A toolbox is 2 ft high, and its width is 3 ft less than its length. If its volume is 80 ft³, find the length and width of the box.​

Refractive index of the given unknown liquid = 0.500.

What is angle?

Angle is a geometric figure formed by two rays, called the sides of the angle, that have a common endpoint, called the vertex. An angle is measured in degrees, with a full circle representing 360°.

The refractive index of a material is a measure of how much light is bent when it enters the material from a medium with a different refractive index. When light enters a material with a higher refractive index, it bends towards the normal. The angle of refraction can be used to calculate the refractive index of a material. In this case, the unknown liquid’s refractive index is determined by measuring the angle of refraction.

The angle of refraction of the unknown liquid was 30 degrees, which was used to calculate the refractive index. Using the equation n1 = 1.0003 x sin (angle 2), the refractive index of the liquid was determined to be 0.50015, which was rounded to 3 decimal places to give a result of 0.500.

The refractive index of a material is an important measure of how light behaves when it interacts with a material. Knowing the refractive index of a material is important for applications such as computing the path of light through optical lenses or calculating the velocity of light in various materials, as well as for analyzing the behavior of materials such as metals, plastics and liquids.

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Answer:

Scalene triangle

Step-by-step explanation:

To determine the type of triangle, we need to compare the lengths of the sides to each other.

If all three sides have the same length, it's an equilateral triangle.

If two sides have the same length and the third is different, it's an isosceles triangle.

If all three sides have different lengths, it's a scalene triangle.

Using the lengths given, we see that all three sides have different lengths, so this is a scalene triangle.

Answer:

an obtuse triangle.

Step-by-step explanation:

To determine the type of triangle with sides of lengths 2, 6, and 7, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we can check whether this condition holds for the three sides of lengths 2, 6, and 7:

2 + 6 > 7 (True)

6 + 7 > 2 (True)

2 + 7 > 6 (True)

Since all three inequalities are true, the given lengths of 2, 6, and 7 form a valid triangle.

To determine the type of triangle, we can use the lengths of the sides and the Pythagorean theorem or trigonometric functions. For this triangle, we can use the Pythagorean theorem to find that the longest side (7) is opposite the largest angle, which is greater than 90 degrees. Therefore, this triangle is an obtuse triangle.

The two functions with the end behavior x→+∞ , f(x) →+∞ are:

f(x) = (1/4)*x + 3

h(x) = 2x - 1

The end behavior of a function studies how the function behaves as x tends to infinity or negative infinity.

The function will tend to positive infinity as x tends to positive infinity if the function increases for x > 0.

Then we need to identifty which of these two functions are increasing, the two increasing ones are:

f(x) = (1/4)*x + 3

h(x) = 2x - 1

These two are linear equations with positive solpes, so these are increasing functions, and as x→+∞ , f(x) →+∞

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }[/tex]

The highlighted part of circle shown below is known as segment.

A segment of a circle is a region of the circle that is bounded by a chord and the arc that it intersects. More specifically, a segment is the region between a chord and a minor or major arc of a circle.

The chord is the straight line that connects two points on the circumference of the circle, and the arc is the curved part of the circumference that lies between these two points. A segment is named according to its chord, for example, the segment determined by the chord AB is referred to as segment AB. The area of a segment of a circle can be calculated using the formula A = (1/2)r^2(θ-sinθ), where r is the radius of the circle, and θ is the central angle of the segment in radians.

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The simplified expression when(17−8c)is subtracted from (−c+5) is 12 - 7c.

When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement. Let's say James and Natalie were tinkering with matchsticks when they had the idea to arrange the sticks into numerical patterns. James used four matchsticks to make the numeral 4 in the air. Adding three additional matchsticks allowed Natalie to create a pattern with two 4s. They understood that they may continue to add three matchsticks each round to make a total of four.

The two expressions are:

17 - 8c and - c + 5

The subtraction of the two expressions are:

17 - 8c - (-c + 5)

17 - 8c + c - 5 = 12 - 7c

Hence, the simplified expression when(17−8c)is subtracted from (−c+5) is 12 - 7c.

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Answer:

Based on the data in the table, we can set up a system of equations to represent the relationship between the number of imports (f(x)) and the number of exports (g(x)):

2x + 3y = z (Equation 1)

4x + 4y = z (Equation 2)

6x + 5y = z (Equation 3)

8x + 6y = z (Equation 4)

In this system, x represents the month number (January = 1, February = 2, etc.), y represents the number of exports, and z represents the total trade (exports plus imports). Each equation represents the data for a specific month.

To solve the system, we can use any method of solving systems of linear equations, such as substitution or elimination. However, we can also observe a pattern in the coefficients of the variables:

2 3 5 8

4 4 6 8

We can see that the coefficients of the x-term (the month number) increase by 2 each time, and the coefficients of the y-term (the number of exports) increase by 1 each time. This suggests that the equation for the nth month (where n is an integer between 1 and 4) can be expressed as:

2n + (n+2)y = z

We can test this by plugging in the values of n and y from any of the given months and verifying that the resulting value of z matches the actual value for that month. For example, if we use the data for March (n=3, y=5), we get:

2(3) + (3+2)(5) = z

6 + 25 = 31

And we can see that the actual value of z for March is indeed 31, which confirms that our equation works.

Using this equation, we can find the solution to the system for any given month by plugging in the appropriate values for n and y. For example, to find the total trade (z) for May (which would correspond to n=5), we can plug in n=5 and solve for z:

2(5) + (5+2)y = z

10 + 7y = z

To find the number of exports for May, we can plug in n=5 and solve for y:

2(5) + (5+2)y = z

10 + 7y = z

10 + 7y = 10 + 2y + 3

5y = -3

y = -3/5

However, since exports cannot be negative, this solution is not valid. This suggests that the data given in the table only applies to the months of January through April, and we cannot use this equation to find the solution for any month beyond April.

In summary, the system of equations represents the relationship between the number of imports and exports for each month from January to April. By observing the pattern in the coefficients of the equations, we can derive a general equation that can be used to find the total trade for any month between January and April. However, we cannot use this equation to find the solution for any month beyond April, as there is not enough data to determine the number of imports and exports for those months.

It is feasible to close Hargett St. between Blount Street and Person Street for a day.

Given the traffic flow model described, it is feasible to close Hargett St. between Blount Street and Person Street for a day. The model states that the average daily traffic flow on Hargett St. is 8,000 vehicles per day, with 3,000 vehicles per hour during peak hours. By closing Hargett St. between Blount Street and Person Street for a day, the average daily traffic flow would be reduced by 8,000 vehicles per day. Thus, the total number of vehicles that would be diverted from Hargett St. on the day of the event would be 8,000 vehicles. This amount of traffic would not be too overwhelming for the surrounding streets to handle, since the model states that the average daily traffic flow for those streets is approximately 4,000 vehicles per day.

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Answer:

25

Step-by-step explanation:

Add all of the sides together

The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units'

Given data ,

Let the exponential growth equation be represented as x ( t )

Now , the average percentage change from the year 2000 - 2009 is calculated by

The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )

The total number of years = 9 years

So , the average percentage change = total percentage / number of years

On simplifying , we get

The average percentage change = 12.21 / 9 = 1.35667 %

b)

The population in 2009 was 37,000,000

So , the population growth rate r = 1.35667 %

And , the population in the years 2015 is given by

The number of years n = 6 years

x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶

On simplifying , we get

x ( t ) = 37,000,000 ( 1.013567 )⁶

x ( t ) = 40,115,896

Hence , the population in the year 2015 is 40,115,896

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A sinusoidal function is a type of periodic function that can be written in the form y = a sin(bx + c) + d, where a is the amplitude, b is the frequency, c is the phase shift, and d is the vertical shift.

Given the parameters in the question, we can plug them into the general form of a sinusoidal function to find the specific function.

Amplitude = 4
Period = 3π
Vertical shift = -8

The period of a sinusoidal function is related to the frequency by the equation period = (2π)/b. Therefore, we can solve for b to find the frequency:

3π = (2π)/b

b = (2π)/(3π)

b = 2/3

Plugging in the given values for amplitude, frequency, and vertical shift, we get the sinusoidal function:

y = 4 sin((2/3)x) - 8

This is the sinusoidal function that satisfies the given conditions. It has an amplitude of 4, a period of 3π, and a vertical shift down 8 units.

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The area of the shape formed from rectangle ABDE is 78 cm².

To find the area of the compound shape, we need to find the area of rectangle ABDE and triangle BCD separately and then add them.

The rectangle ABDE has a length of 15 cm (DE) and a width of 4 cm (AB). Therefore, its area is:

Area of rectangle = length x width = 15 cm x 4 cm = 60 cm²

The triangle BCD has a base of 4 cm (BC) and a height of 9 cm (BD). Therefore, its area is:

Area of triangle = 1/2 x base x height = 1/2 x 4 cm x 9 cm = 18 cm²

Now, add the areas of the rectangle and the triangle to find the total area of the compound shape:

Total area = Area of rectangle + Area of triangle = 60 cm² + 18 cm² = 78 cm²

Therefore, the area of the compound shape is 78 cm².

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The probability of choosing the lists of students from the class is given by combinations C = 2400 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the total ways of choosing the students from the class be C

Now , the total number of boys = 12 boys

The total number of girls = 10 girls

And , the lists are in the order

A = { boy , girl , boy }

B = { girl , boy , girl }

The total number of ways C = A + B

From the combination of selecting boys and girls , we get

The total number of selecting A = 12 x 10 x 11 = 1320 ways

The total number of selecting B = 10 x 12 x 9 = 1080 ways

So , the total number of selecting the lists C = 2400 ways

Hence , the probability of choosing the lists of students from the class is given by C = 2400 ways

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The equation that could that represents the relationship is: m = 27g

Variation is a topic which expresses the relationship between two variables in the form of an equation. The two variables are known as dependent and independent variables.

Considering Mr. Nava's statement, since the number of gallons of gasoline has a direct relationship to the number of miles he travels, then;

m [tex]\alpha[/tex] g

m = kg

where k is the constant of proportionality

This implies that the more the amount of gasoline in his car, then the more the number of mile that he will travel.

Therefore, the equation that represents this relationship is:

m = 27g

where the value of k is 27

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Answer:

  E.  ∆ABE is isosceles

Step-by-step explanation:

Given ∠BAD ≅ ∠BED in ∆ABE you want to know what can be concluded.

An isosceles triangle has sides of equal measure opposite angles of equal measure. The base angles A and E in triangle ABE are given as congruent, so we can conclude ∆ABE is isosceles.

The inverse of the following matrix X is X-1 = ​3/416/4-1/4​​-3/44/30/4​-2/41/41/4​​.

The inverse of a matrix is a matrix that, when multiplied by the original matrix, produces the identity matrix. To find the inverse of the following matrix X, we need to use the formula X-1 = 1/|X| adj(X), where |X| is the determinant of X and adj(X) is the adjoint of X.

First, let's find the determinant of X:
|X| = (1)(-12)(-3) + (2)(-1)(-2) + (2)(3)(-1) - (-2)(-1)(2) - (1)(3)(-2) - (4)(-1)(-3)
|X| = -36 + 4 + -6 + 4 - -6 - -12
|X| = -16

Since the determinant of X is not equal to 0, the inverse of X exists.

Now, let's find the adjoint of X:
adj(X) = ​-12-2-1​​34-30​24−11−3​​

Finally, let's use the formula X-1 = 1/|X| adj(X) to find the inverse of X:
X-1 = 1/(-16) ​-12-2-1​​34-30​24−11−3​​

X-1 = ​3/416/4-1/4​​-3/44/30/4​-2/41/41/4​​

Therefore, the inverse of the following matrix X is X-1 = ​3/416/4-1/4​​-3/44/30/4​-2/41/41/4​​.

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To solve the compound inequality, we need to solve each inequality separately and then combine the solutions using the word "OR."

For the first inequality, 8x+7>55, we can isolate the variable on one side of the inequality by subtracting 7 from both sides:

8x > 48

Next, we can divide both sides by 8 to solve for x:

x > 6

For the second inequality, -5x-1>=-26, we can isolate the variable on one side of the inequality by adding 1 to both sides:

-5x >= -25

Next, we can divide both sides by -5 to solve for x. Remember that when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:

x <= 5

Now we can combine the solutions using the word "OR." In interval notation, this would be (-∞, 5] U (6, ∞). This means that the solution includes all values of x less than or equal to 5 or greater than 6.

So the final answer is:

x ∈ (-∞, 5] U (6, ∞)

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The value of the trigonometric function sin A, tan A, and sec A will be 3/5, 3/4, and 5/4.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Use the triangle to evaluate each function.

Hypotenuse AB has a length of 5, BC has a length of 4, and side AC has a length of 3.

Then the value of the trigonometric function will be

sin A = BC / AB

sin A = 3 / 5

tan A = BC / AC

tan A = 3 / 4

sec A = AB / AC

sec A = 5 / 4

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nvm sorry wrong answer

Answer:-12

Step-by-step explanation:

To solve for y, we can use the second equation to isolate x and substitute the result into the first equation:

2x - 5y = 72

2x = 5y + 72

x = (5y + 72)/2

Now we can substitute this expression for x into the first equation:

3x + 4y = -30

3((5y + 72)/2) + 4y = -30

Simplifying the left side:

(15/2)y + 108 + 4y = -30

Combining like terms:

(23/2)y = -138

Dividing both sides by (23/2):

y = -138 * 2/23

Simplifying:

y = -12

Therefore, the value of y that satisfies both equations is -12.

The answer using positive exponents only is 16x^(24)y^(16).

To simplify the expression (2x^(6)y^(4))^(4), we need to use the properties of exponents. Specifically, we need to use the property that states (a^(m))^n = a^(m*n). This means that when we raise a power to another power, we multiply the exponents.

Using this property, we can simplify the expression as follows:

(2x^(6)y^(4))^(4) = 2^(4) * x^(6*4) * y^(4*4) = 16 * x^(24) * y^(16)

So, the simplified expression is 16x^(24)y^(16).

Therefore, the answer using positive exponents only is 16x^(24)y^(16).

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=24\\ y=1 \end{cases} \\\\\\ 1=\cfrac{k}{24}\implies 24=k\hspace{9em}\boxed{y=\cfrac{24}{x}} \\\\\\ \textit{when x = 3, what's "y"?}\qquad y=\cfrac{24}{3}\implies y=8[/tex]

The domain of the correspondence is {-3, -2.5, 0, 4} and the range is {3, 9, -10}. This correspondence is not a function because it is not a one-to-one correspondence; for example, both -3 and 4 are mapped to the same value of 3.

The question is asking for the domain, range, and whether the correspondence is a function for the given set of ordered pairs: {(-3,3), (-2.5), (0,9), (4,-10)}.

The domain of a correspondence is the set of all possible input values. In this case, the domain is the set of x-values from the ordered pairs: {-3, -2.5, 0, 4}.

The range of a correspondence is the set of all possible output values. In this case, the range is the set of y-values from the ordered pairs: {3, -5, 9, -10}.

A correspondence is a function if each input (x-value) is associated with only one output (y-value). To determine if the given correspondence is a function, we need to check if any x-value is repeated with a different y-value.

In this case, there are no repeated x-values, so each x-value is associated with only one y-value. Therefore, the correspondence is a function.

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The equation which represents the cost of one square foot of flooring is   x = $3.45.

Let the cost of one square foot of flooring be = x,

We know that the store is selling 60 square feet of flooring for $287, which includes a $80 installation fee.

So, the cost of 60 square feet of flooring is

⇒ $287.00 - $80.00 = $207

To find the cost of one square foot of flooring, we divide the cost of 60 square feet by 60,

Which is,

⇒ $207/60 = $3.45

Therefore, the cost of one square foot of flooring is represented by the equation x=$3.45.

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The given question is incomplete, the complete question is

A home improvement store advertises 60 square feet of flooring for $287.00 including a $80 installation fee. Write an equation to represent the cost of one square foot of flooring.

Answer:

Let's use the variable "r" to represent the number of red flowers in each red flower bed.

Then, the total number of red flowers in the garden would be 3r, since there are 3 beds of red flowers.

Similarly, the total number of yellow flowers in the garden would be 3 * 30 = 90, since there are 3 beds of yellow flowers, and 30 flowers in each bed.

So the total number of flowers in the garden is the sum of the red and yellow flowers:

Total number of flowers = 3r + 90

Since there are 135 flowers in the garden, we can set the equation equal to 135 and solve for "r":

3r + 90 = 135

3r = 45

r = 15

Therefore, there are 15 red flowers in each red flower bed, and the total number of red flowers in the garden is 3r = 45. The equation representing the number of red and yellow flowers is:

Total number of flowers = 3r + 90 = 3(15) + 90 = 45 + 90 = 135.

So this equation checks out, as we expect the total number of flowers to be 135.

Answer:

Step-by-step explanation:

Sorry, i can't heip you

Exact Form of the expression is mathematically given as

[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]

Generally, An expression is a combination of variables, numbers, operators, and/or functions that represent a value.

[tex]\sin \left(2 \arccos \left (\frac{1}{3}\right)\right)[/tex]

Evaluate[tex]$\arccos \left(\frac{1}{3}\right)$.[/tex]

sin (2 *1.23095941)

Multiply 2 by 1.23095941.

sin (2.46191883)

The result can be shown in multiple forms.

Exact Form:

[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]

Decimal Form:

0.62853936

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Answer:

13:00

Make a straight line from the vertex of the current Yuri line to 16:15

Step-by-step explanation: