If a radioactive element has a half-life of 4 hours, then x grams of the element dwindles to x/2 grams after 4 hours. If a nuclear reactor has 800 grams of that radioactive element, find the amount of radioactive material after 16 hours.

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

You can multiply, reduce, add, or take this away in mathematics. An expression is put together as follows: Verb, numeric value, and math operator A mathematical formulation is composed of numbers, variables, and procedures (such as addition, subtraction, multiplication or division etc.) Opposing phrases and phrases is possible. An exponential function is any mathematical declaration that has variables, integers, or an mathematical operation. As an instance, the phrase 4m + 5 consists of both the terms 4m and 5, as well as the supplied equation's variable m, each of which is divided by the mathematical sign +.

given

the expression = "  number of one-third cup servings in 4 cups "

= four times one-third

= 4*1/3

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

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Answer & Explanation:

sin Θ = opp/hyp

cos Θ = adj/hyp

tan Θ = opp/adj

csc Θ = hyp/opp

sec Θ = hyp/adj

cot Θ = adj/opp

1.

sin Θ = opp/hyp = (8√2)/18 = (4√2)/9

cos Θ = adj/hyp = 14/18 = 7/9

tan Θ = opp/adj = (8√2)/14 =  (4√2)/7

csc Θ = hyp/opp = 18/(8√2) = (9√2)/(4√2√2) = (9√2)/8

sec Θ = hyp/adj = 18/14 = 9/7

cot Θ = adj/opp = 14/(8√2) = (7√2)/(4√2√2) = (7√2)/8

Answer:

Step-by-step explanation:

The monthly payment on a loan and the total interest that will be paid during the term of the loan can be found using an amortization formula.

Here are the steps to find the monthly payment and total interest for the given loan conditions:

Convert the interest rate to a decimal: 7.5% = 0.075

Divide the interest rate by the number of periods (months) per year: 0.075 / 12 = 0.00625

Find the number of payment periods: 8 years * 12 months/year = 96

Calculate the monthly payment using the amortization formula:

Payment = Loan Amount * (Interest Rate / (1 - (1 + Interest Rate)^(-Number of Payments)))

Payment = $6,200 * (0.00625 / (1 - (1 + 0.00625)^(-96)))

Payment = $79.88

So, the monthly payment on the loan is $79.88.

Calculate the total interest paid over the term of the loan:

Total Interest = (Monthly Payment * Number of Payments) - Loan Amount

Total Interest = ($79.88 * 96) - $6,200

Total Interest = $7,538.88

So, the total interest that will be paid during the term of the loan is $7,538.88.

The required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
When simplifying the expression 4x²y⁴/2x⁷y⁸, we can divide the numerator and denominator by the greatest common factor of each, which is x²y⁴. Doing so gives us:

[tex]$\frac{4x^2y^4}{2x^7y^8} = \frac{4}{2x^5y^4} = \frac{2}{x^5y^4} = \boxed{\frac{2}{x^5y^4}}$[/tex]

Thus, the required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

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The correct choices are 1) B, 2) G, 3) C, 4) I.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

1) The price paid for $60 jeans after a 35% discount is applied can be found as follows:

Discount Amount = 60 * 35% = $21

Price Paid = 60 - 21 = $39

Correct choice is B.

2) The discount amount on a $55 sweatshirt with a 20% discount can be calculated as follows:

Discount Amount = 55 * 20% = $11

Correct choice is G.

3) The 20% tip on a $73 meal can be calculated as follows:

Tip Amount = 73 * 20% = $14.6

Correct choice is C.

4) The 7% sales tax on a new $32,000 car can be calculated as follows:

Tax Amount = 32000 * 7% = $2,240.

Correct choice is I.

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The system of equations to find the number of each type of shot is x + y = 59 and x + 2y = 103

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let x represent the number of 1 point shots and y represent the number of 2 point shot.

The team made 59 successful shots, hence:

x + y = 59      (1)

Also, The team scored 103 points in all, therefore:

x + 2y = 103    (2)

From both equations:

x = 15, y = 44

The team made 15 number of 1 point shots and 44 number of 2 point shot.

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For f(x) =4x+1 and g(x) = x²-5, the answer of (f/g) (x) is D) 4x+1/x²-5, x≠±√5

From the question, we have:

f(x) =4x+1

g(x) = x²-5

If what you are looking for is( f/g) (x), then only place the value of f(x) as the quantifier and g(x) as the denominator. Then the function that satisfies is D.

But here there is a condition that (f/g) (x) applies if the value of x is not √5 or -√5. Because if it becomes an x value then the result will be 0.

We can prove this:

With this equation (f/g) (x)=4x+1/x²-5

let's try to use value of x is √5, it will be

(f/g) (x)=4x+1/x²-5

(f/g) (√5) = 4.√5+1/(√5)²-5

=(4√5+1)/5-5

=(4√5+1) /0

=0

Then, try to use value of x is -√5, it will be

(f/g) (x)=4x+1/x²-5

(f/g) (√5) = 4.(-√5)+1/(-√5)²-5

=(-4√5+1)/5-5

=(-4√5+1) /0

=0

From the results above it proves that option D cannot be used if x= ±√5.

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Answer: (-4, 1)

Step-by-step explanation:

To solve graphically, change each equation into slope-intercept form

(y = mx + b)

3x + 4y = -8

+8 +8

3x + 4y + 8 = 0

-4y -4y

3x + 8 = -4y

Divide both sides by -4 to get y by itself

-3/4x - 2 = y or y = -3/4x - 2

Do the same for the other equation.

-x + y = 5

+x +x

y = 5 + x or y = x + 5

Plug in the equations graphically. The point at which the two lines intercept is your answer.

The correct answer is option d. The length of the given hypotenuse  of a right triangle is 7 cm.

A right triangle has side lengths of 4 centimeters and 5 centimeters, so we can use the Pythagorean Theorem to find the length of the hypotenuse. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse c is given by

[tex]c^2 = 4^2 + 5^2[/tex]

= 16 + 25

= 41

so the length of the hypotenuse is c = √41 = 7 cm.

The answer is d. 7 cm.

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The sample should be milled to a radius that is approximately 7.19 times its original radius in order to increase its work function by 2%.

The work function of a material is related to its surface area, and milling a sample into smaller nano-spheres increases its surface area. The increase in work function can be approximated by the following equation:

ΔW = kTln(A/A₀)

where ΔW is the change in work function, k is Boltzmann's constant, T is the temperature in Kelvin, A is the new surface area of the milled sample, and A₀ is the original surface area of the sample.

To find the size to which the sample should be milled to increase its work function by 2%, we need to rearrange the equation to isolate the new surface area:

A/A₀ = e^(ΔW/kT)

Plugging in the known values, we get:

A/A₀ = e^(0.02 * 5.1 eV / (8.62 * 10⁻⁵ eV/K * 300 K))

= 51.64

The new surface area is 5064% larger than the original surface area.

Since the sample is being milled into nano-spheres, the new surface area is proportional to the square of the radius. Let's call the original radius of the sample "r₀". Then the new radius is:

r = √(A/A₀) * r₀ = √(51.64) * r₀ = 7.19 * r₀

--The question is incomplete, answering to the question below--

"g a gold (au) macro scale sample has a work function of 5.1 ev. to what size should the sample be milled to increase its work function by 2 %? assume that the sample is milled into nano-spheres and give the size in terms of radius. What is the relation between the new radium and original radius?"

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The old will Mr Lim be in 6 years time is 46 years old.

To make solving this problem easier, we need to consider the ages of Mr Lim and his son. For example by multiplying the number x.

Let:

Mr Lim's age = a

His son's age = b

So that,

The ratio of ages in the current year:

Mr Lim's age to his son's age = 5x : 2x

a : b = 5x : 2x

The ratio of ages in the four years ago:

Mr Lim's age to his son's age = 3x : x

(a - 4) : (b - 4) = 3x : x

[tex]\frac{a-4}{b -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3}{1}[/tex]

5x - 4 = 6x - 12

5x - 6x = -12 + 4

-x = -8

x = 8

So that we know the age of Pak Lim's and the age of his son's this year.

Mr Lim's age = 5x

                     = 5 × 8

                     = 40 years old

His son's age = 2x

                     = 2 × 8

                     = 16 years old

After that, we find Mr Lim's age 6 years from now by adding 6 years to this year's age.

Mr Lim's age be in 6 years time = 40 + 6

                                                    = 46 years old

So, the old will Mr Lim be in 6 years time is 46 years old.

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Therefore, Horatio can buy approximately 11.83 gallons of gas. However, since he cannot buy a fractional part of a gallon, the actual number of gallons he can buy is either 11 or 12 gallons.

An equation is a mathematical statement that shows the equality between two expressions. Equations are used to solve problems and find solutions to mathematical or real-world problems. They typically involve variables, which are symbols that represent unknown values, and constants, which are known values that are used in the equation. Equations can take many forms, but they generally follow the pattern: expression = expression. Equations are an important tool in mathematics, science, and engineering, and they can be used to model and analyze many different types of systems and processes.

Here,

Horatio has $230, but he wishes to save $160 and spend $24.95 on an oil change. So the amount of money he has left to spend on gas is:

$230 - $160 - $24.95 = $45.05

To find out how many gallons of gas Horatio can buy with $45.05, we can divide the amount of money by the price per gallon:

$45.05 ÷ $3.81/gallon ≈ 11.83 gallons

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By evaluating a proportional relation, we can see that if 10 fiction books are sold, then 13 non-fiction books are sold.

Here we know that 3 fiction books are sold for every 4 non-fiction books sold.

Then if x fiction books are sold, the number of non-fiction books sold are given by the proportional relation:

y = (4/3)*x

Here we know that 10 fiction books are sold, so x = 10, replacing that we will get:

y = (4/3)*10 = 40/3 = 13.33

So 13 non-fiction books are sold.

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Answer:

Step-by-step explanation:

One quarter = 1/4

1/4 of a number is 6.

We have to find that number by taking

6 times 4 = 24

So, we know that number is 24

What is one-third of the number?

1/3 of 24 = 8

So, the answer is 8.

Answer:

[tex]5b + 7p = 79[/tex]

[tex]7b + 5p = 77[/tex]

Answer:

Step-by-step explanation:

The factored form of a polynomial function with roots r1 and r2 can be found by multiplying two linear factors (x - r1) and (x - r2).

Here are the steps to find the factored form of the polynomial function with roots 3i and 2:

Write the first linear factor: (x - 3i)

Write the second linear factor: (x - 2)

Multiply the two linear factors: (x - 3i)(x - 2)

Expand the product to find the polynomial function:

x^2 - (3i + 2)x + (3i * 2) = x^2 - 2x - 6i

And there you have it, the factored form of the polynomial function with roots 3i and 2 is x^2 - 2x - 6i.

A. A polynomial function A for the total sales of football and baseball jerseys is 26t^4 + 26t^2 + 760

B. The function A is neither even nor odd

a. To find a polynomial function for the total sales of football and baseball jerseys, we simply add the two functions:

A = G + H = 15t^4 + 13t^3 + 10t^2 - 10t + 750 + 11t^4 - 13t^3 + 9t^2 + 8t + 650 = 26t^4 + 26t^2 + 760

b. The function A is neither even nor odd. An even function is one that is symmetrical around the y-axis and an odd function is one that is symmetrical around the origin. The polynomial function A has no symmetry around either the y-axis or the origin, so it is neither even nor odd.

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Based on the information, it can be inferred that the area of the room is 121m².

To calculate the area of the room we must perform the following mathematical procedure:

1. Identify the length of the sides and the base.

2. multiply the length of a side by the base.

3. get the result of the area.

According to the above procedure, the area of the room would be:

According to the above, the area of the room would be 121m². The dimensions of the furniture in the room have no influence in this procedure.

Note: This question is incomplete because there is some information missing. Here is the complete information:

question:

Calculate the area of the room.

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Answer: 75.6, 14.4

Step-by-step explanation:

Note 2 angles are complementary if they adds up to 90 degrees. Lets set x to be the first angle.

x - (x - 61.2) = 90

Then we can know:

2x = 90 + 61.2;

2x = 151.2;

x = 75.6

Now we know the first angle is 75.6, we know the second angle is 75.6 - 61.2 = 14.4. Hope you find this helpful!

Answer:441

Step-by-step explanation:

The probability of spinning a number greater than 4 on a spinner with 6 equal sections is 1 over 3. (option d)

A spinner with 6 equal sections has an equal probability of landing on any of the 6 sections. To find the probability of spinning a number greater than 4, we need to find the fraction of sections that meet this criterion. In this case, there are 2 sections that satisfy this condition (5 and 6).

Therefore, the probability of spinning a number greater than 4 is 2/6, or 1/3.

It's important to remember that when working with probability, the values can only be between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of any event must be a number between 0 and 1, inclusive.

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The future value of this one-time investment of $1,000 in 5 years is equal to: A. $1,082.5.

Mathematically, future value can be calculated by using this formula:

F = P(1 + r)

Where:

Substituting the given parameters into the future value formula, we have the following;

Future value, F = 1,000(1 + 8.25/100)

Future value, F = 1,000(1 + 0.0825)

Future value, F = 1,000(1.0825)

Future value, F = $1,082.5.

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The value of (x + y) in parallelogram ABCD is equal to 150°.

Since ABCD is a parallelogram and ∠ADC is equal to 105°. Additionally, side AB in parallelogram ABCD is produced to point E. This ultimately implies that, angle C (∠C) and angle D (∠D) are adjacent angles of parallelogram ABCD:

∠C + ∠D = 180° (supplementary angles).

x + 105° = 180°

x = 180 - 105

x = 75°

Based on alternate interior angles theorem, ∠y is congruent to ∠x. Therefore, we have the following:

∠y ≅ ∠x

y = 75°

(x + y) = (75 + 75)

(x+ y) = 150°.

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Answer:

Step-by-step explanation:

width is 10 length is 15.

Answer: T = 0.25x + 50, where x represents the number of chirps in 1 minute.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The current area is 60 sq. in. You wish to increase this area to 300 sq. in. by adding x in two dimensions: namely length and width.

These measurements would be 5 + x wide and 12 + x long.

(5 + x)(12 + x) = 300

x^2 + 17x + 60 = 300

Subtracting 300 from both sides and using the quadratic formula for

x^2 + 17x - 240 = 0,

we find that the one reasonable answer for the measure x is 9.2 inches.

The air speed of the plane to cover 360 miles against the wind and with the wind in the given time is equal to 200 miles per hour.

Let 'x' be the speed of the plane fly in still air.

And 'y' be the speed of the wind.

Speed against the wind = x - y

Speed with the wind = x + y

Total distance covered by plane = 360 miles

Time taken against the wind = 2 hours 15 minutes

                                               = 2 ( 1/4 ) hours

                                               = 9 / 4 hours

Time taken with the wind = 1 hour 30 minutes

                                          = 1 ( 1/2 ) hours

                                          = 3 /2 hours

Speed = distance / time

Against the wind :

x - y = 360 / (9 /4 )

⇒x - y = 160___(1)

With the wind:

x + y = 360 / (3 /2)

⇒x + y = 240 ___(2)

Add (1) and (2) we get,

2x = 400

⇒ x= 200miles per hour

⇒y = 40 miles per hour

Therefore, the air speed of the plane as per given condition is equal to 200miles per hour.

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It is possible to choose a and b such that the value of function(x) at any given point is equal to the limit of f(x) as x approaches any value. This guarantees that f is continuous throughout.

A function's limit as x approaches any value must match the value of f(x) at that moment in order for the function to be continuous everywhere. In order to ensure that this need is satisfied, the values of a and b that make up f(x), whether it be a linear equation, polynomial, or another sort of equation, must be chosen. Since the behaviour of the function varies smoothly as x approaches any value, this ensures that the function is continuous throughout. In other words, a and b values must be selected in a way that the function is continuous, i.e., defined and devoid of breaks or discontinuities.

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The complete question is

Find the values of a and b that make f continuous everywhere that f is continuous throughout.

The radius of the circle is equal to the distance between the two points, or LD and LE.

A circle is a safe consisting of all points in a plane that are given distance from a given point the centre the distance from the centre to any point on the circle is known as the radius is alkal is no slider corners and all points along the circle are equidistant from the centre.


mCB= Circumference of the circle is the distance around the outside of the circle.
m/FOB= The formula for finding the circumference of a circle is C=2πr, where C is the circumference, π is 3.14, and r is the radius of the circle.
m/FIG= The formula for finding the area of a circle is A=πr2, where A is the area of the circle, π is 3.14, and r is the radius of the circle.
MAE= Mean Average Error (MAE) is used to measure the accuracy of a model or an algorithm by calculating the average difference between the predicted values and the actual values.
m/COF= The coefficient of friction (COF) is a measure of the resistance of a surface to sliding. It is usually expressed as a ratio of the force of friction to the normal force.
mZAJC= Distance between O and A is the same as the distance between J and C, or mZAJC.
mFG= The length of the arc FG is equal to the product of the central angle and the radius of the circle, or mFG.
MFI= The length of the arc FI is equal to the product of the central angle and the radius of the circle, or MFI.
m/ELD= The length of the line segment ED is equal to the difference between the lengths of the two arcs, or m/ELD.
mFM= The length of the arc FM is equal to the product of the central angle and the radius of the circle, or mFM.
m/AOC= The length of the line segment OC is equal to the difference between the lengths of the two arcs, or m/AOC.
m/AHF= The length of the line segment HF is equal to the difference between the lengths of the two arcs, or m/AHF.
IF= The length of the arc IF is equal to the product of the central angle and the radius of the circle, or IF.
PC= The length of the line segment PC is equal to the difference between the lengths of the two arcs, or PC.
HM= The length of the line segment HM is equal to the difference between the lengths of the two arcs, or HM.
LD and LE are tangent to the circle. This means that the radius of the circle is equal to the distance between the two points, or LD and LE.

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