If the diameter of a circle is
30
30 centimeters, what is the radius of the circle?

Answer:

We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):

sin(a/2) = ±√[(1 - cos(a))/2]

where the ± sign depends on the quadrant of a/2.

To use this formula, we first need to find cos(a). We can do this using the identity:

sin^2(a) + cos^2(a) = 1

Substituting sin(a) = 7/9, we get:

(7/9)^2 + cos^2(a) = 1

Simplifying and solving for cos(a), we get:

cos(a) = ±4/9

Since a is in quadrant I, we take the positive value of cos(a):

cos(a) = 4/9

Now we can use the half-angle formula for sine to find sin(a/2):

sin(a/2) = ±√[(1 - cos(a))/2]

Substituting cos(a) = 4/9, we get:

sin(a/2) = ±√[(1 - 4/9)/2]

Simplifying, we get:

sin(a/2) = ±√(5/18)

Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):

sin(a/2) = √(5/18)

Therefore, the exact value of sin(a/2) is √(5/18)

Answer:

D. 50 square centimeters

The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.

It is important to note that there are different types of trigonometric identities are;

From the image shown, we have;

Using the sine identity

sin θ = opposite/hypotenuse

sin 32 = w/5

find the value

w = 2. 649

To determine the value of angle x , we have;

Using the sine identity

sin x = w/6

sin x = 2. 649/6

sin x= 0. 4416

Take the sine inverse

x = 26. 206 degrees

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Answer: 49,000

48805 is greater than 48500, so it rounds to 49,000

The no of people take more than 19 mins are above 50%

1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding

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Answer:

To find the total surface area of the square pyramid, we need to find the area of each of its faces and add them up.

The pyramid has a square base with sides of 8 inches and each triangular face has an isosceles right triangle shape with two sides of 8 inches and a hypotenuse of 2 x 8 = 16 inches (using the Pythagorean theorem).

The total surface area is then:

Area of the square base: 8 x 8 = 64 square inches

Area of each triangular face: 1/2 x 8 x 8 = 32 square inches (since each triangle is isosceles with base and height of 8 inches)

Total surface area: 4 x 32 + 64 = 192 + 64 = 256 square inches

Therefore, the total surface area of the square pyramid is 256 in². So, the closest answer option is 256 in, 2.

First, let's simplify the expression (4c + 8) + 3c - 2:

(4c + 8) + 3c - 2

= 4c + 3c + 8 - 2 (rearrange terms)

= 7c + 6 (combine like terms)

So the first expression simplifies to 7c + 6.

Next, let's simplify the expression 4c + 2(0.5c + 1):

4c + 2(0.5c + 1)

= 4c + 2(0.5c) + 2(1) (distribute the 2)

= 4c + c + 2 (simplify the parenthesis)

= 5c + 2 (combine like terms)

So the second expression simplifies to 5c + 2.

Now we can compare the two expressions:

7c + 6 vs. 5c + 2

These expressions are not equivalent because they do not have the same coefficients or constants.

Answer:

x = 52

Step-by-step explanation:

The angle x is vertical angle to the 52° angle. Meaning they have the same measurement.

Looking at the options, the answer is x = 52.

Answer:

7/20

its the answer to your question

Answer: $28,383.68.

Step-by-step explanation:

The first step is to determine the number of monthly payments over the 5-year period, which is 5 years x 12 months/year = 60 months.

Next, we can use the formula for the future value of an annuity, which is:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

FV is the future value of the loan (the amount owed at the end of the 5-year period)

P is the initial principal amount ($20,000 in this case)

r is the annual interest rate (6%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the total number of years (5)

Plugging in these values, we get:

FV = $20,000 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12)

FV = $28,383.68

Therefore, the balance owed at the end of the 5-year period would be $28,383.68.

Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

Triangles (a) and (d) are similar because they have the same corresponding angles.

What are triangles ?
A triangle is a closed two-dimensional plane figure with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles are one of the basic shapes in geometry and can be classified into different types based on their side lengths and angle measurements. Some of the common types of triangles include equilateral triangles (where all sides and angles are equal), isosceles triangles (where two sides and two angles are equal), and scalene triangles (where no sides or angles are equal). Triangles have many applications in mathematics, science, and engineering, including in trigonometry, geometry, and physics.

According to the question:
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. In other words, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Additionally, if the ratio of the lengths of the corresponding sides of two triangles is constant, then the triangles are similar. This ratio is called the scale factor of similarity.
Therefore, triangles (a) and (d) are similar because they have the same corresponding angles.

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Q) Which triangles are similar given below?
a. 25,6, 12
b. 16, 8, 25
c. 3,25, 6

The linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450.

What is a linear equation?

A linear equation is a mathematical equation in which the highest power of the variable(s) is one.

ax + b = 0

or

y = mx + b

where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.

Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:

450 - 10x

The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.

The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450

where y is the amount of money Todd has in his savings after x weeks.

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Therefore, the likelihood of getting two even numbers without substitution from a deck of 10 cards with digits 1 through 10 is 2 out of 9.

In most cases, the probability is described as the ratio of positive results compared with all occurrences in the survey region. The formula for probability of recurrence is P(E) = (The total amount of instances that are positive occurrences). (Sample space).

There are 5 even numbers in the set of 10 cards: 2, 4, 6, 8, and 10. The probability of drawing an even number on the first draw is 5/10, or 1/2. After the first card is drawn, there are 4 even numbers remaining in the set of 9 cards.

So the probability of drawing another even number on the second draw, given that the first card was even and was not replaced, is 4/9.

To find the probability of both events occurring (drawing an even number on the first draw and another even number on the second draw), we multiply the probabilities:

P(both even) = (1/2) x (4/9) = 2/9

Therefore, the probability of drawing two even numbers from a set of 10 cards numbered 1 to 10 without replacement is 2/9.

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Answer:

26

Step-by-step explanation:

triangle=180

81 + 73= 154

180 - 154= 26

Answer:

∠m = 26

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

∠81 + ∠73 + ∠m = 180°

Combine like terms.

∠154 + ∠m = 180°

Subtract 154 from both sides.

∠m = 26

The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.

During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.

She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:

Hence,

y = 12 + 8x

where

Therefore,

96 = 12 + 8x

8x = 96 - 12

8x = 84

divide both sides by 8

x = 84 / 8

x = 10.5 hours

Therefore,

hours she rented the boat = 10.5 hours

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Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.

Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.

Solution:

Let x be the quantity of pizzas ordered.

12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.

As a result, the necessary quantity of pizzas is:

[tex]x\geq 3(x-1) \leq x[/tex]

In order to find the best price, we must reduce the total cost, that is determined by:

C(x) = 15x plus 5(x - 1) (x - 1) - 15

Using the cost function's derivative in relation to x, we may calculate:

C'(x) = 20 - 10[tex]/(x-1)^2[/tex]

Finding the critical points by setting the derivative to zero yields the following results:

20 - 10[tex]/(x-1)^2[/tex] = 0

Simplishing, we obtain:

[tex](x-1)^2[/tex]= 2

By solving for x using square root of the both sides, we arrive at:

x = 1 ± √2

The ideal quantity to order is two pizzas because x has to be an integer.

By adding x = 2 to the cost function, we can determine the total cost:

C(2) = 15(2) + 5(2 - 1) - 15 = 22

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Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

5.394366197183099*10^4

Step-by-step explanation:1. Write the number as a decimal 53943.66197183099

2. Make it a new number between 1 and 10

Move the decimal point to make 53943.66197183099 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.

53943.66197183099 -> 5.394366197183099

Our new number is 5.394366197183099. We moved the decimal point 4 times.

Use a calculator and get the values from both equations, 3.83×10^7 and 7.1×10^2 then put the first value 38300000 into a calculator, then divide 38300000/710 and you will get the value 53,943.66197183099. Then run that through a scientific notion calculator to get 5.394366197183099*10^4.

There you go.

Approximately 54,000 horses weigh as much as one cruise ship.

To find out how many horses weigh as much as one cruise ship, we need to divide the weight of the cruise ship by the weight of a horse. In scientific notation, the weight of the cruise ship is 3.83x107 kg and the weight of a horse is 7.1x102 kg.

Dividing the weight of the cruise ship by the weight of a horse, we get:

(3.83x107 kg) ÷ (7.1x102 kg) = 5.4x104

So approximately 54,000 horses weigh as much as one cruise ship.

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For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.

What is expression?

In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.

To find the derivative of the inverse function, we use the formula:

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

First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):

[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]

Now, we can find the derivative of the inverse function:

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

To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:

[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]

To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):

[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]

Now we can find the derivative of the inverse function at x = 3:

[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]

[tex](f^{-1})'(3)[/tex] ≈ 0.052

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Answer:

Step-by-step explanation:

To find Monica's monthly pay after deductions, we need to first calculate her gross pay (before deductions) for the week:

Gross pay = hours worked x hourly rate

Gross pay = 35 hours x $15/hour

Gross pay = $525

Since we know that her total deductions for the week are $475, we can calculate her net pay (after deductions) for the week:

Net pay = Gross pay - total deductions

Net pay = $525 - $475

Net pay = $50

To find her monthly pay after deductions, we need to multiply her weekly net pay by the number of weeks in a month. Since there are approximately 4.33 weeks in a month, we can round up to 4.5 weeks to be safe:

Monthly pay = weekly net pay x number of weeks in a month

Monthly pay = $50 x 4.5

Monthly pay = $225

Therefore, Monica's monthly pay after deductions is $225.

Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.

To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.

Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.

So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:

According to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.

Note: This question is incomplete. Here is the complete information:

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10. The table is mentioned below 11. the product of the number of cubes long and the number of cubes wide is equal to 12. 12. The number of unit cubes needed to make this model is 24.

A cube is a three-dimensional geometric shape that has six square faces, 12 edges, and eight vertices (corners). All six faces of a cube are congruent squares, and all edges have the same length. The cube is a regular polyhedron, meaning that it has congruent faces and angles, and its symmetry group is the group of rotations and reflections that preserve the cube's structure. Cubes are widely used in geometry, mathematics, and physics because of their symmetry and regularity, and they also have practical applications in fields such as architecture and engineering.

10. Different ways a rectangular prism can have a volume of 12 cubic units:

Number of Cubes Long     Number of Cubes Wide Number of Cubes Tall

               1                                      1                                        12

               2                                      2                                        1.5

               2                                      3                                         1

               3                                      2                                         2

               4                                      3                                          1

               6                                      2                                          1

11. The pattern we see is that for each row, the product of the number of cubes long and the number of cubes wide is equal to 12.

12. A rectangular prism that is 4 units long, 2 units wide, and 1 unit tall would have a volume of 8 cubic units. To make a rectangular prism with a volume of 12 cubic units, we can add another layer of 4 cubes to the top of this prism. Therefore, a rectangular prism that is 4 units long, 2 units wide, and 2 units tall would have a volume of 12 cubic units. The number of unit cubes needed to make this model is 24.

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Answer:

Picture number 1: y=1/2x+2

Picture number 2: y=3x-5

Picture number 3 : y=-x

Picture number 4: y=(x+3)^2-2

The value of angle Y (m∠Y) in the given parallelogram is determined as 112⁰.

The value of angle Y is determined by applying the principle of a quadrilateral for the given parallelogram as shown below.

The adjacent angles of a parallelogram are supplementary, that is they add up to 180 degrees, while the opposite angles are equal or congruent.

From the given diagram angle W = angle Y (opposite angles)

angle W + angle Z = 180 (adjacent angles )

angle W = 180 - angle Z

angle W = 180 - 68

angle W = 112

Therefore, angle Y (m∠Y) = 112⁰.

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Answer: m=1/-7

Step-by-step explanation:

2-1/-3-4=1/-7

I don't know if it can be simplified or not

In the circle , the value οf x is 50°.

A secant in geοmetry is a line that tοuches a curve at at least twο different pοints. The Latin wοrd secare, which means tο cut, is where the wοrd secant derives. A secant crοsses a circle at precisely twο pοints when it is a circle. A chοrd is the line segment that the twο pοints determine, i.e., the interval οn the secant whοse ends are the twο pοints.

Remember that a tangent line is οne that crοsses a circle at precisely οne pοint. The term "secant line" describes a line that passes thrοugh twο pοints οn a circle. Secant is a Latin wοrd that means "tο cut," and it is derived frοm secare. A chοrd is the line segment defined by the twο pοints where a secant tοuches a circle in a given space.

Here in the given circle using secant line fοrmula ,

=> 75° = [tex]\frac{1}{2}[/tex] (100°+x)

=> 2×75 = 100+x

=> 150 = 100+x

=> x= 150-100= 50°.

Hence the value of x is 50°.

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All four ratios are equal to 1/3, the scale factor of the dilation is 1/3

In mathematics, a scale factor is a ratio that describes how much larger or smaller an object or shape is in comparison to its original size. In particular, a scale factor is often used to describe the effect of dilation on an object.

Dilation is a transformation in which an object is enlarged or reduced uniformly in all directions from a fixed point known as the center of dilation. The scale factor for dilation is the ratio of the length of the image to the length of the pre-image.

For example, if a square has a side length of 4 units and is dilated by a factor of 2, the resulting image will have a side length of 8 units. In this case, the scale factor for dilation is 2.

More generally, if an object is dilated by a factor of k, then the length of any given segment in the image will be k times the length of the corresponding segment in the pre-image. Thus, the scale factor for dilation is simply k.

To find the scale factor of the dilation, we need to find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD.

We can start by finding the length of each side of trapezoid ABCD:

AB = √[(9-(-3))² + (3-0)²] = √(144+9) = √153

BC = √[(9-9)² + (9-3)²] = 6

CD = √[(-3-9)² + (3-9)²] = √(144+36) = √180

DA = √[(-3-(-3))² + (3-0)²] = 3

Next, we can find the length of each corresponding side of trapezoid A'B'C'D':

A'B' = √[(3-(-1))² + (1-0)²] = √(16+1) = √17

B'C' = √[(3-3)² + (3-1)²] = 2

C'D' = √[(-1-3)² + (1-3)²] = √(16+4) = √20

D'A' = √[(-1-(-3))² + (1-0)²] = √4 = 2

Finally, we can find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD by dividing the lengths of the corresponding sides:

[tex]\frac{A'B'}{AB} =\frac{\sqrt{17} }{153} \\\frac{B'C'}{BC} =\frac{2}{6}=\frac{1}{3} \\\frac{C'D'}{CD} =\frac{\sqrt{20} }{80} =\frac{\sqrt{45} }{445} =\frac{\sqrt{5} }{3\sqrt{5} } =\frac{1}{3} \sqrt{5} \\\frac{D'A'}{DA} =\frac{2}{3}[/tex]

Since all four ratios are equal to 1/3, the scale factor of the dilation is 1/3.

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Answer:

It is not true (equal sign with a slash in it) one side’s 23 and the other side is 20