You are designing a rectangular swimming pool that is to be sent into the ground. The width of the pool is 5 feet more than the depth, and the length is 35 feet more than the depth. The pond holds 2000 cubic feet of water, What are the dimensions of the pool?

The total monthly salary earned by Ram in the month of April 2022 is an amount of 30000 AED before payments and donations.

Word problems are statements that embody a set of algebraic expressions that offers at least one solution. In this case, we have to read the statement, find the equivalent formula and solve for the resulting variable.

After a careful reading, the statement is equivalent to the following formula:

x = x / 3 + x / 4 + x / 20 + x / 10 + 5000 + 3000

4 · x / 15 = 8000    (1)

Where x is Ram's monthly salary.

The solution of (1) is x = 30000.

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Option (b) beta A=0.95 beta B=1.14 is correct regarding the beta of Portfolio A and the beta of Portfolio B.

Given below is the expected return and standard deviation of Assets A and B:

Expected return of A = 15%

Expected return of B = 16%

Standard deviation of A = 21%

Standard deviation of B = 25%

The correlation coefficient between A and B = 0.65

The correlation coefficient between A and market portfolio = 0.75

The correlation coefficient between B and market portfolio = 0.85

The standard deviation of the market portfolio = 22%

We know that, Beta of A = (Correlation between A and market portfolio * Standard deviation of A) / Standard deviation of the market portfolio

Beta of B = (Correlation between B and market portfolio * Standard deviation of B) / Standard deviation of the market portfolio

On substituting the given values, we get: Beta of A = (0.75 * 21%) / 22% = 0.71

Beta of B = (0.85 * 25%) / 22% = 0.97

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The estimate of ∫e^x dx using rectangles with heights given by right-hand endpoints and four subintervals (n = 4) can be determined by evaluating the function at those endpoints and multiplying by the width of each rectangle.

Among the given options, the correct representation of the estimate is:

∫e^x dx is approximately (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2.

This is because we divide the interval [0,2] into four subintervals of equal width, each with a width of 0.5. For the right-hand endpoint approximation, we evaluate the function e^x at those endpoints.

The height of each rectangle is given by e^x evaluated at the right-hand endpoint of each subinterval. The width of each rectangle is 0.5.

By multiplying the height and width of each rectangle and summing them up, we obtain the estimate of the integral.

Therefore, the correct representation is (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2 as an estimate of ∫e^x dx using rectangles with right-hand endpoints and four subintervals.

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Answer:

7

Step-by-step explanation:

So the log thingy is loga(b) = c

a^c = b

So in this one, a = a

b = 7

c = 4

a^4 = 7

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

Answer:

\(m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope\)

(8,3)=(x1,y1)

(10,3)=(x2, y2)

Now,

\(m = \frac{3 - 3}{10 - 8} \\ = 0\)

Answer:

x = 1/2 and y = 3

Step-by-step explanation:

Let

4x + 5y = 17       ......(i)

2x + 4y = 13       .....(ii)

Multiply equation (ii) by 2 to make like 'x' terms. Thus, the new equations are:

4x + 5y = 17       ......(i)

4x + 8y = 26       .....(ii)

Subtract equation (i) from (ii)

4x + 8y - (4x + 5y) = 26 - 17

4x + 8y - 4x - 5y = 9

3y = 9

y = 3

To find x, substitute value of y into any equation

4x + 5y = 17

4x + 5*3 = 17

4x + 15 = 17

4x = 17 - 15

4x = 2

x = 2/4

x = 1/2

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0,

What is the inflection point?

An inflection point of a function is a point on the graph of the function where the concavity (curvature) of the graph changes. In other words, an inflection point is a point where the curve switches from being concave up to concave down, or vice versa.

The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0, because the concavity of the graph changes at that point. To find the value of b such that the function has at least one inflection point over the interval (1,2), we can set x = 1 and x = 2 in the function and solve for b.

If we set x = 1, we get the equation f(1) = 1 + b + 1 = 0. Solving for b, we find that b = -2.

If we set x = 2, we get the equation f(2) = 16 + 2b + 1 = 0. Solving for b, we find that b = -9.

Since the function has an inflection point at x = 0 for any value of b, it will have at least one inflection point over the interval (1,2) for any value of b.

Therefore, the value of b can be any real number.

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Answer:

12. The pattern is adding 7. so the answer is 12

Step-by-step explanation:

Answer:

154 sq ft

Step-by-step explanation:

Area = pi * r^2 with radius r

A = pi * r^2 = 22/7 * 7^2 = 22 * 7 = 154 sq ft

Answer:

\( \sqrt{ \frac{4}{49 {d}^{4} } } = \frac{2}{7 {d}^{2} } \)

Answer:

Step-by-step explanation:

Multiply by x^2 on both sides

9x^2+27x+8=0

Factor.

The answers are -1/3, -8/3

Answer:

Down below.

Step-by-step explanation:

A=2(wl+hl+hw)

A=2(4*5+5*7+7*4)

A=2(20+35+28)

A=2(83)

A=166mm^2

The hydrostatic force on the window is approximately 47,481 Newtons.

We can use the formula for hydrostatic force, which is:

F = ρghA

where F is the hydrostatic force, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity, h is the depth of the window, and A is the area of the window.

First, we need to find the area of the window. Since the window is a semi-circle with diameter 70 centimeters, the radius is 35 centimeters, and the area is:

A = (π/2)r^2

= (π/2)(35 cm)^2

= 1225π/2 cm^2

Next, we need to convert the depth of the window to meters:

h = 2.5 m

We also need the density of water, which is approximately:

ρ = 1000 kg/m^3

Finally, we need the acceleration due to gravity, which we can assume is:

g = 9.8 m/s^2

Now we can plug these values into the formula:

F = ρghA

= (1000 kg/m^3)(9.8 m/s^2)(2.5 m)(1225π/2 cm^2)

≈ 47,481 N

Therefore, the hydrostatic force on the window is approximately 47,481 Newtons.

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The measure of the side J of the triangle ΔIJK will be 43 units.

The law of sines defines the ratio of triangle sides, and their respective sine angles are equivalent. The law of sines is also known as the sine law, sine rule, and sine formula.

Given that in the triangle i = 100 inches,  m∠I=115° and m∠J=23°. The measure of the length J will be calculated as:-

100 / sin115 = J / sin23

J = (100) x sin23 / sin115

J = 100 x 0.43

J = 43 units

The length of side J will be 43 units.

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The triangle with side lengths of 2 mm, 2.5 mm, and 3 mm is not a right triangle because it does not obey Pythagoras theorem.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem states that for a right angled triangle:

Hypotenuse² = Adjacent² + Opposite²

To prove that a triangle with side lengths of 2 mm, 2.5 mm, and 3 mm a right triangle:

3² = 2² + 2.5²

9 = 4 + 6.25

9 ≠ 10.25

The triangle with side lengths of 2 mm, 2.5 mm, and 3 mm is not a right triangle because it does not obey Pythagoras theorem.

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In the case where the particular car Roy wants, enterprise charges an amount of $185 per week with additional 25 cents per mile driven and Avis charges a flat fee of $275 per week, the number of miles driven where renting from enterprise be the less expensive option is less than 3.6 miles.

In the case of enterprise, the cost can be expressed in terms of miles driven, say x as 185 + 25x. In order for the renting from enterprise option to be less expensive than Avis

185 + 25x < 275    

25x < 275 - 185

x < 90/25

x < 3.6 miles

Therefore, if Roy is driving 3.6 miles or less, enterprise option will be the least expensive option.

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Answer: The width is 8 inches

Step-by-step explanation:

Trust me lol also 8 gose into both 96 and 12

Answer:

25

Step-by-step explanation:

To solve this problem, you can use the pythagorean theorem, which is a^2 + b^2 = c^2 where a and b are legs and c is the hypotenuse. We can plug in the values of 15 and 20, and solve for c:

15^2 + 20^2 = c^2

225 + 400 = c^2

625 = c^2

c = 25

This means the hypotenuse is 25.

Answer:

Step-by-step explanation:

So in your account you got $175.29

Then you deposit mean increase the amount of money in your account by $48.75

So: 175.29+48.75 = 224.04

The price is $249.99

So: 249.99 - 224.04 = $25.95

You need to save $25.95 in order to buy your cell phone

To buy the cellphone of worth $249.99, additional $25.95 are required.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

The price of cellphone = $249.99

The amount in saving account = $175.29

Additional amount deposit in account = $48.75

Total amount in account after deposit = 175.29 + 48.75 = 224.04

Since, the price of cellphone is $249.99

And the amount in account = 224.04

So the more amount required = 249.99 - 224.04 = 25.95

To buy the cell phone $25.95 are required.

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Answer:

20.0

Step-by-step explanation:

We can use the distance formula, d = \(\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}\)  to find the length of three sides separately.

AB =  \(\sqrt{(-4+2) ^{2} +(1-3}) ^{2}}\) = \(\sqrt{8}\)

BC =  \(\sqrt{(-2-3) ^{2} +(3+4) ^{2}}\) = \(\sqrt{74}\)

CA =  \(\sqrt{(3+4) ^{2} +(-4-1) ^{2}}\) = \(\sqrt{74}\)

Perimeter = \(\sqrt{74}\) + \(\sqrt{8}\) + \(\sqrt{74}\) = 20.0330776588 units

Answer:

Step-by-step explanation:

Answer:

1,5,3 your welcome

Step-by-step explanation:

The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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Answer:

1 mile/hour is equivalent to 1.47 feet/seconds

Step-by-step explanation:

Given

\(88 ft/s= 60 miles/hr\)

Required

Determine the equivalent of 1 mile/hour

\(88\ ft/s= 60\ miles/hr\)

Express 60 as 60 * 1

\(88\ ft/s= 60 * 1\ mile/hr\)

Divide both sides by 60

\(\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}\)

\(\frac{88\ ft/s}{60}= 1\ mile/hr\)

Reorder

\(1\ mile/hr = \frac{88\ ft/s}{60}\)

Divide 88 by 60

\(1\ mile/hr = 1.46666666667\ ft/s\)

Approximate to 3 significant figures

\(1\ mile/hr = 1.47\ ft/s\)

Hence;

1 mile/hour is equivalent to 1.47 feet/seconds

Answer:

gg

Step-by-step explanation:

ggggftttgxxyuuhhhgg

Answer:

The answer is (6.5,3)

Step-by-step explanation:

The solution is in the image

The endpoints of GH are G(10,1) and H(3,5), then, the midpoint of GH is M(6.5, 3).

Here, we have to find the midpoint of line segment GH, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:

M(x, y) = \(((x_1 + x_2) / 2, (y_1 + y_2) / 2)\)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

In this case, the endpoints of GH are G(10, 1) and H(3, 5).

Let's use the midpoint formula to find the midpoint (M) of GH:

x-coordinate of M = (x-coordinate of G + x-coordinate of H) / 2

x-coordinate of M = (10 + 3) / 2

x-coordinate of M = 13 / 2

x-coordinate of M = 6.5

y-coordinate of M = (y-coordinate of G + y-coordinate of H) / 2

y-coordinate of M = (1 + 5) / 2

y-coordinate of M = 6 / 2

y-coordinate of M = 3

So, the midpoint of GH is M(6.5, 3).

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Answer:

36m

Step-by-step explanation:

The midpoint theorem : the line segment drawn from the midpoint of any two sides of the triangle is parallel to and half of the length of the third side of the triangle.

PT = 2 QS = 16

perimeter of ΔPRT = 3*2 + 7*2 + 8*2 = 36 m