Evaluate. Write your answer as a fraction or whole number without exponents. 6^-2

The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 5

tan 22.5° = n / 10

n = 4.142

Then the perimeter is given as,

P = 8 x 4.142

P = 33.14 units

The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.

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The measure of ∠FGH is 28 - 4x.

A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.

Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.

Using angle sum property, we have:

m∠DEF + m∠FED + m∠FDE = 180

60 - 5x + 2(46 + 2x) + m∠FGH = 180

152 + 4x + m∠FGH = 180

m∠FGH = 180 - 152 - 4x

m∠FGH = 28 - 4x

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The number of each kind of coins Sharah have is 23 dimes and 12 quarters.

Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:

x + y = 35 (the total number of coins)

0.10x + 0.25y = 5.30 (the total value of the coins)

We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x = 35 - y

Now we can substitute this into the second equation:

0.10(35 - y) + 0.25y = 5.30

3.50 - 0.10y + 0.25y = 5.30

0.15y = 1.80

y = 12

Now we can use this value of y to solve for x:

x = 35 - 12 = 23

So Sharah has 23 dimes and 12 quarters.

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Answer:

25%

Step-by-step explanation:

p/w =x/100 for a percentage

93.75/125 = x/100

93.75×100= 9375

9375 = 125x

9375/125 =75

x=75

So she paid 75% of the original price, meaning the jeans were 25% off.

The missing value that cοmpletes the frequency table is 174.

A frequency distributiοn table is a table that displays the number (οr frequency) οf οbservatiοns that fall within each interval after grοuping the data intο intervals. It is an effective tοοl fοr cοmprehending data distributiοn and spοtting patterns οr trends.

Typically, the table has twο cοlumns. The intervals, οr "bins," intο which the data is divided are listed in the first cοlumn. The frequency, οr quantity οf οbservatiοns, that fall intο each bin is displayed in the secοnd cοlumn. Depending οn the data and the level οf precisiοn required, the bins may be identical οr vary in width.

The analysis οf a variety οf data types, including numerical, categοry, and οrdinal data, can be dοne using frequency distributiοn tables. As well as calculating descriptive statistics like the mean, median, and mοde, as well as measures οf variability like the range and standard deviatiοn, they can alsο be used tο generate these statistics.

All things cοnsidered, frequency distributiοn tables οffer a quick and effective apprοach tο summarize a lοt οf data and learn mοre abοut its distributiοn and prοperties.

Tο cοmplete the frequency table, we need tο determine the frequency fοr the interval 28 ≤ x < 30.

We can see frοm the histοgram that the interval 28 ≤ x < 30 has a width οf 2. Since the tοtal frequency is the sum οf the frequencies in each interval, we can use the infοrmatiοn prοvided in the frequency table tο sοlve fοr the missing value:

110 + 36 + 180 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We can simplify this expressiοn:

326 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We knοw that the tοtal frequency is the number οf mοbile phοnes that were tested, sο we can assume that this is a knοwn quantity. Let's say that the manufacturer tested 500 mοbile phοnes. Then we can sοlve fοr the missing frequency:

326 + frequency fοr 28 ≤ x < 30 = 500

frequency fοr 28 ≤ x < 30 = 174

Therefοre, the missing value that cοmpletes the frequency table is 174. The cοmpleted frequency table is:

Battery life, x(hοurs) Frequency

15 < x < 20                   110

20 ≤ x < 22                  36

22 ≤ x < 28                  180

28 ≤ x < 30                   174

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The solutions of the equation  0=x^2-9x+8 are x = 8 and x = 1

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

0=x^2-9x+8

Rewrite as

x^2 - 9x + 8 = 0

Expand the equation

So, we have the following representation

x^2 - 8x - x + 8 = 0

When the equation is factorized, we have

(x - 8)(x - 1) = 0

This gives

x - 8 = 0 and x - 1 = 0

Evaluate

x = 8 and x = 1

Hence, the solutions are x = 8 and x = 1

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is defined as follows:

–3(2x – 5) < 5(2 – x)

Expanding the operations, the solution is obtained as follows:

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x > 5.

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The measure of angle FLI is 56=

The sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.

Therefore the sum of angle in a triangle is 180

Since FIL is right angle , then angle FLI =

180-(90+34)

= 180- 124

= 56°

therefore the measure of angle FLI is 56°

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The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).

To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:

16 + 12x - 12x - 12 < 19x + 12 - 12x - 12

4 < 7x

Solving for x, we can divide both sides by 7:

4/7 < x or x > 4/7

In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.

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Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.

The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:

[tex]log(b*t) = log(h/a)[/tex]

[tex]19 = 19.24 * log(53.89*t)[/tex]

t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10

Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.

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The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.

Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22

Step 2: Solve each inequality for x:
x≤31 and x≥-13

Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31

Step 4: Write the solution in interval notation:
[-13, 31]

So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

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The solution is then:

l = 6cm

w = 2cm

h = 2cm

The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid

then, use the formula: surface area (SA)=2lw+2lh+2hw.

here, we have,

We know that the formula for the volume of a box is:

V = l*w*h

Where:

l = length

w = width

h = height

The formula of the surface area of a box is:

SA = 2(lw+lh+wh)

Based on the given we know the following:

24 =  l*w*h

and

56 =  2(lw+lh+wh)

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:

24 = 6*2*2

Let:

l = 6cm

w =2cm

h =2cm    

Now let's try this on the surface area formula:

56 = 2(6*2+6*2+2*2)

so, 56 = 56

The answer is then:

l = 6cm

w = 2cm

h = 2cm

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Answer:

5x4

Step-by-step explanation:

The dimensions of the rectangle are 20x16

The reducing factor is 0.25.

Multiple 20 * 0.25= 5

Multiple 16 * 0.25= 4

Therefore the new dimensions are 5x4.

Answer:

The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:

For x² - 3x + 2 = 0:

a = 1, b = -3, c = 2

x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2

x = 1 or x = 2

For x² + x + 2 = 0:

a = 1, b = 1, c = 2

x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2

x = (-1 ± i√7) / 2

Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:

(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))

As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².

what is volume ?

Volume in mathematics refers to how much room a three-dimensional object takes up. It is a way to quantify how much enclosed room there is overall in a solid figure. Depending on the shape of the item, a number of formulas can be used to calculate its volume. A rectangular prism's volume, for instance, can be calculated by multiplying its length, breadth, and height, whereas a cylinder's volume can be calculated by dividing its base area by its height. The system being used will determine the unit of measurement for volume, but typical units include cubic metres (m³) and cubic centimetres (cm³).

given

a) V = πr²h, where V is the volume, r is the radius, and h is the height, is the expression for a cylinder's volume. By rearranging the calculation, we can find r:

V/(h) = √12,566.4/(*8)) Equals r ≈ 10 centimetres (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)

Consequently, the cylinder's radius is roughly 10 centimetres.

b) The equation A = r² determines the area of a cylinder's base. Using the r number we just discovered, we have:

A = π(10)² ≈ 314.2 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)

Consequently, the cylinder's base has a surface area of about 314.2 cm².

c) The equation L = 2πrh, where r is the radius and h is the height, determines the lateral area of a cylinder. With the numbers from the problem substituted, we obtain:

L = 2π(10)(8) ≈ 502.7 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)

Consequently, the cylinder's side area is roughly 502.7 cm².

d) The equation S = 2πr² + 2πrh gives the surface area of a cylindrical. Using the r and h numbers we discovered earlier, we have:

S = 2π(10)² + 2π(10)(8) ≈ 942.5 cm² (rounded to the nearest tenth of a centimetre) (rounded to the nearest tenth of a cm)

As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².

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In response to the supplied query, we may state that Therefore, equation  g(12) = 8.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

To find g(3), we substitute x=3 into the function g(x):

g(3) = 2(3)/3

g(3) = 6/3

g(3) = 2

Therefore, g(3) = 2.

To find g(12), we substitute x=12 into the function g(x):

g(12) = 2(12)/3

g(12) = 24/3

g(12) = 8

Therefore, g(12) = 8.

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If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.

If the extra large box is a dilation of the single serving box with a scale factor of 4, then

The ratio of the volumes of the extra large box to the single serving box will be 4³,

We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.

So, the volume of the extra large box will be;

⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,

Therefore, the extra large box will contain 76.8 ounces of cereal.

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The value of the given expression is - x² + 3x - 11 and option b is the correct answer.

Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form. Therefore, A binomial is a two-term algebraic statement that includes a constant, exponents, a variable, and a coefficient.

The given expression is:

(-3x² + 4x) + (2x²-x-11)

-3x² + 4x + 2x² - x - 11

Subtract the like terms:

- x² + 3x - 11

Hence, the value of the given expression is - x² + 3x - 11 and option b is the correct answer.

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There is a zero for f(x) between a and b.

Using the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.

The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.

Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.

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The scale factοr οf dilatiοn is 1/40 and the cοοrdinates οf F" are (1440, 600)

Labelling the image οf the triangle

The image οf the label is attached

The scale factοr οf the dilatiοn

Given that

D'E' = 36 units

Then, we have

D"E" = 0.9 units

The scale factοr is calculated as

Scale factοr = D"E"/D'E'

Sο, we have

Scale factοr = 0.9/36

Evaluate

Scale factοr = 1/40

Sο, the scale factοr οf dilatiοn is 1/40

The cοοrdinates οf F"

This is calculated as

F = F'/Scale factοr

Sο, we have

F = (36, 15)/(1/40)

F = (1440, 600)

The trigοnοmetry ratiοs

The trigοnοmetry ratiοs are calculated as

sin(D") = EF/DF

cοs(D") = DE/DF

tan(D") = EF/DE

Sο, we have the fοllοwing apprοximated values

sin(D") = 15/39 = 0.36

cοs(D") = 36/39 = 0.92

tan(D") = 0.36/0.92 = 0.39

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The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.

The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.

Plugging in the values into the quadratic formula, we get:

x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))

Simplifying the equation, we get:

x = (12 ± √(144-244))/2

x = (12 ± √(-100))/2

Since the square root of a negative number is a complex number, we can write the equation as:

x = (12 ± 10i)/2

Simplifying further, we get:

x = 6 ± 5i

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Work Shown:

[tex]V = \text{Volume of a sphere}\\\\V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*6^3\\\\V = \frac{4}{3}\pi*216\\\\V = \frac{4}{3}*216\pi\\\\V = 288\pi\\\\[/tex]

Answer:

1968 bottles of water

Step-by-step explanation:

24×82=1968

1968 bottles of water

Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

A probability calculated by a series of tests is known as experimental probability.

The given table is as follows:

              1    2    3    4

Jaylon:   6    8    9    7

Paula:    8     5     7   10

To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:

Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)

= 7 / 30

Similarly,

Experimental probability for Paula:

= 10 / 30

Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)

For Jaylon: (7 / 30) × 130 = 30.33

For Paula: (10 / 30) × 130 = 43.33

Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

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The missing table has been attached below.

(a) The function is decreasing at x=2.

(b) The interval where f(x) is increasing is (-3, 3).

(c) The function, f(x) has a relative maximum at x=-3.

To determine whether the function is increasing or decreasing at x=2, we need to find the derivative of f(x) and evaluate it at x=2.

f(x) = x³ - 27x + 5

f'(x) = 3x² - 27

At x=2, f'(2) = 3(2)² - 27 = -15, which is negative.

Therefore, the function is decreasing at x=2.

To find the interval where f(x) is increasing, we need to find the values of x where f'(x) > 0.

f'(x) = 3x² - 27

3x² - 27 > 0

3(x² - 9) > 0

(x - 3)(x + 3) > 0

The critical points are x=-3 and x=3.

We can test each of the intervals created by these critical points to see where f(x) is increasing or decreasing.

When x < -3, f'(x) < 0, so f(x) is decreasing.

When -3 < x < 3, f'(x) > 0, so f(x) is increasing.

When x > 3, f'(x) > 0, so f(x) is increasing.

Therefore, the interval where f(x) is increasing is (-3, 3).

To find the relative maximum of f(x), we need to find the critical points where f'(x) = 0.

3x² - 27 = 0

x² - 9 = 0

(x - 3)(x + 3) = 0

The critical points are x=-3 and x=3.

To determine which of these critical points corresponds to a relative maximum, we need to use the second derivative test.

f''(x) = 6x

At x=-3, f''(-3) = -18, which is negative.

Therefore, f(x) has a relative maximum at x=-3.

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The following system of inequalities is represented by the graph

x+y>3

-x+y< -4

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Consider the  inequalities:

x+y>3-------(1)

-x+y< -4------(2)

Find x and y intercepts of both by considering them as equations by using equal sign in the place of  inequality sign

x+y=3-------(3)

-x+y= -4------(4)

Find x and intercepts of these 2 equations:

we get x intercept when y=0 ( substitute y=0 into the respective equations and find x)

we get y intercept when x=0  ( substitute x=0 into the respective equations and find y)

x intercept of (3) is (3,0)

y intercept of (3) is (0,3)

x intercept of (3) is (4,0)

y intercept of (3) is (0,-4)

plot these points on a the plane and join them with lines

use dotted line and shade under the lines because of less than symbol

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"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.

First, let's apply the distributive property to the first expression:

3(x+2) + 8 = 3x + 6 + 8

Next, let's simplify the expression by combining like terms:

3x + 6 + 8 = 3x + 14

Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.

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Answer:

42

Step-by-step explanation:

you asding it all up

Answer: I think B & C not super sure though