what is the square root of 504 simplified ?

Answer:

Thus, the surface area of a cylinder involving pie is:

\(\:\:\:A=36\pi \:\) in²

or

\(A\approx 113.1\) in²

Step-by-step explanation:

Given

Using the formula to determine the surface area of a cylinder:

\(A=2\pi \:rh+2\pi \:r^2\)

\(A=\left(2\times \pi \times \:2\times 7\right)+\left(2\times \pi \times \:2^2\right)\:\)

\(\:\:\:A=36\pi \:\) in²

Thus, the surface area of a cylinder involving pie is:

\(\:\:\:A=36\pi \:\) in²

or

\(A\approx 113.1\) in²

Answer:

2.95+0.14t=x

i think but ehhh, i am pretty sure about the constant but not to sure about the varibles

Answer: x=0,7

Step-by-step explanation:

Answer:

x=0 or x=7

Step-by-step explanation:

x^2-3x=4x

Subtract 4x from each side. x^2-7x=0

Factor the left side of the equation. x(x-7)=0

Set factors equal to zero. x=0 or x-7=0

x=0 or x=7

(a) 5.2333.41−0.23 × 0.205

= (5.23) * (3.18 - 0.23) * (0.205)

= 8.48013

Rounded to the correct number of significant figures, the result is: 8.48

(b) 4.223-0.085.556×2.3

= (4.14) / (5.556) * (2.3)

= 1.759619378

= 1.76

Rounded to the correct number of significant figures, the result is: 1.76

5) To convert the melting point of tungsten from Fahrenheit to Celsius and Kelvin:

Melting point in Fahrenheit: 6192°F

To convert to Celsius:

°C = (°F - 32) * 5/9

°C = (6192 - 32) * 5/9

°C ≈ 3434.44°C

Rounded to the correct number of significant figures, the result is: 3434°C

To convert to Kelvin:

K = °C + 273.15

K = 3434.44 + 273.15

K ≈ 3707.59K

Rounded to the correct number of significant figures, the result is: 3708K

6) For the volume calculation of the aspirin tablet

Tablet weight: 250 mgTo find the volume, we use the formula:

Volume = Mass / Density

Volume = 250 mg / 1.40 g/cm³

Volume = 250 mg / 1.40 g/cm³ * (1 g / 1000 mg) * (1 cm³ / 1 mL)

Volume ≈ 178.571 cm³

Rounded to the correct number of significant figures, the result is: 179

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The Difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

To find the difference in the amounts that Tsion and Ibrahim paid for their watches, we need to convert the prices to the same currency. We can use the exchange rates given to convert both prices to pounds.

1 Singapore dollar = £0.58

72 Singapore dollars = 72 x £0.58 = £41.76

1 Hong Kong dollar = £0.09

399 Hong Kong dollars = 399 x £0.095 = £37.91

Therefore, Tsion paid £41.76 for the watch and Ibrahim paid £37.91 for the same model of watch.

To find the difference in the amounts paid, we can subtract the smaller amount from the larger amount:

£41.76 - £37.91 = £3.85

Therefore, the difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

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Answer:

above sea level

Step-by-step explanation:

Answer:

27.3 points per game

Step-by-step explanation:

2020/74 = 27.3 points per game

The positions of the keys in a hash table of size n = 7 has been determined and the collisions are resolved by linear probing.

To determine the positions of the keys in a hash table of size n=7 and insert them into the hash table while resolving collisions by linear probing, we need to first apply a hash function that maps the keys to a specific position in the table. Let's assume that we use the simple mod function as the hash function: h(key) = key % 7.
Using this hash function, the keys will be mapped to the following positions in the hash table:
- 34 -> h(34) = 6
- 78 -> h(78) = 1
- 93 -> h(93) = 2
- 5 -> h(5) = 5
- 74 -> h(74) = 4
- 81 -> h(81) = 4
We can see that two keys, 74 and 81, are mapped to the same position in the table (position 4). This is called a collision. To resolve collisions using linear probing, we simply look for the next available position in the table and insert the key there.
Starting from the position of the collision (position 4), we check the next positions in the table sequentially until we find an empty position. The keys will be inserted into the following positions:
- 34 -> position 6
- 78 -> position 1
- 93 -> position 2
- 5 -> position 5
- 74 -> position 4 (original position)
- 81 -> position 5 (next available position after collision)
Therefore, the final hash table with the keys inserted using linear probing will look like this:
0 | |
1 |78|
2 |93|
3 | |
4 |74|
5 |5|
6 |34|

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Answer:

y=2x+8

Step-by-step explanation:

You set the slope to the opposite of -1/2 which is 2/1 or 2.

Then you do b=2(4) (because 4 is the x in the coordinate points)

and solve for b you get 8 so

Y=2x+8

Answer:

number 1

Step-by-step explanation:

The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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Answer:

B is the correct answer

Step-by-step explanation:

Hope this helps:)

The formula can be used to determine the area of the sector bounded by central angle MON is x/360*πr².

The correct option is (A).

The area of a sector of a circle is the amount of space enclosed within the boundary of the sector. A sector always originates from the center of the circle. The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them.

Given: Central Angle= x , radius= r

We know the formula for Area of sector is

=\(\theta\)/360*πr²

= x/360*πr²

Hence,  Area of sector=  x/360*πr².

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Step-by-step explanation:

Given the linear function, w(x) = 3/5x + 2, where the slope, m = 3/5, and the y-intercept is (0, 2).

Start by plotting the y-intercept on the graph. Then, use your slope, m = 3/5 (rise 3 units, run 5 units) to plot other points on the graph.  

Attached is an edited screenshot of your given problem, which shows the plotted points on the graph using the techniques explained in this post.

The function f(x) = (x^2 - 3x + 2)/(3x^2 - x + 3) is continuous over the interval (-∞, +∞).

To determine the interval(s) over which a function is continuous, we need to check for any potential points of discontinuity. In this case, we have a rational function, which is continuous for all x-values except where the denominator is equal to zero. However, in this particular function, the denominator 3x^2 - x + 3 does not have any real roots, and therefore it is never equal to zero.

Since the denominator is never zero, there are no points of discontinuity in the function. Hence, the function f(x) = (x^2 - 3x + 2)/(3x^2 - x + 3) is continuous over the entire real number line, or in interval notation, (-∞, +∞).

Therefore, the interval over which the function f(x) is continuous is (-∞, +∞).

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Answer:  c or d

Step-by-step explanation:

Answer:

I believe A would be the correct one, but I'm not 100% sure, none of the others make any sense and it looks like there may be a typo on A.

Step-by-step explanation:

If Caitlin were to win a huge sum of cash. In total, she has 49 bills. She adds up $1430. There are twenty and fifty-dollar bills available. The equation 20x + 50y = 1430 is the one that best describes the situation.

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.

Given that Caitlin won a bag of cash, she has a total of 49 bills. She adds up to $1430. There are twenty and fifty-dollar notes available.

The system best represents the situation is,

20x + 50y = 1430

Thus, if Caitlin was to win a huge sum of cash. In total, she has 49 bills. She adds up to $1430. There are twenty and fifty-dollar bills available. The equation 20x + 50y = 1430 is the one that best describes the situation.

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It takes approximately 52.7 hours for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value.

The decay of radioactive substances is governed by the following equation:

\(N(t) = N_{0} e^{(-\lambda t)\)

where:

N(t) is the amount of the substance at time t

N₀ is the initial amount of the substance

λ is the decay constant

t is time

The half-life of gallium-67 is 78.2 hours, which means that:

λ = ln(2)/t₁/₂ = ln(2)/78.2 = 0.00887 h⁻¹

Let N be the amount of gallium-67 remaining after time t, and N₀ be the initial amount. Then, we can use the above equation to find the time t required for the activity of the sample to fall to 6.73 percent of its original value:

N/N₀ = 0.0673

\(0.0673 = e^{(-\lambda t)}\)

Taking the natural logarithm of both sides:

ln(0.0673) = -λt

t = ln(1/0.0673)/λ

t = ln(14.84)/0.00887

t ≈ 52.7 hours

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An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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The distance from the bottom of the ladder to the side of the house is approximately 6.42 feet.

In this problem, we have a ladder leaning against the side of a house, creating a right triangle. We're given the angle of elevation (66 degrees) and the height of the top of the ladder above the ground (14 ft).

We need to find the distance from the bottom of the ladder to the side of the house, which is the adjacent side of the triangle.

To solve this, we can use the trigonometric function tangent (tan). The tangent of an angle in a right triangle is equal to the ratio of the opposite side to the adjacent side. In this case, the angle is 66 degrees, and the opposite side is 14 ft.

tan(66) = opposite side / adjacent side

tan(66) = 14 ft / adjacent side

To find the adjacent side, we can rearrange the equation:

Adjacent side = 14 ft / tan(66)

Using a calculator, we find:

Adjacent side ≈ 6.42 ft

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The equation for the radius of the ball, treated as a sphere, in terms of its surface area is given by r = √(A/4π). For a measured surface area of A = 65 cm², the radius can be calculated as r ≈ 2.028 cm. The density of the ball is calculated by dividing its mass by its volume. With a measured mass of M = 75 g, the density is approximately p ≈ 0.86 g/cm³. To convert this density to Pkg/m³, we need to multiply by 1000, resulting in P ≈ 860 kg/m³.

(a) The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. Rearranging the formula to solve for the radius, we get r = √(A/4π). Plugging in the measured surface area A = 65 cm², we can calculate the radius as r ≈ √(65/4π) ≈ 2.028 cm.

(b) The density of an object is calculated by dividing its mass by its volume. In this case, the measured mass is M = 75 g. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. Using the previously calculated radius r ≈ 2.028 cm, we can find the volume V ≈ (4/3)π(2.028)³ cm³. Dividing the mass M by the volume V, we get the density as p ≈ 75 g / [(4/3)π(2.028)³ cm³] ≈ 0.86 g/cm³.

(c) To convert the density from g/cm³ to kg/m³, we need to multiply by a conversion factor of 1000 since there are 1000 g in 1 kg and 1 m³ is equal to 1,000,000 cm³. Therefore, the density in kg/m³ is P ≈ 0.86 g/cm³ * 1000 ≈ 860 kg/m³.

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Answer:

Step-by-step explanation:

If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/

answer: 4.53 the 3 is repeating

Answer:

  a) 56.25 mph

  b) $1.59/lb

Step-by-step explanation:

The units of the "unit rate" tell you the math operation you need to perform.

Miles per hour (mi/h) is found by dividing miles by hours.

  (450 mi)/(8 h) = (450/8) mi/h = 56.25 mi/h

Dollars per pound ($/pound) is found by dividing dollars by pounds.

  ($7.95)/(5 pounds) = (7.95/5) $/pound = 1.59 $/pound

__

Additional comment

In the context of unit rates, "per" means "divided by."

What makes a rate a "unit rate" is the "1 unit" in the denominator. For miles per hour, the denominator is 1 hour. For dollars per pound, the denominator is 1 pound.

The maximum bending stress (σbmax) produced in the section is 44.09 N/mm², which is less than the yield stress (fy) of the material of the beam.

The moment of resistance (Mn) of a section is defined as the moment which is just sufficient to produce the limiting value of the stress in the extreme fibre of the section. Mn is given by: Mn = S.fy

where fy is the yield stress of the material of the beam.

The plastic moment (Mp) is defined as the moment that can be carried by the section when the material at the extreme fibres is stressed to its yield stress. Therefore, Mp = S.fy

Let us calculate the plastic modulus, S = Mp/fy = (501 * 10³) / 250 = 2004 mm3

As we know that Lp is the limiting length and Lr is the non-limiting length.The effective length factor (K) can be calculated by K = (Lr / Lp)^(1/2) = (5.46 / 2.13)^(1/2) = 2.14 Cb = 1.3 (given)

The actual moment of resistance (Mn) of the section is given by Mn = Mp / (Cb.K) = 501 / (1.3 * 2.14) = 178.39kNm. The bending stress (σb) produced in the section is given by σb = (M * y) / I

where M is the bending moment,

y is the distance of the extreme fibre from the neutral axis, and

I is the moment of inertia.

The maximum bending stress (σbmax) produced in the section occurs at the bottom fibre (y = D/2) and is given byσbmax = 6 * M * L / (B * D²)

Where B is the breadth of the section,

D is the depth of the section, and

L is the span of the beam.

Here, σbmax must be less than or equal to the allowable bending stress of the material used. Here, σbmax is the allowable bending stress. As the section of the beam is W35 * 72, the breadth (B) is 254mm and depth (D) is 259mm. Thus, σbmax = (6 * Mn * L) / (B * D²) = (6 * 178.39 * 10³ * 5.46) / (254 * 259²) = 44.09 N/mm². Hence, the maximum bending stress (σbmax) produced in the section is 44.09 N/mm², which is less than the yield stress (fy) of the material of the beam. Thus, the beam is safe under the given conditions.

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If the diagonals of a quadrilateral divide each other proportionally, it is a trapezium.

Let's consider a quadrilateral ABCD, where the diagonals AC and BD intersect at point E. If the diagonals divide each other proportionally, it means that AE/CE = BE/DE.

To prove that the quadrilateral is a trapezium, we need to show that one pair of opposite sides is parallel.

Using the proportionality condition, we can rewrite it as (AE/CE) = (BE/DE) = 1.

By the Converse of the Basic Proportionality Theorem, we know that if two lines are cut by a transversal such that corresponding angles are equal, then the lines are parallel. In this case, AE is parallel to CD, and BE is parallel to AD.

Therefore, we have shown that AB || CD, which is the definition of a trapezium.

If the diagonals of a quadrilateral divide each other proportionally, it can be concluded that the quadrilateral is a trapezium.

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Five other iterated integrals that are equal to the given iterated integral are:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

To find the five other iterated integrals that are equal to the given iterated integral, we need to rearrange the order of integration. We can do this by changing the order of the limits of integration and writing the integral with respect to a different variable first.

The original integral is:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dz dx dy

Now, we can change the order of integration in the following ways:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

Each of these integrals has the same value as the original integral, but with a different order of integration. It is important to note that changing the order of integration can sometimes make the integral easier to evaluate, especially if the integrand has certain symmetries.

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