Study this model of earth, the moon, and the sun. then answer the questions.
in this model, number 1 represents
v
number 2 represents
and number 3 represents
reset
next

Answer:

Therefore, the base-6 representation of 1407 is 1303.

Step-by-step explanation:

To convert the decimal numeral 1407 to base 6, we can use the following steps:

Divide 1407 by 6 and store the quotient and the remainder.

Repeat the division process with the quotient until the quotient is 0.

Write down the remainders in the reverse order to get the base-6 representation of 1407.

So, the steps would look like this:

1407 ÷ 6 = 234 with a remainder of 3

234 ÷ 6 = 39 with a remainder of 0

39 ÷ 6 = 6 with a remainder of 3

6 ÷ 6 = 1 with a remainder of 0

1 ÷ 6 = 0 with a remainder of 1

Writing down the remainders in the reverse order, we get: 1407(10) = 1303_6.

Therefore, the base-6 representation of 1407 is 1303.

Answer:

The answer is B

Step-by-step explanation:

I just took the quiz on edge 2021 the answer is B

Answer:

B is tha answer

Step-by-step explanation:

The standard error of the mean is 10.

The standard error of the mean (SEM) is calculated by dividing the

population standard deviation (σ) by the square root of the sample size (n):

SEM = σ / √n

In this case, the population standard deviation is 40 and the sample size is 16.

Substituting these values into the formula, we get:

SEM = 40 / √16

SEM = 40 / 4

SEM = 10

Therefore, the standard error of the mean is 10.

for such more question on standard error

https://brainly.com/question/22377370

#SPJ11

Answer:

362

Step-by-step explanation:

15xy=5430...therefore 5430divided by 15 is 362...so 362x15 their product is 5430

Answer:

The change is increased by 80%.

Step-by-step explanation:

Divide 36 by 45. This gives you 0.8. Divide 36 by 0.8 and multiply 45 by 0.8 to check your answer. So, it is increased by 80%. To find out how percents change, divide the first number by the second number. Then, take the decimal and move the decimal point over to the right two spaces, or multiply the entire number by 100.

To calculate the amplitude of the electric field in the LIGO beam, we divide the power of 100 kW by the area of a square centimeter.

(a) The amplitude of the electric field in the LIGO beam can be calculated using the formula:

Amplitude of electric field = √(Power / Area)

Converting the power of 100 kW to 100,000 W and the area of a square centimeter to square meters:

Amplitude of electric field = √(100,000 / 0.0001) = √(10^9) = 10^4 V/m

Therefore, the amplitude of the electric field in the LIGO beam is 10,000 V/m.

(b) The phase shift caused by a gravitational wave temporarily lengthening one arm by 10^-18 m can be estimated using the formula:

Phase shift = (2π * d) / λ

Where d is the change in arm length and λ is the wavelength of the laser. In this case, the effective arm length is 1120 km, which is equivalent to 1.12 x 10^6 m, and the laser wavelength is 1064 nm, or\(1.064 x 10^-6 m.\)

Phase shift =\((2π * 10^-18) / (1.064 x 10^-6) = 2π * 10^-12 radians\)

Therefore, the estimated phase shift caused by the gravitational wave is approximately\(6.28 x 10^-12\) radians.

(c) Using Eq. (35.7), the sensitivity of the photodetector can be estimated by relating the minimal electric field strength required to detect a gravitational wave to the phase shift:

Minimal electric field strength = (λ * Amplitude of electric field) / (4π * d)

Substituting the values obtained:

Minimal electric field strength = \((1.064 x 10^-6 * 10^4) / (4π * 10^-12)\)

Simplifying the equation:

Minimal electric field strength = 8.49 x \(10^7\) V/m

Therefore, the estimated sensitivity of the photodetector is approximately 8.49 x \(10^7\) V/m, indicating the minimal electric field strength needed to detect a gravitational wave.

Learn more about divide here:

https://brainly.com/question/15381501

#SPJ11

Jan's number is 12.

To find Jan's number, we need to determine a positive integer that has exactly 16 positive divisors and includes both 12 and 15 as divisors.

Let's consider the prime factorizations of 12 and 15:

12 = 2^2 * 3

15 = 3 * 5

From these prime factorizations, we can see that the common factor between 12 and 15 is 3.

Now, to have exactly 16 positive divisors, the number should be in the form of \(p^a \times q^b \times r^c\), where \(p\), \(q\), and \(r\) are distinct prime numbers, and \(a\), \(b\), and \(c\) are positive integers.

Since 12 has 2^2 * 3 in its prime factorization and 15 has 3 * 5, we can construct the number by considering these factors:

The number will have 2 raised to the power of 2 because it needs to have 12 as a divisor. So far, we have \(2^2\).

Next, we need to include 3 raised to some power. Since 12 already has 3 in its factorization, we don't need to include an additional 3. Thus, we still have \(2^2\) for this part.

Finally, we need to include 5 raised to some power to account for 15 as a divisor. Since 15 already has 5 in its factorization, we don't need to include an additional 5.

Putting it all together, the number that satisfies the conditions is \(2^2 \times 3^1 \times 5^0 = 4 \times 3 \times 1 = 12\).

Therefore, Jan's number is 12.

To know more about divisors , refer here :

https://brainly.com/question/26086130#

#SPJ11

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

Yes, there are diminishing returns to labor in the given production function.

There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.

When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.

Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.

The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.

The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.

Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.

Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.

Learn more about labor

brainly.com/question/984683

#SPJ11

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

The length of AB of the triangle is 13 units.

The side AB of the triangle can be found using cosine law,

Therefore,

c² = a² + b² - 2ab cos C

c² = 7² +  8² - 2 × 7 × 8 cos 120

c² = 49 + 64 - 112 cos 120

c²= 113 - (-56)

c² = 113 + 56

c² = 169

c = √169

c = 13 units

Therefore, the value of AB is 13 units

learn more on triangle here: https://brainly.com/question/3642070

#SPJ1

Answer:

log 12 = 1.0761

Step-by-step explanation:

log 12

=log(3*2*2)

= log 3 +log 2+ log 2

=0.4771+0.3010+0.3010

=1.0761

Answer:

Log 12 = 1.0791

Step-by-step explanation:

=> log (12)

Prime Factorizing 12

=> log (2×2×3)

Using log rule : \(log (a*b) = log a+logb\)

=> Log 2 + log 2 + log 3

Given that log 2 = 0.3010 , log 3 = 0.4771

=> 0.3010 + 0.3010 + 0.4771

=> 1.0791

Step-By-Step Solution for Part 1:

Answer: Equivalent

Step-By-Step Solution for Part 2:

Answer: Equivalent

Step-By-Step Solution for Part 3:

[Replacing y as 2 and z as 3]

Answer: Not Equivalent

Step-By-Step Solution for Part 4:

15n + 5 = 5(3n + 1)

=> 15n + 5 = (5 x 3n) + (5 x 1)

=> 15n + 5 = 15n + 5

Answer: Equivalent

Answer:

Yes 17/20 is bigger than 7/9

Step-by-step explanation:

17 divided by 20 = 0.85

7 divided by 9 = 0.778 ish

17/20 is bigger

The interest to be paid on $120 at 5% rate for 6 years is $36

Simple interest is the amount paid on a principal amount of money that is borrowed or loaned to someone. It is calculated using the formula: SI = (P × R × T) / 100. Where P is the principal amount, R is the rate and T is the time.

From the question;

P = $120

R = 5%

T = 6years

we shall evaluate for the simple interest as follows:

Simple interest = ($120 × 5 × 6)/ 100

Simple interest = $3600/100

Simple interest = $36

Therefore, the interest to be paid on $120 at 5% rate for 6 years is $36.

Read more about simple interest here:https://brainly.com/question/25793394

#SPJ1

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

know more about speeds here

https://brainly.com/question/28224010#

#SPJ11

The parameterization of the line through points p=(3,-5) and q=(8,0) where p corresponds to t=9 and q corresponds to t=12 is given by the equations x = t - 6 and y = t - 14.

To parameterize the line, we need to find equations that express x and y in terms of a parameter t. We can start by determining the slope of the line using the coordinates of points p and q:

slope (m) = (y₂ - y₁) / (x₂ - x₁)

= (0 - (-5)) / (8 - 3)

= 5 / 5

= 1

Now that we have the slope, we can write the equations in point-slope form using point p:

y - y₁ = m(x - x₁)

y - (-5) = 1(x - 3)

y + 5 = x - 3

y = x - 8

Next, we can express x and y in terms of the parameter t by substituting x = 3 + (t - 9) and y = -5 + (t - 9) into the equation above. Simplifying, we get:

y = (3 + (t - 9)) - 8

y = t - 9 - 5

y = t - 14

Therefore, the parameterization of the line through points p and q where p corresponds to t=9 and q corresponds to t=12 is given by the equations x = 3 + (t - 9) and y = -5 + (t - 9), or equivalently, x = t - 6 and y = t - 14.

Learn more about parameterization here:

https://brainly.com/question/31964038

#SPJ11

Answer:

-5

Step-by-step explanation:

3x²y + xy²​

Let x = -1/2 and y = 4

3(-1/2)^2 (4) + (-1/2) (4)^2

Exponents first

3(1/4) (4) + (-1/2) 16

Multiply

3 - 8

Subtract

-5

​

Answer:   \(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\huge \boldsymbol {-5}\)

Step-by-step explanation:                                                                                                                                                                                                                     simplify it                                                                                                                  \(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} 3x^2y+xy^2=xy(3x+y)\)                                                                       evalute                                                                                                        \(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} -\frac{1}{2} \cdot 4 (-3\cdot \frac{1}{2}+4)=-2\!\!\!\!\diagup\cdot\frac{5}{2\!\!\!\!\diagup} =\boxed{-5}\)                                                                                                                                                                                                                                                              

The probability that they're both home is 1/12.

In the given question,

Probability of Maya at home P(A) = 1/3

And probability of Jim at home P(B) = 1/4

The probability that Jim is home given that maya is home P(A∪B) = 1/2

We have to find the probability when they both are at home P(A ∩ B).

As we can see that the probability of both the events are independent

So, we can use

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Therefore,

1/2 = 1/3 +1/4 – P(A ∩ B)

P(A ∩ B) = 7/12 – 1/2

P(A ∩ B) = 1/12

Hence, the probability that they're both home is 1/12.

To learn more about probability link is here.

brainly.com/question/11234923

#SPJ4

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

To learn more on Angles click:

brainly.com/question/28451077

#SPJ1

Therefore, for n > 1, we have: arithmetic series: a(n) = a(n-1) + 3

arithmetic series?

a. The correct notation for the arithmetic series 8 + 11 + ... + 29 would be:

∑(n=1 to 11) (7 + 3n)

The student's error is not specifying the upper limit of the summation, which should be 11 because there are 11 terms in the series.

b. To evaluate the corrected summation notation, we can use the formula for the sum of an arithmetic series:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

In this case, a1 = 8 and an = 29, so we have:

\(Sn = n/2(8 + 29)\\Sn = n/2(37)\)

Substituting n = 11 (the number of terms), we get:

\(S11 = 11/2(37)\\S11 = 203.5\)

Therefore, the sum of the arithmetic series 8 + 11 + ... + 29 is 203.5.

c. The explicit formula for an arithmetic series is:

\(an = a1 + (n-1)d\)

where an is the nth term, a1 is the first term, and d is the common difference between consecutive terms.

In this case, a1 = 8 and d = 3, so we have:

\(an = 8 + (n-1)3\\an = 3n + 5\)

The recursive formula for an arithmetic series is:

\(a(n+1) = a(n) + d\)

where a(n+1) is the next term and a(n) is the current term.

In this case, the first term is a1 = 8, and the common difference is d = 3, so we have:

\(a(n+1) = a(n) + 3\\a(1) = 8\)

To learn more about common difference:

https://brainly.com/question/28584885

#SPJ1

The values of g, h, m, and n are as follows: g = 5,h = 90, m = 2, n = 8

To add vectors in the form of magnitude and angle, we need to separate the magnitudes and angles of the vectors. Let's break down the given vectors:

Vector 1: 5 angle(50)

Magnitude: 5

Angle: 50 degrees

Vector 2: (x=6, y=8)

Magnitude: sqrt(6^2 + 8^2) = 10

Angle: arctan(8/6) = arctan(4/3) ≈ 53.13 degrees

Vector 3: 4 angle(40)

Magnitude: 4

Angle: 40 degrees

Now, let's add the vectors component-wise:

Sum of x-components: 5cos(50) + 6 + 4cos(40) = 50.6428 + 6 + 40.766 = 3.214 + 6 + 3.064 = 12.278

Sum of y-components: 5sin(50) + 8 + 4sin(40) = 50.766 + 8 + 40.6428 = 3.83 + 8 + 2.5712 = 14.4012

To find the magnitude and angle of the resulting vector, we use the formulas:

Magnitude: sqrt((Sum of x-components)^2 + (Sum of y-components)^2)

Angle: arctan((Sum of y-components)/(Sum of x-components))

Magnitude of the resulting vector: sqrt(12.278^2 + 14.4012^2) ≈ 19.0195

Angle of the resulting vector: arctan(14.4012/12.278) ≈ 48.60 degrees

Comparing the magnitude and angle with the given value:

Magnitude: 19.0195 ≈ 8 (g = 5)

Angle: 48.60 ≈ 90 (h = 90)

Therefore, the values of g, h, m, and n are as follows:

g = 5

h = 90

m = 2

n = 8

Note: The values of m and n are not directly related to the vectors provided in the question, so they are assigned arbitrary values for this exercise.

Learn more about vector addition here: brainly.com/question/28875206

#SPJ11

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer:

its finally sorry it tooke so long

Step-by-step explanation:

Answer:

The answer is finally.

Step-by-step explanation: Both would be a compare and contrast text structure and so would similarly. Since would be a cause and effect text structure so the answer has to be finally. You can also tell because it is using key clues like then, after, and finally.

The ball will take around 1.6 seconds to hit the ground when dropped from shoulder height at the top of the 35-foot tall building, considering a gravitational acceleration of 32.2 feet per second squared.

To find the time it takes for the ball to hit the ground, we can use the equations of motion under constant acceleration. The acceleration due to gravity near the surface of the Earth is approximately 32.2 feet per second squared.

First, let's calculate the total distance the ball needs to travel from the top of the building to the ground. The total height is the height of the building plus Carmine's height, which is 35 feet + 5 feet = 40 feet.

Next, we can use the equation:

\(s = ut + (1/2)at^2\)

where:

s = distance (40 feet)

u = initial velocity (0 feet per second since the ball is at rest)

a = acceleration (-32.2 feet per second squared, taking negative because the ball is moving downward)

t = time (unknown)

Plugging in the values:

\(40 = 0t + (1/2)(-32.2)t^2\)

Simplifying the equation:

\(40 = -16.1t^2\)

Dividing both sides by -16.1:

\(t^2 = -2.48\)

Since time cannot be negative in this context, we discard the negative solution. Taking the square root of the positive solution:

t ≈ 1.57 seconds

Therefore, it will take approximately 1.6 seconds (rounded to the nearest tenth) for the ball to hit the ground when dropped from shoulder height at the top of the building.

Learn more about height here: https://brainly.com/question/29131380

#SPJ11

The complete question is:

Carmine drops a ball at shoulder height from the top of a building (building is 35 feet tall, Carmine is 5 feet tall). If the ball is at rest, and is simply dropped, how long will it take, to the nearest tenth of a second, to hit the ground?

Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

To learn more about Polyhedron, refer:

https://brainly.com/question/27231951

#SPJ4

We need to consider the general problem: \[-(ku')' + cu' + bu = f\]If we discretize by the finite element method with four elements.

On the first and last elements, we use linear shape functions, and on the middle two elements, we use quadratic shape functions. The resulting basis functions are given by:The basis functions ϕ1 and ϕ4 are linear while ϕ2 and ϕ3 are quadratic in nature. These basis functions are such that they follow the property of linearity and quadratic nature on each of the elements.

For the structure of the stiffness matrix K, we need to consider the discrete problem given by \[KU=F\]where U is the vector of nodal values of u, K is the stiffness matrix and F is the load vector. Considering the above equation and assuming constant values of k and c on each of the element we can write\[k_{1}\begin{bmatrix}1 & -1\\-1 & 1\end{bmatrix}+k_{2}\begin{bmatrix}2 & -2 & 1\\-2 & 4 & -2\\1 & -2 & 2\end{bmatrix}+k_{3}\begin{bmatrix}2 & -1\\-1 & 1\end{bmatrix}\]Here, the subscripts denote the element number. As we can observe, the resulting stiffness matrix K is symmetric and has a banded structure.

The element [1 1] and [2 2] are common to two elements while all the other elements are present on a single element only. Hence, we have four elements with five degrees of freedom. Thus, the stiffness matrix will be a 5 x 5 matrix and the structure of K is as follows:

$$\begin{bmatrix}k_{1}+2k_{2}& -k_{2}& & &\\-k_{2}&k_{2}+2k_{3} & -k_{3} & & \\ & -k_{3} & k_{1}+2k_{2}&-k_{2}& \\ & &-k_{2}& k_{2}+2k_{3}&-k_{3}\\ & & & -k_{3} & k_{3}+k_{2}\end{bmatrix}$$Conclusion:In this question, we considered the general problem given by -(ku')' + cu' + bu = f. We discretized it by the finite element method with four elements. On the first and last elements, we used linear shape functions, and on the middle two elements, we used quadratic shape functions. We sketched the resulting basis functions. The structure of the stiffness matrix K was then determined by ignoring boundary conditions. We observed that it is symmetric and has a banded structure.

To know more about general problem visit

https://brainly.com/question/24486535

#SPJ11

If the expression \(r(x) = 3x - 1\) and the expression \(s(x) = 2x + 1\) , then the expression equivalent to \(\frac{r}{s} (6)\) is (a) \(\frac{3(6)-1}{2(6) +1}\) .

What are Algebraic Expression ?

The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : \(3x+7\) .

Here the two expressions are given as \(r(x) = 3x - 1\) and \(s(x) = 2x + 1\) ;

we have to find equivalent expression for \(\frac{r}{s} (6)\) ;

By the Division Property of Algebraic Expression ;

it can be written as : \(\frac{r(6)}{s(6)}\) ;

So , Substituting \(x=6\) , in r(x) ,

we get ; \(r(6) = 3(6) - 1\) , ......equation(1)

On Substituting \(x=6\) , in s(x) ,

we get ; \(s(6) = 2(6)+1\) ,  ....equation(2) ;

Substituting the values of r(6) and s(6) from equation(1) and equation(2) in \(\frac{r(6)}{s(6)}\) ;

we get ;

⇒ \(\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}\) ;

Therefore , the expression equivalent to \(\frac{r}{s} (6)\) is \(\frac{3(6)-1}{2(6) +1}\) .

The given question is incomplete , the complete question is

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?

(a) \(\frac{3(6)-1}{2(6) +1}\)

(b) \(\frac{(6)}{2(6)+1}\)

(c) \(\frac{36-1}{26+1}\)

(d) \(\frac{(6)-1}{(6)+1}\)

Learn more about Expression here

https://brainly.com/question/12011094

#SPJ4

Given:

On a map, the scale shown is 1 inch : 5 miles.

Area of park = 75 square miles.

To find:

The area of the park on the map.

Solution:

Ratio of the areas of similar figures is equal to the ratio square of their corresponding sides.

\(\dfrac{\text{Area of park on the map}}{\text{Actual area of the park}}=\dfrac{\text{Side of park in map}^2}{\text{Actual side of park}^2}\)

Let A be the area of the park on the map.

\(\dfrac{A}{75}=\dfrac{1^2}{5^2}\)

\(A=\dfrac{1}{25}\times 75\)

\(A=3\)

Therefore, the area of the park on the map is 3 square inches.