are given all the sides so we have to find the perimeter of the semi circle which is 7.86cm

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The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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Only graph B represents a proportional relationship.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Graph A shows a non-proportional relationship because as x increases, the corresponding y values do not increase or decrease at a constant rate.

Graph B shows a proportional relationship because as x increases, the corresponding y values increase at a constant rate.

Therefore, The slope of graph B is constant and represents the constant of proportionality between x and y.

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The volume of the solid generated when the region bounded by and is revolved about the​ x-axis is (32/5)π units and 8π units.

Volume of the solid:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes needed to fill a solid. If we count the unit cube in a solid, we have 30 unit cubes, so the volume is: 2 units 3 units 5 units = 30 cubic units

According to the Question:

The rose region is revolving about the x-axis and y-axis:

1)Volume = [tex]\pi \int\limits^2_0 {x^4} \, dx[/tex]

                = [tex]\pi \int\limits^2_0 {y^4} \, dx[/tex]

                = π{ (32/5)-0}

                = (32/5)π units.

2)Volume = [tex]\pi \int\limits^4_0 {[(2^2)_2 - (\sqrt{y^2)_1 } } \, dy[/tex]

                = [tex]\pi \int\limits^4_0 {[4 -y] } } \, dy[/tex] = 8π dy

Complete Question:

How do I find the volume of the solid generated by revolving the region bounded by  y = x², y=0, and x = 2 about the x-axis?

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Answer: 31.5

Step-by-step explanation:  
6*4=24 (Shaded Rectangle)

3*5=15  15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5

The probability of at least 30 left-handed individuals in a sample of 100

What is boinomial probability ?

Binomial probability refers to the probability of a particular number of "successes" occurring in a fixed number of independent trials. In other words, it calculates the probability of a specific outcome happening a certain number of times in a given set of trials.

The binomial probability formula is:

P(X=k) = (n choose k) *[tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex]

where:

P(X=k) is the probability of getting k successes in n trials

n is the number of trials

k is the number of successes

p is the probability of success on a single trial

(n choose k) is the binomial coefficient, which represent

He probability of selecting at least 30 left-handed individuals out of a sample of 100 adults in the US can be calculated using the binomial probability formula with x counting the number who are left-handed.

However, we must be careful when applying the formula to this problem because the sample is selected without replacement. The binomial distribution assumes that each trial is independent of the others, which is not the case when sampling without replacement.

In cases where the sample size is much smaller than the population size, the effect of not replacing the selected individuals is negligible. However, when the sample size is a substantial portion of the population size, as in this case, the probability of selecting an individual who is left-handed changes after each selection. This means that the probabilities of each selection are not independent, and the binomial formula cannot be used.

Therefore, to accurately calculate the probability of at least 30 left-handed individuals in a sample of 100 adults selected in the US without replacement, we need to use a different probability distribution, such as the hypergeometric distribution.

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Answer:

15m3 + 16m5

Step-by-step explanation:

3m3 + 3m3 + 9m3 = 15m3

11m5 + m5 = 16m5

Answer:

-10m^5-3m^3

Step-by-step explanation:

3m^3+3m^3=6m^3-9m^3=-3m^3

-11m^5+m^5=-10m^5

Mover the larger exponent first so -10m^5-3m^3

Rhombus question:

Opposite sides are equal so we will set x+25 and 3x-55 equal to each other.

x+25=3x-55

Subtract x to both sides:

25=2x-55

Add 55 to both sides:

2x=80

Divide 2 to both sides:

x=40

Now we will find the value of y. Remember a triangle adds up to 180 degrees, so we will add all 3 angles and set it equal to 180. The square means 90 degrees.

40+25+90+y=180

Combine like terms:

155+y=180

Subtract 155 to both sides:

y=25

Rectangle question:

Given that AE=x+16 and EC=2x-4. To solve this, you will add these two given lines together because AE+EC=AC.

x+16+2x-4

Combine like terms:

3x-12

l & m, solve for x:

Using alternate angles, we will know that 95 and x are supplementary, so they add up to 180.

95+x=180

Subtract 95 to both sides:

x=85

n & m:

Use alternate angles, think about zig zag:

1=8, 2=6, 4=5, 3+5=180

l & m solve for y:

First we will need to find the x value to solve for y. Using alternate angles, the two expressions are equal. So set the equal.

29x+2=30x-1

Subtract 29x to both sides:

2=x-1

Add 1 to both sides:

x=3

Now we will solve for y. Using alternate angles, both expressions are equal to y, we can pick any.

30x-1=y

Substitute:

30(3)-1=y

Calculate:

90-1=y

Calculate:

y=89

hope this helped!

Here’s a tip if you want answers fast. Try putting one problem in one question post. People tend to avoid posts with too much work. Or you can raise the points.

The distance between two points in a coordinate plane can be found by the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

To calculate the distance between two points in a coordinate plane, you can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

For example, if you want to find the distance between the points (2, 3) and (5, 7), you would plug in the values as follows:

d = sqrt((5 - 2)^2 + (7 - 3)^2)

d = sqrt(3^2 + 4^2)

d = sqrt(9 + 16)

d = sqrt(25)

d = 5

Therefore, the distance between two points is d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

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The amount of milk the 3 students drink is 4 11/12 cups of milk

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

Dasia = 2 3/4

Taniya = 1 1/6

Calixte = 8/8

The amount of milk the 3 students drink is calculated as

Total = 2 3/4 + 1 1/6 + 8/8

Evaluate the sum

Total = 4 11/12

Hence, the total is 4 11/12 cups of milk

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The measure of the angles required are,

Angle A = 58.3deg

Angle B = 121.7deg

If two angles sum up to 180 degrees, they are referred to as supplementary angles. When paired, supplementary angles result in a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this case, Angles 1 and 2 are referred to as "supplements" of one another.

Supplementary angles, by definition, add to to a sum of 180deg.

So what we know is:

Angle B + Angle A = 180deg

Angle B - 63.4deg = Angle A

By substitution:

Angle B + (Angle B - 63.4deg) = 180deg

Using the commutative property of addition, we can re-write the equation as:

(Angle B + Angle B) - 63.4deg = 180deg

We can add 63.4deg to both sides of the equation:

(Angle B + Angle B) - 63.4deg + 63.4deg = 180deg + 63.4deg

By simplifying, that gives us:

2(Angle B) = 243.4deg

Dividing both sides of the equation by 2, we can determine the measure of Angle B:

Angle B = 243.4deg/2 = 121.7deg

Now we have the measure of one of the angles, which we can plug back into our first equation:

Angle B + Angle A = 180deg

121.7deg + Angle A = 180deg

Subtracting 121.7deg from both sides, we get:

Angle A = 180deg - 121.7deg = 58.3deg

There’s your answer:

Angle A = 58.3deg

Angle B = 121.7deg

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The probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277 and the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.

(a) Let X be the number of people out of 20 who have the XBB.1.5 variant. X follows a binomial distribution with parameters n=20 and p=0.7. We need to find the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have this specific variant, which can be expressed as P(X ≤ 12).

Using a binomial distribution table or a calculator, we can calculate:

P(X ≤ 12) = ΣP(X=k), for k=0 to 12

P(X ≤ 12) =  0.2277

Therefore, the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277.

(b) Let Y be the number of patients tested until exactly 5 are found to have the XBB.1.5 variant. Y follows a negative binomial distribution with parameters r=5 and p=0.7. We need to find the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the new variant, which can be expressed as P(Y ≥ 8).

Using the negative binomial distribution formula, we can calculate:

P(Y ≥ 8) = ΣP(Y=k), for k=8 to infinity

P(Y ≥ 8) = Σ [(k-1) choose (r-1)] p^r (1-p)^(k-r), for k=8 to infinity

This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(Y ≥ 8) ≈ 0.99872

Therefore, the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.

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The conversion of 71kg to lbs is nearly equal to 156.53 lbs.

The kilogramme (symbol: kg)  is a SI unit of mass.

The pound (symbol: lb) is also the unit of mass.

One pound is nearly equal to 0.45359237 kilograms.

Here we want to convert 71 kilograms to pounds,

As we know that:

1 kilogram equal to 2.20462 pounds

So, for conversion of 71 kg into pound

Multiplying 71 by 2.20462

71 kilograms = 71 x 2.20462 pounds

After simplifying the calculation,

We get:

71 kilograms = 156.52802 lbs

Therefore,  the conversion of 71 kilograms is equal to nearly  156.52802 lbs (rounded to two decimal places).

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if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

A relation is a function if it has only One y-value for each x-value.

Given that f(x) = ax² + bx + c for all x and

if f( -3 ) = 0 and

f( 1) = 0

We need to find the value of b+c

f(-3)=a(-3)² + b(-3) + c

f(-3)=9a-3b+c=0

9a-3b+c=0

We need to find the value of b + c, which is equal to -a.

From equation (2), we have:

a = -b - c

Substituting this value of a in equation (1), we get:

9(-b - c) - 3b + c = 0

-12b - 8c = 0

3b + 2c = 0

b = -(2/3)c

Substituting this value of b in equation (2), we get:

a + (-(2/3)c) + c = 0

a = (1/3)c

Therefore, b + c = -(2/3)c + c = (1/3)c

Hence, if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

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To summarize, the transformations from f(x) to g(x) and h(x) can be described as follows:

g(x) = f(x) - 1: a vertical shift downward by 1 unit

h(x) = f(x - 4): a horizontal shift to the right by 4 units

What did we do?

Starting with the function f(x) = -2x + 6, let's consider the transformations to the functions g(x) = f(x) - 1 and h(x) = f(x - 4).

For g(x) = f(x) - 1, we can see that the function is shifted downward by 1 unit from f(x). This means that every y-value of f(x) will be decreased by 1 to obtain the corresponding y-value of g(x). Therefore, the graph of g(x) will be the same as the graph of f(x), but shifted down by 1 unit.

For h(x) = f(x - 4), we can see that the function is shifted to the right by 4 units from f(x). This means that the input to f(x) will be increased by 4 to obtain the corresponding input to h(x). Therefore, the graph of h(x) will be the same as the graph of f(x), but shifted to the right by 4 units.

To summarize, the transformations from f(x) to g(x) and h(x) can be described as follows:

g(x) = f(x) - 1: a vertical shift downward by 1 unit

h(x) = f(x - 4): a horizontal shift to the right by 4 units

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The standard deviation of the content weight distribution is historically 0.04 fluid ounces. a mean setting of 12 ounces will result in 50% of the bottles having less than the advertised weight. This statement is false.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Since the weight of the contents in the bottles follows a normal distribution, we can use the standard normal distribution to calculate the proportion of bottles that have contents below the advertised weight.

Let's define the random variable X as the weight of the contents in a bottle.

Then, we can standardize X by subtracting the mean weight (12 fluid ounces) & dividing by the standard deviation (0.04 fluid ounces):

Z = (X - μ) / σ

where μ = 12 and σ = 0.04.

We want to find the proportion of bottles that have contents below 12 fluid ounces, which is equivalent to finding the probability that Z is less than 0 -

P(Z < 0) = 0.5

This means that 50% of the bottles will have contents below the advertised weight if the mean setting is 12 ounces.

However, the problem states that state law requires that no more than 0.3% of the bottles can have contents below the advertised weight.

This means that we need to find the probability that Z is less than some value such that the area under the standard normal distribution to the left of that value is 0.003.

We can find this value using a standard normal distribution table or calculator -

P(Z < z) = 0.003  

z ≈ -2.88

Therefore, the mean setting needs to be adjusted such that the mean weight of the contents is at least 12 + (-2.88) x 0.04 = 11.856 fluid ounces to ensure that no more than 0.3% of the bottles have contents below 12 fluid ounces.

Therefore, the statement in false.

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The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]

y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]

To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:

X' = AX, where X = [x y], A = [22 60; -6 -16]

The matrix exponential of A can be calculated as follows:

[tex]e^{(At)}[/tex] = I + At + [tex]\frac{(At)^{2}}{2!}[/tex] + [tex]\frac{(At)^{3}}{3!}[/tex] + ...

where I is the identity matrix and t is the variable of integration.

We can substitute A and t = 1 into the formula to get:

[tex]e^{A}[/tex]= I + A + [tex]\frac{(A)^{2}}{2!}[/tex] + [tex]\frac{(A)^{3}}{3!}[/tex]+ ...

= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...

= [1 + 22 + [tex]\frac{44}{2!}[/tex] - [tex]\frac{256}{3!}[/tex]*60 + [tex]\frac{192}{2!}[/tex] - [tex]\frac{768}{3!}[/tex];

-6 + [tex]\frac{(-6)}{2!}[/tex] + [tex]\frac{96}{3!}[/tex] - 16 + [tex]\frac{(-104)}{2!}[/tex]+ [tex]\frac{272}{3!}[/tex]]

= [[tex]\frac{29}{3}[/tex] [tex]\frac{102}{3}[/tex];

[tex]\frac{-13}{3}[/tex]  [tex]\frac{-4}{3}[/tex] ]

Now we can use the initial conditions to find the constants of integration. We have:

X(0) = [x(0) y(0)] = [5 3]

So,

[[tex]e^{A}[/tex]] [[tex]c_{1}[/tex]] = [5]

[[tex]c_{2}[/tex]] [3]

Multiplying both sides by the inverse of [tex]e^{A}[/tex], we get:

[[tex]c_{1}[/tex]] = [29/3 102/3]^(-1) [5]

[[tex]c_{2}[/tex]] [-13/3 -4/3] [3]

Solving this system of linear equations, we get:

[tex]c_{1}[/tex] = -4/3

[tex]c_{2}[/tex] = 2/3

Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]

y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]

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The value of the constant k is 12.

By Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, and the product of the roots is c/a. Therefore, we have:

m + (m-1) = 7 (sum of the roots)

m(m-1) = k (product of the roots)

Expanding the first equation, we get:

2m - 1 = 7

Solving for m, we get:

m = 4

Substituting m = 4 into the second equation, we get:

4(4-1) = k

Simplifying, we get:

12 = k

Therefore, the constant k is equal to 12.

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The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.

Number of dollars in one hour is equal to 37 dollars.

Relation between year and hour .

1 year = 12 months

1 month = 31, 30 or 28 days

Total number of days in a year = 365 days

Number of hours in 1 day = 24 hours

Number of hours in 365 days = ( 365 × 24 ) hours

                                                 = 8760 hours

In 1 hour = 37 dollars

⇒ 8760 hours = ( 37 × 8760 ) dollars

⇒ 8760 hours = ( 324,120 ) dollars

⇒ 1year = (  324,120  ) dollars

Therefore, the number of dollars in a year is equal to  324,120 dollars.

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Check the picture below.

The value of x such that  the angles LFDE and LFDB are supplementary is:

17º

If LFDE and LFDB are supplementary, then their sum is 180°. Therefore, we can write an equation using this information:

m∡FDE + m∡LFDB = 180°

Substituting the given expressions for m∡FDE and m∡LFDB, we get:

(3x - 15)° + (5x + 59)° = 180°

Combining like terms and simplifying, we get:

8x + 44 = 180

Subtracting 44 from both sides of the equation, we get:

8x = 136

Dividing both sides of the equation by 8, we get:

x = 17

Therefore, the value of x that makes LFDE and LFDB supplementary is 17.

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Answer:

Gram.

Step-by-step explanation:

Triangles

Looking at the image, It is safe to say there are two similar triangles having similar base and sides there.

Triangle BAC has the same base as Triangle DAC

Therefore, the vertices of the angle B is equivalent to the vertice of angle D

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