\((\frac{3a}{4b} -\frac{4b}{3a})^2\)

The cost of one banana will be 46 cents. We find it by solving the linear equation.

Given,

The number of apples = 4.

The number of Bananas = 5.

The total cost of apples and bananas = 3.70.

Let, the cost of an apple is 'a'.

Let, the cost of an apple is 'b'.

The equation will be, 4a + 5b = 3.70.

The cost of one apple is given as 35 cents.

Now, we have to find the cost of one banana.

By substituting, we get

4(0.35) + 5b = 3.70.

1.40 + 5b = 3.70.

5b = 2.30

b = 0.46.

Therefore, the cost of one banana is 46 cents.

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The complete question could be as follows:

Luke buys 4 apples and 5 bananas at a total cost 0f $3.70. If the cost of one apple is 35 cents, find the cost of one banana.

Answer:

False

Step-by-step explanation:

Dividing integers is opposite operation of multiplication. But the rules for division of integers are same as multiplication rules. Though, it is not always necessary that the quotient will always be an integer.

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please give brainliest

Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

To solve for the mileages at which company A will charge less than company B, we can set up the following inequality:
A < B
where A is the cost of renting from company A and B is the cost of renting from company B. We can plug in the given information to get:
x ≤ A
x > B = y + 40z
where x is the number of miles driven, y is the initial fee for company B, and z is the additional cost per mile for company B.
Now we can substitute the given values to get:
x ≤ A
x > y + 40z
For company A, the cost is a flat rate with unlimited mileage, so A is just the cost listed for one day of rental. Let's say that cost is $100.
For company B, the initial fee is $50 and the additional cost per mile is $0.25. So:
y = 50
z = 0.25
Now we can plug in these values and solve for x:
x ≤ 100
x > 50 + 40(0.25)
x > 65
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

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17 is the integer expressed in base 10.

Given that,

The base 7 representation of a positive integer is AB and its base 5 representation is BA, where A and B are digits from 1 to 4, inclusive.

We have to find what is the integer expressed in base 10.

We know that,

Base 7 representation of a positive integer AB.

Can be written as 7A+B in base 10.

Base 5 representation of BA can be written as 5B+A in base 10.

So, 7A+B= 5B+A

6A=4B

A=2/3B

Now, A and B must be in 1 to 4.

The digits between 1 and 4 who are 2/3 of another is 2 and 3.

A=2 and B=3

So,

Base 7 is 23

And Base 5 is 32

Base 7 is 23 is 17 of base 10.

And Base 5 is 32 is 17 of base 10.

A=17

Therefore, 17 is the integer expressed in base 10.

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a. the estimated thickness of the boundary layer at the stern of the ship is approximately 1.211 × 10^(-4) ft , b. The density of seawater at 40°F is approximately ρ = 64.14 lb/ft³, c. since we don't have the drag force value, we cannot provide an accurate estimation of the power required.

(a) To estimate the thickness of the boundary layer at the stern of the ship, we can use the Prandtl's boundary layer thickness equation. The boundary layer thickness (δ) can be approximated as δ ≈ 5√(ν/U), where ν is the kinematic viscosity of seawater and U is the velocity of the ship.

First, let's convert the ship's speed from knots to feet per second: 15 knots = 15 × 1.15078 = 17.2617 ft/s

The kinematic viscosity of seawater at 40°F is approximately ν = 1.107 × 10^(-6) ft²/s.

Using these values, we can calculate the boundary layer thickness: δ ≈ 5√(1.107 × 10^(-6) / 17.2617) ≈ 5 × 2.422 × 10^(-5) ≈ 1.211 × 10^(-4) ft

Therefore, the estimated thickness of the boundary layer at the stern of the ship is approximately 1.211 × 10^(-4) ft.

(b) The total skin friction drag acting on the ship can be estimated using the equation: D = 0.5 * ρ * U^2 * A * Cd, where ρ is the density of seawater, U is the velocity of the ship, A is the wetted area of the ship, and Cd is the drag coefficient.

The wetted area (A) can be approximated as A ≈ 2 * L * (b + D), where L is the length, b is the beam (width), and D is the draft (depth) of the ship.

Using the given dimensions: A ≈ 2 * 1000 * (270 + 80) ≈ 2 * 1000 * 350 ≈ 700,000 ft²

The density of seawater at 40°F is approximately ρ = 64.14 lb/ft³.

Now, we need the drag coefficient (Cd), which depends on the ship's shape and flow conditions. Without additional information, it's challenging to estimate accurately. Typically, model tests or computational fluid dynamics (CFD) simulations are conducted to determine Cd.

(c) To calculate the power required to overcome the drag force, we can use the equation: P = D * U, where P is the power and D is the drag force. However, since we don't have the drag force value, we cannot provide an accurate estimation of the power required.

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To find the width of the rectangular frame, we need to set up an equation using the given information about the total area of 160 square inches.

The area of a rectangle is given by the formula length multiplied by width. In this case, the length is represented by the expression 2x + 8, and the width is represented by the expression 2x + 6. So, we can set up the equation: (2x + 8)(2x + 6) = 160

Now, let's solve this equation step by step: 1. Expand the equation: 4x^2 + 12x + 16x + 48 = 160 2. Combine like terms: 4x^2 + 28x + 48 = 160 3. Move 160 to the other side of the equation: 4x^2 + 28x + 48 - 160 = 0 4. Simplify: 4x^2 + 28x - 112 = 0 So, the correct equation to solve for the width of the rectangular frame with a total area of 160 square inches is:

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The measure of the arc BED is 218°

This means that we need to find the angle of the arc BED on the given circle.

We need to remember that the total angle on a circle is 360°.

We can also see that the angle between B and C is 52°, and the angle between C and D is 90° (that is what the little square means).

And the angle between B and D (measured counterclockwise) is the angle we want to find, and it will be equal to 360° minus the two angles above, then we will get:

measure of the arc = 360° - 52° - 90°

measure of the arc = 218°

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Answer:

no se ve

Step-by-step explanation:

The equations of values of x and y =0 that will maximize the revenue.

The marginal revenue equations, to calculate the partial derivatives of the revenue function with respect to each variable, x and y.

Given the revenue function:

t(x, y) = 110x + 180y + 3x² - 4y² - xy

The marginal revenue with respect to x, rx(x, y), the partial derivative of t(x, y) with respect to x, while treating y as a constant:

rx(x, y) = ∂t/∂x = 110 + 6x - y

Similarly, the marginal revenue with respect to y, ry(x, y),the partial derivative of t(x, y) with respect to y, while treating x as a constant:

ry(x, y) = ∂t/∂y = 180 - 8y - x

The production levels that will maximize revenue, both marginal revenue equations equal to zero and solve as a system of equations.

Setting rx(x, y) = 0:

110 + 6x - y = 0

Setting ry(x, y) = 0:

180 - 8y - x = 0

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Answer:

D

Step-by-step explanation:

Remember that parallel lines have equal slopes.

So, if the green line is parallel to the red line, and the slope of the green line is -2, this means that the slope of the red line must also be -2!

So, our answer is D.

And we're done!

Answer: D

Step-by-step explanation:

If the slope of The green line is -2 and it is parallel to the red line, the slope of the red line must also be -2

-x + y > -4; x + y < 3 is  the inequality whose solution set is represented by this graph.

What is the inequality in math?

The boundary lines are both dashed, so there will be no "or equal to" as part of the inequality symbols (eliminates the second choice).

The downward sloping line has x- and y-intercepts that are both 3, so it will have the equation in intercept form

 x/3 + y/3 = 1

Multiplying by 3 gives x+y=3. The shading is below it, so the inequality with that line as the boundary is

 x + y < 3

This inequality is only part of the last choice.

The upward sloping line has x- and y- intercepts of 4 and -4, so its equation in intercept form is

 x/4 + y/-4 = 1

Multiplying by -4 gives -x+y=-4. The shading is above it, so the inequality with that boundary line is

-x + y > -4

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Answer:

Yes, the boys caught the same ratio of catfish to trout.

Step-by-step explanation:

First, find the ratios of catfish to trout for both Darnel and Lester.

Darnel's ratio is 4:8, since he caught 4 catfish and 8 trout.

This can be simplified to 1:2 by dividing each number by 4.

Lester's ratio is 3:6, since he caught 3 catfish and 6 trout.

This can be simplified to 1:2 by dividing each number by 3.

So, both of their ratios are 1:2.

Yes, the boys caught the same ratio of catfish to trout.

Answer:

25% increase

Step-by-step explanation:

To find percentage increase or decrease, use this equation:

{ [ ( Final ) - ( Initial ) ] / ( Initial ) } * 100

In this problem, 4 is the initial weight and 5 is the final weight. Now, let's plug these values into the problem to solve for percentage increase in the puppy's weight.

[ ( 5 - 4 ) / 4 ] * 100

[ 1 / 4 ] * 100

25%

So, the puppy's weight increased by 25% in three months.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

I am pretty sure it is 22m

Step-by-step explanation:

minus 2

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Answer:

x=1

Step-by-step explanation:

in photo

The important similarity between the uniform and normal probability distributions is that the mean and the median of both distributions are equal

In a normal probability distribution, we have:

Mean = Median

In a uniform probability distribution, we have:

Mean = Median

This means that:

In both distributions, the mean and the median are equal

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Answer:

y = 2x - 4

Step-by-step explanation:

To solve this problem, we must first calculate the slope of the line AB using the formula:

\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

where:

m ⇒ slope of the line

(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line

Therefore, for line AB with points A = (2, 5) and B = (4, 4) :

\(m_{AB} = \frac{5 - 4}{2 - 4}\)

⇒ \(m_{AB} = \frac{1}{-2}\)

⇒ \(m_{AB} = -\frac{1}{2}\)

Next, we have to calculate the slope of the line BC.

We know that the product of the slopes of two perpendicular lines is -1.

Therefore:

\(m_{BC} \times m_{AB} = -1\)      [Since BC and AB are at right angles to each other]

⇒ \(m_{BC} \times -\frac{1}{2} = -1\)

⇒ \(m_{BC} = -1 \div -\frac{1}{2}\)      [Dividing both sides of the equation by -1/2]

⇒ \(m_{BC} = \bf 2\)

Next, we have to use the following formula to find the equation of line BC:

\(\boxed{y - y_1 = m(x - x_1)}\)

where (x₁, y₁) are the coordinates of a point on the line.

Point B = (4, 4) is on line BC, and its slope is 2. Therefore:

\(y - 4 =2 (x - 4)\)

⇒ \(y - 4 = 2x - 8\)         [Distributing 2 into the brackets]

⇒ \(y = 2x-4\)

Therefore, the equation of line BC is y = 2x - 4.

Explanation

to know the total bill amount we need to add the tip to the total,so

Step 1

find the value of the tip

it means to find the tip amount you need multiply the bill by 0.23,hence

Step 2

finally , add the values to know the total restaurant bill including the tip amount

So, the answer is $138.3627.

I hope this helps you

To find the largest area you can enclose with a single-strand electric fence and m units of wire at your disposal, you need to optimize the dimensions of the rectangular plot.

Let's denote the length of the rectangular plot as L and the width as W. The perimeter of the plot can be calculated as P = L + 2W.

Since one side of the plot is already bounded by the river, we have L + W = m. Rearranging this equation, we get L = m - W.

To find the largest area, we need to maximize the function A = L * W. Substituting the value of L, we have A = (m - W) * W.

Expanding the equation, we have A = mW - W^2.

To find the maximum value of A, we take the derivative of A with respect to W and set it equal to zero: dA/dW = 0.

Differentiating, we get m - 2W = 0. Solving for W, we have W = m/2.

Substituting this value back into the equation for L, we have L = m/2.

Therefore, the dimensions of the largest area are L = m/2 and W = m/2.

To find the area, we substitute these values into the equation for A: A = (m/2) * (m/2) = m^2/4.

In conclusion, the largest area that can be enclosed is m^2/4, with dimensions L = m/2 and W = m/2.

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Using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

So, liters of water when mixed with 10 lemon juice:

Solve, the expression as follows:

Therefore, using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

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The correct question is given below;
Four liters of water are mixed with 6 juiced lemons to make lemonade. how many liters of water should be mixed with 10 juicer lemons to obtain the same result? (pls kinda show work)

A) 4 2/3

B) 5 1/3

C) 6 1/3

D) 6 2/3

E) 8 1/3

Answer:

[see below]

Step-by-step explanation:

Point slope form is:

\(y-y_1=m(x-x_1)\)

(x1, y1) - a point

m - slope

We are given the point of (2, -7), and the slope of -5.

\(y-y_1=m(x-x_1)\rightarrow y-(-7)=-5(x-2)\rightarrow\boxed{y+7=-5(x-2)}\)

Hope this helps.

4320 the number of permutations of the letters abcdefg that contain the string bcd.

The number of permutations that contain the string BCD is obtained by multiplying the number of arrangements from Step 1 and the fixed arrangement of BCD from Step 2.

Total permutations = 24 x 1 = 24 We can do this by using the concept of permutations with restrictions.

Let's consider the string bcd as a single letter. Then, we need to arrange the remaining letters along with this 'new' letter.

This can be done in 6! ways (since there are 6 letters left to be arranged).

However, in each of these arrangements, the string bcd can be arranged in 3! ways among themselves.

Therefore, the required number of permutations will be: 6! x 3! = 4320

So, there are 4320 permutations of the letters abcdefg that contain the string bcd.

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Answer: IF you have two equations with the 2 variables, x and y, you can substitute one y-value with the other, then solve.

Step-by-step explanation:  For example:

y = 2x + 4

3x+y = 9

We can substitute the value of y from the first equation, 2x + 4, into the second equation.  So, the second equaton becomes:

3x + 2x + 4 = 9

Now solve for x:

5x + 4 = 9

5x = 5

x = 1

This value of x then can be used to find y, by substituting in the value "1" for x in the first equation:

y = 2x + 4 = 2(1) + 4 = 2 + 4 = 6

So, the solution to this linear system is (1, 6)

SOLUTION:

Step 1:

Since the two figures are similar, it means that they have properties in common.

Step 2:

In the bigger figure, the side given is 10in and its area is 100 square inches meaning (10 in x 10 in).

Step 3:

In the smaller figure, the side given is 8in, and from step 1, we can see that the two figures are similar, so the area of the smaller figure will be (8 in x 8 in) = 64 square inches.

CONCLUSION:

The area of the smaller figure is 8in x 8in = 64 square inches

The vegetarian ratio would presumably be: 5 million / (5 million + 50 million) = 0.100 which is equivalent to 10%.

To calculate the proportion of vegetarians to non-vegetarians in Bradley's country, one needs to first assess the amount of vegetarians and non-vegetarians living there.

This can be accomplished through reliance on surveys, census data, or further research methods. By dividing the number of vegetarians in comparison to the total number of both vegetarians and non-vegetarians, one can generate a ratio that reveals this information.

For example, let's say Bradley's country contains 5 million vegetarians among a general population of 50 million people. The vegetarian ratio would presumably be: 5 million / (5 million + 50 million) = 0.100 which is equivalent to 10%.

Similarly, as Bradley attempts to distinguish appropriate vegetable, meat, and dessert recipes for his cookbook - 10%, 18%, and 42% respectively - he can utilize this same formula. As an example it could be assumed that if there are 150 recipes in total then 15 would incorporate vegetables as part of their contents - 10% out of 150 recipes - while 30% or 27 recipes would idealized around containing meat components as well as 70% or 63 desserts.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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The probability of reaching into the box and randomly drawing the chip numbered 146 is 0.0027 or 1/364.

Probability is the chance or likelihood of an event taking place.

In this case, we are trying to determine the probability of drawing a chip numbered 146 from a box containing 364 plastic chips numbered 1 through 364.

To solve this, we will use the formula:

probability of an event = number of favorable outcomes / total number of possible outcomes.

Let's find out the favorable and total number of outcomes.

Favorable outcomes: The number of chips numbered 146 is only one.

Therefore, the number of favorable outcomes is 1.
Total number of outcomes: There are 364 plastic chips numbered 1 through 364 in a box.

Therefore, the total number of outcomes is 364.
Hence, the probability of reaching into the box and randomly drawing the chip numbered 146 can be calculated using the formula:

probability of an event = number of favorable outcomes / total number of possible outcomes.

Thus, the probability of drawing the chip numbered 146 is:

Probability = 1/364 or 0.0027 (rounded to four decimal places).

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The sum of the squares of the roots of the quadratic equation 2x^2 - 3x + 27 = 0, where the roots are imaginary, is approximately 11.25.

For a quadratic equation in the form ax^2 + bx + c = 0, the sum of the squares of the roots can be found using the following formula: (Sum of the roots)^2 - 2(Product of the roots).

In this case, the quadratic equation is 2x^2 - 3x + 27 = 0. Since the roots are imaginary, they will be in the form of complex numbers of the form a + bi.

To find the sum of the roots, we can use the fact that the coefficient of the linear term (bx) divided by the coefficient of the quadratic term (ax^2) gives the negative sum of the roots. So, the sum of the roots is -(-3/2) = 3/2.

To find the product of the roots, we can use the fact that the constant term (c) divided by the coefficient of the quadratic term (a) gives the product of the roots. So, the product of the roots is 27/2.

Using the formula mentioned earlier, (Sum of the roots)^2 - 2(Product of the roots), we can calculate the sum of the squares of the roots as (3/2)^2 - 2(27/2) = 9/4 - 27 = -63/4.

Rounding this value to the nearest hundredth, we get approximately -15.75. However, since the question asks for the answer as a decimal rounded to the nearest hundredth, and the sum of the squares of the roots cannot be negative, we take the absolute value and round it, giving us approximately 15.75.

Therefore, the sum of the squares of the roots of the quadratic equation 2x^2 - 3x + 27 = 0, where the roots are imaginary, is approximately 11.25.

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