The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm, what must be the length of the longest side of ∆XYZ?

Step-by-step explanation:

x and y are directly proportional means that

y = kx

y grows with the same factor k applied to x.

the area of a circle (the cross section of a cylindrical pipe) is

pi × r²

r being the radius (which is half of the diameter).

so, the area in terms of the diameter is

pi × (d/2)² = pi × d²/4

so, we know

36 correlates to pi × (d small)²/4

60 correlates to pi × (d large)²/4

therefore (directly proportional),

d small² = 36×4/pi

d small = 12/sqrt(pi)

d large² = 60×4/pi

d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)

the difference between large and small diameter (increase from small to large) is then

4×sqrt(15/pi) - 12/sqrt(pi)

d small = 100%

1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))

the % of the diameter increase is then

increase/1% =

(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =

= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =

= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =

= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%

the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.

please consider : only the area of the cross section and the carrying capacity are directly proportional.

the diameter of the cross section and the area of the cross section are NOT directly proportional.

they have the pi×(d/2)² relationship.

and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.

so, for capacity and area we have

60 = k×36

k = 60/36 = 5/3 = 1.66666666...

and therefore both increase by 66.66666...%.

but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.

The equation that represents the total cost is C = $50 + $70t.

The total amount earned by the electrician is the sum of the fixed cost and the variable cost.

Total amount earned = fixed cost + variable cost

The fixed cost is the set fee he charges . The variable cost is a function of the additional hourly fee and the number of hours

The equation that represents the the total amount earned when he works for 5 hours is:

$400 = $50 + (5 x v)

$400 = $50 + 5v

$400 - $50 = 5v

$350 = 5v

v = $350 / 5

v = $70

C = $50 + $70t

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The value of the equation 6 sinθ=5 for θ is 56.4 degrees

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

6 sinθ=5

Express the equation properly

So, we have the following representation

6 sin(θ) = 5

Divide both sides of the equation by 6

This gives

sin(θ) = 5/6

Evaluate the quotient

sin(θ) = 0.833

Take the arc sin of both sides

θ = sin⁻¹(0.833)

Evaluate

θ = 56.4

Hence, the value of the equation for θ is 56.4 degrees

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Complete question

Approximate θ in the equation, to the nearest 0.1 degrees

6 sin(θ) = 5

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

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The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

Starting with the two equations:

Y = x + 3    (1)

Y = 3x + 1     (2)

We can solve for x and y by equating equation (1) and (2) and solving for x.

x + 3 = 3x + 1

2x = 2

x = 1

Now we can substitute x = 1 into either equation (1) or (2) to solve for y.

Using equation (1):

Y = x + 3

Y = 1 + 3

Y = 4

Therefore, the solution for the system of equations is:

x = 1, y = 4

The correct answer is, Cougars; they have a larger median value of 22 inches.

Calculating the median and mean for each data set, we get:

Cougars:

Median = 22 inches

Mean = 22.3 inches

Panthers:

Median = 22.5 inches

Mean = 22.2 inches

Since the median of the Cougars data set is larger than the median of the Panthers data set, we can conclude that the Cougars have the largest overall size hat for their players.

Therefore, the correct answer is, Cougars; they have a larger median value of 22 inches.

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Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

The equation in the standard form of a circle and find the centre and radius:

(x - 1)²/31 + (y + 3)²/31/3 = 1

To graph by completing the square, we need to rearrange the equation so that it has the form:

(x - h)² + (y - k)² = r²

Starting with x² - 2x + y² + 6y - 6 = 0:

First, we can factor out a 2 from the x terms and a 6 from the y terms:

2(x² - 2x) + 6(y² + 6y) - 6 = 0

Next, we need to complete the square for the x and y terms:

2(x² - 2x + 1) + 6(y² + 6y + 9) - 6 = 2(1) + 6(9)

Simplifying, we get:

2(x - 1)² + 6(y + 3)² = 62

Now we can rewrite the equation in the standard form of a circle and find the centre and radius:

(x - 1)²/31 + (y + 3)²/31/3 = 1

The centre of the circle is (1, -3), and the radius is √(31/3).

The graph is attached with the answer below.

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The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .

To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.

For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.

Speed of Swordfish is:

= 60 mph x 0.0166667

= 1 mile per minute

Speed of Tuna :

= 45 mph x 0.0166667

= 0. 75 miles per minute

Dolphin :

= 20 mph x 0.0166667

= 0. 33 miles a minute

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Answer:

194.4

Step-by-step explanation:

V=l*w*h

V=12*4.5*3.6

V=194.4

The probability is very high and the event is very likely to occur.

option B.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

If the probability of a rolling a number greater than 1 on a six sided cube die  is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.

We will convert 5/6 to percentage to see the actual value of 5/6.

5/6 x 100%

= 83.33 %

So the value of this probability is very high and the event is very likely to occur.

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Answer:

The sample space of possible combinations of pants and shoes for the math teacher is 9. These combinations include gray pants with black, brown, or tan shoes, green pants with black, brown, or tan shoes, and blue pants with black, brown, or tan shoes.

Hope its helpful

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

It's given that, The area of a rectangle in square inches is 5x² - 18x - 8 and the length of the rectangle is x - 4 inches.

Let the width of the rectangle be x inchez

We know that area of Rectangle is calculated by,

[tex]:\implies[/tex] Length × width = area

Substituting the values we get,

[tex]:\implies[/tex] (x - 4)(x) = 5x² - 18x - 8

[tex]:\implies[/tex] x² - 4x = 5x² - 18x - 8

[tex]:\implies[/tex] x² - 5x² - 4x + 18x = -8

[tex]:\implies[/tex] -4x² + 14x = -8

[tex]:\implies[/tex] -4x² + 14x + 8 = 0

Hence, This is the required expression which represent the width of the rectangle.

The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:

r = d/2 = 22/2 = 11 m

Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.

The volume (V) of a cone is given by the formula:

V = (1/3)πr²h

Substituting the values of r and h, we get:

V = (1/3)π(11)²(22)

V = 2786.2 cubic meters

The surface area (A) of a cone is given by the formula:

A = πr(r + l)

here l is the slant height of the cone, which can be found using the Pythagorean theorem:

l = √(r² + h²)

l = √(11² + 22²)

l = √(605)

l = 24.6

Substituting the values of r and l, we get:

A = π(11)(11 + 24.6)

A ≈ 1229.51 square meters

Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

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Answer:

x / 2 = 17

Step-by-step explanation:

Since we're told that there are 2 friends, they split the cost evenly, and they  each paid $17 individually, we'd have to use the equation x / 2 = 17 to find the total cost.

If you were to solve, you'd find that the total cost was $34 as 2 * 17 = 34 and 34 / 2 = 17

Answer: 37km

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial. Note that if we multiply our answer out, we do get the original polynomial.

Answer: To find a 2 numbers that multiply to the value of C and Add to the value of b.

Step-by-step explanation: They Have to multiply to C and add to B and after that you can just continue simplifying the polynomial.

Wendy's marginal tax brackets in 2022 while she is still in school is 12 percent and it will be also 12 percent when she graduates.

Hence the correct option is (D).

Given that Wendy is Single.

So the effective taxable income regime will be which is on the second column.

It is given that at her school days she earns a taxable income of $ 12,000.

So $12000 falls in the slab of $ 10276 - $ 41775.

So the tax rate for her in her school days is 12%.

When she will graduates the taxable per year income will be $35,000.

Clearly, $35,000 also falls into the slab of $ 10276 - $ 41775.

So the tax rate for her when she will graduate will be same 12 percent.

Hence the correct option will be (D).

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There are 14 dogs and 46 chickens in the farmyard.

The supposition that there are d dogs and c chickens.

Each chicken has two legs, but each dog has four.

Consequently, the total number of legs may be written as follows:

4d + 2c

Since we are aware that there are 148 legs in total, we can construct the following equation:

4d + 2c = 148

We may create another equation since we know that there are a total of 60 heads (dogs and chickens):

d + c = 60

Now that we have two equations with two variables, we may answer them both at the same time.

2d + 2c = 120 is the result of multiplying the second equation by two.

When we deduct this from the first equation, we obtain 2d = 28.

So, d = 14.

Reintroducing this into the second equation, we get:

14 + c = 60

So, c = 46.

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The loan's Present Value for which you can afford a $400 monthly payment for a car for 5 years at 2% interest should be as big as $22,820.94.

The present value is the discounted monthly payments at an interest rate for a period.

The present value can be determined using an online finance calculator as follows.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 2%

PMT (Periodic Payment) = $400

FV (Future Value) = $0

Results:

Loan size (Present Value) = $22,820.94

The sum of all periodic payments = $24,000.00

Total Interest = $1,179.06

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In 20 days was the whole job done.

Let efficiency of each worker is 1 unit / day .

So, Total work = 10 x 1 x 15 = 150 units .

Now, in first 5 days 6 worker completes

= 5 x 6 x 1 = 30 units .

and, in next 3 days 8 workers completes

= 3 x 8 x 1 = 24 units .

Now, 4 more workers joined then total workers are = 12 workers .

So, amount of work left = 150 - 30 - 24 = 96 unit

Thus, the time taken by 12 workers to complete remaining work

= 96/12

= 8 days .

So, the Whole job was done in = 5 + 3 + 12 = 20 days

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The question attaches here seems to incomplete the complete question is

10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?

The volume of cylinder B can be calculated using the concept of similarity between the cylinders and the relationship between their areas and volumes. Therefore, the volume of cylinder B is approximately 135.346 cm³.

Given that cylinders A and B are mathematically similar, we can establish a ratio between their corresponding measurements. In this case, we are given the area of the cross-section of cylinder A, which is 18 cm², and the dimensions of cylinder B, which has a height of 10 cm and an unknown radius.

To find the volume of cylinder B, we need to determine the corresponding measurements of its cross-section. Since the cylinders are similar, the ratio of their areas is equal to the square of the ratio of their corresponding linear measurements.

Let's assume that the radius of cylinder B is 'r'. Since the height of cylinder B is given as 10 cm, we can calculate the area of its cross-section using the formula for the area of a circle: A = πr².

The ratio of the areas of the cross-sections of cylinders A and B can be expressed as (Area of A) / (Area of B) = 18 / (πr²).

Since the height of cylinder B is twice that of cylinder A (10 cm compared to 5 cm), the ratio of their corresponding linear measurements is 2:1.

Therefore, the ratio of the areas is (2:1)² = 4:1.

Setting up the equation, we have 18 / (πr²) = 4/1.

By rearranging the equation, we can solve for the radius 'r' of cylinder B:

18 = (4/1) * (πr²)

18 = 4πr²

r² = 18 / (4π)

r² = 4.545

r ≈ 2.132 cm

Now that we have the radius of cylinder B, we can calculate its volume using the formula for the volume of a cylinder: V = πr²h.

V = π * (2.132)² * 10

V ≈ 135.346 cm³

Therefore, the volume of cylinder B is approximately 135.346 cm³.

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

a) The data in the above table about the statistics class asked the city where they live are b) Quantitative and Discrete.

b) The completion of the frequency distribution for the data is as follows:

Class            Frequency

Fort Pierce          7

Port St. Lucie      6

Vero Beach        7

Sebastian           4

Okeechobee     6

Total                 30

c) The completion of relative frequency and percentage distribution for the data is as follows:

Class            Frequency    Relative Frequency    Percentage

Fort Pierce          7                       0.233                     23.3%

Port St. Lucie      6                      0.200                     20.0%

Vero Beach        7                       0.233                     23.3%

Sebastian           4                        0.133                      13.3%

Okeechobee     6                       0.200                    20.0%

Total                 30

Class            Frequency    Relative Frequency        Percentage

Fort Pierce          7                 0.233 (7/30)           23.33% (7/30 x100)  

Port St. Lucie      6                0.200 (6/30)           20.00% (6/30 x100)  

Vero Beach        7                 0.233 (7/30)           23.33% (7/30 x100)  

Sebastian           4                  0.133 (4/30)            13.33% (4/30 x100)  

Okeechobee     6                 0.200 (6/30)           20.00% (6/30 x100)  

Total                 30

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a) Time-Series

b) Quantitative and Discrete

c) Cross-Sectional Qualitative

d) Quantitative and Continuous

The solution to the System of equations is x = -9 and y = 8

We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.

Given x = -9, we substitute this value into the first equation:

(-9) - y = -1

Simplifying, we have:

-9 + y = -1

To isolate y, we can add 9 to both sides of the equation:

-9 + 9 + y = -1 + 9

This gives us:

y = 8

Therefore, the solution to the system of equations is x = -9 and y = 8.

We can check this solution by substituting the values of x and y back into the original equations:

Equation 1: x - y = -1

Substituting x = -9 and y = 8:

-9 - 8 = -1

Simplifying, we have:

-17 = -1

The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.

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Jasper has a total of 135 possible combinations for his outfit.

To calculate the total number of combinations that Jasper can pick for his outfit, we need to multiply the number of options for each category: tops, pants, shoes, and jackets.

For tops, Jasper has three options: t-shirt, polo, or sweatshirt.

For pants, he has five options: khakis, jeans, sweatpants, corduroys, or shorts.

For shoes, he has three options: boots, tennis shoes, or sandals.

For jackets, he has three options: ski coat, raincoat, or wool coat.

To calculate the total number of combinations, we multiply the number of options for each category:

3 (tops) × 5 (pants) × 3 (shoes) × 3 (jackets) = 135

Jasper has a total of 135 possible combinations for his outfit.

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