In circle H with m/GHJ = 82 and GH = 12 units, find the length of arc GJ.
Round to the nearest hundredth.
H

======================================================

Explanation:

See the diagram below.

The diagram shows we have a right triangle with these side lengths:

We'll use the pythagorean theorem to find c

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\c = \sqrt{(8)^2 + (5.5)^2}\\\\c = \sqrt{94.25}\\\\c \approx 9.7082\\\\c \approx 9.7\\\\[/tex]

Mrs. Durham and Brett are about 9.7 meters apart.

Answer:

y=½x-6

Step-by-step explanation:

m= ½

equation of the line: y-y1=m(x-x1)

y+5=½(x-2)

y=½x-6

Answer:

[tex]y =\dfrac{1}{2}x-6[/tex]

Step-by-step explanation:

Point-slope formula

[tex]y-y_1=m(x-x_1)[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}[/tex]

Answer: The answer is D. 72 cu ft.

Step-by-step explanation:

The total pounds of science books that sanya carried is; 6⁷/₈ pounds

From the attached Line Plot, we can see the book weights.

Now, we are told that Sanya carried all the books weighing 2¹/₄ pounds and 2³/₈ pounds.

From the line plot we see that;

Number of books weighing 2¹/₄ pounds are 2 books

Number of books weighing 2³/₈ pounds is 1 book

Thus;

Total weight of books carried by Sanya = 2(2¹/₄) + 1(2³/₈)

Total weight = 4¹/₂ + 2³/₈

Total Weight = 6⁷/₈ pounds

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a) a= 2×40 = 160°

b) b = 60/2 = 30°

c) c = 40°

d) d = 115°

The relationship between dollars delivered and rand received represents a function.

Corresponds to a mathematical relationship between two variables, x and y, where the set of x values ​​is associated with a y value. Being expressed by the formula:

Therefore, in the exchange rate question, x is the independent variable, that is, the value of $100, and y will correspond to the dependent variable, which is the value of rand that will be received in relation to the dollar.

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Answer:

48 weeks

Step-by-step explanation:

This is a division problem.

6 / (1/8) = 6/1 × 8/1 = 48

Answer: 48 weeks

They are written in term of power to the base of a function. The value of n that will make both expression equal is 2/9

They are written in term of power to the base of a function. Given the expression below:

[tex]216^{n-2}=\frac{1}{36}^{3n}[/tex]

This can be further simplified as:

[tex]6^3^{n-2}=(6^{-2})^{3n}\\6^{3n-2}=6^{-6n}[/tex]

Cancel the base to have:

3n-2 = -6n
3n+6n = 2

9n = 2

n = 2/9

Hence the value of n that will make both expression equal is 2/9

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Answer: irrational number

Step-by-step explanation:

Let us write it out.

      [tex]\displaystyle \frac{23}{\sqrt{3} }[/tex]

Next, we will define ratoinal and irrational.

      A rational number is a number that can be written as a whole number, fraction, or decimal that ends / repeats.

      An irrational number is any number that cannot be turned into a fraction.

Let us see which category the number given falls into.

      [tex]\displaystyle \frac{23}{\sqrt{3} } = 13.27905619\;\;\;\;\;\;\text {it goes on...}[/tex]

This means  [tex]\frac{23}{\sqrt{3} }[/tex] is an irrational number.

Answer:

− (8b − x) (5b + x)

Step-by-step explanation:

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

There is no flaw in the steps. Hence, the correct option is A.

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Using the given information, the radius of the sphere to the nearest meter is 13m

From the question, we are to determine the radius of the sphere

Using the formula for calculating the volume of a sphere,

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

Where V is the volume

and r is the radius

From the given information,

V = 9198 m³

Then,

[tex]9198 = \frac{4}{3} \times \pi r^{3}[/tex]

[tex]9198 = \frac{4}{3} \times 3.14 \times r^{3}[/tex]

[tex]4 \times 3.14 \times r^{3} = 9198 \times 3[/tex]

[tex]4 \times 3.14 \times r^{3} = 27594[/tex]

[tex]r^{3} = \frac{27594}{4 \times 3.14}[/tex]

[tex]r = \sqrt[3]{\frac{27594}{4\times 3.14} }[/tex]

r = 12.99995 m

r ≅ 13 m

Hence, the radius of the sphere to the nearest meter is 13m.

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This answer does look right to me.

The number of cans the school will collect is T = 190 c.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

Each class is challenged to collect 190 cans.

If there are c classes in the school.

Then, the number of Cans can be collected is:

= Number of classes x number of cans each class collect

=  c x 190

= 190 c

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The total area of the fields that Ram has is  170,900 square meters ( 170900 m²)

From the question, we are to determine the total area of the fields that Ram has

Since the fields are square in shapes, we will use the formula for calculating the area of a square

The area of a square can be calculated by using the formula,

A = s²

Where A is the area

and s is the side

For the first field

s = 350 m

∴ A = 350²

A = 122500 m²

For the second field

s = 220 m

∴ A = 220²

A = 48400 m²

Then,

The total area of the fields = 122500 m² + 48400 m²

The total area of the fields = 170900 m²

Hence, the total area of the fields that Ram has is  170,900 square meters ( 170900 m²)

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A cube is a three-dimensional solid object having six square faces. The measure of the length of the diagonal of the face of the cube is 12.2 cm.

A cube is a three-dimensional solid object having six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron.

Given the length of an edge of the cube is √75 cm, therefore, the length of the diagonal of the face of the cube will be √2 times the length of an edge of the cube. Thus, the measure of the length of the diagonal of the face of the cube is,

Length of the diagonal of the face = √2 × √75 = 12.2 cm

Hence, the measure of the length of the diagonal of the face of the cube is 12.2 cm.

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Answer: ITS B (12.2)

Step-by-step explanation:

I am the lizard king, I can do anything.

Answer:

£15.20

Step-by-step explanation:

butter : sugar : flour = 2 : 1 : 9

Total mass for 1 recipe = 30 g

2 + 1 + 9 = 12

12x = 30

x = 30/12

x = 2.5

For 1 scone:

butter = 2x = 2(2.5) g = 5 g

sugar = x = 2.5 g

flour = 9x = 9(2.5) g = 22.5 g

Cost for 1 scone:

butter: 5 g × £2.50/(500 g) = £0.025

sugar: 2.5 g × £1.60/(1000 g) = £0.004

flour: 22.5 g × £0.6/(1500 g) = £0.009

Cost for 1 recipe = £0.025 + £0.004 + £0.009 = £0.038

Cost for 400 scones = 400 × £0.038 = £15.20

Answer: £15.20

An exponential function that represents the population is y = 5 (7)ˣ. And the population after 5 days will be 84035.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

The table is shown.

The exponential equation is given as

y = abˣ

Then at x = 1, y will be 35. Then we have

35 = ab ...1

Then at x = 2, y will be 245. Then we have

245 = ab² ...2

On solving equations 1 and 2. Then we have

a = 5 and b = 7

Then the exponential function will be

y = 5 (7)ˣ

Then the population after 5 days will be

y = 5 (7)⁵

y = 5 x 16807

y = 84035

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Answer:

Step-by-step explanation:

1. The moment he started: 3 bacteria

1st hour: 3*2 bacteria = 3*[tex]2^{1}[/tex] bacteria

2nd hour: 3*2*2 bacteria = 3*[tex]2^{2}[/tex] bacteria

3rd hour: 3*2*2*2 bacteria = 3*[tex]2^{3}[/tex] bacteria

etc.

Each hour the number of bacteria multiplies by 2 (the power of 2 is increased by 1), therefore, [tex]B=3*(2)^{n}[/tex]

2. Exponential function has the form of [tex]f(x)=ab^{x}[/tex]

if a is greater than 0 and b is greater than 1, then it's exponential growth.

The answer is:

[tex]y=4^{x}[/tex]  (4 > 1)

3. If smth increases by 2.5% each time, that means that at first you had 100% and then it became 100%+2.5% = 102.5%. So each time we multiply the value by 1.025 (100*1.025=102.5).

4. Linear equation form: [tex]y=ax+b[/tex]

Quadratic equation form: [tex]y=ax^{2} + bx + c[/tex]

Exponential equation form: [tex]y=ab^{x}[/tex]

In this case, a = 3.8, b = -5.5, c = -4.8

5. (a) square root

(b) linear

(c) exponential

(d) quadratic

6. Each year the car's worth is multiplied by 0.82 (82%). Therefore, after n years, the value will be: V = 27 500 * [tex]0.82^{n}[/tex]

7. Neither first, nor second differences are constant in case of an exponential relation, because we do not add but multiply.

Ex. [tex]y=2^{x}[/tex]

values: 1 2 4 8 16 32...

1st diff: 1 2 4 8 16...

2nd diff: 1 2 4 8...

8. (a) [tex]7^{11} / 7^{7} = 7^{11-7} = 7^{4}[/tex]

(b) [tex](\frac{4}{9})^{12} *(\frac{4}{9})^{5} =(\frac{4}{9} )^{12+5}=(\frac{4}{9})^{17}[/tex]

(c) [tex]4^{11} / (4^{5})^{3} =4^{11} / 4^{5*3}=4^{11} /4^{15}=4^{11-15}=4^{-4}[/tex]

(d) [tex]8^{-6}*8^{3}=8^{-6+3}=8^{-3}[/tex]

Answer:

745.31

Step-by-step explanation:

20x25=500

(2(12.5)pie)/2=245.435

245.435+500=745.31

The domain of the function where the function is decreasing is (-∞, 1). Then the correct option is D.

The domain means all the possible values of the x and the range means all the possible values of the y.

The function is given below.

f(x) = x² - 2x + 5

The equation can be written as

f(x) = x² - 2x + 1 + 4

f(x) = (x - 1)² + 4

Then the domain of the function where the function is decreasing will be (-∞, 1).

Then the correct option is D.

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If an event is likely to occur, the probability that the event will occur is between 3/4 and 1.

Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

If the probability lies between 0 and 1/5, it is likely that the event would not occur. If the probability lies between 1/5 and 1, it is likely that the event would occur.

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Answer:

75% and 100%

Step-by-step explanation:

The probability spectrum is (the spaces are supposed to be equal):

|----------------------|--------------------|--------------------|---------------------|

0%                    25%               50%              75%                   100%

impossible   unlikely          equal            likely                  certain

The number of combinations of plays that is possible will be 2.

Let the number of combinations be represented by x.

From the information given, we are informed that the touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points.

Therefore, this will be:

7x + 3x + 2x = 24

12x = 24

x = 24/12

x = 2

Therefore, there are 2 combinations.

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Using proportions, the amount that Sally can expect to receive from social security annually is given by:

c. $19,153.26.

A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.

She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:

A = 0.42 x 45603 = $19,153.26.

Which means that option C is correct.

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Answer:

each hot dog costs $3

Step-by-step explanation:

$18÷6 hotdogs=$3 or $3×6 hotdogs=$18

Answer:

x = 8

z = 65

Step-by-step explanation:

Through various rules, we are able to assert: (6x + 67)° = 115°.

Now, we want to solve for x:

6x + 67 = 115

6x = 48

x = 8

We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.

The solution to the function [tex]f(x) = 2\sqrt{x - 2}[/tex] when x = 2 is 0

The equation of the function is given as:

[tex]f(x) = 2\sqrt{x - 2}[/tex]

When x = 2, we have:

[tex]f(x) = 2\sqrt{2 - 2}[/tex]

Evaluate the difference

[tex]f(x) = 2\sqrt{0}[/tex]

Evaluate the exponent of 0

f(x) = 2 * 0

Evaluate the product

f(x) = 0

Hence, the solution to the function when x = 2 is 0

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Answer:

that 2 out of 20 ratio you have 18 to 1 odds of getting these

Step-by-step explanation:

I think the question should be m<-2.2 according to your number line

the answer is graphed. I hope it helps

Answer:B

Step-by-step explanation: this is because when it is greater than, it goes right, and if there is no "equal to" it is closed circle and B has a closed circle going to the right of -2.2