Let $m$ be the smallest integer whose cube root is of the form $n+r$, where $n$ is a positive integer and $r$ is a positive real number less than $1/1000$. Find $n$.

The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

Here, we have,

Given ,

the circle with radius 8 and center (1, 3).

so, we have,

the center of circle (h,k) = (1,3) and radius, r = 8

we know that,

Equation of the circle = (x-h)² + (y-k)² = r²

so, we get,

⇒ (x - 1)² + (y - 3)² = 64

⇒ x² - 2x + 1 + y² - 6y + 9 = 64

⇒ x² + y² - 2x - 6y - 54 = 0 (on simplification)

Hence, The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

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The upper bound of the probability is P(|X - 3| ≥ 0.44) ≤ 5 / 0.44^2 ≈ 32.37e-2.

By the Chebyshev inequality, for any positive number k, we have:

P(|X - E[X]| ≥ k) ≤ Var[X] / k^2

In this case, we want to find P(|X - 3| ≥ 0.44), which is equivalent to P(X - 3 ≥ 0.44 or X - 3 ≤ -0.44). So we choose k = 0.44 and use the inequality:

P(|X - 3| ≥ 0.44) ≤ Var[X] / 0.44^2

Substituting Var[X] = 5 and solving for the upper bound of the probability, we get:

P(|X - 3| ≥ 0.44) ≤ 5 / 0.44^2 ≈ 32.37e-2

Rounding to six decimal places, we have:

P(|X - 3| ≥ 0.44) ≤ 0.323666

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The exponential function that represents this situation is f(x) = 857000 * (1.134)ˣ

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

Inital subscribers, a = 857000

Rate of increase, r = 13.4%

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

The function of the situation is

f(x) = a * (1 + r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 857000 * (1 + 13.4%)ˣ

So, we have

f(x) = 857000 * (1.134)ˣ

Hence, the function is f(x) = 857000 * (1.134)ˣ

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The probability of event A or B occurring (P(A or B)) is 0.5680, which corresponds to option c. To solve this problem, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Since events A and B are independent, we know that P(A and B) = P(A) * P(B)

Substituting the given probabilities, we get:

P(A or B) = 0.40 + 0.28 - (0.40 * 0.28)
P(A or B) = 0.68 - 0.112
P(A or B) = 0.568

Therefore, the answer is c. 0.5680.

If events A and B are independent, we can find the probability of A or B occurring (P(A or B)) by using the formula: P(A or B) = P(A) + P(B) - P(A) * P(B).

Given the probability of event A (P(A)) is 0.40 and the probability of event B (P(B)) is 0.28, we can plug these values into the formula:

P(A or B) = 0.40 + 0.28 - (0.40 * 0.28) = 0.40 + 0.28 - 0.112 = 0.568.

So, the probability of event A or B occurring (P(A or B)) is 0.5680, which corresponds to option c.

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The surface area and volume of the cube, in inches² is 96 in² and 64 in²

The formula for calculating the surface area and volume of a cube is expressed as:

[tex]\sf S = 6L^2[/tex]

[tex]\sf V=(l\times w)\times h[/tex]

L is the side length of the cube

Given that L = 4 in. Substitute the given parameter into the formula:

[tex]\sf S = 6(4)^2[/tex]

[tex]\sf S = 6(16)[/tex]

[tex]\sf S = 96 \ in^2[/tex]

[tex]\sf V=(4\times4)\times4[/tex]

[tex]\sf V=16\times4[/tex]

[tex]\sf V=64 \ in^2[/tex]

Hence the surface area and volume of the cube, in inches² is 96 in² and 64 in²

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The set of all real numbers for which the function is defined is the domain of the function.

We have the function is:

h(x) = −log(3x−8) + 5

The logarithmic function is defined only for real numbers that are greater than 0. Hence, this implies that (3x-8) must be greater than 0.

=> 3x - 8 > 0

=> 3x > 8

=> x > 8/3

Thus, the domain of the given function is all real numbers that are greater than 8/3.

Domain will be in interval is:

(8/3, infinity)

The values of x for which the function, f(x) is undefined and the limit of the function does not exist is the vertical asymptote of a function.

The given function is undefined when 3x-2 will be equal to 0.

The equation will be in the form and solve for 'x'.

3x - 8  = 0

3x = 8

x = 8/3

The value of x is 8/3.

Therefore, the vertical asymptote of the given function is x=8/3.

Find the limiting value of the given function when x approaches the vertical asymptote,

h(x) = -log(3x - 8) + 5

h(x) = infinity

Therefore, as x  approaches the vertical asymptote,  [tex]h(x)[/tex] →[tex]\infty[/tex]  and as x approaches to positive [tex]\infty[/tex], h(x) →[tex]-\infty[/tex]

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A unit vector u in the direction opposite of ⟨−6,−3,−1⟩ is ⟨6/√46, 3/√46, 1/√46⟩. To find a unit vector in the opposite direction of ⟨−6,−3,−1⟩.

We first need to find the magnitude of this vector:
||⟨−6,−3,−1⟩|| = √((-6)^2 + (-3)^2 + (-1)^2) = √46
Then, to find the opposite direction, we simply negate each component ⟨6, 3, 1⟩. Finally, to find the unit vector in this direction, we divide by the magnitude:
u = ⟨6/√46, 3/√46, 1/√46⟩

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The availability of the web hosting service over the past 100 days is 99.5%.

The term availability means the degree to which a system like web hosting is in specified operable and committable state at the start of a mission.

We will find the downtime first.

Given that:

Hosting provider has been up 99% of the time, the downtime is:

= 100 days x (1 - 0.99)

= 1 day

The total time that the service should have been available is:

= 100 days x 24 hours/day

= 2400 hours

The availability as the ratio of uptime to total time is

= (2400 - 12) / 2400 x 100%

= 0.995 x 100%

= 99.5%.

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If you have 174 assignments and complete 4 assignments per week, it would take you 43 weeks to finish your work. That is roughly 294 days, given that there are approximately 7 days in a week.

If this is the actual amount of work you need to complete, I applaud you mate. Good luck.

Gradients are an important concept in many fields of science and engineering, providing a quantitative measure of how a particular variable changes over space or time.

A gradient is a term used in mathematics and physics to describe the change in a variable over a certain distance. It refers to the rate at which a variable changes as you move from one point to another. In the context of temperature, for example, a temperature gradient would describe how the temperature changes as you move from one location to another. This can help in understanding the spatial distribution of temperature and other variables in various contexts, such as weather forecasting, climate studies, or even engineering applications.

A gradient is a measure of change in a variable, like temperature or pressure, over a specified distance, providing valuable information about the spatial distribution and variations in these variables.

A gradient can be positive, indicating an increase in the variable as you move in a particular direction, or negative, indicating a decrease. In the case of temperature, a positive gradient would mean that the temperature is increasing as you move in a particular direction, while a negative gradient would mean that the temperature is decreasing.

One important application of gradients is in the study of heat transfer. The rate at which heat flows from one location to another is proportional to the temperature gradient between the two locations. In other words, the greater the difference in temperature between two points, the faster heat will flow between them.

Overall, gradients are an important concept in many fields of science and engineering, providing a quantitative measure of how a particular variable changes over space or time.

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We cannot determine the probability of the number of 0's being different from the number of 1's without additional information. The probability depends on the length of the bit string.

However, we can state that if the length of the bit string is odd, then the probability of having an equal number of 0's and 1's is zero, and therefore the probability of having a different number of 0's and 1's is 1. On the other hand, if the length of the bit string is even, then the probability of having an equal number of 0's and 1's is positive, and therefore the probability of having a different number of 0's and 1's is less than 1.

In general, if we let n be the length of the bit string, then the probability of having an equal number of 0's and 1's is given by the binomial coefficient C(n, n/2) divided by 2^n, and the probability of having a different number of 0's and 1's is 1 minus this value.

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Shop A offers 3 rulers for £1.50, which is equivalent to £0.50 per ruler.

Shop B offers 5 rulers for £2, which is equivalent to £0.40 per ruler.

Therefore, Shop B offers the cheapest price.

To purchase 45 rulers, we can buy 9 sets of 5 rulers from Shop B, which would cost:

9 × £2 = £18

Alternatively, we could buy 15 sets of 3 rulers from Shop A, which would cost:

15 × £1.50 = £22.50

Therefore, the cheapest price for 45 rulers is £18 from Shop B.

The cheapest price for 45 rulers would be to buy them from Shop B, which would cost £18.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

First, find the cost per ruler at each shop:

At Shop A, you can buy 3 rulers for £1.50, so the cost per ruler is £1.50 ÷ 3 = £0.50.

At Shop B, you can buy 5 rulers for £2, so the cost per ruler is £2 ÷ 5 = £0.40.

So, Shop B has a cheaper price per ruler.

Next, you need to find the total cost of buying 45 rulers from Shop B.

Since the cost per ruler is £0.40, you can multiply this by the number of rulers to get the total cost:

Total cost = £0.40 × 45 = £18.

Therefore, the cheapest price for 45 rulers is £18 at Shop B.

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The relative frequency of English majors can be calculated as 3/20 = 0.15 or 15%

The relative frequency of English majors in the sample can be calculated by dividing the number of English majors (which is 3) by the total number of students in the sample (which is 20).
So, the relative frequency of English majors can be calculated as:
3/20 = 0.15 or 15%
This means that out of the 20 students in the sample, 15% of them are English majors.
It's worth noting that relative frequency is a way of expressing the proportion of a particular category or value in a dataset, as a percentage of the total. It is a useful tool for understanding the distribution of data and identifying patterns or trends within it. In this case, we can see that English majors are a relatively small proportion of the sample, compared to economics, math, and psychology majors.

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Answer:

top left

Step-by-step explanation:

the line has a similar amount of dots above and below it,

Probability that a student chosen at random from class is not a psychology major = 0.82

Probability is a branch of mathematics which tells about the occurrence of any event.

The sum of the probability of an event to occur and the probability of the same event not to occur is always equal to 1.

Mathematically, we can represent it as mentioned below:

P(E) + P(E') = 1

where P(E) = Probability of an event to occur.

And P(E') = Probability of an event not to occur.

According to the question,

The probability that a student chosen at random from class is a psychology major = P(E) = 0.18

As we know,

P(E) + P(E') = 1

Hence, Probability that a student chosen at random from class is not a psychology major = P(E') = 1 - P(E) = 1 - 0.18 = 0.82

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The given question is incomplete, complete question is:

The probability that a student chosen at random from your class is a psychology major is 0.18.

What is the probability that a student chosen at random from your class is not a psychology major?

The probability of getting between 1 and 9 heads in 10 tosses is approximately 0.998 or 99.8%.

To solve this problem, we need to use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

X is the number of heads

n is the number of tosses

p is the probability of getting a head in a single toss

(n choose k) is the binomial coefficient, which represents the number of ways to choose k heads from n tosses

In this case, we want to find the probability of getting between 1 and 9 heads in 10 tosses, inclusive. So we need to calculate:

P(1 ≤ X ≤ 9) = P(X = 1) + P(X = 2) + ... + P(X = 9)

To simplify the calculation, we can use the complement rule:

P(1 ≤ X ≤ 9) = 1 - P(X = 0) - P(X = 10)

where P(X = 0) and P(X = 10) represent the probabilities of getting 0 and 10 heads, respectively.

Using the binomial distribution formula, we can calculate:

P(X = 0) = (10 choose 0) * 0.5^0 * 0.5^10 = 0.0009765625

P(X = 10) = (10 choose 10) * 0.5^10 * 0.5^0 = 0.0009765625

So:

P(1 ≤ X ≤ 9) = 1 - P(X = 0) - P(X = 10) = 1 - 2 * 0.0009765625 = 0.998046875

Therefore, the probability of getting between 1 and 9 heads in 10 tosses is approximately 0.998 or 99.8%.

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So, the slope (rate of change) between the points (3, 2) and (6, 10) is 8/3 or approximately 2.67.

To find the slope between two points, you can use the "slope formula." The slope formula is given by:
slope (m) = (y2 - y1) / (x2 - x1)
In this case, you are given the two points (3, 2) and (6, 10). Let (x1, y1) = (3, 2) and (x2, y2) = (6, 10).
Step 1: Subtract the y-coordinates: y2 - y1 = 10 - 2 = 8
Step 2: Subtract the x-coordinates: x2 - x1 = 6 - 3 = 3
Step 3: Divide the difference of y-coordinates by the difference of x-coordinates: m = 8 / 3
So, the slope (rate of change) between the points (3, 2) and (6, 10) is 8/3 or approximately 2.67.

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There are a total of 5 ways that paul can make 34 cents using only dimes and pennies.

to find the number of ways paul can make 34 cents using only dimes and pennies, we can use a systematic counting method called "brute force." we will need to consider all possible combinations of dimes and pennies that add up to 34 cents, and count the total number of valid combinations.

we can start by using dimes to see how many of them can fit into 34 cents. since each dime is worth 10 cents, the maximum number of dimes that can be used without going over 34 cents is 3, giving a total value of 30 cents. we can then use the remaining cents to make up the difference. there are several possible ways to do this:

- 4 pennies: this combination uses 3 dimes and 4 pennies.- 3 pennies: this combination uses 3 dimes and 3 pennies.

- 2 pennies: this combination uses 2 dimes and 14 pennies.- 1 penny: this combination uses 1 dime and 24 pennies.

- 0 pennies: this combination uses 0 dimes and 34 pennies. note that this method can be used to solve similar problems with different amounts and types of coins. however, as the number of coins and the values increase, the number of possible combinations can become very large, making the brute force method impractical. in those cases, other methods such as generating   function   s or dynamic programming may be more appropriate.

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The values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .

We have,

When a Triangle is a right angled Triangle then the ratios used to determine the sides and the angles of the triangle are called Trigonometric Ratio.

It is given that in triangle EFG , right angled at F ,

EG = 8 , FG = 2

By Pythagoras theorem

The length of EF is

8² = 2² + EF²

EF = √(64-4) = √60 = 2√15

The value of the trigonometric ratios is

sin E = Perpendicular / Hypotenuse

sin E = 2 / 8 = 1/4

sin G =  2√15 / 8 = √15 / 4

sec G = 1 / cos G = Hypotenuse / Base = 8 / 2 = 4

Therefore the values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .

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complete question:

Right △EFG has its right angle at F, EG=8, and FG=2.

What is the value of the trigonometric ratio of an angle of the triangle?

Drag a value to each box to match the trigonometric ratio with its value.

TanE=

SinG=

SecG=

(4,1/4, 4√15/15, √15/15, √15/4)

(PLEASE ANSWER ASAP, ALSO IF YOU KNOW ANY OF THE OTHER ANSWERS TO THE PRE-CALUCLUS-TRIGONOMETRY SEMESTER TEST 6.04 PLEASE HELP!)

Given that a ≡ b (mod n), it means that a and b have the same remainder when divided by n.

Step 1: Understand the notation a ≡ b (mod n). This notation means that when both a and b are divided by n, they have the same remainder.

Step 2: Apply the definition of modular arithmetic. If a ≡ b (mod n), there exists an integer k such that a = b + kn.

Step 3: Divide both sides of the equation by n. When you do this, you'll see that the remainder of a/n and b/n is the same, since the term kn is divisible by n and does not affect the remainder.

In conclusion, when a ≡ b (mod n), it means that both a and b have the same remainder when divided by n.

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You will need to refill the tank 1 time during the journey.

Distance means the total movement of an object with no regard to direction. It means how much ground an object has covered despite its starting or ending point.

To get number of times the tank needs to be refilled, we will divide the total distance of the journey by the distance the car can travel with a full tank.

Number of times the tank needs to be refilled = Total distance / Distance traveled per tank

Given:

Gas tank capacity = 20 gallons

Distance traveled per gallon = 25 miles

Total distance of the journey = 725 miles

Distance traveled per tank = Gas tank capacity × Distance traveled per gallon

= 20 gallons * 25 miles/gallon

= 500 miles

The number of times the tank needs to be refilled is:

= 725 miles / 500 miles

= 1.45

= 1 times.

Translated question:

A car with a gas tank of 20 gallon can go 25 miles with 1 gallon of gasoline If the tank is full at beginning of a journey of 725 miles, how many How often do you have to refill the tank?

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The matrix format and coefficient matrix of the systems is mentioned below.

a) [tex]\left[\begin{array}{ccc}-2&-3\\-1&4\end{array}\right][/tex]   b)  [tex]\left[\begin{array}{ccc}0&-3\\-2&1\end{array}\right][/tex]   c) [tex]\left[\begin{array}{ccc}-2&0\\1&0\end{array}\right][/tex]    d) [tex]\left[\begin{array}{ccc}-2&-1\\0&-4\end{array}\right][/tex]    e) [tex]\left[\begin{array}{ccc}1&-2\\-2&4\end{array}\right][/tex]    

f) [tex]\left[\begin{array}{ccc}0&-6\\0&6\end{array}\right][/tex]    

In linear algebra, a system of linear equations can be represented in matrix format. Each equation is a linear combination of the variables, and the coefficients are arranged in a matrix known as the coefficient matrix. The right-hand side of the equations is also arranged in a matrix, called the constant matrix.

a) The system x′ = −2x − 3y, y′ = −x + 4y can be represented in matrix format as:

| x′ | | -2 -3 | | x |

| y′ | = | -1 4 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}-2&-3\\-1&4\end{array}\right][/tex]  

b) The system x′ = −3y, y′ = −2x + y can be represented in matrix format as:

| x′ | | 0 -3 | | x |

| y′ | = | -2 1 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}0&-3\\-2&1\end{array}\right][/tex]  

c) The system x′ = −2x, y′ = x can be represented in matrix format as:

| x′ | | -2 0 | | x |

| y′ | = | 1 0 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}-2&0\\1&0\end{array}\right][/tex]    

d) The system x′ = −2x − y, y′ = −4y can be represented in matrix format as:

| x′ | | -2 -1 | | x |

| y′ | = | 0 -4 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}-2&-1\\0&-4\end{array}\right][/tex]    

e) The system x′ = x − 2y, y′ = −2x + 4y can be represented in matrix format as:

| x′ | | 1 -2 | | x |

| y′ | = | -2 4 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}1&-2\\-2&4\end{array}\right][/tex]    

f) The system x = −6y, y′ = 6y can be represented in matrix format as:

| x | | 0 -6 | | y |

| y′ | = | 0 6 | * | y |

The coefficient matrix is the 2x2 matrix on the right-hand side of the equation, which is:

[tex]\left[\begin{array}{ccc}0&-6\\0&6\end{array}\right][/tex]    

In summary, each system of linear equations can be represented in matrix format, and the coefficient matrix is simply the matrix of coefficients on the right-hand side of the equation.

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Thus, the integral of xe^yds on the circle from (2,0) to (5,4) is equal to 207/8 e^4 - 23/8.

To solve this problem, we will use the line integral formula:
∫(P dx + Q dy) = ∫(P(x,y) dx + Q(x,y) dy)

where P and Q are the x and y components of the vector field F(x,y) = (xe^y, 0).

First, we need to parameterize the given circle. We can do this by using the parametric equations:

x = 2 + 3t
y = 4t

where 0 ≤ t ≤ 1.

Next, we can compute the differential ds:

ds = √(dx^2 + dy^2) = √(9 + 16) dt = 5 dt

Now, we can substitute the parametric equations and ds into the line integral formula:

∫(P dx + Q dy) = ∫(xe^y dx) = ∫(xe^y dx/dt dt) = ∫((2+3t)e^(4t) 3 dt)

Evaluating the integral gives:

∫(xe^yds) = ∫((2+3t)e^(4t) 3 dt) = 207/8 e^4 - 23/8

Therefore, the integral of xe^yds on the circle from (2,0) to (5,4) is equal to 207/8 e^4 - 23/8.

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The probability that at least one bulb out of 12 will stop working during holiday season making all of lights go out on string is given by 0.2153.

Number of bulbs working throughout the holiday season = 12

Chance of each bulb working throughout the holiday season = 98%

Let A be the event that at least one bulb stops working during the holiday season, .

Making all of the lights go out, and let B be the event that all bulbs work throughout the holiday season.

Find P(A), the probability of event A.

Use the complement rule to find P(A),

P(A) = 1 - P(B)

To find P(B), we need to calculate the probability that each of the twelve bulbs works throughout the holiday season,

0.98¹² = 0.7847

So, the probability that all bulbs work throughout the holiday season is 0.7847.

This implies,

P(A) = 1 - P(B)

       = 1 - 0.7847

       = 0.2153

Therefore, probability that at least one bulb will stop working during  holiday season, making all of the lights go out on the string is 0.2153.

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In this exercise, we are given a vector x and two different bases B and C, and we are asked to find the coordinate vectors of x with respect to each of these bases, as well as the change of basis matrices between B and C, and between C and B.

To find the coordinate vectors of x with respect to bases B and C, we need to express x as a linear combination of the basis vectors in each of these bases. This gives us the column vectors [x]B and [x]C, respectively.

To find the change of basis matrix from B to C, we need to express each basis vector in B as a linear combination of the basis vectors in C, and then arrange the coefficients in a matrix. Similarly, to find the change of basis matrix from C to B, we need to express each basis vector in C as a linear combination of the basis vectors in B and arrange the coefficients in a matrix.

Using the change of basis matrix from B to C, we can compute [x]C by multiplying [x]B by this matrix. Similarly, using the change of basis matrix from C to B, we can compute [x]B by multiplying [x]C by this matrix. We can compare our answers to the coordinate vectors obtained directly from the basis vectors to check our calculations.

Overall, this exercise tests our understanding of coordinate vectors and change of basis matrices, which are important concepts in linear algebra. By working through these computations, we can gain a deeper intuition for how vectors behave under different bases, and how we can use change of basis matrices to switch between different coordinate systems.

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The surface area of the prism is equal to 98 square feet.

To calculate the surface area of a triangular prism with a rectangular base, we need to determine the areas of the rectangular and triangular faces and add them together.

area of one triangle face = 1/2 × 3.5ft × 4ft = 7 ft²

area of the two triangle faces = 2 × 7 ft² = 14 ft²

area of one rectangle face = 7ft × 4ft = 28 ft²

area of the three rectangle faces = 3 × 28 ft² = 84 ft²

surface area of the prism = 14 ft² + 84 ft²

surface area of the prism = 98 ft²

Therefore, the surface area of the triangular prisms is calculated to be equal to 98 square feet.

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The  two linearly independent solutions to the homogeneous portion of the differential equation are:

y_1 = 1

y_2 = t

The homogeneous portion of the differential equation is obtained by setting the right-hand side equal to zero:

de'' = 0

The characteristic equation is:

r^2 = 0

which has a repeated root r = 0. Therefore, the general solution to the homogeneous equation is:

y_h = c_1 + c_2 t

where c_1 and c_2 are arbitrary constants.

To find two linearly independent solutions, we can choose two different values for c_1 and c_2. For example, we can choose c_1 = 1 and c_2 = 0, which gives:

y_1 = 1

and we can choose c_1 = 0 and c_2 = 1, which gives:

y_2 = t

Both of these solutions are linearly independent because they are not multiples of each other. Therefore, the two linearly independent solutions to the homogeneous portion of the differential equation are:

y_1 = 1

y_2 = t

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Answer:

8 people went

Step-by-step explanation:

A school is going to the movies. The tickets cost 4 dollars per person with a 5-dollar entry fee. If the trip costs 37 dollars, how many people went?

The Lorenz curve is a graphical representation of income distribution in a country. The function f(x) measures the cumulative percentage of total income earned by the corresponding percentage of the population ranked by income.

Therefore, if the lowest 1/10 of the population earns 1/100 of the total income earned by everyone in the country, then f(1/10) would represent the cumulative percentage of total income earned by the bottom 10% of the population.

The Lorenz curve is a graphical representation of income distribution in a country. It measures the cumulative percentage of total income received by the cumulative percentage of the population.

In this case, if the lowest 1/10 of the population earns 1/100 of the total income, then f(1/10) represents the cumulative percentage of income earned by the lowest 10% of the population.

So, for this country, f(1/10) = 1/100. This means that the lowest 10% of the population earns 1% of the total income in the country.

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