Acellus
Acellus
Length of Arcs
Find the length of AB. Leave
your answer in terms of π.
27
A
20° AB =[?]T
B
l'o

The numbers chosen by the Anjali, which when rounded off to 1 decimal place , becomes equal are: 987.47 and 987.53.

The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.

Here is the general rounding rule:

Consider these two numbers:

987.47 and 987.53.

rounded off to 1 decimal place, they becomes:

987.5 (as 7 is greater than 5, it will get rounded off and 1 is added to previous number of 7).

and 987.5 (as is less than 5 , so 53 will be taken as 5 only)

Thus, the numbers chosen by the Anjali, which when rounded off to 1 decimal place , becomes equal are: 987.47 and 987.53.

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Answer:

ion kno fr

Step-by-step explanation:

Answer:

6 quarts

Step-by-step explanation:

2 pints = 1 quart

4 cups = 1 quart

• 5 pints of orange juice

5 pints = 5/2 =>2.5 quarts

• 6 cups of grape juice

6 cups = 6/4 => 1.5 quarts

• 8 cups of apple juice

8 cups = 2 quarts

2.5 + 1.5 + 2 = 6 quarts

Answer:

3. 211.6 feet

4. 59.04 degrees.

Step-by-step explanation:

3.

To find how much wire Mark Wolfman needs for the tallest tower in the park, we can use trigonometry. Let's call the height of the tower "h". We know that the wire is attached to the top of the tower and to a stake in the ground that is 44 feet away from the base of the tower. The wire makes a 78 degree angle with the flat ground.

We can use the tangent function to find the height of the tower:

tan(78) = h / 44

Multiplying both sides by 44, we get:

h = 44 * tan(78)

So the height of the tower is approximately 207 feet.

To find how much wire is needed, we can use the Pythagorean theorem:

wire length = sqrt(h^2 + 44^2)

Substituting the value we found for "h", we get:

wire length = sqrt(207^2 + 44^2)

Simplifying, we get:

wire length = 211.6

So Mark Wolfman needs approximately 211.6 feet of wire.

4.

To find the angle of depression of the swimmer's dive, we need to consider the triangle formed by the swimmer, the buoy, and the point on the lake bottom directly below the buoy. We know that the buoy is 30 feet away from the swimmer and the chain connecting it to the bottom of the lake is 50 feet down.

The angle of depression is the angle between the swimmer's line of sight and the horizontal. Since the swimmer is looking downward toward the chain, the angle of depression is the same as the angle formed by the horizontal and the line connecting the swimmer to the chain.

Using trigonometry, we can find the tangent of this angle:

tan(angle of depression) = opposite / adjacent

tan(angle of depression) = 50 / 30

tan(angle of depression) = 5/3

Taking the arctangent of both sides, we get:

angle of depression = arctan(5/3)

Using a calculator, we find that the angle of depression is approximately 59.04 degrees.

the proof by mathematical induction involves establishing the basis step, proving the inductive step, and using mathematical induction to show that the formula holds true for all non-negative integers.

The problem asks us to determine whether each of the proposed recursive definitions is a valid definition of a function f from the set of non-negative integers to the set of integers. If it is well defined, we are asked to find a formula for f(n) when n is a non-negative integer and to prove that the formula is valid.    

After finding the formula for f(n), we are asked to prove its validity using mathematical induction. To do this, we first need to establish the basis step and the inductive step.

The basis step is the first step in the proof by mathematical induction. We need to prove that the formula holds true for the smallest value of n, which is usually 0 or 1. In this case, we need to prove that P(0) and P(1) are true.

Next, we need to prove the inductive step. This involves assuming that the formula holds true for some arbitrary value of n and using that assumption to prove that the formula also holds true for n+1.

To prove that the formula holds true for all non-negative integers, we need to show that the basis step and inductive step are both true. We can then conclude that the formula is valid for all non-negative integers by mathematical induction.

The proof of the inductive step can be completed by assuming that P(1) ∧ P(2) ∧ ... ∧ P(k) is true, and then using this assumption to prove that P(k + 1) is true. This is usually done by manipulating the formula for f(n) and using algebraic properties to show that the formula holds true for n+1.

In summary, the proof by mathematical induction involves establishing the basis step, proving the inductive step, and using mathematical induction to show that the formula holds true for all non-negative integers.

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Answer:

about like 4-5

Step-by-step explanation:

its 4 or 5

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine what Paul will pay or receive, we need to calculate his total tax liability and compare it to the amount he already paid in federal tax.

For 2021, the tax brackets and rates for individuals filing married separately are as follows:

10% on taxable income up to $9,950

12% on taxable income over $9,950 up to $40,525

22% on taxable income over $40,525 up to $86,375

24% on taxable income over $86,375 up to $164,925

32% on taxable income over $164,925 up to $209,425

35% on taxable income over $209,425 up to $523,600

37% on taxable income over $523,600

First, we need to determine which tax bracket Paul falls into based on his taxable income of $27,205. Since his income is between $9,950 and $40,525, he falls into the 12% tax bracket.

To calculate his total tax liability, we can use the following formula:

(total taxable income) x (tax rate) - (tax credit) = total tax liability

Plugging in the numbers for Paul, we get:

($27,205) x (0.12) - ($1,630) = $2,267.60

Note that we subtract a tax credit of $1,630 since Paul is filing married separately and has taxable income below the phase-out threshold for the credit.

Now, we can compare Paul's total tax liability of $2,267.60 to the $3,410 he already paid in federal tax. Since he paid more than his total tax liability, he will receive a refund of:

$3,410 - $2,267.60 = $1,142.40

Therefore, Paul will receive a refund of $1,142.40 from the federal government.

We cannot determine the probability that a newly selected adult is older than 62 because there is not much to do with the distribution other than the sample and standard deviation and skewness of the distribution.

Most US workers retire at 64, but data show that the average age varies by state. For example, the average retirement age in Washington, DC is about 67, while many states such as Iowa, Kansas, Maryland, Vermont, and Texas have the average retirement age of 65. 61 in Alabama, Kentucky and Michigan or Alaska and West Virginia.

The average probability of  retirement age has increased in recent years. In 1986, the average retirement age was 62 for men and 57 for women. From 2016, the average retirement age increased to 65 for men and 63 for women. Changes in SSI, reductions in workplace pensions, and even longer life expectancy can cause many to delay retirement for at least a few years.

Plus, with Social Security benefits averaging just $1,503 per month and declining pensions, seniors are expected to find their retirement savings and maximize their income spending. It will also cause them to postpone their holidays.

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Answer:

85.6 cm²

Step-by-step explanation:

You can divide this shape with a horizontal line:  trapezoid and a rectangle

Total Area = Area of trapezoid + Area of rectangle

                  = (1/2)(b₁ + b₂)(h) + (b)(h)

                  = (1/2)(6+10)(7.2) + (10)(2.8)

                  = 57.6 + 28

                  = 85.6 cm²

Answer:

A fast and easy surface area of a rectangular prism calculator to find just what its name suggests.

Step-by-step explanation:

l=13in

w=7

h=6

A=422in squared

According to the given information Megen would have to work for 9 hours to make option 2 the better pay option.

A rate is a ratio that compares two different kinds of quantities, usually measured in different units. It is often expressed as a quantity per unit of time, such as miles per hour, or dollars per hour.

Let's assume that Megen works x hours.

Option 1: Megen will earn 5.5x dollars.

Option 2: Megen will earn 0.15 dollars for the first hour of work and 3(0.15) = 0.45 dollars for each additional hour of work. Therefore, Megen will earn:

0.15 + 0.45(x - 1) = 0.45x - 0.3 dollars.

Now we need to find the value of x such that option 2 is better than option 1:

0.45x - 0.3 > 5.5x

Simplifying and solving for x:

0.3 > 5.05x

x < 0.0594

Since Megen cannot work a negative number of hours, we need to round up to the nearest hour. Therefore, Megen would have to work at least 1 hour for option 2 to be the better pay option.

Therefore, according to the given information Megen would have to work for 9 hours to make option 2 the better pay option.

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Answer:

A: The straight-line depreciation equation is a linear equation of the form:

Value = initial value - (rate of depreciation) x (age)

Where the "rate of depreciation" is the amount by which the value decreases each year. In this case, the initial value is $43,500, and the car depreciates over a period of 12 years. So, you can calculate the rate of depreciation as:

Rate of depreciation = (initial value - final value) / (age)

Where the final value is zero (since the car is totally depreciated after 12 years). Therefore, you have:

Rate of depreciation = ($43,500 - $0) / 12 years = $3,625 per year

Substituting this into the formula, you get:

Value = $43,500 - $3,625 x (age)

Where "value" is the current value of the car after "age" years.

B: You want to find how long it will take for the car to be worth 25% of its value. Let's call this time "t". Then you have:

0.25($43,500) = $10,875 = $43,500 - $3,625t

Solving for "t", you get:

$3,625t = $43,500 - $10,875 = $32,625

t = $32,625 / $3,625 = 9 years

Therefore, it will take 9 years for the car to be worth 25% of its value.

C: You want to find how much the car will be worth in 10 years. Substituting "age = 10" into the equation derived in part A, you get:

Value = $43,500 - $3,625 x 10 = $7,750

Therefore, the car will be worth $7,750 in 10 years.

The total taxes on Mr. Kramer's new car are:

1,440 + 351.48 = 1,791.48 dollars.

What is the rate?

A rate is a measurement of how one quantity changes with respect to another quantity, usually expressed as a ratio. For example, if a car travels 120 miles in 2 hours, its speed (or rate) is 60 miles per hour (120 miles divided by 2 hours).

The sales tax rate is 0.06, which means Mr. Kramer will pay 0.06 dollars for every dollar of the price.

The price of the car is 24,000 dollars, so the sales tax will be:

0.06 * 24,000 = 1,440 dollars

The property tax rate is 14.62 dollars for every 1000 dollars of the price.

To calculate the property tax on the car, we need to divide the price by 1000 and then multiply by the tax rate:

(24,000 / 1000) * 14.62 = 351.48 dollars

Therefore, the total taxes on Mr. Kramer's new car are:

1,440 + 351.48 = 1,791.48 dollars.

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Answer:

Step-by-step explanation:

You want to identify factors of 12mn that appear on the list.

Often, we are interested in prime factors of a number or expression. These are integers or expressions that are divisible only by themselves and 1. Here, the expression 12mn written in terms of its prime factors is ...

   2 · 2 · 3 · m · n

The product of any subset of these factors is a factor of 12mn. Such products include ...

It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.

The formula for calculating the time it takes a population to triple with a constant relative growth rate of 10% per year is:

Time (in years) = ln(3) / ln(1.10)

The natural logarithm of 3 (ln(3)) is 1.09861228866811, and the natural logarithm of 1.10 (ln(1.10)) is 0.095310179804325.

Therefore, the calculation of the time it takes a population to triple with a constant relative growth rate of 10% per year is:

Time (in years) = 1.09861228866811 / 0.095310179804325 = 11.52

It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.

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Answer:

The volume of the sphere is 2304π ft³.

Step-by-step explanation:

The formula for the volume of a sphere is:

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

where r is the radius of the sphere.

Given the radius of the sphere is 12 feet, substitute r = 12 into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\dfrac{4}{3} \cdot \pi \cdot 12^3\\\\&=\dfrac{4}{3} \cdot \pi \cdot 1728\\\\&=\dfrac{6912}{3} \cdot \pi \\\\&=2304\pi\; \sf ft^3 \end{aligned}[/tex]

Therefore, the volume of the sphere in terms of π is 2304π ft³.

The 3rd one

Step-by-step explanation:

I'm 99.9% sure it's right

I'm really sorry if not!

hope this helps

Table 3 represents a linear function.

How to determine the table that represents a linear function?

In a linear function, the change in the y-value is proportional to the change in the x-value by a constant rate, known as the slope. We can calculate the slope of Table 3 by selecting any two points and using the formula:

slope = (y2 - y1) / (x2 - x1)

For example, if we choose the points (-2, -4) and (2, 0), we get:

slope = (0 - (-4)) / (2 - (-2)) = 4 / 4 = 1

This means that for every increase of 1 in the x-value, the y-value increases by 1. We can confirm that this holds for all the other points in Table 3 as well, indicating that it represents a linear function.

The other tables do not represent linear functions because the change in the y-value is not proportional to the change in the x-value at a constant rate.

Answer:

Step-by-step explanation: ??? There is no picture

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{59\% of 640}}{\left( \cfrac{59}{100} \right)640}\implies 377.6[/tex]

Answer:

377.6

Step-by-step explanation:

640÷10=64 to find 10%

64×5=320 to find 50%

640÷100=6.4 to find 1%

6.4×9=57.6 to find 9%

320+57.6=377.6

answer: 377.6

Answer:

x = 26

Step-by-step explanation:

the 3 angles lie on the straight line DAC and sum to 180° , that is

4x - 8 + 34 + 76 - x = 180

3x + 102 = 180 ( subtract 102 from both sides )

3x = 78 ( divide both sides by 3 )

x = 26

The angles of the given Rhombus are:

The above are arrived at using the qualities of a Rhombus and the theorem of alternate angles.

A rhombus is a quadrilateral with certain properties that distinguish it from other types of quadrilaterals. The key properties of a rhombus are:

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Given the information about the circle, the value of x is 7.3

A circle is simply a round shape that has no corners or line segments. It is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

The value of x based on the information given will be:

10x + 38 = 111

10x = 111 - 38

10x = 73

Divide

x = 73 / 10

x = 7.3

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For a sample of radioactive material,

a) The half-life of the radioactive material with that it disintegrates to 90% of the original amountb is equals to the 6.58 years.

b) The time is 2.12 years, at which the material disintegrates to 80% of the original amount.

We have, a sample of radioactive material disintegrates to 90% of the original amount after one year. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. Let the original/ initial amount of a sample of radioactive material = y₀ and after t year amount of material = y₀/2. After one year, amount of sample of radioactive material = 90% of y₀. Now, radioactive decay equation form is y(t) = y₀( 0.90)ᵗ ,

We have to calculate value of t when y = y₀/2.

=> [tex]\frac{ y_0}{2} = y_0( 0.90)^t[/tex]

=> 1/2 = (0.90)ᵗ

Taking natural logarithm both sides

=> ln( 1/2) = ln ( 0.90)ᵗ

=> ln( 1/2) = t ln ( 0.90)

=> t = ln(1/2)/ln(0.90)

=> t = 6.579 ~ 6.58 years

b) Now, we have to determine value of t when material disintegrates to 80% of the original amount. Let t years be required time here. So, 80% of y₀ = y₀ ( 0.90)ᵗ

=> 0.80y₀ = y₀( 0.90)ᵗ

Taking natural logarithm both sides

=> ln( 0.80 ) = ln( 0.90)ᵗ

=> ln( 1/2) = t ln( 0.90)

=> t = ln(0.80)/ln(0.90)

=> t = 2.117 ~ 2.12years

Hence, required value of time is 2.12 years.

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Therefore , the solution of the given problem of unitary method comes out to be  able to afford the festival because 120 is larger than 70.

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

The following chart allows us to determine each person's earnings:

=> Person 1: 2 hours times $8 per hour  =  $16

=>  Person 2: $4 hours x $8 per hour  =  $32 per person

=>Person  3: 3 hours x $8 per hour = $24 per person.

=> Person 4: 5 hours x $8 per hour  =  $40.

=> Person 5: One hour times $8 per hour equals $8.

Each person needs to bring at least $70 in order to join the festival. As a result, the disparity shown below can be used to describe this circumstance:

=> 16 + 32 + 24 + 40 + 8 ≥ 70

Simplifying the inequality's left side, we obtain:

=> 120 ≥ 70

We can infer that all of the friends were able to afford the festival because 120 is larger than 70.

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The coordinates of the image after the translation are:

A′(−1, 1), B′(7, 1), C′(3, 5)

So the answer is (D) A′(−1, 1), B′(7, 1), C′(3, 5).

What are coordinates ?

Coordinates are pairs of numbers that locate a point in a space or on a plane. In two-dimensional space, or the Cartesian plane, a point is located by an ordered pair of real numbers (x, y), where x represents the horizontal distance and y represents the vertical distance. These numbers are called the coordinates of the point.

The horizontal line is called the x-axis, and the vertical line is called the y-axis. The point where the x-axis and y-axis intersect is called the origin, and it is assigned the coordinates (0, 0).

According to the question:
To translate a figure, we add or subtract a constant value to the x and/or y coordinates of each vertex. In this case, we want to translate triangle ABC 7 units to the right. So, we will add 7 to the x-coordinate of each vertex.

The coordinates of A are (-8, 1). Adding 7 to the x-coordinate gives:

A′ = (-8 + 7, 1) = (-1, 1)

The coordinates of B are (0, 1). Adding 7 to the x-coordinate gives:

B′ = (0 + 7, 1) = (7, 1)

The coordinates of C are (-4, 5). Adding 7 to the x-coordinate gives:

C′ = (-4 + 7, 5) = (3, 5)

Therefore, the coordinates of the image after the translation are:

A′(−1, 1), B′(7, 1), C′(3, 5)

So the answer is (D) A′(−1, 1), B′(7, 1), C′(3, 5).

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The price of one adult ticket is approximately $3,977.27, and the price of one child ticket is approximately $4,636.37.

Let's use the system of linear equations to solve this problem.

Let x be the price of an adult ticket and y be the price of a child ticket. We can create two equations based on the information given:

To solve this system of linear equations, we can use either substitution or elimination. In this case, we'll use elimination.

First, multiply the first equation by 17 and the second equation by 9 to make the coefficients of y the same:

Now, subtract the second equation from the first equation:

(170x + 153y) - (126x + 153y) = 1,385,500 - 1,210,500

44x = 175,000

Now, divide both sides of the equation by 44 to solve for x:

x = 175,000 / 44

x ≈ 3,977.27

Now that we have the price of an adult ticket, we can plug the value of x back into either equation to solve for y.

We'll use the first equation:

10(3,977.27) + 9y = 81,500

39,772.70 + 9y = 81,500

Now, subtract 39,772.70 from both sides of the equation:

9y = 41,727.30

Now, divide both sides of the equation by 9 to solve for y:

y = 41,727.30 / 9

y ≈ 4,636.37

So, the price of one adult ticket is approximately $3,977.27, and the price of one child ticket is approximately $4,636.37.

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The question in English is:

In a theater, 10 adult tickets and 9 children's tickets cost $81,500; 17 tickets for children and 14 for adults cost $134,500. Find the price of one adult and one child ticket.