How to Calculate the Value of Pi? (Pi Formula)

Answer:A 1.23 x 102hr

Step-by-step explanation:

It will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

What is the volume of the cylinder?

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

The volume of the cylinder-shaped vat can be calculated as follows:

V = π * r^2 * h

= π * 32.5^2 * 33.9 ft^3

The mass of the liquid in the vat can be calculated as the product of its volume and density:

m = d * V

= 1.77 g/mL * π * 32.5^2 * 33.9 ft^3

The time it takes to fill the vat can be calculated as the ratio of the mass of the liquid to the rate at which it is spilling out of the hose:

t = m / (12,757.9 g/s)

Converting the volume to liters, the density to kg/m^3, and the time to hours, the answer is approximately 1.23 x 10^2 hours.

Hence, it will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

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End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.

Here,

End behavior of a function f specifies how the function's graph behaves at the "ends" of the x-axis. In other words, when we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ), the end behavior of a function explains the graph's trend.

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Check the picture below.

first off let's get the area of the "circular ring", and then let's add to that the area of the innermost circle with a radius of 6.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=14\\ r=10 \end{cases}\implies A=(14^2-10^2)\implies A=96\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi (6)^2\implies A=36\pi \\\\[-0.35em] ~\dotfill\\\\ 96\pi ~~ + ~~36\pi \implies 132\pi ~~ \approx ~~ \text{\LARGE 414.69}~in^2[/tex]

AUC - B = 17 and AUB = 1, 2, 8, 9, 10, The partition of S formed by A, B, and C is not Au(B-C) = 1, 2, 8, 9, 10, or 17.

Finding the union of A and B requires us to identify every element that is either in A, B, or both. Here, A = 17 and B = 8, 9, and 10 respectively. So AUB = {1, 2, 8, 9, 10, 17}.

Finding (AUC) - B requires us to identify the components of the union of A and C minus the components of B. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, (AUC) - B = 17.

To determine Au(B-C), we must first identify the components of the union of A and the difference between B and C. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, Au(B-C)=1, 2, 8, 9, 10, and 17.

d. S cannot be partitioned by A, B, or C since S includes items that are not present in any of those three. As an illustration, elements 1 and 2 are present in S but not in A, B, or C. Therefore, S cannot be divided into A, B, and C.

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Richard has a 1/5 probability of accurately answering all of the questions.

Probability is simply the possibility that something will happen.

When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

The study of events that fit into a probability distribution is known as statistics.

How likely something is to happen is determined by its probability.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

So, we know he probability formula which is:

P(E) = Favourable events/Total events

So, the correct answers are 10 and there are 10*5 total options.

Then, P(F) = 10 and P(T) = 10*5 = 50.

Now, insert values in the formula and calculate as follows:

P(E) = Favourable events/Total events

P(E) = 10/50

P(E) = 1/5

Therefore, Richard has a 1/5 probability of accurately answering all of the questions.

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Complete question:

Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended a class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.)

What is the probability that he will answer all questions correctly?

The quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

A Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given that, the solution of a quadratic equation is {0, 2},

The equation of a quadratic polynomial in form sum and product of solutions is given by,

x²-(α+β)x+αβ = 0, where α, β = solution of equation

α+β = 0+2

α+β = 2

αβ = 0×2

αβ = 0

Therefore, equation is x²-2x+0 = 0

Hence, the quadratic equation whose solution set is {0, 2}, is: x²-2x = 0

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y = -x - 9 is the equation of the line that passes through the points (-5. -4) and (-2, -7).

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a line Pass through the points (-5. -4) and (-2, -7)

The slope-intercept form of the equation of a line:

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

m = (-7 + 4)/(-2 + 5)

m = -3/3

m = -1

Thus the equation of the line will be:

y = - x  +b

Since, point (-5, -4) passes through the equation of the line

-4 = 5 + b

b = -9

So,

The equation of the line:

y = -x - 9

Therefore, the equation of the line that passes through the points (-5. -4) and (-2, -7) is y = -x - 9.

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Note that the correlation coefficients matched with the correct association are given as follows:

0.52: Moderate association

-0.86: Strong association

0.93: Strong association

-0.66: Moderate association

-0.01: Weak association

A correlation coefficient is a quantitative measure of a statistical connection between two variables.

The variables might be two columns from a specified data set of observations, commonly referred to as a sample, or two factors of a multivariate random variable with a known distribution.

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The volume of a rectangular prism is a measure of the space occupied by the prism. It is calculated by multiplying the area of the base of the prism by its height.

In a rectangular prism, the base is a rectangle, and the height is the perpendicular distance between the top and bottom faces of the prism.

To find the volume of the rectangular prism, we simply multiply the length, width, and height of the prism. The length and width give us the area of the base, and the height gives us the perpendicular distance between the top and bottom faces. So, the formula for the volume of a rectangular prism is:

V = length * width * height

In this case, the height of the rectangular prism is 10 inches, the width is 19 inches, and the length is 20 inches. So, we can plug these values into the formula and calculate the volume:

V = 20 * 19 * 10

V = 3800 cubic inches

So, the volume of the rectangular prism is 3800 cubic inches.

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A rectangular prism has a height of 10 inches in a width of 19 inches and a length of 20 inches in what is the volume of the prism​?

We need only multiply the rectangular prism's length, breadth, and height to determine its volume. The area of the base is determined by the length, breadth, and height, while the angle between the top and bottom faces is determined by the height. So, the following is the formula for a rectangle prism's volume:

V: length, breadth, and height

In this instance, the rectangular prism measures 10 inches in height, 19 inches in breadth, and 20 inches in length. As a result, we can determine the volume by entering these values into the formula:

V = 20 * 19 * 10

Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

Let 'x' be Elena's score in the first game and 'y' be Elena's score in the second game.

We know that the total score for the two games is 478, so we can write the following equation:

x + y = 478

We also know that the score in the second game is 30 more than 3/4 of Elena's score in the first game. We can write this as:

y = x + 30

Substituting this into the first equation gives:

x + x + 30 = 478

Simplifying gives:

2x + 30 = 478

Subtracting 30 from both sides gives:

2x = 448

Dividing both sides by 2 gives:

x = 224

So, Elena's score in the first game is 224. Substituting this value into the equation for the second game gives:

y = 224 + 30

So, Elena's score in the second game is 254.

In summary, Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

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The number of yards of ribbon used to make small barrettes is 3 yards and the number of yards of ribbon used to make large barrettes is 7 yards.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, Destiny is using ribbon to create girls' hair barrettes.

Let the number of yards of ribbon used to small barrettes be x and the number of yards of ribbon used to large barrettes be y.

For a craft fair in Booneville, she made 12 small barrettes and 14 large barrettes, using a total of 148 yards of ribbon.

Now, the equation is 12x+14y=148 -------(i)

For another craft fair in Newport, she made 12 small barrettes and 10 large barrettes, which used a total of 116 yards.

So, the equation is 12x+10y=116 -------(ii)

Subtract equation (ii) from equation (i), we get

12x+14y-(12x+10y)=148-116

4y=32

y=8

Substitute y=7 in equation (i), we get

12x+14(8)=148

12x+112=148

12x=36

x=3

Therefore, the number of yards of ribbon used to make small barrettes is 3 yards and the number of yards of ribbon used to make large barrettes is 7 yards.

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Answer:

For a random sample of 4 players, the sampling distribution of the sample mean age would have:

the mean wouldn't be close to 26.8 years, as a sample mean will be an unbiased estimator of the population mean but the sample here is far smaller than a sample of 50.

A larger standard deviation compared to the standard deviation of individual player ages (4.2 years), as the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 4 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (4).

For a random sample of 50 players, the sampling distribution of the sample mean age would have:

A mean close to 26.8 years, as the sample mean will be an unbiased sample mean for a sample of 4 players, as the standard deviation of the estimator of the population mean.

A smaller standard deviation compared to the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 50 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (50).

[tex]f'(-2) = 4[/tex]This means that the rate of change of the function is 4 for all values of x within the given interval.

The derivative of a polynomial function tells us the rate of change of the polynomial function at any given point. Therefore, if we look at the table above, we can see that for x = -2, the derivative of the function (f') is equal to 4. So the statement that [tex]"f'(-2) = 4"[/tex] is true for -2 < x < 6.

The derivative of a polynomial function is a measure of the rate of change of the function at any given point. In the table provided, we can see that for x = -2, the derivative of the function (f') is equal to 4. As such, this statement is true for the interval -2 < x < 6 since f'(-2) = 4. This means that the rate of change of the function is 4 for all values of x within the given interval.

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It will take 0.6431 years or approximately 7.7 quarters for the investment to grow to $8935.

Raina deposited $5000 into an account with a 9. 4% annual interest rate, compounded quarterly.

To calculate the time it takes for an investment to grow to a certain amount at a given interest rate, you can use the formula:

T = [tex]\frac{log(\frac{A}{P}) }{log(1+\frac{r}{n}) }[/tex]

where:

T is the time in years

A is the final amount ($8935)

P is the initial amount ($5000)

r is the annual interest rate (9.4%)

n is the number of times compounded per year (quarterly = 4 times)

Plugging in the values, we get:

T = (log(8935 / 5000)) / (log(1 + 0.094 / 4))

T = [tex](\frac{log(1.787)}{log(1.0225)} )[/tex]

T = 0.6431 years or approximately 7.7 quarters (rounded to 2 decimal places).

Therefore, it will take 0.6431 years or approximately 7.7 quarters.

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The point satisfies both equation 1 and 2" and "The point is a solution to the system.

An equation is a mathematical statement that shows the equality of two expressions. Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.

To check whether a point is a solution to a system of equations, we can substitute the values of the variables into the equations and see if the resulting expressions are equal.

So, for the point (-3, -2), we can substitute these values into the equations:

Equation 1: -7x - 4y = 29

Substituting x = -3 , y = -2:

-7(-3) - 4(-2) = 29

21 + 8 = 29

29 = 29

Equation 2: 3x = -7 + y

Substituting x = -3 , y = -2:

3(-3) = -7 + (-2)

-9 = -9

Since both equations are true, the point (-3, -2) satisfies both equation 1 and 2, and is a solution to the system.

Therefore, the true statement from the list is "The point satisfies both equation 1 and 2" and "The point is a solution to the system".

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The value of the expression when x = 2 is

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

10(x + 2) + 10 • 2

The expression 10(x + 2) + 10 * 2 for x = 2 is:

10(2 + 2) + 10 * 2

So, we have the following representation

10 * 4 + 10 * 2 =

So, we have the following representation

40 + 20

Lastly, we have

= 60

So, the answer is B. 60.

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[tex]\huge\begin{array}{ccc}A.&\left(\frac{f}{g}\right)(x)=\frac{\sqrt[3]{2x}}{2x+1},&x\neq-\frac{1}{2}\end{array}[/tex]

We have the functions:

[tex]f(x)=\sqrt[3]{2x}\\\\g(x)=2x+1[/tex]

Let's define the domain of the functions:

[tex]D_f:x\in\mathbb{R}\\\\D_g:x\in\mathbb{R}[/tex]

Make the function

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{\sqrt[3]{2x}}{2x+1}[/tex]

Let's define the domain of the function:

[tex]D:2x+1\neq0\\\\2x+1-1\neq0-1\\\\2x\neq-1\\\\\dfrac{2x}{2}\neq\dfrac{-1}{2}\\\\x\neq-\dfrac{1}{2}[/tex]

The required pmf is P(X=x) = [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

A probability mass function (pmf) is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value. Let X be a discrete random variable on a sample space S . Then the probability mass function f(x) is defined as. f(x)=P[X=x]. f ( x ) = P [ X = x ] .

as given, if 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation.

so,

Let X denote the number of firms that violate at least one regulation from 10 randomly selected firms out of 70 firms of which 28 violate at least one regulation.

P(X=x)

= Hyper(x; n = 10, M = 28, N = 70)

= h(x; 10, 28, 70)

= [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

Thus, the required pmf is P(X=x) = [tex]\frac{\binom{28}{x}\binom{70 - 28}{10 - x}}{\binom{70}{10}}[/tex]

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The required pmf is P(X=x) = 28Cx * (70-28)C(10-x))/70C10

A probability mass function (pmf) is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value. Let X be a discrete random variable on a sample space S . Then the probability mass function f(x) is defined as. f(x)=P[X=x]. f ( x ) = P [ X = x ] .

as given, if 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation.

so,

Let X denote the number of firms that violate at least one regulation from 10 randomly selected firms out of 70 firms of which 28 violate at least one regulation.

P(X=x)

= Hyper(x; n = 10, M = 28, N = 70)

= h(x; 10, 28, 70)

= 28Cx * (70-28)C(10-x))/70C10

Thus, the required pmf is P(X=x) = 28Cx * (70-28)C(10-x))/70C10

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The difference between the two girl at first is 120 - 24 = 96 weet.

I determined the answer by using algebra. I started by defining the original number of weet that Sally had as x. Then, I used the information given in the problem to set up two equations:

       x = 24

Now that I know that Sally originally had 24 weet, I can use that information to find the original number of weet that Devi had. According to the problem, Devi had five times as many weet as Sally, so:

Finally, I subtracted Sally's original number of weet (24) from Devi's original number of weet (120) to find the difference between the two:

So, the difference between the two girls at first was 96 weet.

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The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

The probability that a randomly selected school or district uses digital content is 72%. To find the probability that a randomly selected school uses digital content and uses it as part of their curriculum, we need to divide the number of schools that use digital content and use it as part of their curriculum (6) by the total number of schools (20). This gives us 6/20 or 30%. Therefore, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

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Answer:

Let x be the number of bottles of water that Yui buys, and y be the number of sports drinks. The first equation represents the total number of bottles:

x + y = 6

The second equation represents the total cost:

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Solving the first equation for y in terms of x:

y = 6 - x

Substituting this expression for y into the second equation:

1.5x + 2.5(6 - x) = 10

Expanding and simplifying the right side:

1.5x + 15 - 2.5x = 10

-x + 15 = 10

Subtracting 15 from both sides:

-x = -5

Dividing both sides by -1:

x = 5

Substituting this value for x back into y = 6 - x:

y = 6 - 5

y = 1

So Yui buys 5 bottles of water and 1 bottle of sports drink.

Step-by-step explanation:

k=2.081, f(x) is continuous at x=3. So correct option is A.

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous. Mathematicians up until the 19th century mostly used intuitive ideas of continuity and only took into account continuous functions. To formalize the idea of continuity, the epsilon-delta definition of a limit was established.

Since f(x)[tex]\left \{ {{k^{3}+x } for x < 3 \atop {\frac{16}{k^{2}-1 }for x\geq 3 }} \right.[/tex]

We have to check continuity at x=3, for the value of k.

So, [tex]\lim_{x \to-3 \ } f(x)= \lim_{x \to +3\ } f(3)[/tex], eq.(1)

[tex]\lim_{x \to -3\ } f(x)=k^{3} + 3\\ \lim_{x \to +3\ } f(x)= \frac{16}{k^{2}-3 } and f(3)=\frac{16}{k^{2}-3 } \\from eq.(1)\\k^{3}+3=\frac{16}{k^{2} -3}[/tex]

By option (A), put k= 2.081= 2.081³ + 3= [tex]\frac{16}{2.081^{2} -3}[/tex]

=9.01189744+3= [tex]\frac{16}{4.330561-3}[/tex]

=12.01189744=[tex]\frac{16}{1.330561}=12.0118974[/tex]

Hence, k=2.081, f(x) is continuous at x=3.

So, option A is correct.

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The mass of the salt in the tank after t minutes is t kg. The tank begins to overflow after 300 minutes, and the mass of the salt in the tank is 300 kg.

a. To determine x(t), the mass of the salt in the tank after t minutes, we can use the principle of mass balance:

x(t) = 0.5 * [Vin(t) - Vout(t)]

where

Vin(t) = the volume of brine solution that flows into the tank after t minutes

Vout(t) = the volume of brine solution that flows out of the tank after t minutes.

Vin(t) = 4t

Vout(t) = 2t

Therefore:

x(t) = 0.5 * [4t - 2t] = 0.5 * 2t = t

So, the mass of the salt in the tank after t minutes is t kg.

b. To determine the mass of the salt when the tank begins to overflow, we need to find the time when the volume of brine solution in the tank reaches 600l.

Vin(t) - Vout(t) = 600

4t - 2t = 600

2t = 600

t = 300

So, the tank begins to overflow after 300 minutes, and the mass of the salt in the tank is 300 kg.

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Using the concept of sine rule and cosine rule, the value of angle ACB is

36.64°

The sine rule is a mathematical formula used in trigonometry to find the relationship between the sides and angles of a triangle. It states that the sine of one of the angles in a triangle is equal to the ratio of the length of the side opposite that angle, divided by the length of the hypotenuse. The formula can be written as:

sin(A) = a / c

where A is one of the angles in the triangle, a is the length of the side opposite angle A, and c is the length of the hypotenuse. The sine rule is commonly used to find the length of one side of a triangle when the lengths of the other two sides and one angle are known. Another form of the sine rule is the "ambiguous case" formula, which can be used to find one of the angles in a triangle when the lengths of all three sides are known:

a / sin(A) = b / sin(B) = c / sin(C)

where A, B, and C are the angles in the triangle, and a, b, and c are the lengths of the sides.

In the given problem, we can simply substitute the values into the formula and then solve for the unknown angle.

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

But since we don't know the value of BC, we can find that first using cosine rule.

a² = b² + c² - 2(bc) cos A

a² = 9² + 6² -2(9)(6)cos80

a² = 98.23

a = √98.23

a = 9.9

Going back to using sine rule;

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

9.9 / sin 80 = 6 / sin C

sin C = (6 sin 80) / 9.9

sin C = 0.5968

C = sin⁻¹(0.5968)

C = 36.64°

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It will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

To find the unit rate for each person, divide the number of boxes they can fold by the time it takes them to fold them:

Dionne: 175 boxes / 50 minutes = 3.5 boxes/minute

Elia: 120 boxes / 40 minutes = 3 boxes/minute

Next, divide the total number of boxes to be folded (210) by each person's unit rate:

Dionne: 210 boxes / 3.5 boxes/minute = 60 minutes

Elia: 210 boxes / 3 boxes/minute = 70 minutes

So, it will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

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Answer:

6

Step-by-step explanation:

70 sign up

11.5 each visit  assuming w visits

so to get to 139

11.5w +70=139

11.5w =69

w= 6

There are 4 possible nitrogenous bases, so for each position in the DNA sequence there are 4 options to choose from. Therefore, in a single base position there are 4 possible mutations. In a double base position, there are 4 * 4 = 16 possible mutations. This means that for 11 double base positions, there are 11 * 16 = 176 possible double letter mutations.

DNA (Deoxyribonucleic Acid) is the genetic material that encodes the instructions for the development and function of all living organisms. DNA is made up of four nitrogenous bases: adenine (A), cytosine (C), guanine (G), and thymine (T).

The sequence of these nitrogenous bases is what determines the genetic information of an organism. Mutations are changes in the DNA sequence that can occur naturally or as a result of environmental factors.

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Answer:

Step-by-step explanation:

76

Answer:

Step-by-step explanation:

x = -2

F(x)=1.5(2)^x=0.375 , G(x)=-3(1/4)^x=-48

x=0

F(x)=1.5(2)^x=3, G(x)=-3(1/4)^x=-3

x=1/2

F(x)=1.5(2)^x=1.06 , G(x)=-3(1/4)^x=-6