Write the fraction in simplest form. *
8/12

The diameter of the circular fountain is 13.6 feet, while its circumference is 21.352 feet to the nearest hundredth.

The diameter is the line drawn that divides the circle into two while the circumference is the perimeter of the circle. Both are a measure of the radius of a circle.

Diameter, D = 2r

where r is the radius of the circle

Circumference = 2πr = πD

where π = 3.14

Given that the circular fountain has a radius of 6.8 feet

Diameter =  2 × 6.8 feet = 13.6 feet

Circumference = 3.14 × 13.6 feet

Circumference = 21.352 feet (to the nearest hundredth)

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Answer:

[tex]x= 8\sqrt{2}[/tex]

Step-by-step explanation:

This is a 45, 45, 90-degree triangle.

You can tell because whenever there is a 90 degree angle (right angle) and a 45-degree angle, the last angle must be 45, too, making it 45, 45, 90.

In such a triangle, the hypotenuse is equal to some number (x) times the square root of 2.

To get 16, you must eliminate that radical 2, so you have to multiply by a square root. We know that the square root of 2 times the square root of 2 is 2, so then now we only need to get a constant to multiply it by 16.

This constant would be 8.

We know this because sqrt(2) times 8(sqrt 2) gives us 2 times 8, or 16.

Now that we know what x is, we have the solution.

The legs of a 45,45,90 degree triangle are equal to the number we need to multiply the square root of 2 by to get 16, 8(sqrt 2)

That is our answer: 8(sqrt 2)

Answer:

Step-by-step explanation:

-5x-1>9

add 1 to both sides

-5x>10

divide by negative 5

x<-2

the sign flips since you divided by a negative

and your answer is x<-2

Marina's debt to income ratio is given as follows:

27.75%.

The debt to income ratio is obtained as the sum of all debts divided by the sum of all incomes.

The sum of all debts is given as follows:

1400 + 350 + 140 + 130 + 600 = 2620.

The sum of all incomes is given as follows:

8900 + 350 + 190 = 9440.

Hence the ratio is given as follows:

2620/9440 = 0.2775.

As a percent, the ratio is given as follows:

0.2775 x 100% = 27.75%.

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The values of F, G and H are given as follows:

F = 5, G = 29, H = 1.

The expression at the right side of the equality represents the entire expression after the least common factor is applied at the left side.

The least common side of the denominators is given as follows:

(x - 3)(4x + 7).

Hence the simplified numerator is given as follows:

(2x + 1)(4x + 7) + (-3x + 2)(x - 3).

Expanding the operations, and combining the like terms, we have that:

(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 8x² + 18x + 7 - 3x² + 11x - 6.

(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 5x² + 29x + 1.

Then the equality of the two numerators is given as follows:

5x² + 29x + 1 = Fx² + Gx + H.

Hence the values of the letters are given as follows:

F = 5, G = 29, H = 1.

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The reduced price of the item will be $44.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the price of an item has been reduced by 20%. The original price was $55.

The reduced price of the item will be calculated as,

Price  = 55 x ( 100% - 20 %)

Price = 55 x ( 1 - 0.2

Price = ( 55 x 0. 8 )

Price= $44

Hence, the price of the item will be $44.

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Answer:

35⁰

Step-by-step explanation:

because the sum of the interior angle of triangle is 180⁰ so 90+55+x=180

x=35

The probability that all the balls are green when we randomly select them is:

P = 0.044

We know that a bag contains 4 white, 5 red and 6 green balls, then there are a total of:

4 + 5 + 6 = 15 balls.

The probability of getting a green one is given by the quotient between the number of green balls and the total number of balls, so for the first one we have:

p = 6/15

Now for the next ball, because we already took one, now there are 5 green balls and 14 in total, so the probability is:

q = 5/14

The probability for the last one is calculated in a similar way, we will get:

z = 4/13

The joint probability (the probability of getting the 3 green balls in a row) is given by the product of the probabilities above, here we will get:

P = *q*z = (6/15)*(5/14)*(4/13) = 0.044

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

Where:

A = the final value of the account

P = the initial value of the account ($56,700)

r = the annual interest rate (6.3%)

t = the number of years

n = the number of compounding periods per year (4)

So, the equation would be:

A = 56,700 * (1 - 0.063)^(t/4)

A = 56,700 * (1 - 0.063)^(14/4)

A = $24,988.18

So, the account will be worth $24,988.18 after 14 years, if the rate of loss stays 6.3% compounded quarterly.

On solving the provided question, we can say that angles MOP + NOP = MON; x = 140/4 = 35 and MOP = NOP = 2(35) +1 = 71

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

here, angles

MON = 142°, m MOP= 2x+1, and  NOP = 2x+1

so, MOP + NOP = MON

2x+1 + 2x + 1 = 142

4x = 140

x = 140/4 = 35

MOP = NOP = 2(35) +1 = 71

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It would not be unusual for a household to have three dogs, as the data you provided shows that there are households in the small town with three dogs.

The frequency of households with three dogs is 173, which is the third highest number after households with one or two dogs. Therefore, having three dogs in a household is not uncommon in this small town,

Frequency refers to the number of times an event or a value occurs within a specific data set. It can be represented as a count or a percentage. In statistics, frequency is used to describe the distribution of data, which can help to identify patterns and trends. For example, in the data you provided, the frequency of households with three dogs is 173, which means that there are 173 households in the small town that have three dogs. It's a way to understand how common or rare is something in the dataset. By counting the number of times each value appears on the dataset and organizing it, we can have a better understanding of how the variable is distributed.

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The equation 7.5s + 1.6t - 4.2s is simplified to give a result of

The given equation 7.5s + 1.6t - 4.2s is simplified by following the mathematical operator that is acting on the values after a consideration of like terms

The variables in the equation are t and s

terms in t: 1.6

terms in s: 7.5, -4.2

collecting like terms

this will lead to rearranging the equation to give

7.5s - 4.2s + 1.6t

using the mathematical operator (addition and subtraction)

= 3.3s + 1.6t

unlike terms cannot be operated on, because of this the answer is 3.3s + 1.6t

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The zero of the function g(x) is x = -4

A function is a relationship between inputs where each input is related to exactly one output. A function is generally denoted by f(x) where x is the input.

It should be noted that based on the information, we want to find the value of x. This will be illustrated thus:

To find the zeros of a function g(x), we solve the equation g(x) = 0 for x. That is:

g(x) = (x + 4) / (x - 6)

0 = (x + 4) / (x - 6)

0(x - 6) = (x + 4)

0 = (x + 4)

x + 4 = 0

x = -4

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The programming code that gives instructions to other parts of the computer.

Computer programming code is typical referral source code. Source code is a set of instructions written using a computer programming language that tells a computer what to do.

It is written in a language that a computer can understand, and is usually written in a text file. Source code is the foundation of all computer programming and software development, and it is the basis for creating applications, programs, and websites. Source code is written in a language such as C++, Java, or Python and is compiled and then translated into machine language that the computer can understand and execute.

The source code is then tested and debugged to ensure that it works correctly. Source code is an essential part of software development and is the foundation for successful software projects.

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The statement "(Bob) ≤ {Bob, Carol, Ted, Alice}" is False.

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

Bob) ≤ {Bob, Carol, Ted, Alice}

Here, (Bob) is a singleton set which contains the element "Bob", while {Bob, Carol, Ted, Alice} is a set.

In general, the notation "A ≤ B" is used to indicate that set A is a subset of set B, which means that all elements of A are also elements of B.

Therefore, in this case (Bob) is not a subset of {Bob, Carol, Ted, Alice} because it is not a set of distinct elements, it is just a single element.

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Answer:

D.

Step-by-step explanation:

y - 12 means that 12 is being subtracted from y.

Subtracting 12 from y means decreasing y by 12.

Answer: D.

Answer: 8 pounds

Step-by-step explanation: Let’s first identify the main key details

Strawberry- 2 pounds

Apple- 6 more of strawberry

What is 6+2

8

The apple weighs 8 pounds.

Hope this helped

Answer:

A is correct answer I guess but if you hhj have been able to worked something out put me on

Answer: h = 16

Step-by-step explanation:

       We will isolate the variable, h, with inverse operations and simplifying to solve for h.

   Given:

[tex]\displaystyle -\frac{5}{6}h-\frac{2}{3}h=-24[/tex]

   Multiply both sides of the equation by 6:

       ➜ Why would we do this? This allows us to work without fractions.

-5h - 4h = -144

   Combine like terms:

-9h = -144

   Divide both sides of the equation by -9:

h = 16

We are aware that a Kites two opposite angles are equal. We are aware that a quadrilateral's total number of angles equals 360 degrees. As a result, x and y have values of 80° and 110°.

The space a kite encloses is known as the area of the kite. A quadrilateral with two sets of neighbouring sides that are equal is referred to as a kite. A kite is made up of four angles, four sides, and two diagonals.

The product of the lengths of a kite's diagonals divides its area in half. A kite's area is calculated using the formula Area = 12 (d)1 (d)2.

Important Notes

By subtraction of known angle measurements from 180 degrees, one can determine the value of X in triangles. If you know at least two angles, you can subtract them from 180 to discover the third angle that is lacking since the sum of all the angles in a triangle must equal 180 degrees.

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Answer: I can't solve all of them but I will give tips. i repeats in cycles so i^1 is sqrt-1, i^2 is -1, i^3 is -i and i^4 is 1. Look at the exponent and first divided out 4 then use the  1 2 3 answers. When you divided i and a number such as (1-i)/1+i) multiply by the conjugate of the denominator which is 1-i. To find conjugate replace the + with a -.

Step-by-step explanation:

The equation for the variable G after changing the subject of the formula is; G = (T/MF) - (4/F)

The subject of a formula is defined as the variable that is being worked out. It can be recognized to be the letter that is on its own on one side of the equal sign. For example, in the formula for the area of a rectangle given as;

A = b * h

area = base × height , the subject of the formula is A.

We are given the formula;

T = M(4 + FG)

Divide both sides by M to get;

T/M = 4 + FG

Subtract 4 from both sides to get;

(T/M) - 4 = FG

Divide both sides by F to get;

G = (T/MF) - (4/F)

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Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.

A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).

whole = 0,1,2,3,4,5,6,7,8,9,10,11........….

rational = 12/23,3,3/4,5/6,...…

irrational =  [tex]\sqrt{98}[/tex]

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Solving the provided question, we can say that the equation we have here are y=-x+3 and y=3x-4 and y=x+2, so values of y are as => 0, 5 and 5.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation we have here are

y=-x+3

y=3x-4

y=x+2

and the value of the x = 3

so values of y are as => 0, 5 and 5

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A regular polygon's outer angle is 40° in length and has 9 sides.

We have,

360°

It is given that each exterior angle is 40∘.

40 ∘ .

Consequently, the polygon's number of sides = Measure of all exterior angles added together Every external aspect

= 36040 = 9.

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The equation as per the information that has been provided, the answer will be computed as:

The function's limit indicates its value as the independent variable gets closer to a certain point.

Finding the limit as the independent variable approaches both the positive and negative limits is necessary to determine whether a function's limit is present. If both limits are the same, the limit of the function is present.

L=limx→0.5(cos(x)+2sin(3x))

L=cos0.5+2sin3×0.5

L=0.87+2sin1.5

L=0.87+2(0.99)

L=0.87+1.99

L=2.86

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Answer: 63 bottle caps

Step-by-step explanation:

3591 caps collected

57 days

3591/57=63

Caps collected per day 63 caps

So on solving the provided question, we can say that mean rate for satellite television from a sample of households was $49.00 per month 29 * 49 = $1421

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate :Divide by how many digits there are after adding up all the digits. the total divided by the count.

here the data vales are

12+76+4+89+55+6+8+7+4/9

261/9

29

so , mean rate for satellite television from a sample of households was $49.00 per month 29 * 49 = $1421

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Answer:Hi! The answer will be B I got a 100 on my test and i also did this before.

The total volume of cough syrup that the pharmacist will have left would be = 2,400ml. That is option B.

A pharmacist is an individual trained and licensed to dispense the correct amount of prescribed medication.

The volume of the cough syrup the pharmacist has = 4.3L

But 1 L = 1000 ml

4.3 L = 4.3 × 1000 = 4300ml

The volume of the available syrup bottle brought by the pharmacist = 1,900 ml

The quantity of syrup transferred to a bottle = 1,900 ml

Therefore the amount remaining = 4300 - 1900 = 2,400ml.

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The expression 14b shows the total number of beads in one necklace.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Kylie used b beads to make each necklace.

She made 14 necklaces.

So,

the total number of beads,

= 14 x number of beads in one necklace.

The total number of beads,

= 14 x b

The total number of beads,

= 14b

Therefore, 14b is the required expression.

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The time that Mrs James have her eyes open than closed will be 13 19/20 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.

The more time that she have her eyes open than closed will be:

= 15 1/2 - (1/10 × 15 1/2)

= 15 1/2 - 1 11/20

= 13 19/20

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