y=mx b that intersects the x-axis at (1,3) & crosses at y-axis at (-4,-5)

Given the figure, we have to find the value of y.Using the angle sum property of a quadrilateral, we know that the sum of angles in a quadrilateral is 360 degrees.

Therefore:

∠A + ∠B + ∠C + ∠D = 360°

We know that

∠A = 600°,

∠B = 120°, and

∠C = 100°

∠A + ∠B + ∠C + ∠D = 360°

600° + 120° + 100° + ∠D = 360°

820° + ∠D = 360°

∠D = 360° - 820°

∠D = -460°

Since angle D is not possible to be negative, we know that there must be a mistake in the diagram. We need to make sure that the figure is correct before we can find the value of y.

Therefore, the value of y cannot be determined with the information given in the figure.

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The surface area of the new and revised above-ground pool in terms of x is 2πr * (3x - 3).

To find the surface area of the new and revised above-ground pool, we need to consider the change in depth and its effect on the original pool's surface area.

The original pool has a depth of 3x and the surface area can be calculated by multiplying the depth by the circumference of the pool's base. Assuming the base is circular, the circumference is given by 2πr, where r is the radius.

So, the surface area of the original pool is 2πr * 3x.

When converting to an above-ground pool with a reduced depth of 3, the new depth becomes (3x - 3). The new surface area can be calculated using the same formula, but substituting the reduced depth: 2πr * (3x - 3).

Therefore, the surface area of the new and revised above-ground pool in terms of x is 2πr * (3x - 3).

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To simplify the expression f(x) - g(x) where f(x) = x + 4 and g(x) = x^2 + 3x - 2, we substitute the given functions into the expression and simplify it. The simplified form will be in terms of x and will represent the difference between the two functions.

To simplify f(x) - g(x), we substitute the given functions:

f(x) - g(x) = (x + 4) - (x^2 + 3x - 2)

Expanding the expression, we get:

f(x) - g(x) = x + 4 - x^2 - 3x + 2

Combining like terms, we have:

f(x) - g(x) = -x^2 - 2x + 6

Therefore, the simplified form of f(x) - g(x) is -x^2 - 2x + 6. This expression represents the difference between the functions f(x) and g(x) in its simplest form.

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The fully transformation that maps triangle A to triangle B involves a combination of translation, rotation, and scaling operations.

To map triangle A to triangle B, we can apply a series of transformations. First, we can perform a translation to move triangle A to the desired position. Translation involves shifting the entire triangle in a specific direction. Once the translation is applied, the vertices of triangle A will be in the correct position relative to triangle B.

Next, we can apply a rotation transformation to align the orientation of triangle A with triangle B. Rotation involves rotating the triangle around a specific point or axis. By adjusting the rotation angle, we can ensure that the corresponding vertices of the two triangles match up.

Finally, we can apply a scaling transformation to adjust the size of triangle A to match the size of triangle B. Scaling involves uniformly expanding or shrinking the dimensions of the triangle. By scaling triangle A appropriately, we can ensure that the corresponding sides of the triangles are proportional.

By combining these three transformations—translation, rotation, and scaling—we can fully map triangle A to triangle B, ensuring that the positions, orientations, and sizes of the triangles are aligned.

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Adrienne invested $1200 in account A and $1600 in account B.

Let's set up a system of equations to represent the given information. We are given that the total amount invested is $2800, so we have the equation a + b = 2800.

The interest earned from account A is given as 39% of the amount invested in account A, which can be represented as 0.39a.

Similarly, the interest earned from account B is 5% of the amount invested in account B, represented as 0.05b. The total interest earned is $128, so we have the equation 0.39a + 0.05b = 128.

Solving this system of equations can be done using various methods, such as substitution or elimination. One way to solve is by substitution.

From the first equation, we can solve for a in terms of b: a = 2800 - b. Substituting this into the second equation, we get 0.39(2800 - b) + 0.05b = 128.

Simplifying and solving for b, we find b = $1600. Substituting this value back into the first equation, we get a = $1200.

Therefore, Adrienne invested $1200 in account A and $1600 in account B.

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A 9kg bag of peas would cost $32.22 at the same rate as a 5kg bag based on the given details.

To find the cost of a 9kg bag of peas at the same rate, we can use the concept of direct proportion.

The cost of the peas is directly proportional to the weight of the bag. This means that the cost per kilogram remains the same.

Let's calculate the cost per kilogram of peas:

Cost per kilogram = Total cost / Total weight

= $17.91 / 5kg

Cost per kilogram = $3.58/kg

Now, we can calculate the cost of a 9kg bag of peas:

Cost of 9kg bag = Cost per kilogram * Weight of the bag

= $3.58/kg * 9kg

Cost of 9kg bag = $32.22

Therefore, a 9kg bag of peas would cost $32.22.

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Answer: To find out how much a 5-ounce serving of the frozen Scandinavian vegetable mix costs, we need to calculate the cost per ounce first.

Given that a 2 ¾-pound bag costs $0.88 per pound, we can calculate the cost per pound as follows:

Cost per pound = $0.88

Since there are 16 ounces in a pound, we can calculate the cost per ounce by dividing the cost per pound by 16:

Cost per ounce = Cost per pound / 16

Cost per ounce = $0.88 / 16

Cost per ounce ≈ $0.055

Now, to find the cost of a 5-ounce serving, we can multiply the cost per ounce by 5:

Cost of a 5-ounce serving = Cost per ounce * 5

Cost of a 5-ounce serving ≈ $0.055 * 5

Cost of a 5-ounce serving ≈ $0.275

Therefore, the cost of a 5-ounce serving of the frozen Scandinavian vegetable mix is approximately $0.275, which is closest to option (b) $0.28.

The equation x^3 = y^5 represents a relationship between two variables, x and y, raised to different exponents. This equation states that the cube of x is equal to the fifth power of y.

To better understand this relationship, we can take the cube root of both sides to isolate x: x = y^(5/3). This equation shows that x is equal to the fifth root of y raised to the power of 5/3.

In simpler terms, it means that if we raise y to the power of 5/3 and then take the cube root of that result, we will obtain x.

This equation allows us to relate x and y and determine the value of one variable based on the value of the other.

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The equivalent expression that combines like terms for the new price of the item is b(0.57).

To write an equivalent expression by combining like terms for the new price of the item with a 43% discount, we can simplify the expression b - 0.43b.

First, let's understand the given expression: b represents the original price of the item, and 0.43b represents the amount of the discount (43% of the original price).

To combine like terms, we can factor out the common term 'b' from both terms in the expression:

b - 0.43b = b(1 - 0.43).

Next, we can simplify the expression within the parentheses:

1 - 0.43 = 0.57.

Finally, substituting the simplified expression back into the original equation, we get:

b - 0.43b = b(0.57).

Therefore, the equivalent expression that combines like terms for the new price of the item is b(0.57).

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Marcus ends up paying $37.70 for the two shirts. To calculate the final price Marcus pays for the shirts, we need to follow these steps:

Calculate the discounted price of each shirt: Since the shirts are on a 30% off rack, the discounted price of the first shirt is 0.70 * $28.99 = $20.29, and the discounted price of the second shirt is 0.70 * $30.29 = $21.20.

Calculate the total cost of the shirts before tax: The total cost of the two shirts is $20.29 + $21.20 = $41.49.Apply the additional 10% off discount: To calculate the final price after the additional discount, we need to subtract 10% from the total cost. 10% of $41.49 is 0.10 * $41.49 = $4.15. Subtracting this amount from the total cost gives us $41.49 - $4.15 = $37.34.

Add the sales tax: To calculate the final price including the 6% sales tax, we need to add 6% of $37.34 to the total cost. 6% of $37.34 is 0.06 * $37.34 = $2.24. Adding this amount to the total cost gives us $37.34 + $2.24 = $39.58.

Rounding to the nearest cent, Marcus ends up paying $39.59 for the two shirts. Therefore, the correct answer is option a. $39.59.

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Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is less.

When comparing a fixed principal loan to a fixed payment loan, the key difference lies in how the interest is calculated. In a fixed principal loan, the interest is based on the initial principal amount and remains constant throughout the loan term.

On the other hand, in a fixed payment loan, the interest is calculated based on the outstanding principal balance, which reduces over time as payments are made. As a result, the interest payments decrease gradually over the loan term.

Due to the nature of a fixed principal loan, where the interest is calculated based on the initial principal amount, the total interest paid over the loan term is lower compared to a fixed payment loan. Since the principal amount remains the same, the interest payments do not decrease over time.

In contrast, a fixed payment loan typically has higher total interest payments because the interest is calculated based on the outstanding principal balance, which is higher at the beginning of the loan term and decreases gradually as payments are made.

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Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.  

a) less

b) more  

c) same

The angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.

To find the angle, we can use the concept of similar triangles. The person's height, the length of the shadow, and the distance between the person and the tip of the shadow form a right triangle.

Let's denote the angle of the sun above the horizon as "θ". We can use the tangent function to find the angle:

tan(θ) = opposite/adjacent

In this case, the opposite side is the person's height (5.94 ft) and the adjacent side is the length of the shadow (9.74 ft).

tan(θ) = 5.94/9.74

To find the angle θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(5.94/9.74)

Using a calculator, we can evaluate this expression to find that θ is approximately 34.45 degrees.

Therefore, the angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.

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The value of q is 4.  two lines are parallel if their slopes are equal. To find the slope of the first line, rearrange it into the form y = mx + b, where m is the slope.

This gives us qx - 7y = 10 - 20, which simplifies to qx - 7y = -10. Therefore, the slope of the first line is q/7. The slope of the second line is -3/4. For the lines to be parallel, their slopes must be equal, so q/7 = -3/4. Solving this equation gives q = 4.

To find the value of q for which the lines qx−7y+10=20 and 4y+3x+9=0 are parallel to each other, we need to compare their slopes.

First, we rearrange the first equation into the form y = mx + b, where m represents the slope. The equation becomes qx - 7y = -10 after simplification. Comparing this equation with the standard form y = mx + b, we can see that the slope of the first line is q/7.

The second equation is already in the form y = mx + b. Its slope is -3/4.

For two lines to be parallel, their slopes must be equal. Therefore, we set the slopes equal to each other and solve for q:

[tex]q/7 = -3/4[/tex]

Cross-multiplying gives us:

[tex]4q = -21[/tex]

Finally, dividing both sides of the equation by 4, we find:

[tex]q = -21/4[/tex]

So, the value of q that makes the two lines parallel is q = -21/4, or approximately -5.25.

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Answer:

Precise measurements and calculations are necessary to achieve the desired pH of 12.00.

Step-by-step explanation:

To convert a sodium hydroxide solution with a pH of 13.00 to a pH of 12.00, you would need to decrease the concentration of hydroxide ions (OH-) in the solution. One way to achieve this is by diluting the solution with a neutral solvent, such as water.

Here's a step-by-step process:

Determine the volume of the sodium hydroxide solution you want to prepare with a pH of 12.00. Let's assume you want to prepare 100 mL of the new solution.

Calculate the amount of water needed to dilute the solution. Since you want to decrease the concentration of hydroxide ions, you need to add water. The amount of water needed depends on the desired concentration and the initial concentration.

pH is a logarithmic scale, so the difference in pH values represents a 10-fold difference in concentration. Since the pH is decreasing from 13.00 to 12.00, you need to dilute the solution by a factor of 10.

Therefore, to dilute 100 mL of the sodium hydroxide solution by a factor of 10, you would need to add 900 mL of water.

Mix the sodium hydroxide solution with the calculated amount of water. Ensure thorough mixing to obtain a homogeneous solution.

By diluting the sodium hydroxide solution with water, you decrease the concentration of hydroxide ions, resulting in a lower pH value. However, it's important to note that pH is a logarithmic scale, so small changes in concentration can result in significant changes in pH.

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The total number of pennies on Rows 1-4 (the first 32 squares) is 232. The content loaded formula can be used to calculate the total number of pennies on the Rows 1-4 of the first 32 squares.

formula = 2^(n-1) + 2^(n-2) + 2^(n-3) + 2^(n-4) + 2^(n-5) + ……+ 2^1 + 2^0Where n = the number of rows The first four rows of the chessboard have 2^(4-1) = 8, 2^(4-2) = 4, 2^(4-3) = 2, and 2^(4-4) = 1 pennies respectively .The total number of pennies on the first 32 squares (Rows 1-4) is calculated using the following formula; Total = 8 + 4 + 2 + 1 = 15For the first four rows (the first 32 squares), the total number of pennies is 15. Hence, the correct option is 15.

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If Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

The recipe calls for 1/4 cup of corn grits for every 1/2 cup of water. To find out how much water Henry will need if he uses 1 1/2 cups of corn grits, we can set up a proportion.

Let's assume x represents the amount of water needed in cups. The proportion can be written as:

1/4 cup of corn grits / 1/2 cup of water = 1 1/2 cups of corn grits / x cups of water

To solve the proportion, we can cross multiply:

(1/4) × x = (1 1/2) × (1/2)

Simplifying the right side of the equation:

(1/4) × x = (3/2) × (1/2)

x/4 = 3/4

To isolate x, we can multiply both sides of the equation by 4:

x = (3/4) × 4

x = 3

Therefore, if Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

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The correct symbol to make the statement true is: -56 < -55

To make the statement true, we need to choose the correct symbol between -56 and -55.

The options are:

-56 > -55 (greater than)

-56 < -55 (less than)

-56 = -55 (equal to)

-56 ≥ -55 (greater than or equal to)

-56 ≤ -55 (less than or equal to)

In this case, the correct symbol to make the statement true is:

-56 < -55

Therefore, the correct statement is: -56 < -55.

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Amilia has 20 times as many toothpicks as Tim. Tim has 3 tooth picks. Amilia has 60 tooth picks.

To determine how many times as many toothpicks Amilia has compared to Tim, we can divide the number of toothpicks Amilia has by the number of toothpicks Tim has.

Amilia has 60 toothpicks, while Tim has 3 toothpicks.

To calculate the ratio, we divide the number of toothpicks Amilia has by the number of toothpicks Tim has:

60 / 3 = 20

Therefore, Amilia has 20 times as many toothpicks as Tim. This means that the number of toothpicks Amilia has is twenty times greater than the number of toothpicks Tim has. It indicates a significant difference in the quantity of toothpicks possessed by the two individuals.

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A combination of the sum of two complex numbers is 15 - 19i

To find the sum of two complex numbers, add their real parts separately and add their imaginary parts separately.Now, we need to find the sum of the following complex numbers.

(-4i) + (10 - 5i) -3

5i -3 - 5i

6 - 4i 6 - 6i

Add the real parts, which are (-4) and 10.

Therefore, the real part is (10 - 4) = 6.

Add the imaginary parts, which are (-5) and (-3).

Therefore, the imaginary part is (-5 - 3) = -8.

Thus, the sum of (-4i) and (10 - 5i) is 6 - 8i.

Now, we need to find the sum of the following complex numbers.

(-3 − 5i) + (6 − 4i) + (6 − 6i)

First, we add (-3 − 5i) and (6 − 4i) to find the sum.

(−3 − 5i) + (6 − 4i) = (3 − 5i)

Then we add (3 − 5i) and (6 − 6i) to find the sum.

(3 − 5i) + (6 − 6i) = 9 − 11i

Therefore, the sum of (-3 - 5i), (6 - 4i) and (6 - 6i) is 9 - 11i.

Now we have to write our answer as a combination of the sum of two complex numbers, which we found earlier.

6 - 8i + 9 - 11i = 15 - 19i

Thus, the final answer is 15 - 19i.

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The number of times Felipe's stamp collection is contained within his uncle Carlo's collection is 52.5 times.

Felipe has 36 stamps in his collection, and his uncle Carlo has 1890 stamps in his collection. To determine how many times Felipe's collection fits into Carlo's collection, we can divide the number of stamps Carlo has by the number of stamps Felipe has.

1890 / 36 = 52.5

Therefore, Felipe's stamp collection is contained within his uncle Carlo's collection approximately 52.5 times.

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The correct option is D, which has the equation (y+13)²/144 - (x+5)²/25 = 1.

The hyperbola x²/16 - y²/9 = 1 has its center at (0, 0), its transverse axis along the x-axis, and its foci at (-c, 0) and (c, 0),

Where c is the distance from the center to the foci.

The formula for the distance from the center to the foci is c = √(a² + b²), Where a is the distance from the center to a vertex on the transverse axis, and b is the distance from the center to a vertex on the conjugate axis.

In this case,

a² = 16, so a = 4, and b² = 9, so b = 3.

Therefore, c = √(16 + 9) = 5.

So, we are looking for a hyperbola with one focus at (-5, 0) or (5, 0).

Option A has a focus at (13, 5) and a focus at (13, -5), so it does not have a focus in common with the given hyperbola.

Option B has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.

Option C has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.

Option D has a focus at (-5, -13) and (-5, 13), so it has a focus in common with the given hyperbola. Therefore, the correct answer is D.

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The complete question is:

Which hyperbola has one focus in common with the hyperbola  x²/16 - y²/9 = 1.

In each round, half of the remaining teams are eliminated.7th round: 2 - 1 = 1 team eliminated The sequence shows the progressive elimination of teams as the tournament progresses.

The sequence that represents the number of teams that have been eliminated in round n of the badminton tournament. This pattern continues until there is only one team left, which becomes the winner of the tournament.

It can be written as follows:

1st round: 128 - 64 = 64 teams eliminated

2nd round: 64 - 32 = 32 teams eliminated

3rd round: 32 - 16 = 16 teams eliminated

4th round: 16 - 8 = 8 teams eliminated

5th round: 8 - 4 = 4 teams eliminated

6th round: 4 - 2 = 2 teams eliminated

7th round: 2 - 1 = 1 team eliminated

In each round, half of the remaining teams are eliminated. This pattern continues until there is only one team left, which becomes the winner of the tournament. The sequence shows the progressive elimination of teams as the tournament progresses.

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The  statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

The figure shows a pair of parallel line segments on a coordinate grid: Line segment GH runs from (-1, -1) to (3, -1), and line segment EF runs from (-1, -2) to (3, -2).

To determine the characteristics of line segments E'F' and G'H' after being translated 2 units to the right, we need to apply the translation to the endpoints of the original line segments.

Applying a translation of 2 units to the right:

Endpoint E: (-1, -2) + (2, 0) = (1, -2)

Endpoint F: (3, -2) + (2, 0) = (5, -2)

Endpoint G: (-1, -1) + (2, 0) = (1, -1)

Endpoint H: (3, -1) + (2, 0) = (5, -1)

Now, let's analyze the statements:

a) Line segments E'F' and G'H' do not intersect and are closer together than EF and GH.

  This statement is false. E'F' and G'H' do not intersect, but they are not closer together than EF and GH. They are actually farther apart.

b) Line segments E'F' and G'H' intersect at (-2, 0) and are two times farther apart than EF and GH.

  This statement is false. E'F' and G'H' do not intersect at (-2, 0). They have different coordinates for their endpoints.

c) Line segments E'F' and G'H' intersect at (0, -2) and are two times closer together than EF and GH.

  This statement is false. E'F' and G'H' do not intersect at (0, -2). They have different coordinates for their endpoints.

d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

  This statement is true. E'F' and G'H' do not intersect, and they have the same distance between them as EF and GH.

Therefore, the correct statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

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The discounted-price of the game system is $154.00, given the original-cost of a video game system is $175 and Raymond works in an electronics store and gets a 12 percent employee discount.

The discounted price, we need to find 12% of $175 which is equal to: [tex]\frac{12}{100}\times175=21[/tex]

The employee discount is $21.

We need to subtract this discount from the original cost:

175 - $21 = 154

So, the discounted price of the game system is $154.00.

Therefore, the correct option is $154.00

The discounted price of the game system is indeed $154.00.

The original cost of the game system is $175, and

Raymond receives a 12% employee discount.

We calculate 12% of $175, which is $21.

By subtracting this discount from the original cost, we get $154.00, which is the final discounted price.

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To show that the lorry is traveling below the speed limit, we need to convert its speed from meters per second to kilometers per hour and compare it to the speed limit of 50 km/h.

The lorry's speed is given as 13.6 m/s. To convert this to kilometers per hour, we multiply it by the conversion factor: Speed (km/h) = Speed (m/s) * (3.6 km/h) = 13.6 * 3.6 = 48.96 km/h. Comparing the lorry's speed of 48.96 km/h to the speed limit of 50 km/h, we can see that the lorry is traveling below the speed limit.

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The exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.

To find the exact value of tangent (19π/12), we can use the trigonometric identity:

tangent (θ) = sin (θ) / cos (θ).

First, let's find the values of sin (19π/12) and cos (19π/12).

Using the unit circle, we can determine that sin (19π/12) = -1/2 and cos (19π/12) = -√3/2.

Now we can substitute these values into the tangent formula:

tangent (19π/12) = sin (19π/12) / cos (19π/12) = (-1/2) / (-√3/2).

Simplifying the expression by multiplying the numerator and denominator by 2/√3:

tangent (19π/12) = (-1/2) * (2/√3) / (-√3/2) = (1/√3).

To rationalize the denominator, we multiply the numerator and denominator by √3:

tangent (19π/12) = (1/√3) * (√3/√3) = √3/3.

Therefore, the exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.

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The total number of women at the college is 250. The total enrollment, including both men and women, is 420.

Let's assume the number of men is 7x and the number of women is 5x. According to the given information, 7x = 5x + 460. Solving this equation, we find x = 230. Substituting this value back, we find the number of women is 5x = 5 * 230 = 1150. The total enrollment is the sum of the number of men and women, which is 7x + 5x = 12x = 12 * 230 = 2760. Therefore, the total number of women is 1150, and the total enrollment is 2760.

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There are 217 bacteria there now.

A percentage is defined as the ratio that can be expressed as a fraction of 100.

We have:

initial count (P) = 155

growth rate (r) = 40% = 0.4 (from the image)

current count = P(1 + r)

current count = 155(1 + 0.4)

current count = 155(1 .4)

current count = 217

Therefore, 217 bacteria are there now.

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Complete Question

Check attached image

The value of the variable x in the given figure is given by 19.1 ft.

Here in the given picture the given two triangles are similar triangles.

For the similar triangles, the ratios of the similar sides are equal.

So here the side with 9.3 ft of first triangle is similar with the side with x ft and the side of 1.7 ft of first triangle is similar with the side with 3.5 ft.

By the condition then,

x/9.3 = 3.5/1.7

x = 9.3 * (3.5 / 1.7) = 19.1 [rounding off to the nearest first decimal place]

Hence the value of x in the given figure is 19.1 ft.

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The question is incomplete. The complete question will be -

The average height is 1.4m and the total height of the other three children is given by T = 2.95 m

Given data,

To find the total height of the other three children, we first need to determine the combined height of Nosiku, Naza, and Tom.

Given that the average height of Nosiku, Naza, John, and Tom is 1.4m, and John's height is 1.25m, we can calculate the total height of the other three children as follows:

Total height of the other three children = Average height * Number of children - John's height

Total height of the other three children = ( 1.4m x 3 ) - 1.25m

T = 4.2m - 1.25m

T = 2.95m

Hence , the total height of the other three children (Nosiku, Naza, and Tom) is 2.95 meters.

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