A linen service is delivering clean tablecloths to restaurants on its list of clients. A delivery is made to a restaurant in Morristown and then another in Newberg. These two restaurants are 30 centimeters apart on a map. The map uses a scale of 3 centimeters = 2 kilometers. What is the actual distance between the two restaurants?

Answer:

The equivalent will be:

\(\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}=\left(\:x^{\frac{2}{7}}\right)\left(y^{-\frac{3}{5}}\right)\)

Therefore, option 'a' is true.

Step-by-step explanation:

Given the expression

\(\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}\)

Let us solve the expression step by step to get the equivalent

\(\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}\)

as

\(\sqrt[7]{x^2}=\left(x^2\right)^{\frac{1}{7}}\)      ∵ \(\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\)

\(\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\)

\(=x^{2\cdot \frac{1}{7}}\)

\(=x^{\frac{2}{7}}\)

also

\(\sqrt[5]{y^3}=\left(y^3\right)^{\frac{1}{5}}\)         ∵  \(\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\)

\(\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\)

\(=y^{3\cdot \frac{1}{5}}\)

\(=y^{\frac{3}{5}}\)

so the expression becomes

\(\frac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\)

\(=\left(\:x^{\frac{2}{7}}\right)\left(y^{-\frac{3}{5}}\right)\)            ∵ \(\:\frac{1}{y^{\frac{3}{5}}}=y^{-\frac{3}{5}}\)

Thus, the equivalent will be:

\(\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}=\left(\:x^{\frac{2}{7}}\right)\left(y^{-\frac{3}{5}}\right)\)

Therefore, option 'a' is true.

Answer:

The location of point T is \(\vec T = (7.5, 2.25)\). Graph is included at the end of the explanation as attachment.

Step-by-step explanation:

The SQ : QT ratio means that there are 4 units of SQ for each 3 units of QT. Vectorially speaking, we notice that:

\(\overrightarrow {SQ} = \frac{4}{7}\cdot \overrightarrow {ST}\) (Eq. 1)

\(\overrightarrow{QT} = \frac{3}{7}\cdot \overrightarrow {ST}\) (Eq. 2)

Now, we eliminate \(\overrightarrow{ST}\) by equalizing (Eq. 1) and (Eq. 2):

\(\frac{7}{3} \cdot \overrightarrow{QT} = \frac{7}{4}\cdot \overrightarrow{SQ}\) (Eq. 3)

From Linear Algebra, we know that:

\(\frac{7}{3}\cdot (\vec T - \vec Q) = \frac{7}{4}\cdot (\vec Q-\vec S)\) (Eq. 3b)

And we clear \(\vec T\)

\(\frac{7}{3}\cdot \vec T -\frac{7}{3}\cdot \vec Q = \frac{7}{4}\cdot \vec Q -\frac{7}{4}\cdot \vec S\)

\(\frac{7}{3}\cdot \vec T = \frac{49}{12}\cdot \vec Q - \frac{7}{4}\cdot \vec S\)

\(\vec T = \frac{3}{7}\cdot \left(\frac{49}{12}\cdot \vec Q-\frac{7}{4}\cdot \vec S\right)\)

\(\vec T = \frac{7}{4}\cdot \vec Q-\frac{3}{4}\cdot \vec S\)

If we know that \(Q(x,y) = (3, 0)\) and \(S(x, y) = (-3,-3)\), then we have that \(T(x,y)\) is:

\(\vec T = \frac{7}{4}\cdot (3, 0) - \frac{3}{4}\cdot (-3, -3)\)

\(\vec T = \left(\frac{21}{4}, 0 \right) + \left(\frac{9}{4},\frac{9}{4}\right)\)

\(\vec T = \left(\frac{21+9}{4},\frac{0+9}{4} \right)\)

\(\vec T = \left(\frac{15}{2}, \frac{9}{4}\right)\)

\(\vec T = (7.5, 2.25)\)

At last we plot the segment with all points described on statement. We can check the result in the attachment set below.

Answer:

250 bottles and 150 bags of trail mix.

Step-by-step explanation:

You multiply 250 times 3.5 and get 875. Then you multiply 150 times 4 and get 600. Then add 875 plus 600 and get 1475.

Answer:

250 bottles and 150 bags

The required hole size is 0.466775 inches

When expressing a whole number and a fraction together, decimals are utilized. Here, we shall use a "." (also known as a decimal point) to demarcate the full number from the fraction. Say, for instance, that you intend to bring a cone of ice cream. You are informed by the vendor that ice cream costs $2 and 50 cents. Now, if you wanted to sum up this cost in a single number, you would say that an ice cream cone costs $2.50.

The main objective is to express the hole sizes in a decimal form such that the holes are to be 1/32 inch larger in diameter than the studs.

Given that, the diameter of the switchboard is 0.4365 inches.

Converting 1/32 into decimal we get 0.03125

Calculate the hole size as shown below.

0.03125 + 0.4365 = 0.46775

Thus, the required hole size is, 0.46775 inches.

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Answer:

27,36,45

Step-by-step explanation:

Pythagorean theorem

\(a^{2} +b^{2} =c^{2}\)

\(6^{2}+ 9^{2}\\ =117\\\neq 12^{2}\)

\(7^{2}+ 10^{2}\\ =149\\\neq 12^{2}\)

\(16^{2}+ 18^{2}\\ =580\\\neq 25^{2}\)

\(27^{2}+ 36^{2}\\ =2025\\= 45^{2}\)

To solve the given ordinary differential equation (ODE) with initial conditions, we will use the method of power series expansion.

Let's assume that the solution to the ODE is given by a power series: y = Σ(a_n * x^n), where a_n represents the coefficients to be determined.

Taking the derivatives of y, y', and y'' with respect to x, we have:

y' = Σ(a_n * n * x^(n-1))

y'' = Σ(a_n * n * (n-1) * x^(n-2))

Substituting these series into the ODE, we get:

3000 * 2 * x * y + x * y' - y'' = x

Expanding this equation and grouping the terms by powers of x, we can equate the coefficients of each power of x to zero. This allows us to determine the coefficients a_n.

Using the given initial conditions, y(1) = 1, y'(1) = 3, and y''(1) = 14, we can substitute x = 1 into the power series and solve for the coefficients a_n.

After determining the coefficients, we can substitute them back into the power series expression for y(x) to obtain the specific solution to the ODE that satisfies the initial conditions.

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Answer:

sorry can't help didn't understand

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's simplify ~

\(\qquad \sf  \dashrightarrow \:( - 2 - 5i) - ( - 4 + 6i)\)

\(\qquad \sf  \dashrightarrow \: - 2 - 5i + 4 - 6i)\)

\(\qquad \sf  \dashrightarrow \: - 2 + 4 - 5i- 6i)\)

\(\qquad \sf  \dashrightarrow \:2 - 11i\)

Therefore, A is the Correct choice !

82 kg is equal to 180.77844 pounds and 2892.24704 ounces.

Weight is a measure of how heavy an object is, and it is typically measured in units such as pounds (lbs) and ounces (oz). The kilogram (kg) is also a unit of weight, and it is the base unit of mass in the International System of Units (SI).

To convert the pounds to ounces, we know that 1 pound is equal to 16 ounces. To get the ounces from pounds, we can multiply the pounds by 16, so 180.77844 pounds is equal to 2892.24704 ounces.

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The area of the shaded region of the figure is 100.53 square cm

The area of the shaded part is solved by finding the area of the two parts and subtracting

This can be done using the formula below

area of the shaded part = π(R² - r²)

Where 'R = 4 cm + 2 cm = 6 cm

r = 2 cm

plugging in the values we have

area of the shaded part = π(R² - r²)

area of the shaded part = π(6² - 2²)

area of the shaded part = π(36 - 4)

area of the shaded part = 32π

area of the shaded part = 100.53 square cm

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Answer:

x = 107/15

Step-by-step explanation:

Our first step should be to turn all of the mixed fractions into improper fractions. So, 1 2/3 becomes 5/3, and -2 1/5 becomes -11/5. We now get -1/4(x + 5/3) = -11/5. Now we should divide both sides by -1/4, and we get x + 5/3 = -11/5 x -4 = 44/5. So x + 5/3 = 44/5. We want the denominator to be equal on both sides so a common denominator could be 15. 5(5)/3(5) = 25/15. 44(3)/5(3) = 132/15. So now we have x + 25/15 = 132/15. We subtract both sides by 25/15 and we get x = 107/15.

The solution of the given equation −1/4(x+1 + 2/3)=−2 + 1/5 is x = 83/15.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

As per the given equation,

−1/4(x+1 + 2/3) = −2 + 1/5

-1/4(x + 5/3) = -9/5

x + 5/3 = 9/5 x 4

x = 36/5 - 5/3

x = 83/15

Hence "x = 83/15 is the answer to the given problem, 1/4(x+1 + 2/3)=2 + 1/5".

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If the gradient of AB is 0, the coordinates of point A and B are (-4, 2) and (6, 2) respectively.

If the gradient of line AB is 0, it means that the line is horizontal. In this case, we can determine the coordinates of points A and B using the information given.

Since the midpoint of line AB is (1,2), we can infer that the average of the x-coordinates of A and B is 1, and the average of the y-coordinates is 2.

Let's assume that point A has coordinates (x₁, y₁) and point B has coordinates (x₂, y₂).

Since the midpoint of line AB is (1,2), we can write the following equations:

(x₁ + x₂) / 2 = 1 (1)

(y₁ + y₂) / 2 = 2 (2)

We also know that the length of line AB is 10 units.

Using the distance formula, we can express this as:

√((x₂ - x₁)² + (y₂ - y₁)²) = 10 (3)

Since the gradient of line AB is 0, the y-coordinates of points A and B must be the same. Therefore, y₁ = y₂. We can substitute this into equations (1) and (2):

(x₁ + x₂) / 2 = 1 (1')

y₁ = y₂ = 2 (2')

Now, let's substitute y₁ = y₂ = 2 into equation (3):

√((x₂ - x₁)² + (2 - 2)²) = 10

√((x₂ - x₁)²) = 10

(x₂ - x₁)² = 100

Taking the square root of both sides, we get:

x₂ - x₁ = ±10

Now, we have two cases to consider:

Case 1: x₂ - x₁ = 10

From equation (1'), we have:

(x₁ + x₁ + 10) / 2 = 1

2x₁ + 10 = 2

2x₁ = -8

x₁ = -4.

Substituting x₁ = -4 into equation (1), we find:

(-4 + x₂) / 2 = 1

-4 + x₂ = 2

x₂ = 6

Therefore, in this case, point A has coordinates (-4, 2), and point B has coordinates (6, 2).

Case 2: x₂ - x₁ = -10

From equation (1'), we have:

(x₁ + x₁ - 10) / 2 = 1

2x₁ - 10 = 2

2x₁ = 12

x₁ = 6

Substituting x₁ = 6 into equation (1), we find:

(6 + x₂) / 2 = 1

6 + x₂ = 2

x₂ = -4

Therefore, in this case, point A has coordinates (6, 2), and point B has coordinates (-4, 2).

To summarize, if the gradient of AB is 0, there are two possible solutions:

A(-4, 2) and B(6, 2)

A(6, 2) and B(-4, 2).

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The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. Ellis has started a vegetable garden.

He bought 15 bags of soil and 3 bags of fertilizer for 282.72.

He realized he did not have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.

Let the cost of each bag of soil be x and the cost of a bag of fertilizer be y.

Then we have the linear equations,

15x + 3y = 282.72

5x + 2y = 107.23

On solving the equations 1 and 2, we have

x = 16.25 and y = 12.99

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

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Answer:

the answer is A

Step-by-step explanation:

It is an acute angle but is larger than 40

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Hello!

Let's write this system below:

Notice that I divided it into two equations, i) and ii).

I'll isolate the variable X in equation i), look:

From now on, we will use this value when referring to X.

So, let's replace where's X in equation ii) by (-7 +3y):

At this moment we know the value of the variable Y as 2. So, we can choose any of the equations and replace this value.

Let's replace Y in the first equation now:

So, the solution of this system is x = -1 and y = 2.

Answer:

(-1, 2)

Step-by-step explanation:

x-3y = -7

3x+y = -1     <===== multiply this equation by 3 to get

9x + 3y = -3   <=====add this to first equation ( this will eliminate 'x')

10x = -10     so x = -1

  use this value of 'x 'in any of the equations to compute 'y'

      -1 -3y = -7      

           -3y = -6

              y =  2

The value of GJ and and JH will be 6.5 and 9.19 respectively

What is angle of elevation?

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Given data ,

The angle of elevation θ = 45°

The value of GH = 6.5

Now , the ΔJGH is a right triangle , so by Trigonometric relations

tan θ = JG / GH

tan 45° = 1

Therefore , 1 = JG / GH

1 = JG / 6.5

So , JG = GH = 6.5  

Now to calculate JH , we use the Pythagoras Theorem ,

where JH² = JG² + GH²

Substituting the values for JG and GH , we get

And JH² = 6.5² + 6.5²

              = 42.25 + 42.25

              = 84.5

taking square root on both sides

Therefore , JH = 9.19

Hence , The value of GJ and and JH will be 6.5 and 9.19 respectively

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Answer:

10,250

Step-by-step explanation:

Correct me if I am wrong But,

Answer: it would be 12

Step-by-step explanation: because if you times 12 twice you would get 144

Answer:

Step-by-step explanation:

Answer:

You didnt show the table, not sure how to answer

Step-by-step explanation:

Answer:

D. 48

Step-by-step explanation:

f(x) = 5x^2 + 2 and g(x) = x^2 - 1; find g(f(-1))

First, we have to find f(-1). You will take the f(x) equation and substituute-1 for x

f(x) = 5x^2 + 2

f(-1) = 5(-1)^2 + 2

f(-1) = 5(1) + 2

f(-1) = 5 + 2

f(-1) = 7

Now we know f(-1) is equal to 7, which means g(f(-1)) is the same thing as g(7). We will be using the g(x) equation now and substitute 7 for x.

g(x) = x^2 - 1

g(7) = 7^2 - 1

g(7) = 49 - 1

g(7) = 48

The correct is 48 (D).

Answer:

D

Step-by-step explanation:

Answer: 2/8

Step-by-step explanation:

Answer:

1. Animals.

2. Plants.

3. Fungi

4. Protists.

5. Monerans.

6. Kingdom.

7. Botany.

8. Reproductive parts.

9. Vegetative parts.  

10. Epidermis.

Step-by-step explanation:

1. Insects, birds: Animals. All insects and birds are living organisms generally referred to as animals.

2. Moss, trees: Plants. Moss and trees are living organisms generally referred to as plants.

3. Yeast, molds: Fungi. They belong to a kingdom of multi-cellular eukaryotic organisms which can't make or produce their own food (heterotrophs).

4. Protozoa, red algae: Protists. They belong to a kingdom of single-celled (unicellular) eukaryotic microscopic organisms.

5. Bacteria, blue-green algae: Monerans. They belong to a kingdom of single-celled (unicellular) prokaryotic organisms without a nuclear cell membrane.

6. Five main groups of all living things: Kingdom. These are namely Kingdom Animalia, Kingdom Fungi, Kingdom Plantae, Kingdom Monera and Kingdom Protista

7. The study of plants: Botany.

8. Flowers, fruits, and seeds: Reproductive parts.

9. Roots, stems, and leaves: Vegetative parts.

10. Provides plant cover on leaves and roots: Epidermis.

Answer:

I think C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

comment if it was correct