A walkway forms one diagonal of a square playground. The walkway is 24 m long. How long is a side of the​ playground?

Based on flow velocity, 4.132 feet per second is the correct response to the question.

A vector number called velocity is used to explain how quickly an object changes its position with respect to time. Its definition is that it is the displacement (change in position) of an object per unit of time, which takes into account both the magnitude (speed) and direction of the object's motion.

We must determine the pipe's cross-sectional area. The following formula provides the cross-sectional area of a pipe:

A = πr²

where r is the pipe's radius.

Since the pipe's diameter is specified as 6 inches, the radius may be determined as being equal to half of the diameter:

r = 6/2 = 3 inches

To translate this to feet:

r = 3/12 = 0.25 feet

Now we may apply the cross-sectional area formula:

A = πr² = π(0.25)² = 0.196 ft²

Next, we can use the formula for velocity of flow:

v = Q/A

where A is the pipe's cross-sectional area and Q represents the flow rate.

Inputting the values provided yields:

v = 0.81/0.196 = 4.132 fps

As a result, the 6-inch-diameter pipe's flow velocity is roughly 4.132 feet per second.

To know more about velocity, visit:

https://brainly.com/question/29110645

#SPJ1

Answer:

$13.00 per person

Step-by-step explanation: you divide $26 by 2

Alright, let's take this step by step.

First, let's understand what an ordinary annuity is. An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. For example, if you save $100 every year for 5 years, that’s an ordinary annuity.

Now, let’s understand the formula to calculate the future value (FV) of an ordinary annuity:

FV = P x ((1 + r)^n - 1) / r

Where:

- FV is the future value of the annuity.

- P is the payment per period (how much you save each time).

- r is the interest rate per period (in decimal form).

- n is the number of periods (how many times you save).

Let’s solve each part:

a) $500 per year for 6 years at 8%.

P = 500, r = 8% = 0.08, n = 6

FV = 500 x ((1 + 0.08)^6 - 1) / 0.08

  ≈ 500 x (1.59385 - 1) / 0.08

  ≈ 500 x (0.59385) / 0.08

  ≈ 500 x 7.4231

  ≈ 3701.55

So, the future value of $500 per year for 6 years at 8% is about $3,701.55.

b) $250 per year for 3 years at 4%.

P = 250, r = 4% = 0.04, n = 3

FV = 250 x ((1 + 0.04)^3 - 1) / 0.04

  ≈ 250 x (1.12486 - 1) / 0.04

  ≈ 250 x (0.12486) / 0.04

  ≈ 250 x 3.1215

  ≈ 780.38

So, the future value of $250 per year for 3 years at 4% is about $780.38.

c) $1,000 per year for 2 years at 0%.

P = 1000, r = 0% = 0.00, n = 2

FV = 1000 x ((1 + 0.00)^2 - 1) / 0.00

  = 1000 x (1 - 1) / 0.00

  = 1000 x 0

  = 0

Wait, something went wrong, because we know that if we save $1000 for 2 years with no interest, we should have $2000. This is a special case, where we just sum the contributions because there's no interest:

FV = 1000 x 2

   = 2000

So, the future value of $1,000 per year for 2 years at 0% is $2,000.

An annuity due is similar to an ordinary annuity, but the payments are made at the beginning of each period instead of the end. To convert the future value of an ordinary annuity to an annuity due, you can use the following formula:

FV of Annuity Due = FV of Ordinary Annuity x (1 + r)

a) Reworked

FV of Annuity Due = 3701.55 x (1 + 0.08)

                 ≈ 3701

.55 x 1.08

                 ≈ 3997.67

b) Reworked

FV of Annuity Due = 780.38 x (1 + 0.04)

                 ≈ 780.38 x 1.04

                 ≈ 810.80

c) Reworked

FV of Annuity Due = 2000 x (1 + 0.00)

                 = 2000 x 1

                 = 2000 (This doesn't change because there's no interest).

And there you have it! The future values for both ordinary annuities and annuities due!

Answer:

Answers b homies

Step-by-step explanation:

F(x)=3/2x+30

The function models of the given graph would be f(x) = 15x + 30 which is the correct answer would be an option (B)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

Take two points (6, 120) and (0, 30) in the graph

Here x₁ = 0, y₁ = 30, x₂ = 6 and y₂ = 120

Let the equation of linear function would be

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Subtitute the values of x₁ = 0, y₁ = 30, x₂ = 6 and y₂ = 120

y - 30 = (120 - 30)/(6 - 0 )[x -0]

y - 30 = (90/6)x

y = 15x + 30 or

f(x) = 15x + 30

Therefore, the function models of the given graph would be f(x) = 15x + 30.

Learn more about the graph here:

brainly.com/question/16608196

#SPJ2

There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with \(0\leq r < d\) such that \(a=dq+r\)

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

Learn more about integers here: https://brainly.com/question/20521181

#SPJ4

Answer:

key details, because it tells you more about the story

Answer:

C

Step-by-step explanation:

The expected value with a sample size of 20 and a probability of 0.25 will be 5.

The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.

E(x) = 20 x 0.25

E(x) = 5

The expected value with n = 20 and p = 0.25 will be 5.

More about the expected value link is given below.

https://brainly.com/question/13945225

#SPJ1

Answer:

that would be 8 if you divide them

Answer:

A=∫

1

3

x

2

dx

A=[

3

x

3

]

1

3

A=(

3

27

−

3

1

)

A=

3

26

Answer:

110

Step-by-step explanation:

5/6 of 132 is 110

y = x^2 represents a nonlinear function.

A linear function has the form of y = mx+b where m and b are constants and x is variable, the graph of a linear function is always a straight line. A nonlinear function is any function that is not linear, the graph of a nonlinear function is not a straight line.

y = x^2 is nonlinear because the variable x is squared, a quadratic function and its graph is a parabola.

y=2x is a linear function and its graph is a straight line, increasing linearly with x.

y = x is also a linear function and its graph is also a straight line, increasing linearly with x.

y = x+2 is a linear function and its graph is also a straight line with a y-intercept of 2, increasing linearly with x

So, y = x^2 represents a nonlinear function, and it is the correct answer.

The value of x when the tangents intersect is 24.

The theorem of tangent intersection states that the the measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's use the theorem to find the value of x in the circle as follows:

61 = 1 / 2 × ((10x + 1) - (5x - 1))

61 = 1 / 2 × (10x - 5x + 1 + 1)

61 = 1 / 2 × (5x + 2)

61 = 1 / 2 (5x + 2)

61 = 5 / 2 x + 1

61 - 1 = 5 / 2 x

60 = 5 / 2 x

cross multiply

5x = 120

divide both sides by 5

x = 120 / 5

x = 24

learn more on tangent intersection here: https://brainly.com/question/21481562

#SPJ1

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

Learn more about polynomial here;

https://brainly.com/question/29153822

#SPJ4

5. x=60

6. x= 31, y=57

7. x=36, y=144, z=90

Answer:

2 + 2 ㏑2

Step-by-step explanation:

y = x (e^x)

to dy/dx (slope), we need to perform the product rule:

if y = f(x) g(x), where both f(x) and g(x) are functions in x, then dy/dx = f(x) g'(x) + f'(x) g(x).

let u = x (dy/dx = 1) and v = e^x ( dv/dx = e^x).

then dy/dx = u (dv/dx) + v (du/dx)

= x (e^x) + e^x. this is the slope.

at x = ㏑2:

dy/dx = ㏑2 (e^㏑2) + e^㏑2

= ㏑2 (2) + 2

= 2 + 2 ㏑2

The number of lumps fitted along the box is 16.

To determine the number of lumps fitted along the box, we need to consider the dimensions of the box and the number of lumps in each row and layer.

Given that five lumps are fitted across the box, we can conclude that there are five lumps in each row.

Let's assume that the number of lumps fitted along the box is represented by "x." Since there are three layers in the box, the total number of lumps in each layer would be 5 (the number of lumps in a row) multiplied by x (the number of lumps along the box), which gives us 5x.

Considering there are three layers in the box, the total number of lumps in the box would be 3 times the number of lumps in each layer: 3 * 5x = 15x.

Given that there are 240 lumps in the box, we can equate the equation: 15x = 240.

By dividing both sides of the equation by 15, we find x = 16.

For more such questions on lumps,click on

https://brainly.com/question/33234555

#SPJ8

Answer:

The inequality 3y + x < 3x - y - 8 is represented by option D.

Step-by-step explanation:

The inequality 3y + x < 3x - y - 8 is represented by option D.

To see this, we can rearrange the inequality to get all the x and y terms on one side, like so:

3y + x < 3x - y - 8

4y < 2x - 8

2y < x - 4

y < (1/2)x - 2

This shows that y is less than a linear function of x, with a slope of 1/2 and a y-intercept of -2. Visually, this represents a downward-sloping line on a graph. Therefore, option D is the correct answer.

The values of a1 = [ 3], a2 = [ 9 ], and b = [ 48] and b is not a linear combination of a1 and a2. The correct answer is (a).

To check if b is a linear combination of a1 and a2, we need to see if there exist scalars x and y such that:

x * a1 + y * a2 = b

Substituting the given values, we get:

x * [3] + y * [9] = [48]

[-3] [-9] [-48]

This system of linear equations can be solved using standard methods, such as Gaussian elimination. However, we can quickly see that there are no values of x and y that satisfy the equation.

First, note that the first two rows of the equation system are linearly dependent, since the second row is a multiple of the first row. Therefore, we only have two independent equations to solve for three unknowns (x, y, and z).

If we subtract the first equation from the second equation, we get:

6y = 0

This implies that y = 0. Substituting y = 0 in the first equation, we get:

3x = 48

This implies that x = 16. Substituting these values in the third equation, we get:

0 ≠ -48

Since there are no values of x and y that satisfy the equation system, we can conclude that b is not a linear combination of a1 and a2. Therefore, the answer is (a) b is not a linear combination.

To know more about linear combination:

https://brainly.com/question/29551145

#SPJ4

Hey there!

Let's solve this equation.

\(-6x-10=-40\)

Add 10 to both sides.

\(-6x-10+10=-40+10=-6x=-30\\-6x=-30\)

Divide both sides by by -6.

\(\frac{-6x}{-6} =\frac{-30}{-6}\)

Simplify the fraction by dividing -30 by -6.

\(-30/-6=5\\ x=5\)

x=5 is your answer.

Hope this helps!

\(\text{-TestedHyperr}\)

Answer: 23.6 (rounded to the nearest tenth)

Step-by-step explanation:

The surface area of a square pyramid net can be found by adding the areas of the base and the four triangular faces.

First, find the area of the base by multiplying the length and width of the square base.

Area of base = length × width

Next, find the area of one of the triangular faces by using the formula:

Area of triangle = 0.5 × base × height

Since there are four triangular faces in a square pyramid, multiply the area of one triangle by four to find the total area of the triangular faces.

Area of triangular faces = 4 × (0.5 × base × height)

Finally, add the area of the base and the area of the triangular faces to find the total surface area of the square pyramid net.

Surface area = Area of base + Area of triangular faces

= (length × width) + (4 × (0.5 × base × height))

= (length × width) + (2 × base × height)

So, the surface area of a square pyramid net is the sum of the area of the base and the area of the four triangular faces.

To know more about surface area click below:

https://brainly.com/question/29298005#

#SPJ11

the other solution is\(\frac{-9}{5}\)

Answer:

Solution given:

\(5x^2 -11x-36=0\)

doing middle term factorization

we need to get 11 by subtracting product of 5 and 36.

5*36=180=2*2*3*3*5

we get 11 by subtracting 5*2*2-3*3=20-9

substituting value of 11 as (20-9)

now

\(5x^2 -(20-9)x-36=0\)open bracket

\(5x^2 -20x+9x-36=0\)

taking common from each two terms

5x(x-4)+9(x-4)=0

again taking common

(x-4)(5x+9)=0

either

x-4=0

x=4

or

5x+9=0

5x=-9

x=\(\frac{-9}{5}\)

Step-by-step explanation:

Following are the calculation to the given equation:

Given:

\(\to 5x^2 - 11x - 36 = 0\)

one solution:

\(x=4\)

To find:

other solution=?

Solution:

\(\to 5x^2 - 11x - 36 = 0\\\\\to 5x^2 - (20-9)x - 36 = 0\\\\\to 5x^2 - 20x+9x - 36 = 0\\\\\to 5x(x - 4)+9(x - 4) = 0\\\\\to (x - 4) (5x+9) = 0\\\\\to x - 4=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x+9 = 0\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x = -9\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{-9}{5}\\\)

Therefore, another solution is "\(-\frac{9}{5}\)".

Learn more:

brainly.com/question/3044722

To find the rate of change of y with respect to time t, we need to take the derivative of the function y = 500(1-0.2)^t with respect to t:

dy/dt = 500*(-0.2)*(1-0.2)^(t-1)

Simplifying this expression, we get:

dy/dt = -100(0.8)^t

Therefore, the rate of change of y with respect to t is given by -100(0.8)^t. This means that the rate of change of y decreases exponentially over time, and approaches zero as t becomes large.

Answer:

AB || CE, so we have triangle DEO, two of whose angles are 100° and 26° (from point D, draw DE such that CD + DE = CE intersects BO). The third angle of this triangle measures 54°, so

x = 180° - 54° = 126°.

Answer:

20 pints per hour

Step-by-step explanation:

60/6 = 10

10 x 4 = 40

40 pints/hour in the morning

60/3 = 20

20 x 1 =20

20 pints/hour in the afternoon

40 - 20 = 20

20 pint/hour difference

Answer:

\(7-8x+4y=-21\)

Step-by-step explanation:

\(2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21\)

Answer:

Step-by-step explanation:

Answer:

yes because 42+82 is greater than 96

it will just about fit through the door

hope this helps! :)

Answer:

20 days

Step-by-step explanation:

Number of books sold each day for 40 days :

The first quartile (Q1) = 2

For the 25% of the days = 2 books were sold

Hence 0.25 * 40 = 10 days, 2 books or less were sold

The upper quartile (Q3) = 12 books

For up to 75% of the days = 0.75 * 40 = 30 days ; 12 books or less were sold

To obtain the number of books sold between 2 and 12 ; we subtract :

(30 days - 10 days) = 20 days

Answer:

20

Step-by-step explanation:

Let x = length and y = width

You would have 2 lengths, so 2x and 3 widths, so 3y

Those need to equal total length of fence:

2x + 3y = 1200

The 3 widths would equal total fence minus the 2 lengths:

3Y = 1200-2x

Solve for y: y = 400 -2/3x

Area = length x width = xy. Replace y :

Area = x(400-2/3x) = 400x-2/3x^2

Differentiate:

400-4x/3 =0

4x/3 = 400

4x = 1200

X = 300

Y = 400-2/3(300) = 200

The dimension would be 300 ft x 200 ft