i need help pls hurry.thsnks

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Answer:

the slope is 11 and the y intercept is 6

y = mx + b

m= 11

b= 6

In this utility function, the term 6X represents the utility derived from consuming good X, while the term -Y represents the disutility or loss of satisfaction from consuming good Y. By subtracting Y from 6X, Chloe's preferences reflect the substitution relationship she perceives between the two goods.

A utility function describes an individual's preferences and the satisfaction they derive from consuming different goods. In Chloe's case, she believes that 6 units of good X can fully replace the satisfaction derived from consuming 1 unit of good Y. Therefore, we can construct a utility function based on this substitution ratio.

Let's denote the quantity of good X as X and the quantity of good Y as Y. Since Chloe believes that 6 units of X perfectly substitute 1 unit of Y, we can express her utility function as:

U(X, Y) = 6X - Y

It's important to note that utility functions are subjective and specific to an individual's preferences. Chloe's utility function captures her belief that 6 units of X are equivalent to 1 unit of Y, but it may not hold true for other individuals with different preferences or perceptions of substitutability between the goods.

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Answer:

The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180. A polygon with 18 sides has an interior angle sum of 2880 degrees.

Step-by-step explanation:

Answer:

2880 degrees.

Step-by-step explanation:

The sum of the measures of any polygon is the number of sides minus two multiplied by 180. A polygon with 18 sides has an interior angle sum of 2880 degrees.

Hope this helps!

Brain-List?

Thus, the value of the function for the given Laplace transformation is:

y(t)=(1/6)*∫[0,t]sin(6(t-u))du+30u(t-3)sin(6(t-3))

To take the Laplace transform of both sides of the given differential equation, we will use the fact that L{y''(t)}=s^2Y(s)-s*y(0)-y'(0) and L{g(t)}=G(s), where G(s) is the Laplace transform of g(t).

Thus, we have:
s^2Y(s)-s*0-0+36Y(s)=G(s)

Simplifying:
Y(s)(s^2+36)=G(s)

Solving for Y(s):
Y(s)=G(s)/(s^2+36)

To take the inverse Laplace transform of both sides, we will use the fact that L^-1{F(s)/s}=∫[0,∞]f(t)dt and L^-1{F(s)/(s^2+w^2)}=1/w*sin(wt).

Thus, we have:
y(t)=L^-1{Y(s)}=L^-1{G(s)/(s^2+36)}

Breaking up G(s) into two terms based on the definition of g(t), we have:
y(t)=L^-1{(t/(s^2+36))+(30e^(-3s)/(s^2+36))}

Taking the inverse Laplace transform of the first term:
L^-1{(t/(s^2+36))}=∫[0,t](1/6)*sin(6(t-u))du

Taking the inverse Laplace transform of the second term:
L^-1{(30e^(-3s)/(s^2+36))}=30u(t-3)sin(6(t-3))

Thus, our final solution for y(t) is:

y(t)=(1/6)*∫[0,t]sin(6(t-u))du+30u(t-3)sin(6(t-3))

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Answer:

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

Step-by-step explanation:

Total yards of fabrics = 6 yards

you need to cut it in two pieces where one is two feet longer than the other.

First piece= x feet

Second piece= x+2 feet

Convert 6 yards to feet

6 yards = 18 feet

First piece + second piece = total piece of fabrics

x + (x+2) = 18

x + x + 2 = 18

2x + 2 = 18

2x = 18 - 2

2x = 16

Divide both sides by 2

x = 16 / 2

x = 8 feet

8 feet = 2.66667 yards

x + 2

= 8 + 2

= 10 feet

10 feet = 3.33333 yards

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

Answer: yes

Step-by-step explanation:

It is because for every x value there is a y and the x value does not repeat to any y values.

Answer:

No because the slope isnt constant, the y changes higher and higher while the x stays constant

Step-by-step explanation:

Hope this helps!:)

Answer:

7.28011

d=(−7−(−5))2+(−6−1)2−−−−−−−−−−−−−−−−−−−−√

d=(−2)2+(−7)2−−−−−−−−−−−√

d=4+49−−−−−√

d=53−−√

d=7.28011

Answer:

Step-by-step explanation:

distance= root (x2-x1)^2 + (y2-y1)^2

= root (-7+5)^2+(-6-1)^2

= root 4+49

= root 53

= 7.28

(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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The type of set that allows you to position rollers diagonally and set from multiple points of origin is an oblong set.

An oblong set is a type of parallel set consisting of two parallel rectangular bars or blocks, with rollers positioned diagonally between them. The oblong shape of the set allows for the rollers to be positioned at a diagonal angle, which can be useful when setting up workpieces that need to be adjusted at an angle or from multiple points of origin.

In contrast, a half oval set and a half circle set are both types of circular sets that consist of rollers positioned in a semi-circular shape. These types of sets are useful for supporting workpieces that have a curved or circular shape, but they do not provide the flexibility to position rollers at a diagonal angle or from multiple points of origin.

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By using the concept of combinations, there are 13,122,848 ways.

For getting the number of ways to distribute 30 people into 4 distinct rooms with the given conditions, we will use the concept of combinations.

In the case of 2 people in room 3 and 26 in room 4, the number of ways to distribute them is:
²⁸C₂ = 28! / (2!(28-2)!) = 378

After calculating the total number of ways, we find that there are 13,122,848 ways to distribute 30 people into the 4 distinct rooms with the given conditions.

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The variance of the distribution is 0.964.

What is the variance?

The squared deviation from the mean of a random variable is referred to as variance in probability theory and statistics. The square of the standard deviation is another common way to express variation. Variance is a measure of dispersion, or how far apart from the mean a group of data are from one another.

Here, we have

Given:

x    P(r)

0    0.130

1      0.346

2     0.346

3      0.154

4       0.026

We have to find the variance of the distribution.

Var(X) = E(X²) - (E(X))²...(1)

E(X²) = ∑x²Pₓ(X=x)

E(X²) = 0×0.130 + 1²×0.346 + 2²×0.346 + 3²×0.154 + 4²×0.026

E(X²) = 3.532

Now,

E(X) = ∑xPₓ(X=x)

E(X) =  0×0.130 + 1×0.346 + 2×0.346 + 3×0.154 + 4×0.026

E(X) = 1.604

Now, we put the value of E(X) and E(X²) in equation (1) and we get

Var(X)  = 3.532 - (1.604)²

Var(X)  = 0.95918

Var(X)  = 0.964

Hence, the variance of the distribution is 0.964.

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Answer:

So we need to transfer 37 red and 73 blue marbles from Box A to Box B.

Step-by-step explanation:

Let x be the number of red marbles to be transferred from Box A to Box B, and let y be the number of blue marbles to be transferred from Box A to Box B. Then the total number of marbles in each box after the transfer is:

Box A: 200 + 90 - x - y = 290 - x - y Box B: 80 + 100 + x + y = 180 + x + y

We want 80% of the marbles in Box A and 50% of the marbles in Box B to be red, so we can set up the following equations:

0.8(290 - x - y) = 232 - 0.8x - 0.8y (80% of Box A is red) 0.5(180 + x + y) = 90 + 0.5x + 0.5y (50% of Box B is red)

To solve for x and y, we can set these two expressions equal to each other:

232 - 0.8x - 0.8y = 90 + 0.5x + 0.5y

Simplifying and rearranging, we get:

1.3x + 1.3y = 142 13x + 13y = 1420 x + y = 110

So we need to transfer a total of 110 marbles from Box A to Box B. To find the number of red marbles to transfer (x), we can use the first equation:

0.8(290 - x - y) = 232 - 0.8x - 0.8y 232 - 0.8x - 0.8y = 232 - 0.8x - 58 0.8y = 58 y = 72.5

Since we can't have a half marble, we'll round up to 73 blue marbles to transfer. Therefore, the number of red marbles to transfer is:

x = 110 - 73 = 37

So we need to transfer 37 red and 73 blue marbles from Box A to Box B.

The fraction which is recommended as value of iron in 1 cup of oatmeal as per the given relation is equal to 2/15.

As given in the question,

Daily recommended value of iron in the given cup of oatmeal

3 / 4 cup of oatmeal  gives  1/10 daily value of iron.

Fraction recommended as daily value of iron is given by :

⇒ 3 /4 cup of oatmeal = 1 /10 value of iron

⇒ 1 cup of oatmeal = ( 1 × 4 ) / ( 3 × 10 ) value of iron

⇒ 1 cup of oatmeal = ( 4 ) / ( 30 ) value of iron

⇒ 1 cup of oatmeal = ( 2 ) / ( 15 ) value of iron

Therefore, the fraction recommended as daily value of iron is equal to

( 2/15 ).

The above question is incomplete, the complete question is :

In 3/4 cup of oatmeal, there is 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron is in 1 cup of oatmeal? ( multiplication and division equation)

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(a) The total debt function is D(t) = 13(t+8)sqrt(t^2+16t) + C, where C is the constant of integration.

(b) The total debt will exceed $180,000 in approximately X years.

The given information provides us with the rate at which the company incurs debt over time, represented by D′(t) = 78(t+8)sqrt(t^2+16t) dollars per year. To find the total debt function, we need to integrate this rate function.

In the first step, we integrate D′(t) with respect to t. The integral of 78(t+8)sqrt(t^2+16t) is calculated to be 13(t+8)sqrt(t^2+16t) + C, where C represents the constant of integration.Now, let's delve deeper into the explanation of the main answer. The total debt function, D(t), is obtained by integrating the given rate function, D′(t), with respect to time. Integration involves finding the antiderivative of the rate function, which effectively accumulates the debt over time.

The integration process results in the function 13(t+8)sqrt(t^2+16t) + C, where C represents the constant of integration. This function provides a mathematical representation of the total debt at any given point in time since the company began.To clarify, the constant of integration, C, represents an unknown value that arises during integration. In this context, C accounts for any initial debt the company had before the specified time frame, t=0, and other factors not included in the given information. Thus, it allows for flexibility in accounting for additional variables.

To determine the number of years it takes for the total debt to exceed $180,000, we set the total debt function, D(t), greater than $180,000 and solve for the corresponding value of t. By substituting D(t) = $180,000 into the total debt function D(t) = 26(t^2 + 16t)^(3/2) + C, we can solve for the value of t. This will give us the approximate number of years it will take for the company's debt to exceed $180,000.

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Applying the knowledge of fractions, the bigger one is: one-sixth of 138.

Fractions can be defined as a part of a digit or number, and are not whole numbers. For example, a third is 1/3, one-sixth is 1/6, which are both fractions.

Therefore, let's evaluate each statement:

1/3 of 45 = 1/3 × 45 = 15

1/6 of 138 = 1/6 × 138 = 23

Therefore, the bigger of the two is: one-sixth of 138.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

Check the picture below, so that happens when h = 0.

\(\stackrel{h}{0}~~ = ~~-5t^2+15t\implies 0=-5t(t-3)\implies 0=t(t-3)\implies t= \begin{cases} 0\\ 3~\checkmark \end{cases}\)

now, notice, 0 is also a solution, which means at 0 seconds the ball was touching the ground, well, it was kicked "from" the ground, so at 0 seconds it was initially on the ground anyway.

Answer:

c. start fraction 5 over 6 end fraction

Step-by-step explanation:

there are six numbers on a cube

1, 2, 3, 4, 5, 6

there are 5 other numbers other than 6

5/6

5 = other than 6

6 = total numbers

Answer:

29,500

Step-by-step explanation:

is 50% percent and that is how much will increase. =)

Hence proved that if n is a power of 2, then\(i = \theta (log_2 n).\)

We have n as a power of 2, so we can write n as:

\(n = 2^k\)

Taking logarithm base 2 on both sides, we get:

\(log_2 n = k\)

Now, let's substitute i = 0, 1, 2, ..., k in the given equation:

\(2^i\)= θ(i)

\(2^{(2i)}\) = θ(i)

\(2^{(3i)} = \theta(i)\)

...

\(2^{(k+i)}\) = θ(i)

We can see that the expression on the left side of each equation is exactly \(n^{(2i/k)}\), so we can write:

\(n^{(2i/k)}\) = θ(i)

Taking logarithm base 2 on both sides, we get:

\((2i/k) log_2 n = log_2 \theta(i)\)

Simplifying, we get:

\(i = (k/2) log_2 \theta (i) + C\)

where C is a constant that depends on the value of i.

Since \(k = log_2 n\), we can substitute k in the above equation:

\(i = (log_2 n/2) log_2 \theta(i) + C\)

Simplifying, we get:

\(i = (1/2) log_2 n log_2 \theta (i) + C'\)

where C' is a constant that depends on the value of i.

Thus, we can conclude that:

\(i = \theta(log_2 n)\)

Therefore, we have shown that if n is a power of 2, then\(i = \theta (log_2 n).\)

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Hey there!

7 5/8

= 7 * 8 + 5 / 8

= 56 + 5 / 8

= 61 / 8

= 61 ÷ 8

= 7.625

Reciprocal form for fraction is basically the bottom number switched from the top number

Therefore, your answer is: 7 8/5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer: 1 tablespoon

Step-by-step explanation:

To determine whether the given vectors v = (1, -3) and v = (-2, -1) form a basis for R2, we need to check if they are linearly independent and span the entire R2 space.

To check for linear independence, we set up a linear combination equation where the coefficients of the vectors are unknown (let's call them a and b). We equate this linear combination to the zero vector (0, 0) and solve for a and b:

a(1, -3) + b(-2, -1) = (0, 0)

Simplifying this equation gives two simultaneous equations:

a - 2b = 0

-3a - b = 0

Solving these equations simultaneously, we find that a = 0 and b = 0, indicating that the vectors are linearly independent.

To check for span, we need to verify if any vector in R2 can be expressed as a linear combination of the given vectors. Since the vectors are linearly independent, they span the entire R2 space.

Therefore, the given vectors v = (1, -3) and v = (-2, -1) form a basis for R2 as they are linearly independent and span the entire R2 space.

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Answer:

1/8

Step-by-step explanation:

Answer:

1/8 or option A for edge 2020

Step-by-step explanation:

I got it right in the warm up ^^

Hope this helps!!

Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:

f'(x) = 3/x - 6x² - 8/(x^5).

The function is given by:

f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4

The derivative of a sum is the sum of the derivatives, hence:

f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'

The derivative of a constant is of zero, hence:

Hence:

f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.

The derivative of the logarithm is given by:

ln(h(x))' = (1/h(x)) x h'(x).

Hence:

(ln(x^3))' = 3x²/x³ = 3/x.

The derivative of the power of x is given by:

[x^n]' = nx^(n-1).

Hence:

Hence the derivative of the function is given by:

f'(x) = 3/x - 6x² - 8/(x^5).

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False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.

What does the term "echelon form" mean?

What purpose does echelon matrix serve?

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