The function f(x) = 300(0.5)x/100 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after Round to the nearest whole number.

The commutative property is given by a×b=b×a

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Given here: The law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Let the two numbers be a and b

Then we get a×b=b×a

Hence, The commutative property is given by a×b=b×a

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In linear equation, 300 boxes does the machine package in 5 ​minutes .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

In 5 minutes the machine package does

                     = 5*60

                        = 300 boxes.

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Answer:

Step-by-step explanation:

Ivy is incorrect. An ellipse would also fit her definition(since an ellipse has no corners and a shape that is round and closed)

Ethan is correct. A circle is a set of all points some fixed distance away from some fixed point.

Ebuka is incorrect. A half circle will also fit her definition.

The distance that the student can travel in "t" hours if the speed is constant is:

distance = (2 mi/h)*t

Here we need to remember the relation between time, distance, and speed:

distance = time*speed.

Solving for speed, we will get:

Speed = distance/time

Here, we know that the student can travel 1/2 of a mile in 1/4 of an hour, then we have:

With that, we can find the speed:

speed = (1/2 of a mile)/(1/4 of an hour) = 2 miles per hour.

Then the distance that the student can paddle in "t" hours is written as:

distance = (2 mi/h)*t

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No, V is not a vector space with the operations defined in this way. Because the operations defined in this question do not satisfy the properties required for V to be a vector space.

A vector space is a collection of objects (vectors) that can be added together and multiplied ("scaled") by numbers, called scalars. These operations must satisfy certain properties to be considered a vector space.

For example, one of the properties is the associativity of vector addition, which means that (u + v) + w = u + (v + w) for any vectors u, v, and w in V. However, with the given definition of +, we have (U + V) + W = (UV-1) + W = U(VW-1) which is not equal to U + (V + W) = U(VW-1)

Another property is the distributivity of scalar multiplication over vector addition, which means that c(u + v) = cu + cv for any scalar c and any vectors u and v in V. But with the given definition of ., we have C(U+V) = C(UV-1) which is not equal to C.U + C.V = CUV-1

Furthermore, with the definition given the additive identity and the existence of additive inverse are not guaranteed.

Therefore, V is not a vector space with the operations defined in this way.

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Answer: D. base currency

Step-by-step explanation: In the foreign exchange market, currencies are traded in pairs.  A currency pair consists of two currencies, with one currency being quoted against the other.

In a currency pair, the base currency is the first currency listed.  It is the currency against which the exchange rate is quoted.  In the case of USD/CAN, USD is the base currency.  The base currency serves as a reference point for calculating exchange rates. It helps determine the value of the quote currency which  is the second currency listed in a currency pair.  It represents the value of the quote currency needed to purchase one unit of the base currency.  

Furthermore, changes in the exchange rate reflect the strength or weakness of the base currency relative to the quote currency.

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The center and the radius of the circle (x – 2)²+ (y + 1)² = 5 are

(2, -1) and √5, respectively.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

The equation of the circle,

(x – 2)²+ (y + 1)² = 5.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Comparing the equations, we get,

h = 2 and k = -1 and r = √5

That means,

the center = (2, -1) and the radius = √5

Therefore, the center = (2, -1) and the radius = √5.

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Using equation, the number of large drinks is 126.

A drink stand is selling small drinks for $2 each and large drinks for $4 each. One day, a total of 150 drinks were sold for $552.

The number of large drinks sold can be calculated as follows:

Using equation,

let

x = number of small drinks

y = number of large drinks

Hence,

2x  + 4y = 552

x + y = 150

multiply equation(ii) by 2

2x  + 4y = 552

2x + 2y = 300

subtract equation(ii) from equation(i)

2y = 252

divide both sides by 2

y = 252 / 2

y = 126

Therefore,

number of large drinks = 126

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The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account. Simple interest doesn't compound, which means a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

The simple interest earned can be calculated by using this formula

A = P(1 + rt)

Where,

A is the future value.

P is the principal value.

r is the interest rate.

t is the time.

Now Substituting the values into the formula, we have,

A = 16,000[1 + (0.08 × 3)]

A = 16,000[1 + 0.24]

A = 16,000× 1.24

Future value, A = $19,840.

Following that, we will compute the monthly payment over a 36-month period as follows:

Monthly payment = Future value/Time

Monthly payment = 19,840/36

Monthly payment = $551.11

Similarly, we will compute the credit card's compound interest:

A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾

A = 16000[1 + 0.025]⁸⁴

A = 16000× 1.025⁸⁴

A = 9000 × 3.49258954

Future value, A = $45425.80

Following that, we will compute the monthly payment over an 84-month period as follows;

Monthly payment = Future value/Time

Monthly payment = 45425.80/84

Monthly payment = $540.78.

Hence, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

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Answer:

x=3/5, y=-11/5. (3/5, -11/5).

Step-by-step explanation:

7x+6y=-9

y=-2x-1

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

7x+6(-2x-1)=-9

7x-12x-6=-9

-5x-6=-9

-5x=-9+6

-5x=-3

x=-3/-5=3/5

y=-2(3/5)-1=-6/5-1=-6/5-5/5=-11/5

The length of the triangle DEF f is 4.3 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The sine law can be used to find the side of a triangle. Therefore, let's find the side f of the triangle using sine law.

Therefore,

a / sine A = b / sin B = c / sin C

Hence,

e / sin E = f / sin F

E = 180 - 104 - 52

E = 24 degrees

Therefore,

1.8 / sin 24 = f / sin 104

cross multiply

1.8 sin 104 = f sin 24

divide both sides by sin 24

f = 1.8 sin 104  / sin24

f = 1.8 × 0.97029572627 / 0.40673664307

f = 1.7465323073 / 0.40673664307

f = 4.29277407617

f = 4.3 units

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The value of y is 58 and RS is 55.25 and ST is 17.5.

Equation is an expression that consists of variables, constants, and operators, and expresses a relationship between them. It is a mathematical statement that two expressions are equal. Equations can be used to solve a wide variety of problems in mathematics, science, engineering, and other fields. Examples of equations include the Pythagorean Theorem, the equation of a circle, and the equation of a line. Equations can be written in a variety of forms, such as symbolic, graphical, and numerical.

The value of y can be found by solving the equation 8y+4=58. By subtracting 4 from both sides, we get 8y=54.

Dividing both sides by 8, we get y=6.75.

Therefore, RS=8y+4=8(6.75)+4=55.25 and

ST=2y+4=2(6.75)+4=17.5.

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The next number in the given pattern is 1/4

What is Geometric Progression ?

Geometric progression can be defined as the sequence of numbers in which the common ratio between any consecutive numbers is same.

Given sequence ,

1/324  , 1/108 , 1/36 , 1/12

Lets check whether they are in Geometric sequence or not.

So,

r = 1/108  /  1/324

r = 324/108

r = 3

And

r = 1/36  /  1/108

r = 108/36

r = 3

So, The common ratios are same , it is in Geometric sequence

So , the next term could be

= 1/12  *  3

= 1/4

So, the next term could be 1/4

Hence, The next number in the given pattern is 1/4

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The final result of  algebra is: (6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)This is the simplified form of the given expression.

Simplification is the process of making an expression or equation simpler and easier to understand or work with. In mathematics, simplification often involves combining like terms, removing unnecessary operations, or reducing the number of terms in an expression. The goal of simplification is to obtain an equivalent expression that is clearer, more manageable, and easier to interpret.

Here ,

is the step by step process:

(6x ^ 3 - x ^ 2 - 14x + 5):(2x - 1)

Step 1: Divide 6x^3 by 2x and write the quotient 3x^2.

Step 2: Multiply the denominator (2x - 1) by the quotient (3x^2)

Step 3: Subtract the result from the numerator and bring down the next term of the numerator ( x^2)

Step 4: Repeat the process by dividing the x^2 by 2x and write the quotient -x.

Step 5: Multiply the denominator (2x - 1) by the quotient (-x)

Step 6: Subtract the result from the numerator and bring down the next term of the numerator ( -14x)

Step 7: Repeat the process by dividing the -14x by 2x and write the quotient -7

Step 8: Multiply the denominator (2x - 1) by the quotient (-7)

Step 9: Subtract the result from the numerator and bring down the next term of the numerator (5)

Step 10: We can see that the degree of the remainder is less than the degree of the denominator so we can write the remainder as 5/(2x-1)

So the final result is:(6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)

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A contour map/ plot is a way of representing a function with a two-dimensional input and a one-dimensional output.

Contours are obtained by intersecting the surface with the horizontal plane using the equation z = c. So the contour equation at height c is f(x,y) = c.

There are three types of contour lines displayed on the map:

Intermediate, Index, Supplement. The index line is the thickest contour line, and the points along the line are usually function numbered. Contours do not branch or split. Page 5 Steep slopes are represented by dense contour lines. Contour lines never intersect, but they can touch.

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Answer: Function B

Step-by-step explanation: Function A's equation would be y = x + 3 and although they have a greater y-intercept (starting point on x) the rate of change is less than Function B.

Answer:  192 oz

Step-by-step explanation:

thats the answer

On solving the provided question, by LCM after 2520 minutes, all 3 movies will begin at the same time.

The number that is the smallest of two or more natural numbers' common multiples is known as the Lowest Common Multiple (LCM) in mathematics.

IF we look from mathematical point  of view, the question is just asking what is the smallest numbers that is divisible by 120, 140 and 90, which is the L.C.M of these 3 number.

For instance, 12 is the least frequent multiple of 4 and 6. As a result, 12 is the lowest common multiple such that its elements are 4 and 6.

If we look at what the question ask, all the movies will begin at the same time if all the multiples of 120, 140 and 90 have a number in common and should be smallest.

Hence, after solving for L.C.M., we get 2520 as the L.C.M.

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Answer:

07(-x)-7(3)

Step-by-step explanation:

7(-x-3)

-7x-21

07(-x)-7(3)

-7x-21

The value of (fxg)(-3) if f(x)=5x-1 and g(x) =2x^2+1 will be 94.

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B. It is a relation “f” in which each element of set “A” is mapped with only one element belonging to set “B”. Also in a function, there can’t be two pairs with the same first element.

f(x)=5x-1

g(x) =2x^2+1

fxg = 5(2x^2+1) - 1

fxg = 10x^2 + 5 - 1

fxg = 10x^2 + 4

fxg(-3) = 10(-3)^2 + 4

fxg(-3) = 10(9) + 4

fxg(-3) = 90 + 4

fxg(-3) = 94

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The answer is  $350

By ranking the wages of a group of employees in descending order, you may determine the median base salary by finding the wage that is in the Middle of the distribution . 50 percent of earnings fall below the median, while 50 percent of salaries rise above the median.

The average of a set of numbers is known as the mean. If there are five salaries involved and the mean is $360, the total can be calculated by

Average = Total / number

Total = (Average)(Number)

Total = $360 * 5 = $1800

Four of the wages are spoken for, so we add them up and take $1800 out of the equation to get our result.

so $340 + $340 + $345 + $425 = $1450

and $1800 - $1450 = $350

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The approximate distance around the circular field is 172.7 feet.

A diagram of a roundabout is being designed to improve driver safety on a busy road.  The radius of the circular field planned for landscaping is 27.5 feet.

Therefore, the approximate distance around the outside of the circle can be calculated as follows:

The distance around the circle is the circumference of the circle.

Hence,

circumference of a circle = 2πr

where

Therefore,

distance around the circle = 2 × 3.14 × 27.5

distance around the circle = 172.7 feet

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Qualitative with 2 possible outcomes of variable is required to construct a confidence interval for a population proportion.

The goal of qualitative research is to collect and analyze non-numerical (descriptive) data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality. In-depth interviews, focus groups, or observations are frequently used in this kind of study to gather the information that is rich in context and detail.

To investigate complicated phenomena or to learn more about people's viewpoints and experiences on a certain subject, qualitative research is frequently used. It is especially helpful for academics who wish to comprehend the meaning that individuals attribute to their experiences or who want to identify the fundamental causes of people's conduct. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches.

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Answer:

a

Step-by-step explanation:

Due to the fact that many people only call their doctors when they are ill once or twice a year, the data is skewed toward the lower levels.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. Each column's data count or percentage of occurrences are shown on the vertical y-axis. Data distribution patterns can be seen visually using columns.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values).

Therefore, the correct answer is option b) The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

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Answer:

220√3

Step-by-step explanation:

220 x tan60°

220√3

When he has six and one-fourth feet of wood and one-half foot is needed for each birdhouse, he can create 12 birdhouses out of it.

Simply put, the unit technique is used to extract a single unit value from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.

given

Kevin has six and one fourth feet of wood = 6 + 1/4 = 25/4

one half foot for each birdhouse = 1/2

so  number of birdhouses = 25/4 / 1/2 = 25/2

When he has six and one-fourth feet of wood and one-half foot is needed for each birdhouse, he can create 12 birdhouses out of it.

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[tex](\dfrac{2}{9} )^2[/tex]

Can be written as:

[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]

To multiply two fractions, you need to multiply the numerator by the numerator and multiply the denominator over the denominator.

Multiply:

[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]

[tex]\dfrac{2\times2}{9\times9}[/tex]

[tex]=\fbox{$\dfrac{4}{81} $}[/tex]