how many miles is 60,000 inches

The required maximum area of the rectangle is 17.5m

The perimeter of a rectangle is = 70m.

We have to find The maximum area of rectangle .

A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.

Maximum area of rectangle is = 70 / 4

                                                   = 17.5

The required value of maximum area of the rectangle is 17.5m.

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the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle

The evaluations are:

i. 11!  = 39916800

ii. 24! = 2.045 x 10^37

Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;

5! = 5 x 4 x 3 x 2 x 1!

   = 120

To evaluate the given expressions;

a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!

       = 39916800

Also,

b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!

          = 204484017332398 x 10 ^23

          = 2.045 x 10^37

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There is higher variability of y with large values of x.

There is a non linear relation between x and y.

We observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.

Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.

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The missing parameters of the regular polygons are listed below:

Case 1: θ = 45°, a = 10.864 cm

Case 2: θ = 72°, s = 5.812 cm

In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:

Central angle

θ = 360 / n

Relationship between apothema and side length

a = s / [2 · tan (180 / n)]

Where:

Now we proceed to find missing parameters:

Case 1: s = 9 cm, n = 8

θ = 360 / 8

θ = 45°

a = (9 cm) / [2 · tan (180 / 8)]

a = 10.864 cm

Case 2: a = 8 cm, n = 5

θ = 360 / 5

θ = 72°

s = 2 · a · tan (180 / n)

s = 2 · (8 cm) · tan (180 / 5)

s = 5.812 cm

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Answer:

Perimeter of rhombus = 4(9.7) = 38.8 cm

Area of rhombus = 4(1/2)(6.2)(7.4)

= 91.76 cm^2

The statement that could be true for the domain of g is g(-4) = -11.

option A.

The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.

The given statements that could be true for g is calculated as follows;

Option A: g(-4) = -11

Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.

Therefore, this could be true.

Option B: g(-13) = 20

Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.

Option C: g(0) = 2

We are given that g(0) = -2, so option C is not true.

Option D: g(7) = -1

Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.

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Answer: 15y2 - 19y + 6 = 0

Step-by-step explanation:

The first term is,  15y2  its coefficient is  15 .The middle term is,  -19y  its coefficient is  -19 .The last term, "the constant", is  +6 Step-1 : Multiply the coefficient of the first term by the constant   15 • 6 = 90 Step-2 : Find two factors of  90  whose sum equals the coefficient of the middle term, which is   -19 .

The single transformation that maps shape P onto shape Q is given as follows:

Reflection over the line y = 1.

Examples of transformations are given as follows:

The orientation of the figure changed, hence it underwent a reflection.

The intercepts are given as follows:

y = 4 and y = -2.

The line of reflection is the mean of the coordinates of the intercepts, hence:

(4 - 2)/2 -> y = 1.

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There are 25% chance of 5 more people in the party.

Hence option (a) is correct.

Relative frequency = (number of times of occurrence of an event )/ (number of trials)

For the given table

relative frequency for 1 people = 0.05 = 5%

relative frequency for 2 people = 0.46 = 46%

relative frequency for 3 people = 0.18 = 18%

relative frequency for 4 people = 0.22 = 22%

relative frequency for 5 people = 0.06 = 6%

relative frequency for 6 people = 0.03 = 3%

Since relative frequency for 1 people is 5%

Therefore,

Relative frequency for 5 people is = 5x5%

                                                         = 25 %

Hence,

Relative frequency of 5 more people 25%.

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Answer: 34.9

Step-by-step explanation: 100 - 65.1

Therefore, the correct answer is option C that is LM is reflected over the y-axis to L'M.

In mathematics, a transformation refers to a change in the position, shape, or size of a geometric figure. Transformations can be classified into four types: translation, rotation, reflection, and dilation.

Here,

The transformation of LM to L'M' involves both translation and reflection. To see the translation, we can compare the x- and y-coordinates of L and L', as well as M and M':

The x-coordinate of L' is 5 units more than the x-coordinate of L: -2 = -7 + 5.

The y-coordinate of L' is 2 units less than the y-coordinate of L: -4 = -2 - 2.

The x-coordinate of M' is 5 units more than the x-coordinate of M: 5 = 0 + 5.

The y-coordinate of M' is 2 units less than the y-coordinate of M: 3 = 5 - 2.

Therefore, we can conclude that LM is translated 5 units right and 2 units down to L'M'. This eliminates options OB and OD. To see the reflection, we can compare the x-coordinates of L and M, and their respective x-coordinates in L' and M':

The x-coordinate of L is negative and the x-coordinate of M is positive.

The x-coordinate of L' is negative and the x-coordinate of M' is positive.

Therefore, we can conclude that LM is reflected over the y-axis to L'M'. This eliminates option OA. Therefore, the correct answer is option OC.

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a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.

b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.

Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.

Probability is represented as a fractional value using decimals, fractions, or percentages.

The percentage of students taking a math class =79%

The percentage of students taking an English class = 70%

The percentage of students taking both classes = 67%

Let the event that a student is taking a math class = m

Let the event that a student is taking an English class = e

The probability of m is p(m) = 0.79

The probability of e is p(e) = 0.70

The probability of m and e is p(m and e) = 0.67

The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)

The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)

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The other value of x where g(x) = 15 is 16 in the absolute value function

Since the vertex of the absolute value function is at (10,0), the equation for the function can be written as:

g(x) = a|x - 10|

To find the value of a, we can use the fact that the function passes through the point (4,15):

15 = a|4 - 10|

15 = 6a

a = 2.5

So the equation for the absolute value function is:

g(x) = 2.5|x - 10|

To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:

2.5|x - 10| = 15

|x - 10| = 6

x - 10 = 6 or x - 10 = -6

x = 16 or x = 4

Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.

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The [tex]f^{-1}[/tex] inverse of f  of each

1) (x + 1)/2

2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]

3) 3 - 4x

4) [tex](x+5)^{1/3}[/tex]

5) [tex]\sqrt{x + 4}[/tex]

1) function f(x) = 3x + 1

let f(x) = y

y = 3x + 1

y - 1 = 3x

(y - 1)/3 = x

x obtained is [tex]f^{-1}[/tex]

and y will be x

[tex]f^{-1}[/tex] = (x-1)/3

2) equation f(x) = 4x² - 1

let f(x) = y

y = 4x² - 1

y + 1  = 4x²

(y + 1 )/4 = x²

x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]

x obtained is [tex]f^{-1}[/tex]

and y will be x

[tex]f^{-1}[/tex] =  [tex]\sqrt{\frac{x + 1}{4} }[/tex]

similarly,

3) f(x) = 3-x/4

y = 3-x/4

4y = 3 - x

x = 3 - 4x

[tex]f^{-1}[/tex] =  3- 4x

4) y = x³ - 5

y + 5 = x³

x = [tex](y + 5)^{1/3}[/tex]

[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]

5) y = x² - 4

y + 4 = x²

x = √y + 4

[tex]f^{-1} = \sqrt{x + 4}[/tex]

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Answer:

6

Step-by-step explanation:

bc

The value of x it the nearest tenth of degree is 25.6°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/ hyp

cos( tetha) = adj/ hyp

tan( tetha) = opp/ adj

Here, the hypotenuse is 92 and adjascent to the to the angle x is 63

therefore to calculate x we use cosine function

cos x = 83/92

cos x = 0.902

x = cos^-1( 0.902)

x = 25.6° ( nearest tenth)

therefore the value of x is 25.6°

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Answer:

f(1) = 1

Step-by-step explanation:

Open holes on a graph means that the function is not defined at that point, so we ignore the open hole.

At f(1), there is both an open hole at y=-2 and a closed hole at y=1

We ignore the open hole as it is not defined so the answer would be the closed hole, y = 1

So f(1) is 1

A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3

B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5

A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.

Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.

3x² - 2 + x² + 2xy + 5

Combine like terms:

4x² + 2xy + 3

Part B: Number of canned food still remaining to be collected is calculated below.

(6x² - 2xy + 8) - (4x² + 2xy + 3)

Open bracket:

6x² - 2xy + 8 - 4x² - 2xy - 3

Combine like terms:

2x² - 4xy + 5

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Answer:

it would be 9x

Step-by-step explanation:

because subtract 3 from 12 and leave the x

The table is completed as follows:

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the first row, when x = 0.2, y = 2, hence the constant is given as follows:

k = y/x

k = 2/0.2

k = 10.

Hence the equation is:

y = 10x.

Then the numeric values are given as follows:

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The number of sun flowers with a height  of 27¹/₂ inches or more are 4 more than those with a height of less than 27¹/₂ inches

A dot plot, which is also known as a strip plot or dot chart, is a simple form of data visualization that comprises of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.

The number of heights below 27¹/₂ inches that exists in the given dot plot is seen to be 8 in number.

Similarly, the number of dot plots that exists above or equel to 27¹/₂ inches from the given dot plot are 12 in number.

Therefore, we can say that:

Difference in total number for both parameters = 12 - 8= 4

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The perimeter of the composite figure is 46 metres.

The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.

Therefore, the perimeter of the figure can be found as follows:

perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12

perimeter of the shape = 11 + 9 + 11 + 15

perimeter of the shape =20 + 11 + 15

perimeter of the shape = 31 + 15

perimeter of the shape = 46 metres

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Answer:

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]

[tex]\large\underline{\textsf{What is Area?}}[/tex]

[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]

[tex]\textsf{as the sides of a shape.}[/tex]

[tex]\underline{\textsf{How are we able to find Area?}}[/tex]

[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]

[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]

[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]

[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]

[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]

[tex]\large\underline{\textsf{Formula;}}[/tex]

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\underline{\textsf{Plug in Values;}}[/tex]

[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]

[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]

[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56

what is synthetic division ?

Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).

In the given question,

To use synthetic division to rewrite the fraction, we first set up the problem like this:

   -3 | 4    17    14    -3    0    2

       |     -12    -15    3   0

       +----------------------------------

          4     5    -1     0    0    2

The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.

We then proceed to perform synthetic division as follows:

Bring down the first coefficient, which is 4, and write it under the horizontal line.

Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.

Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.

Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.

Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.

Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.

Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.

The result of the synthetic division is:

4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56

Therefore, we have rewritten the fraction in the desired form:

4x⁵+17x⁴+14x³-3x²+2

---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)

         x+3

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The solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5

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

The equation 100+ (n - 2)² = 149

Express as

100+ (n - 2)² = 149

Subtract 100 from both sides of the equation

So, we have the following representation

(n - 2)² = 49

Take the square root of both sides

n - 2 = 7 and n - 2 = -7

Add 2 to both sides

n = 9 and n = -5

Hence, the solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5

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The median is the accurate reflection of the data

501, 900, 971, 977, 1071

The mean would be

summation of the values

mean = 884

The median is the value that occurs in the middle = 971

The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data

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Answer:

f(-1)=0

Step-by-step explanation:

To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :

[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]

[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0

Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.

The quarterly interest rate is 4% / 4 = 1%.

Let's use the formula for the future value of an annuity:

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

where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:

FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01

FV = $2500 x (5.409 - 1) / 0.01

FV = $2500 x 540.9

FV = $1,352,250

Therefore, there will be $1,352,250 in the account when the man retires at age 71.

If line A is parallel to line B then the value of x is 18.

Given that a line A is parallel to line B

We have to find the value of x

3x+7x=180

Combine the like terms

10x=180

Divide both sides by 10

value x=18

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