The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?

Answer:

We can use the Pythagorean theorem to solve this problem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we know that the two sides have lengths of 2 cm and 6 cm, and we are trying to find the length of the third side, which we'll call x. We also know that the third side is not the hypotenuse, so we can't just assume that it's the longest side.

Using the Pythagorean theorem, we can write:

x^2 + 2^2 = 6^2

Simplifying, we get:

x^2 + 4 = 36

Subtracting 4 from both sides, we get:

x^2 = 32

Taking the square root of both sides, we get:

x = sqrt(32)

Simplifying, we get:

x = 4sqrt(2)

So the length of the third side is 4sqrt(2) centimeters.

Answer:

Step-by-step explanation:

The situation is modeled by the linear equation:

t = $5*x

We know that Brenda earns $5 each week for chores. The variable x represents the number of weeks brenda did her chores, and t represents the total dollars she earned.

Then if she works for x weeks, the amount that she earns is x times $5, then the equation will be a linear one:

t = $5*x

That is the equation.

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The equivalent expressions is solved to give the quantity four ninths end quantity to the power of x. Option C

An algebraic expression can be described as an expression that is made up of terms, factors, coefficient, variables and constants.

These expressions are also composed of mathematical operations.

Also note that index forms are mathematical forms used to represent numbers too large or too small.

From the information given, we have that;

(2/3)²⁽ˣ⁾

expand the bracket, we get;

(2/3)²ˣ

Find the square of both the numerator and denominator, we get;

(4/9)ˣ

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The correct values to fill in the missing information are:

Claim: The claim is that the proportion of American adults who eat salad once per week is different from 50%, which corresponds to the null hypothesis H0: p = 0.5.

Opposite: The opposite of the claim is that the proportion of American adults who eat salad once per week is equal to 50%, which corresponds to the alternative hypothesis H1: p = 0.5 (Note that in this case, the alternative hypothesis is the opposite of the claim since we are testing for a difference from 50% in the claim).

Therefore, the claim is H0: p ≠ 0.5 (two-tailed test), and the opposite is H1: p = 0.5 (two-tailed test).

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There are 462 different possible lineups of 5 songs that can be composed from the given list of 11 songs.

We need to use the idea of combinations to figure out how many different lineups of musical entertainment can be made. A way to select objects from a larger set without regard to their order is called a combination.

In this problem, we have to choose five songs from an 11-song list. We would like to know how many different ways there are for us to select five songs from the eleven that are available, where the order of the songs in the lineup is irrelevant. We can use the combination formula to solve this.:

n choose k = n! / (k! * (n - k)!)

where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to and including that number.

In this case, we have 11 songs to choose from and we want to choose 5 songs. So we can plug these values into the formula:

11 choose 5 = 11! / (5! * (11 - 5)!)

= (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)

= 11,880 / 120

= 462

Consequently, there are 462 unique potential setups of 5 tunes that can be created from the given rundown of 11 melodies.

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I actually do not know because I am still in grade 6

• Concept: Exponents

• Solution:

You want to simplify the expression 4⁰×4².

We will use basic exponent properties for this.

First bear in mind that anything to the power of 0 is 1.

So that means that 4⁰ = 1.

We're not done yet because we still need to simplify the other part:

4².

Don't forget that:

Because

4² = 4×4 which is 16

So we have 1 times 16 or just 16.

Answer: choice "c": 16

Answer:

42, 41, 123

Step-by-step explanation:

3, 2, 6, 5, 15, 14

- 1 x3. - 1. x3. - 1

you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.

Answer:

The next three numbers are 42, 41, and 123

Step-by-step explanation:

3 - 1 = 2

2 * 3 = 6

6 - 1 = 5

5 * 3 = 15

15 - 1 = 14

The pattern is subtracting one and then multiplying by three.

14 * 3 = 42

42 - 1 = 41

41 * 3 = 123

The single payment Jacob would make in 24 months from now, to pay off the two obligations under the new agreement is $7,620.

We shall be solving this using the formula for Simple Interest,

The interest accrued on each payment can be calculated using the formula for Simple Interest:

Interest = Principal × Rate × Time

where:

Principal = amount borrowed,

Rate = simple interest rate,

Time = time period in years.

Under the original agreement, Jacob shall make two payments of $3000 each, one 6 months from now and the other 12 months from now.

For payment1, the interest accrued would be:

Interest1 = $3000 × 0.10 × (6/12) = $150

For payment2, the interest accrued would be:

Interest2 = $3000 × 0.10 × (12/12) = $300

So the total amount Jacob was to pay under the original agreement is:

Total1 = $3000 + $150 + $3000 + $300 = $6,450

Now let's calculate the amount Jacob would have to pay under the new agreement.

Original principal for each payment is $3000.

The interest accrued on the sum of both payments can be calculated using the same formula for simple interest:

Interest3 = ($3000 + $150 + $3000 + $300) × 0.10 × (24/12) = $720

So the total amount Jacob would pay under the new agreement is:

Total2 = $3000 + $150 + $3000 + $300 + $720 = $7,620

So, Jacob would make a single payment of $7,620, 24 months from now,

to pay off both loans under the new agreement.

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Answer:

[tex]m = \frac{4 - ( \sqrt[3]{ - 6} + 4)}{0 - ( - 6))} = \frac{ \sqrt[3]{6} }{6} = .303[/tex]

So the average rate of change of g(x) over -6 < x < 0 is about .303.

$15 is the cost of a 6-ounce serving cost.

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Given: If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting.

EP = 24 lb costing $45

1/4th lost during roasting.

Remaining = 24 lb - (1/4) of 24 lb

= 24 lb - 6 lb

= 18 lb

Now, this roast should match the cost of the original EP.

Cost per lb = (cost of beef originally)/(quantity of roasted beef)

= 45/18 dollar per lb

Cost of 6-ounce serving cost = (45/18)×6 = $15.

Hence, $15 is the cost of a 6-ounce serving cost.

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Answer: The 22% discount was calculated as R551 (rounded to the nearest rand).

Step-by-step explanation:

To calculate the discount, we need to determine what percentage of the original price R2 499 the discount of R551 represents.

The formula to calculate the percentage discount is:

Discount percentage = (Discount amount ÷ Original price) x 100%

Substituting the values given in the question, we get:

Discount percentage = (551 ÷ 2499) x 100%

Discount percentage = 0.22088 x 100%

Discount percentage = 22.088%

Therefore, the discount given was 22%.

The simplest form of the expression "(14ab³)/(7a⁻²b⁻¹)" is represented by the expression (d) 2a³b⁴.

To simplify the expression (14ab³)/(7a⁻²b⁻¹), we first simplify the terms with the same base,

First, we simplify the coefficients "14" and "7" by dividing them to get:

⇒ (14ab³)/(7a⁻²b⁻¹) = 2ab³/a⁻²b⁻¹;

Next, we simplify the variables "a" and "b" by subtracting the exponents of "a" and "b" in the denominator respectively,

We get,

⇒ 2ab³/a⁻²b⁻¹ = 2a¹⁻⁽⁻²⁾b³⁻⁽⁻¹⁾ = 2a¹⁺²b³⁺¹ = 2a³b⁴,

Therefore, the simplest form of the expression (14ab³)/(7a⁻²b⁻¹) is 2a³b⁴, the correct option is (d).

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The given question is incomplete, the complete question is

Look at this expression. (14ab³)/(7a⁻²b⁻¹),

Which of the following is the simplest form of the expression above?

(a) 2a⁻²b⁻³

(b) 2a⁻¹b²

(c) 2[tex]a^{-\frac{1}{2} }[/tex]b⁻³

(d) 2a³b⁴.

(7) The volume of the triangular based prism is 41.16 m³.

(8) The volume of the haxagonal based prism is 1793.4 cm³.

Volume is the space ocuppied by a solid shape.

(7) To calculate the volume of the triangular based prism, we use the formula below

Formula:

Where:

Substitute these values into equation 1

(8) Also, to calculate the volume of the hexagon based prism, use the formula below

Where:

SUbstitute these values into equation 2

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The scatter plots that do not show a linear relationship are B and C

The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.

The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.

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Answer:

Let's assume the number of boys in the school as "B".

Then, the number of girls can be expressed as "B - 28".

According to the problem, the total number of students is 1176. Therefore, we can write an equation as follows:

B + (B - 28) = 1176

Simplifying the above equation, we get:

2B - 28 = 1176

Adding 28 to both sides, we get:

2B = 1176 + 28

2B = 1204

Dividing both sides by 2, we get:

B = 602

Therefore, there are 602 boys in the school.

The value of the missing side x is 12. 6

We have that the Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides.

From the information given, we have that;

(4√5)² = 8² + y²

find the square values

80 = 64 + y²

collect the like terms

y² = 16

y = 4

Also, using the Pythagorean theorem, we have;

x² = 4² + 12²

find the squares and substitute the values

x² = 16 + 144

x² = 160

Find the square root

x = 12. 6

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Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 12 yards long.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Litre and in3 are the symbols for cubic measurements. However, in order to determine an object's dimensions, you must be aware of its volume. It's common practise to translate an object's weight onto metric units like kilogrammes.

Here,

Let's use "x" yards to represent the unknown leg of the right triangular pyramid's base.

A pyramid's volume can be calculated using the following equation: => => Volume = (1/3) * Base Area * Height

In this instance, the height of the pyramid is 14 yards, and its base is a right triangle with legs that are 8 yards and 'x' yards in length.

Consequently, we can formulate the equation for the pyramid's volume as follows:

=> 168 = (1/3) * (8 * x) * 14

The simplified formula gives us 168 = (4/3) * 14 * x.

We may find "x" by dividing both sides of the equation by

=> [(4/3)*14]: 168 / [(4/3)*14] = x.

=> x = 12

Therefore, the other leg of the right triangular pyramid's base is 12 yards long.

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The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days

Work rate is the rate at which a specified work is completed.

The number of days it will take 10 workers to create 20 products = 40 days

Therefore;

The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days

Where 1 worker can create 20 products in 400 days, then;

The work rate for one worker indicates;

The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5

5 workers will take = 400 days ÷ 5 = 80 days

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Answer:

The area of the shaded region is 27 units^2.

Step-by-step explanation:

Area of outer square = 6^2 = 36 units^2

Area of inner square = 3^2 = 9 units^2

Area of shaded region

= 36 units^2 - 9 units^2 = 27 units^2

The area of a shaded region in a unit grid can be found either by subtracting the area of unshaded regions from the total grid area or by adding up the areas of identifiable shapes within the shaded region.

To find the area of the shaded region without counting every square, you can use a few different strategies, such as identifying and subtracting the area of unshaded regions from the total grid area, or recognizing and adding together larger, easily countable shapes within the shaded region.

For example, if your grid is 10x10 units, the total area would be 100 square units. If, within that grid, there are 20 unshaded squares, you can subtract this from the total area to find the area of the shaded region. So, 100 total square units - 20 unshaded square units = 80 shaded square units. This approach works best when the number of unshaded squares is relatively small or easily countable.

Alternatively, if the shaded region forms easily identifiable shapes (like a 5x5 square or a 3x10 rectangle), you can add the areas of these shapes together to get the total shaded area. This approach works best when the shaded region forms a few large, simple shapes.

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A statement which could be true for g is that: D. g(-13) = 20.

In Mathematics and Geometry, a domain can be defined as the set of all real numbers for which a particular function is completely defined.

Since the domain of this function is given by -20 ≤ x ≤ 5, it simply means that the value of x must between -20 and 5. Also, with a range of -5 ≤ g(x) ≤ 45, the value of x must between -5 and 45.

By extrapolating the function, we can deduce that:

g(0) = -2

g(-9) = 6

g(-13) = 20

In this context, we can reasonably infer and logically deduce that based on the answer options provided, g(-13) = 20 is the only statement that could be true for the function g.

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The variables I₁ and I₂ using the matrix algebra and using the Cramer's rule are I₁ = 1 and I₂ = 1

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

15I₁ + 5I₂ = 20

25I₁ + 5I₂ - 30 = 0

Rewrite as

15I₁ + 5I₂ = 20

25I₁ + 5I₂ = 30

Rewrite as

I₁     I₂

15    5    20

25   5    30

From the question, the matrix form is

AI = b

Ths matrix A from the above is

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

Ths matrix B from the above is

[tex]B = \left[\begin{array}{c}20&30\end{array}\right][/tex]

And, we have the matrix I to be

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

Start by calculating the inverse of A from

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

So, we have:

|A| = 15 * 5 - 5 * 25

|A| = -50

The inverse is

[tex]A^{-1} = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right][/tex]

Recall that

AI = b

So, we have

[tex]I = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right] * \left[\begin{array}{c}20&30\end{array}\right][/tex]

Evaluate the products

[tex]I = -\frac{1}{50}\left[\begin{array}{c}5 * 20 + -5 * 30&-25 * 20 + 15 *30\end{array}\right][/tex]

[tex]I = -\frac{1}{50}\left[\begin{array}{c}-50&-50\end{array}\right][/tex]

Evaluate

[tex]I = \left[\begin{array}{c}1&1\end{array}\right][/tex]

Recall that

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

So, we have

I₁ = 1 and I₂ = 1

Recall that the determinant of matrix A calculated in (a) is

|A| = -50

Replace the first column in A with b

So, we have

[tex]AI_1 = \left[\begin{array}{cc}20&5&30&5\end{array}\right][/tex]

Calculate the determinant

DI₁ = 20 * 5 - 30 * 5

DI₁ = -50

Replace the second column in A with b

So, we have

[tex]AI_2 = \left[\begin{array}{cc}15&20&25&30\end{array}\right][/tex]

Calculate the determinant

DI₂ = 15 * 30 - 20 * 25

DI₂ = -50

So, we have

I₁ = DI₁ / |A| = -50/-50 = 1

I₂ = DI₂ / |A| = -50/-50 = 1

So, we have

I₁ = 1 and I₂ = 1

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The value of y in the triangle is 20.

What is the triangle?

A triangle is a polygon with three sides and three angles. It is the simplest and most basic polygon in Euclidean geometry.

According to the given information:

From the figure, we can say that ΔABC and ΔABI are similar.

we can write proportions as

[tex]\frac{y}{30} =\frac{30}{y+25}[/tex]

y(y+25) = 30*30

[tex]y^{2}[/tex]+25y=900

[tex]y^{2}[/tex]+25y-900 = 0

On solving we can use quadratic formula y = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation y^2 + 25y - 900 = 0, we can identify a = 1, b = 25, and c = -900.

Plugging these values into the quadratic formula, we get:

y = (-25 ± √(25^2 - 4 * 1 * -900)) / (2 * 1)

Simplifying further:

y = (-25 ± √(625 + 3600)) / 2

y = (-25 ± √(4225)) / 2

y = (-25 ± 65) / 2

Now we can solve for two possible values of y:

y = (-25 + 65) / 2 = 40 / 2 = 20

y = (-25 - 65) / 2 = -90 / 2 = -45

So the two possible values of y that satisfy the given equation are y = 20 and y = -45.

distance cannnot be negative, so the value of y is 20.

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The measures of the angles are

MSR = 42

MSCQ = 138 degree

mSQR = 318 degrees

mQV = 42 dgerres

MSCQ + MSCR = 180

MSR = MSCR = 42

MSCQ + 42 = 180

MSCQ = 138 degree

MSQR = 360 - 42

= 318 degrees

MQV = MSR vertically opposite

= 42 degree

MQSR = 1/2 x 42

= 21 degrees

MQV = 1/2 x 180 = 90 degrees

The measures of the angles have been solved for

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The length of ST is 24.

In geometry, a tangent is a line that touches a curve at a single point, without crossing over the curve at that point. This point of contact is called the point of tangency.

For example, in a circle, a tangent is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at the point of tangency.

Tangents are important in geometry because they allow us to find the slope of a curve at a specific point. The slope of the tangent line at a point on a curve is equal to the derivative of the function representing the curve at that point.

To find the length of ST, we need to find the length of SR and add it to the length of RT.

Using the tangent-tangent theorem, we know that RP is perpendicular to RT at point R. Therefore, angle RPT is a right angle.

We can use the Pythagorean theorem to find the length of RT. Let's call the length of RP "a" and the length of PT "b". Then, we have:

a² = (x+6)² + b² (from right triangle PQR)

a² = (2x-9)² + (b+3)² (from right triangle PSR)

Setting these two equations equal to each other, we have:

(x+6)² + b² = (2x-9)² + (b+3)²

Expanding and simplifying, we get:

x² - 24x + 90 = 0

Solving for x using the quadratic formula, we get:

x = (24 ± √(24² - 4190)) / (2*1) = 15 or 6

Since x cannot be negative, we take x = 15.

Now we can use the Pythagorean theorem to find the length of SR:

a² = (2x-9)² + (b+3)²

a² = (2*15-9)² + (b+3)²

a² = 276 + (b+3)²

We also know that SR = 3, so:

3² = (b+3)²

9 = b² + 6b + 9

b² + 6b - 0 = 0

Solving for b using the quadratic formula, we get:

b = (-6 ± √(6² - 410)) / (2*1) = -3 or 0

Since b cannot be negative, we take b = 0.

Therefore, we have:

a² = (x+6)² + b²

a² = (15+6)² + 0²

a² = 441

So, RT = a = √(441) = 21.

Finally, we have:

ST = SR + RT = 3 + 21 = 24.

Therefore, the length of ST is 24.

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To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.

In the graph: The red line represents y=3x+2 and the blue line represents y=x-2

Explain the term straight line

A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.

According to the given information

To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.

First, we can find the point of intersection by setting the two equations equal to each other:

3x + 2 = x - 2

Simplifying, we get:

2x = -4

x = -2

Substituting this value of x back into one of the equations, we get:

y = (-2) - 2 = -4

So the solution to the system of equations is the point (-2, -4).

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Juan's claim is plausible based on the given function because the maximum height of the ball is 62.875 feet, which is higher than the 50-foot light tower.

To prove that Juan hit the ball over the 50-foot light tower, we need to find the maximum height of the ball using the given function h(x) = -16x^2 + 60x + 4 and show that the maximum height is greater than 50 feet.

The maximum height of the ball occurs at the vertex of the parabolic function h(x), which is given by the formula x = -b/2a, where a = -16 and b = 60.

Substituting these values into the formula, we get:

x = -b/2a = -60/(2*(-16)) = 1.875

So the ball reaches its maximum height after 1.875 seconds. To find the maximum height, we can substitute this value of x into the original function h(x):

h(1.875) = -16(1.875)^2 + 60(1.875) + 4 = 62.875

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Answer:

if f(x) = 3x, g(x) = x+4, and h(x) = x²-1, Find [h•(f•g)](3)

{h • (f • g)}(3) = 440

Step-by-step explanation:

To find {h • (f • g)}(3), we need to first evaluate the innermost function, f • g, then substitute the result into the outer function, h, and finally evaluate the resulting expression at x = 3.

Let's start by finding f • g:

f • g = f(g(x))

Substitute g(x) into f(x):

f • g = f(x + 4)

Now substitute f(x) into the above expression:

f • g = 3(x + 4)

Simplify:

f • g = 3x + 12

Now we can substitute this result into h(x):

h • (f • g) = h(3x + 12)

Substitute x = 3 into the above expression:

h • (f • g) = h(3(3) + 12)

Simplify inside the parentheses:

h • (f • g) = h(9 + 12)

Simplify further:

h • (f • g) = h(21)

Now let's evaluate h(21):

h(x) = x² - 1

h(21) = (21)² - 1

Simplify:

h(21) = 441 - 1

Final result:

{h • (f • g)}(3) = 440

The number of hours Matt babysits his sister is 1 and half hours.

Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.

Let the number of half an hours Matt babysits his sister be x.

Matt made $18.50

So, equation is 5.50x+2 =18.50

5.50x=16.50

x=16.50/5.50

x= 3

Which means 1 and half hours he babysits his sister.

Therefore, the number of hours Matt babysits his sister is 1 and half hours.

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