What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.

60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce

Let x be the amount of herb that costs $1.00/oz and y be the total amount of the mixture that costs $2.20/oz.

The total weight of the mixture is:

= y=x+40

The total cost of the mixture is:

4(40) + 1x = 2.20y

160 + x = 2.20 (x + 40) .......Substitute y using the expression from the first equation

160 + x = 2.20x + 88 .........Subtract 160 and x from both sides

1.20x = 72 .........Divide both sides by 1.20

x = 60

The herbalist must mix 60 oz of the herb that costs $1.00/oz to the mixture, therefore we can say that:

60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce

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Answer: We can use the Pythagorean theorem to find the length of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse and the width and length of the rectangle are the other two sides.

Let's use "l" to represent the length of the rectangle:

l^2 + 14^2 = 29^2

l^2 = 29^2 - 14^2

l^2 = 561

l = sqrt(561)

l ≈ 23.67 feet

Now that we know the length and width of the rectangle, we can use the formula for the perimeter, which is the sum of all four sides:

Perimeter = 2 * length + 2 * width

Perimeter = 2 * 23.67 + 2 * 14

Perimeter = 47.34 + 28

Perimeter = 75.34 feet

Therefore, the perimeter of the rectangle is approximately 75.34 feet.

Step-by-step explanation:

When calculating the price of an order that has been paid in advance, the school supplier will use the following formula:

4n - 2

The ordering cost formula is useful for calculating the economic order quantity and gives businesses insight into how

much of an item is necessary to meet customer demand and fulfill sales goals.

These ordering costs can include shipping fees, unexpected transportation costs, inspection fees and other expenses

necessary to acquire inventory products. Essentially, any money your company spends to place and receive inventory

orders accounts for the purchasing and ordering costs.

Where n represents the number of boxes purchased.

The school supplier sells boxes of A4 paper for £4, and a £2 discount is given on any order paid for in advance.

Formula for calculating what to charge for any order paid in advance:

To calculate the price for an order paid in advance, the formula 4n - 2 should be used.

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Answer:

We can use the formula for exponential growth:

A = P(1 + r)^t

where:

A = final amount

P = initial amount

r = annual growth rate (as a decimal)

t = time (in years)

Let's plug in the values:

P = 540

r = 0.039

t = 2035 - 2015 = 20

A = 540(1 + 0.039)^20

A ≈ 891

Therefore, the local government of Central Village can predict there will be approximately 891 houses in 2035.

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r)^n

where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of years

In this case, we want to find the final amount (the number of houses in 2035), given the initial amount (540 houses in 2015), the annual interest rate (3.9%), and the number of years (20 years from 2015 to 2035).

So, we can plug in the values and solve for A:

A = 540(1 + 0.039)^20

A = 540(1.039)^20

A = 540(2.011)

A = 1086.54

Rounding to the nearest whole number, we get:

A ≈ 1087

Therefore, the local government of Central Village can predict there will be about 1087 houses in 2035.

Answer:

5760

Step-by-step explanation:

Answer: y = -12x + 63

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope of the line, which is -12, and a point that the line passes through, which is (6,-9).

Using the point-slope form of a linear equation, we have:

y - (-9) = -12(x - 6)

Simplifying this equation, we get:

y + 9 = -12x + 72

Subtracting 9 from both sides, we get:

y = -12x + 63

Therefore, the equation of the line in slope-intercept form is y = -12x + 63.

the first institution has 441 and the second institution has 189.

We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:

Let x be the multiplier of the ratio.

Then, we have:

7x is the first institution.

3x is the second institution.

From the problem, we know that the sum of the two institutions is 630:

7x + 3x = 630

Simplifying the left side, we get:

10x = 630

Dividing both sides by 10, we get:

x = 63

Now that we know the value of x, we can find the number of each institution:

First institution = 7x = 7(63) = 441

Second institution = 3x = 3(63) = 189

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(a) The simplest interest is $12.

(b) The simplest interest is 5 cents.

(c) The simplest interest is $360.

(d) The simplest interest is $15.

What is the interest rate?

In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.

The formula of simple interest is I = P × R × T

(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years

The simple interest is

500 × 0.08 × (1/4)

= $12

(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years

The simple interest is

50 × 0.12 × (1/12)

=$0.5

= 5 cents

(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years

The simple interest is

1000 × 0.18 × 2

=$360

(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years

The simple interest is

600 × 0.15 × (60/360)

=$15

P is principal, R is known as rate of interest.

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Answer:

5

Step-by-step explanation:

The mode is the most commonly occurring number in a set of numbers. In this one it is 5.

Answer: x = 18.9 to 1dp

Step-by-step explanation: Using SOH CAH TOA,

Sin 25 = 8/x

Making x subject of the formula:

x = 8/Sin 25

x = 18.92961267

x = 18.9 to 1dp

Answer: Acute

Step-by-step explanation:

Acute - Less than 90 degress

Straight - Exactly 180 degrees

Obtuse - More than 90 degrees

Right - Exactly 90 degrees

[tex]\mathcal{A} = \pi r^{2} = \pi (11^{2}) = 121 \pi \ ft^{2}[/tex]

Answer:

121 pi divide to 4

Step-by-step explanation:

the answer is 121 pi divide to 4. please see it on the picture.

The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is y = [tex]358,000(0.9975)^{t}[/tex]. So  correct option is D) .

Annual rate can also be used to describe growth rates or changes in other types of measurements, such as population growth or inflation. For example, if the population of a city grows by 2% per year, the annual rate of population growth is 2%.

It is important to note that when annual rates are used to describe financial products or investments, they may be compounded over time. Compounding refers to the process of earning interest on interest, which can significantly increase the total amount of interest owed or earned over time. Therefore, it is important to carefully consider the effects of compounding when evaluating financial products or investments.

The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is:

y = [tex]358,000(0.9975)^{t}[/tex]

Therefore, the correct option is D) y = [tex]358,000(0.9975)^{t}[/tex].

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The 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.

Given that the first letter in the name has to be a capital letter and the number of letters in the name is 6, find how many 6-letter names are possible.There are 26 capital letters in the English alphabet. Since the first letter must be a capital letter, we have 26 choices for the first letter.There are 26 lowercase letters in the English alphabet. We have 26 choices for each of the 5 remaining letters of the name.Using the multiplication principle of counting, the total number of possible 6-letter names with a capital first letter is:26 × 26 × 26 × 26 × 26 × 26=26⁶= 26 * 26 * 26 * 26 * 26 * 26 = 308915776 Therefore, there are 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.

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One way to approach this problem without using a calculator is to group the numbers by their place value (i.e., thousands, hundreds, tens, and ones), and then add them together.

For example,

For thousands:

User A has 3 thousands,

User B has 4 thousands,

User C has 2 thousands,

User E has 7 thousands.

There are no thousands for User D.

So the total number of thousands is 3+4+2+7 = 16 thousands.

For hundreds:

User A has 550 hundreds (since 3550 = 3 x 1000 + 550),

User B has 0 hundreds (since 4000 is a multiple of 1000),

User C has 450 hundreds (since 2450 = 2 x 1000 + 450),

User D has 10 hundreds,

User E has 0 hundreds (since 7000 is a multiple of 1000).

So the total number of hundreds is 550+0+450+10+0 = 1010 hundreds.

For tens and ones:

Since all the numbers are in thousands or hundreds, there are no tens or ones to add.

Therefore, the total amount of data stored on the server is:

16 thousands + 1010 hundreds = 16,100 GB

Therefore , the solution of the given problem of variable comes out to be John worked for four hours and Max worked for nine.

A variable is a quality that can be evaluated expression and have various values. Height, age, salary, province of birth, academic status, and style of residence range are a few examples of variables.

Here,

Let's use the variables "J" and "M" to denote the respective number of hours done by John and Max. Next, we can formulate the formulae in the following system:

=> J + 5 = M (Max put in five hours more than John did.)

=> 15J + 10M = 150 (They prepared a total of 150 sandwiches) (They made a total of 150 sandwiches)

This system can be resolved using replacement. By deducting 5 from both sides of the first equation, we can find "J" in terms of "M":

=> J = M - 5

Now, we can enter the following formula in place of "J" in the second equation:

=> 15J + 10M = 150

Using J = M - 5 as a substitute, 15(M - 5) Plus 10M = 150.

=> 15M - 75 + 10M Equals 150 (distributing the 15) (distributing the 15)

=> 25M = 225 (adding 75 to both ends) (adding 75 to both sides)

=> M = 9

Max thus put in nine hours of labour. John worked a total of __ hours, so we can re-enter ___ into the first calculation as follows:

=> J + 5 = M

=> J + 5 Equals 9 (M replaced with 9)

=> J = 4

John spent 4 hours at work.

The answer is that John worked for four hours and Max worked for nine.

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Answer:

2.14 (rounded to the nearest tenth)

Step-by-step explanation:

Let's assume that the length of the slide is represented by the variable "x".

Based on the information provided in the question, Bridgette walks 1 meter from the end of the slide back to the ladder and climbs 3 meters to reach the top of the slide again. Therefore, the total vertical distance Bridgette covers in one trip down and up the slide is 1 + x + 3 = x + 4 meters.

The length of the slide is the hypotenuse of a right triangle formed by the slide and the total vertical distance Bridgette covers in one trip down and up the slide. Using the Pythagorean theorem, we can write: x^2 = (x + 4)^2 - 1^2

Simplifying this equation, we get: x^2 = x^2 + 8x + 16 - 1

7x = 15

x = 2.14 (rounded to the nearest tenth)

Therefore, the length of the slide is approximately 2.1 meters.

Answer:

---------------------------------

The slide and ladder form a right triangle with:

Let the length of the slide be s, this is a hypotenuse.

Find s using Pythagorean:

The probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

What is the formula to calculate standard deviation?

The formula to calculate standard deviation is:

SD = sqrt [(Σ(xi - μ)²) / N]

Where, SD = standard deviation

x = individual data points

μ = mean of the sample

N = sample size

What is the formula for z-score?

The formula for z-score is:

z = (x - μ) / σ

Where,

z = z-score

x = raw score

μ = mean of the population

σ = standard deviation of the population

Given that, The average BMI (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5.

To find the probability that a randomly selected 9-year-old has a BMI greater than 26.8, we have to find the z-score.

z = (x - μ) / σz = (26.8 - 18.4) / 4.5z = 1.86

Now, we have to find the probability from the z-table, which is 0.9686. But we have to find the probability greater than 26.8, so we have to subtract it from 1.1 - 0.9686 = 0.0314 ≈ 0.031

Therefore, the probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

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Mariya made a mistake in the third step of her work by multiplying both sides of the inequality by -13 instead of dividing.

An inequality is a mathematical statement that compares two values or expressions using a symbol such as <, >, ≤, or ≥. It indicates that one value is not equal to another, and may be greater than or less than it.

This resulted in a change of the direction of the inequality from less than or equal to (≤) to greater than or equal to (≥). Therefore, the correct inequality would be a ≥ -13 × -16. The solution of this inequality is a ≥ 208.

When graphing the solution, the solution set will include all values of a greater than or equal to 208, which can be represented by a shaded line to the right of the point 208 on a number line.

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Answer: 0.008

Step-by-step explanation:

1/10 of 0.08

of is the same as multiplying

1/10 x 0.08= 1/10 x 8/100= 8/1000

8 divided by 1000= 0.008

Answer:

37.03 sq. mm.

Step-by-step explanation:

got it right on usa test prep

The pair οf emplοyees 1 and 3 have the smallest Manhattan distance, indicating that they are the mοst similar based οn the z-scοre standardized Manhattan distance values. Therefοre, the answer is Emplοyees 1 and 3

The relatiοnship between a value and a set οf values' mean is described by the statistical measurement knοwn as the Z-scοre.

Manhattan distance = [tex]|z^1 - z^2| + |z^3 - z^4| + ... + |zn-1 - zn|[/tex]

The z-scοres fοr each variable are calculated as fοllοws:

z-scοre = (x - mean) / standard deviatiοn

Emplοyee 1:

Age z-scοre = (25 - 27.33) / 1.2472 = -1.8616

Salary z-scοre = (48000 - 51666.67) / 9930.77 = -3.6915

Emplοyee 2:

Age z-scοre = (35 - 27.33) / 1.2472 = 6.1420

Salary z-scοre = (72000 - 51666.67) / 9930.77 = 2.0505

Emplοyee 3:

Age z-scοre = (27 - 27.33) / 1.2472 = -0.2645

Salary z-scοre = (53000 - 51666.67) / 9930.77 = 1.4256

Distance between emplοyees 1 and 2: |(-1.8616) - 6.1420| + [(-3.6915) - 2.0505] = 13.3956

Distance between emplοyees 1 and 3: |(-1.8616) - (-0.2645)| + [(-3.6915) - 1.4256] = 4.7236

Distance between emplοyees 2 and 3: |(6.1420) - (-0.2645)| + [(2.0505) - 1.4256] = 8.5020

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Answer:i got u :uuuuuuuuuuuuuu

Work Shown:

[tex]A = P*(1+r/n)^{n*t}\\\\2P = P*(1+r/1)^{1*3}\\\\2 = (1+r)^{3}\\\\(1+r)^{3} = 2\\\\1+r = \sqrt[3]{2}\\\\r = -1+\sqrt[3]{2}\\\\r \approx 0.25992\\\\[/tex]

That converts to 25.992% after moving the decimal point two spots to the right. Round this value however your teacher instructs.

The theorem holds for all real numbers x and the other case is that x < 5.

option C.

A real number is a value that represents a quantity along a continuous number line. Real numbers can be either rational or irrational. Rational numbers are numbers that can be expressed as a ratio of two integers, such as 1/2, 3/4, or -7/8.

For the given question, if one of the cases is that x > 5, we can determine the other case by considering the definition of absolute value:

If x > 5, then ∣x-5∣ = x-5 (since x-5 is positive),

so x + ∣x-5∣ = x + (x-5) = 2x - 5

which is clearly greater than or equal to 5.

If x < 5, then ∣x-5∣ = -(x-5) (since x-5 is negative),

so x + ∣x-5∣ = x - (x-5) = 5,

which is also greater than or equal to 5.

Therefore, the theorem holds for all real numbers x.

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The complete question is below:

Theorem: For any real number x, x+∣x−5∣≥5. In a proof by cases of the theorem, there are two cases. One of the cases is that x > 5.

What is the other case?

A. x≤0

B. x≤5

C. x<5

D. x<0

The diameter οf the cup is 6 centimeters.

A circle's diameter is defined as a line thrοugh the centre that jοins the circumference at bοth ends. It is twice as lοng as the circle's radius. In οther wοrds, the line that splits a circle in half evenly at its centre is the diameter οf the circle.

The diameter οf a circle is equal tο twice its radius.

Therefοre, tο find the diameter οf the cup, we need tο multiply the radius by 2:

Diameter = 2 x Radius

Diameter = 2 x 3 cm = 6 cm

Hence, the diameter οf the cup is 6 centimetres.

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The volume of the hexagonal prism is the amount of space in the prism

The volume of the hexagonal prism is 212.4 cubic units

The given parameters are:

Base area = 36 square units

Height = 5.9 units

The volume is then calculated as:

Volume = Base area x Height

So, we have:

Volume = 36 x 5.9

Evaluate the product

Volume = 212.4

Hence, the volume of the hexagonal prism is 212.4 cubic units

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Answer: 4.1

Step-by-step explanation: To find a missing leg you must square both numbers, then subtract the leg you do have from the hypotenuse ( 33.64 -  16.81) to get the squared number for the missing leg ( 16.83). You then have to find the square root of that number and round to the nearest tenth (4.1).

After answering the provided question, we can conclude that As a result, expression 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre

An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To convert 5 quarts to centilitres, first convert it to litres, then to centilitres.

1 gallon = 0.946352946 litres (conversion factor from customary system)

5 quarts equals 5 x 0.946352946 litres equals 4.73176473 litres

100 centilitres = 1 litre (conversion factor from metric system)

4.73176473 litres = 4.73176473 multiplied by 100 centilitres per litre = 473.176473 centilitres

As a result, 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre.

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Answer:

Step-by-step explanation:

8:2 doubled is 16:4