A square plot of land has a building 80 ft long and 50 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 18,500 ft2, what are the dimensions of the entire plot of land?

Answer:

y=1/6x

Step-by-step explanation:

Given that y= # of pushups and x = time, you can do 4 pushups in 24 seconds

therefore, 6y=x

In otherwords, y=1/6x

Hope this helped! :)

a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Answer:

SAS

Step-by-step explanation:

side angle side

Answer: 2 points

Step-by-step explanation:

Therefore, the equation of the line tangent to the graph of f(x) = x^4 + 2x^2 at the point where f'(x) = 1 is:y = -3x + 13/16 or y = 3x + 1/16.

The given function is f(x) = x^4 + 2x^2. We are to find the equation of the tangent line to this function at the point where f'(x) = 1. Let's first find the derivative of f(x) as follows:f(x) = x^4 + 2x^2f'(x) = 4x^3 + 4xAt the point where f'(x) = 1, we have:1 = 4x^3 + 4x4x^3 + 4x - 1 = 0Solving for x using the Rational Root Theorem gives:x = (-1/2) or x = (1/2) or x = (√5)/2 or x = -(√5)/2Substituting each of these values of x back into the original function gives the corresponding y-coordinates:f(-1/2) = (-1/16) + 1/2 = 7/16f(1/2) = (-1/16) + 1/2 = 7/16f(√5/2) ≈ 4.84f(-√5/2) ≈ 4.84Thus, there are two points where f'(x) = 1: (-1/2, 7/16) and (1/2, 7/16). We can now use the point-slope form of the equation of a line to find the tangent line at each of these points. For example, at the point (-1/2, 7/16), the slope of the tangent line is:f'(-1/2) = 4(-1/2)^3 + 4(-1/2) = -3Thus, the equation of the tangent line is:y - (7/16) = -3(x + 1/2)Simplifying:y = -3x + 13/16Similarly, at the point (1/2, 7/16), the slope of the tangent line is:f'(1/2) = 4(1/2)^3 + 4(1/2) = 3Thus, the equation of the tangent line is:y - (7/16) = 3(x - 1/2)Simplifying:y = 3x + 1/16

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An equation of the line tangent to the graph of,

\(f(x) = x^4 + 2x^2\)

The required equation is \(y = 3x - \frac{3}{16}\)

We know that if the line tangent to the graph of the function f(x) at the point (a,f(a)) exists, then it passes through the point (a,f(a)) and has the slope f'(a).

The slope of the function is f'(x) = 4x³ + 4x.

We want to find an equation of the line tangent to the graph of the function f(x) = x⁴ + 2x² at the point

where f'(x) = 1.

So, we have, f'(x) = 1 = 4x³ + 4x

Thus, solving this equation,

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

\(x^3+x-\frac{1}{4} = 0\)

Thus, the roots of the polynomial,

\(x^3 + x - \frac{1}{4} = 0\)

are

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

Now, we have to find the point of the function

\((\frac{1}{2}, f(\frac{1}{2}))\)

where the slope is 1.

We have,

\(f(x) = x^4 + 2x^2\)

\(f(\frac{1}{2}) = (\frac{1}{2})^4 + 2(\frac{1}{2})^2 = \frac{9}{16}\)

So, the point is ,

\((\frac{1}{2}, \frac{9}{16})\)

Therefore, an equation of the line tangent to the graph of

\(f(x) = x^4 + 2x^2\)

at the point

\((\frac{1}{2},\frac{9}{16})\)

where f'(x) = 1 is:

\(y - \frac{9}{16} = (4(\frac{1}{2})^3 + 4(\frac{1}{2}))(x - \frac{1}{2})\)

\(y - \frac{9}{16} = 3(x - \frac{1}{2})\)

Therefore,

is the required equation.

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The coefficient of x⁵y⁶ in (xy)¹¹ is 462.

The coefficient of x⁵y⁶ in (xy)¹¹ is:

Identify the powers of x and y in the term x⁵y⁶.

The powers are 5 and 6, respectively.

Since (xy)¹¹ is raised to the 11th power, we need to find the binomial coefficient using the formula:

C(n, k) = n! / (k!(n-k)!),

where n is the power (11 in this case) and k is the power of x (5 in this case).

Calculate the binomial coefficient:

C(11, 5) = 11! / (5!(11-5)!) = 11! / (5!6!) = 462.

Therefore, the coefficient of x⁵y⁶ in (xy)¹¹ is 462.

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Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

Answer:

2 4 6 8 10 12 14 16.....................................................

Answer:

even numbers are

Step-by-step explanation:

2,4,6,8,10,12,14,16,18,20,24,26 and so on

Answer:

The only common factor would be 1 only.

Step-by-step explanation:

If you don't believe me, then you might as well calculate yourself or find the gcf or lcm

Answer:

No

Step-by-step explanation:

Given:

a = 28

b = 47

c = 55

a² + b² = c²

28² + 47² = 55²

784 + 2209 = 3025

2993 ≠ 3025

No because the 2 legs don't equal the hypotenuse

Given the values q = 2.0 μC and d = 0.91 m, the total potential at point P due to the four point charges is 70.32 volts.

To find the total potential at point P due to the four point charges, we can use the formula for the electric potential due to a point charge:

V = k * q / r

where V is the potential, k is the electrostatic constant (8.99 × 10⁹ N m²/C²), q is the charge, and r is the distance from the charge to the point where we want to calculate the potential.

In this case, we have four point charges, each with a value of q = 2.0 μC. Let's label them as Q1, Q2, Q3, and Q4. The distance from each charge to point P is d = 0.91 m.

Since we want to find the total potential, we need to calculate the potential due to each individual charge and then sum them up.

Let's calculate the potential due to each charge:

V1 = k * Q1 / r1

V2 = k * Q2 / r2

V3 = k * Q3 / r3

V4 = k * Q4 / r4

where r1, r2, r3, and r4 are the distances from each charge to point P.

Now, let's substitute the given values into the equations:

k = 8.99 × 10⁹  N m²/C²

Q1 = Q2 = Q3 = Q4 = 2.0 μC = 2.0 × 10⁻⁶ C

r1 = r2 = r3 = r4 = 0.91 m

Calculating the potentials:

V1 = (8.99 × 10⁹N m²/C²) * (2.0 × 10⁻⁶ C) / 0.91 m= 17.58 V

V2 = (8.99 × 10⁹N m²/C²) * (2.0 × 10⁻⁶ C) / 0.91 m= 17.58 V

V3 = (8.99 × 10⁹ N m²/C²) * (2.0 × 10⁻⁶ C) / 0.91 m= 17.58 V

V4 = (8.99 × 10⁹ N m²/C²) * (2.0 × 10⁻⁶ C) / 0.91 m= 17.58 V

Now, we can calculate the total potential by summing up the individual potentials:

Total potential at point P = V1 + V2 + V3 + V4

To find the total potential, we sum up the individual potentials:

Total potential at point P = V1 + V2 + V3 + V4

= 17.58 V + 17.58 V + 17.58 V + 17.58 V

= 70.32 V

Therefore, the exact total potential at point P due to the four point charges is 70.32 volts.

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Answer:

Ratio is 1:4 or 1 dog for 4 cat

Step-by-step explanation:

Data :

Dogs = 5

Cats = 20

To find ratio

  20/ 5 = 4

S0

Relationship is 1:4

1)the total return on the investment after 5 years is $75,796.16.

2)the total amount to be paid back after 4 years is $15,266.41.

3)the total return on the investment after 2 years is $5,780.25.

4) the total worth of the investment after 7 years is $207.89.

1. Calculating total return on investment: We are given,Principal invested = $52,400

Rate of interest = 6%

Time period = 5 years

Interest compounded annually.

Using the formula for the compound interest, we get:Total return = $75,796.16

Therefore, the total return on the investment after 5 years is $75,796.16.

2. Calculating the total amount to be paid back:We are given,Principal borrowed = $10,400

Rate of interest = 12.7%

Time period = 4 years

Interest compounded semiannually.Using the formula for the compound interest, we get:

Total amount paid back = $15,266.41

Therefore, the total amount to be paid back after 4 years is $15,266.41.

3. Calculating total return on investment:We are given,Principal invested = $5,300

Rate of interest = 2.9%

Time period = 2 years

Interest compounded annually.Using the formula for the compound interest, we get:

Total return = $5,780.25

Therefore, the total return on the investment after 2 years is $5,780.25.

4. Calculating the total worth of investment: We are given,Principal invested = $100

Rate of interest = 8.2%

Time period = 7 years

Interest compounded annually.

Using the formula for the compound interest, we get:Total worth of investment = $207.89

Therefore, the total worth of the investment after 7 years is $207.89.

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Answer:

D

Step-by-step explanation:

\(f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5\)

Therefore, the correct answer is choice D. Hope this helps!

CD = (1.328/Re^(1/2)) for laminar boundary layer flow.

a) The boundary conditions of the 3rd order polynomial is that the velocity at the edge of the boundary layer is zero and the velocity at the outer edge of the boundary layer is equal to the free stream velocity.

b)Using the above boundary conditions, C1, C2, and C3 can be determined as follows:

Applying n = 0 to the equation, we obtain u = 0, which is the velocity at the edge of the boundary layer.

Therefore, C1 = 0.

Applying n = 1 to the equation, we obtain u/u∞ = 0.99, which is the velocity at the outer edge of the boundary layer. Therefore, C3 = 0.99∞

Applying the continuity equation, we obtain C2 = C1/2

c)dp/dx = μ*d2U/dy2dp/dx is the pressure gradient, µ is the dynamic viscosity of the fluid.

d) The boundary layer thickness expressed in the form 8/x is given as,

δ = 8/ [2.45(C1/Cf)1/2]

∫0∞ [(u∞ - u)/u∞]1/2dy

Here, Cf = (τw)/(1/2ρu∞^2).

Thus, the boundary layer thickness expressed in the form 8/x is,

δ = 0.37xRe^(-1/5)

e)The momentum thickness expressed in the form 0/x is given as,

θ = ∫0∞ [(u∞ - u)/u∞](1/2)1/2dy

Thus, the momentum thickness expressed in the form 0/x is,

θ = (C2/10) x (Re)^(-1/2)

f) The displacement thickness expressed in the form 8*/x is given as,

δ* = ∫0∞ [(u∞ - u)/u∞]dy

Thus, the displacement thickness expressed in the form 8*/x is,

δ* = (C2/30) x (Re)^(-1/2)

g) The skin friction coefficient, Cf is given as,

Cf = τw/(1/2ρu∞^2)

Thus, Cf = (0.455/Re^0.5) for laminar boundary layer flow.

h)The drag coefficient, CD is given as,

CD = (2F)/(ρu∞^2L)

= 2Fd/(ρu∞^2L)

Therefore, CD = (1.328/Re^(1/2)) for laminar boundary layer flow.

i)The drag force on both sides of the plate is given as,

F = ∫0^L τw dx

= 2∫0^(L/2) τwdx.

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Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

Answer:

5x+3x=8x

8x = 32

x=32/8 = 4

boys are 4 x 5 = 20

girls are 4 x 3 = 12

Step-by-step explanation:

Add the ratios together: 5 + 3 = 8

Divide total students by 8:

32 / 8 = 4

Multiply each ratio by 4 to find the number of each:

Boys = 4 x 5 = 20

Girls = 3 x 4 = 12

There are 20 boys.

Answer:

i think it's D mybe

Step-by-step explanation:

The expected value of a game represents the average amount of money that a player can expect to win or lose per game. The expected value of the game is $0.25.

Two heads: The probability of getting two heads is 1/4 (since the first coin can be either heads or tails, and the second coin must match). The player wins $1 in this case. Two tails: The probability of getting two tails is also 1/4. The player wins $1. Head and tail: The probability of getting a head and a tail is 1/2 (since the first coin can be either heads or tails and the second coin must be the opposite).

The player loses $1 in this case. To calculate the expected value, we multiply each outcome's probability by its corresponding monetary value and sum them up: (1/4 * $1) + (1/4 * $1) + (1/2 * -$1) = $0.25. Therefore, the expected value of the game is $0.25. On average, a player can expect to win $0.25 per game in the long run.

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Answer:

The Percent of Blue sqaures out of the total for Group A is 75%.

The Percent of Blue sqaures out of the total for Group B is 60%.

The Percent of Blue sqaures out of the total for Group C is 66.66666%.

Answer:

14.25

Step-by-step explanation:

5.7*5/2=14.24*2/5, and 5.7*5/2=14.25

The person that can drive further on a 40 gallons of gasoline would be = Carl

Gasoline is a type of fossil fuel that is used by the engine of vehicles and is being converted from chemical energy to mechanical energy.

For Laura;

The distance covered = 260 miles

The quantity of gasoline used = 10 gallons

therefore the mile covered per gallon;

260 miles = 10 gallons

X miles = 1 gallon

X miles = 260/10 = 26 miles

For Carl;

The distance covered = 270

The quantity of gasoline used = 8 gallons

Therefore the mile covered per gallon;

270 miles = 8 gallon

X miles = 1 gallon

X miles = 270/8

X miles = 33.8 miles

Therefore the person that will drive further on a 40 gallons of gasoline would be = Carl since he drives 33.8 miles with 1 gallon of gasoline.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer: all numbers 9 and up.

Step-by-step explanation:

As it is given that, a cylinder has a height of 15 yards and the volume of the cylinder is 15,260.4 cubic yards and we are here to find the radius of the cylinder.

\( \: \)

We know that,

\({ \longrightarrow\qquad{\frak {\pmb{ \pi {r}^{2}h = Volume_{(cylinder) } }}}} \\ \\\)

Where,

\( \: \)

Now, we will substitute the given values in the formula :

\( \: \)

\({ \longrightarrow\qquad{\sf {\pmb{ 3.14 \times {r}^{2} \times 15 = 15260.4 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \times 47.1 = 15260.4 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} = \dfrac{15260.4}{47.1} }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \ = 324 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ r = \sqrt{324} }}}} \\ \\\)

\({ \longrightarrow\qquad{ \underline{ \boxed{\pmb {\frak{ r = 18 } }}}}} \: \: \: \bigstar\\ \\\)

\( \: \)

Therefore,

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Here we are given height and volume of the cylinder. To find the radius of the cylinder We will substitute the value of height and volume in give formula:

Volume of cylinder = πr²h

➝ 15,260.4 = 22/7 × (r)² × 15

➝ 15,260.4 = (r)² × 330/7

➝ 15,260.4 = (r)² × 47.1

➝ 15,260.4/47.1 = (r)²

➝ 324 = (r)²

➝ √324 = r

➝ 18 = r

Hence,

Answer:

1 5/3 or 3/5

2. 25/9 or 9/25

3.9/25*15=5.4

Given, the equation that represents the height of an object:

First, we will find the velocity of the object which is the first derivative of the height using the method of the limits

We will find the value of the function y(t) when t = 3, and when t = 3+h

Substitute y(3+h) and y(3) into the expression of the limit

Where a = 0

d) compute the instantaneous velocity at t = 3

So, the answer will be:

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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