Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function. π y=4cos x + 10 ... The amplitude is The period is. The displacement is (Type an exact

To find the length of a rectangle with given coordinates, you need to use the distance formula. The distance formula is a mathematical formula that is used to find the distance between two points in a plane.

The distance formula is given by -

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points, and d is the distance between the points.

To find the length of a rectangle, you will need to use the distance formula to find the distance between two points that are on opposite sides of the rectangle. For example, you can use the distance formula to find the length of the rectangle by finding the distance between the points \((x_1, y_1)\)and \((x_2, y_2)\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points on opposite sides of the rectangle.

For example, consider a rectangle with the following coordinates:

(1, 1); (1, 5); (5, 5); and (5, 1)

To find the length of this rectangle, you can use the distance formula to find the distance between the points (1, 1) and (1, 5). The distance formula is:

d =\(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

= \(\sqrt{(1 - 1)^2 + (5 - 1)^2}\)

=\(\sqrt{0 + 16}\)

= \(\sqrt{16}\)

= 4

Therefore, the length of the rectangle is 4 units.

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The area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom is 0.0125.

In statistics, the chi-square distribution is a continuous probability distribution that is widely used in inferential statistics. The area to the right of a certain value can be calculated using a chi-square table or a computer program. In this case, we want to find the area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom. Using a chi-square calculator or a chi-square table, we can determine that this area is 0.0125. This means that there is a 1.25% chance of getting a chi-square value greater than 23.337 with 12 degrees of freedom. This type of calculation is often used in hypothesis testing and other statistical analyses.

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Answer:

The width is 6 and the length is 9.

Step-by-step explanation:

Factors of 54: (1, 54), (2, 2), (3, 18), and (6, 9)

6 and 9 would work because 6+3=9

Answer:

x = 225

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths and c is the hypotenuse.

Substituting in the values:

(x - 3)^2 + 9^2 = x^2

Then, we isolate x:

(x - 3)^2 + 81 = (x - 3)(x - 3) + 81 = x^2 - 6x + 9 + 81 = x^2 - 6x + 90 = x^2

(Subtract x^2 from both sides)

- 6x + 90 = 0

(Add 6x to both sides, I also flipped the equation to put x on the left side)

6x = 90

(Divide both sides by 6)

x = 15

To double-check, substitute x with 15:

(15 - 3)^2 + 9^2 = 15^2

Simplify:

144 + 81 = 225 (true)

Answer: This is written in Expanded form.

Step-by-step explanation: The number is 6,915, to write a number in expanded form, write it's place values by the number it's in.

Ex: Expanded form of 5,731: 5,000 + 700 + 30 + 1

The given series converges only when x = 0

To determine the values of x for which the series n!x⁵ⁿ converges, we can use the ratio test, which states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges, and if the limit is greater than 1, the series diverges.

Applying the ratio test to the series, we obtain |aₙ ₊ ₁ /aₙ| = |(n+1)! x⁵(n+1)/(n! x⁵)| = |(n+1)x⁵|. We simplify this expression to obtain |(n+1)x⁵|.

We then take the limit as n approaches infinity of |(n+1)x⁵|. If x is not equal to zero, this limit will approach infinity, since n+1 grows without bound as n approaches infinity, and x⁵ is a constant factor that does not affect the growth rate. In this case, the limit will be greater than 1, indicating that the series diverges.

However, if x is equal to zero, then the limit of |(n+1)x⁵| is zero, indicating that the series converges.

Therefore, the series n!x⁵n converges only when x is equal to zero.

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The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.

Toothpaste company

Large tubes

Small tubes

1) Sparkling

100 per hour

200 per hour

2) Bright White

100 per hour

250 per hour

3) Fresh!

200 per hour

250 per hour

4) Mint

150 per hour

150 per hour

Formula for comparative advantage is

CA=rate of producing large tubes/rate of producing small tube

For 1 Sparkling:

CA = 100/200

CA = 0.5

For 2 Bright White:

CA = 100/250

CA = 0.5

For 3 Fresh:

CA = 200/250

CA = 0.8

For 4 Mint:

CA = 150/150

CA = 1

thus, to place the companies in order of greatest comparative advantage to least comparative advantage in  producing large tubes of toothpaste is 4, 3, 1, 2.

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Complete question:

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in

producing large tubes of toothpaste.

2.1.3.4

4.1,2,3

4,3,1,2

Save and Exit

Next

Submit

Mark this and retum

Answer:

7x+2x=7-1

9x=6

9÷6= 9/6

Step-by-step explanation:

Move numbers with (x) on one side turning it into (-)

x = 6/5

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation:

 7x − 2x = −1 + 7

Combine like terms:

 5x = −1 + 7

Calculate the sum or difference:

 5x = 6

Divide both sides of the equation by the coefficient of variable: 

x = 6 ÷ 5

Calculate the product or quotient: 

x = 1.2

Express the number in fractions:

 x= 6/5

Answer:

x = 6/5

Answer:

See below

Step-by-step explanation:

If Sean's dad is 6 feet 4 inches tall. Then the height of Sean and his mom will be 4 feet and 9 inches and 5 feet and 3 inches.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Sean is three-fourths his dad's height and one-half foot shorter than his mom.

If Sean's dad is 6 feet 4 inches tall.

Then the height of Sean and his mom will be

Let x be the height of Sean and y be the height of his mother.

Then we have

x = (3/4)(6.33)

x = 4.75

x = 4 feet and 9 inches

Then we have

     x = y - 1/2

4.75 = y - 0.5

    y = 4.75 + 0.5

    y = 5.25

    y = 5 feet and 3 inches

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Answer: x= 4.5 or x= 9/2

Step-by-step explanation:

Step-by-step explanation:

(x - 6) - (4.5 - x) = -1.5

remove the brackets

x - 6 - 4.5 + x = -1.5

2x - 10.5 = -1.5

2x = 9

x = 4.5

To sketch the regions corresponding to the events and determine if they are of product form, we need to consider the given conditions for each event and analyze their graphical representations.

(a) Event: {X - Y ≤ 2}

Sketch: This event represents the region below the line X - Y = 2 in the xy-plane.

Product Form: No, this event is not of product form.

Limits of Integration: Assuming the limits of integration for X are a and b, and for Y are c and d, the double integral with limits of integration will be:

∫∫ fX,Y(x, y) dxdy, where a ≤ x ≤ b and c ≤ y ≤ x - 2

(b) Event: {max(X - Y) < 6}

Sketch: This event represents the region below the line max(X - Y) = 6 in the xy-plane.

Product Form: No, this event is not of product form.

Limits of Integration: Assuming the limits of integration for X are a and b, and for Y are c and d, the double integral with limits of integration will be:

∫∫ fX,Y(x, y) dxdy, where a ≤ x ≤ y + 6 and c ≤ y ≤ d

(c) Event: {|X| < |Y|}

Sketch: This event represents the region where the absolute value of X is less than the absolute value of Y.

Product Form: Yes, this event is of product form.

Limits of Integration: Assuming the limits of integration for X are a and b, and for Y are c and d, the double integral with limits of integration will be:

∫∫ fX,Y(x, y) dxdy, where -y ≤ x ≤ y and c ≤ y ≤ d

(d) Event: {|X - Y| ≤ 2}

Sketch: This event represents the region where the absolute value of X - Y is less than or equal to 2.

Product Form: Yes, this event is of product form.

Limits of Integration: Assuming the limits of integration for X are a and b, and for Y are c and d, the double integral with limits of integration will be:

∫∫ fX,Y(x, y) dxdy, where y - 2 ≤ x ≤ y + 2 and c ≤ y ≤ d

(e) Event: {X/Y ≤ 1}

Sketch: This event represents the region below the line X/Y = 1 in the xy-plane.

Product Form: No, this event is not of product form.

Limits of Integration: Assuming the limits of integration for X are a and b, and for Y are c and d, the double integral with limits of integration will be:

∫∫ fX,Y(x, y) dxdy, where a ≤ x ≤ y and c ≤ y ≤ d

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The Cynic believes that when the Meek inherit the Earth, there will be a shift towards an easier and less complicated life.

In general, the Cynics believed in living a simple and ascetic life, free from materialism and societal norms.

It can be assumed that the Cynics may believed that the inheritance of the Earth by the meek would lead to a shift in values and beliefs towards simplicity, frugality, and self-sufficiency, rather than wealth, power, and status. This is a stark opposite to the world as it currently is as this world has wealth and power as the most power defining factors of status.

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The balance due on the note at the date of maturity is ​$1010.13.

The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.

Given permission to apply the US rule

In the United States, a year is deemed to have 360 days for the purposes of calculating interest.

Given that the principal is $ 2000,

Interest rate = 4% = 0.04

The effective date is April 1.

The whole amount is $1,000.

May 1 = partial payment

Duration = 30 days (May 1 - April 1)

Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67

So value = $ 2000 + $6.67 = $6.67

Partial payment received = $1,000

As a result, value = $ 1006.67 = $2006.67 - $ 1000

Time T= 31

Interest = PTR * 31/360 * 0.04 = 3.46

So the total value is $1006.67 + $3.47 = $1010.13.

The note's outstanding balance at maturity is $1010.13.

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Step-by-step explanation:

commision = 7% of $9000

commision = 7/100 * $9000

commision = $630

The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

What is mean ?

mean can be defined as the ratio of sum of the total observations and the number of total observations.

Given set of data

11,13,17,20,22,25,27,31,31,33

Mean  =  11 +13+17+20+22+25+27+31+31+33/10

= 230/10

 =23

Hence  mean = 23

The (n/2)th term= the 5th term

                       =22

The  (n/2+1) term = The  6th term

= 25

The median = 22+25/2

                  =23.5

Range = Highest term - lowest term

          =33- 11

           =22

Here lower half {11,13,17,20,22}

The middle number of lower half is first quartile.

Q₁ = 17

And lower half is{25,27,31,31,33}

The middle number of upper half is third quartile.

Q₃=31

Interquartile Range =Q₃-Q₁

                               =31-17

                                =14

Hence, The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

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Step-by-step explanation:

None is better they have the same score in percentage.

Answer:

She scored equally well in both tests.

Step-by-step explanation:

Convert to percentages:

25/30 = 5/6 = 5*100/6 = 83.3 %

35/42 = 5/6 = 83.3%.

a single expression that represents the capacity of both gas tanks combined the combined capacity of both gas tanks is "15x2 + 0x + 0", which can be simplified to "15x2".

An expression is a mathematical phrase that combines numbers, variables, and operations such as addition, subtraction, multiplication, and division.

Capacity refers to the maximum amount that something can hold, such as the volume of a container or the number of people that can be accommodated in a room.

According to the given information:

To find the combined capacity of both gas tanks, we need to add the volumes of the two tanks. So we have:

Combined capacity = volume of larger tank + volume of smaller tank

= (8x^2 + 2x - 1) + (7x^2 - 2x + 1)

Simplifying this expression by combining like terms, we get:

Combined capacity = 15x^2

Therefore, the capacity of both gas tanks combined can be represented by the expression "15x^2". This is a single term polynomial expression that represents the total capacity of the two gas tanks in cubic inches.

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Based on the given information, with a mean completion time of 41.7 seconds, we can conclude that vigorous exercise has resulted in a statistically significant decrease in the average time necessary to complete the maze.

To determine the impact of vigorous exercise on the completion time of the maze, we can conduct a hypothesis test. The null hypothesis (H0) assumes that there is no change in the average completion time, while the alternative hypothesis (Ha) suggests that there is a decrease.

By comparing the observed mean completion time of 41.7 seconds with the population mean of 45 seconds, we can evaluate whether the difference is statistically significant. Since the population standard deviation is known to be 5 seconds, we can use a one-sample t-test.

Calculating the test statistic, we find that t = (41.7 - 45) / (5 / √10) ≈ -3.08. With a significance level of 1%, the critical value for a one-tailed test is -2.756. Since -3.08 is smaller than -2.756, we reject the null hypothesis.

Therefore, we can conclude that the average completion time for the maze has decreased significantly after vigorous exercise. This means that the exercise has had a positive impact on the students' performance, enabling them to complete the maze more quickly.

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The approximate 95% confidence interval is (14.69, 18.51).

What is the confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given:

H₀ : μ = 15

H₁ : μ > 15

The test statistic t = ( x - μ) /(s/√n)

= (16.6 - 15)/(8√70/))

= 1.67

P-value = P(T > 1.67)

= 1 - P(T < 1.67)

= 1 - 0.9503

= 0.0497

At a 5% significance level, since the P-value < α (0.0497 < 0.05), so we should reject H₀.

So at a 5% significance level, there is sufficient evidence to conclude that employees spend more than 15 minutes on average on non-business activities.

The point estimate for the population mean (x) = 16.6

SE = (s/√n) = 8/√70 = 0.9562

At a 95% confidence interval, the critical value is t* = 1.995

The 95% confidence interval for the population mean is

x± t* (s/√n)

= 16.6 ± 1.995 × (8/√70)

= 16.6 ± 1.91

= 14.69, 18.51

Hence, the approximate 95% confidence interval is (14.69, 18.51).

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The formula for the nth term, an, of the given sequence is an =  (-1)ⁿ⁺¹ * n² / (6n + 5), where the numerator alternates between positive and negative perfect squares, and the denominator increases by a constant difference of 6.

To find the formula for the nth term, we need to analyze the pattern in the given sequence.

The numerators alternate between positive and negative perfect squares: 1, -4, 9, -16, ...

The denominators increase by a constant difference of 6: 5, 11, 17, 23, ...

Based on this pattern, we can observe that the numerator is given by (-1)ⁿ⁺¹ * n². The exponent (n+1) ensures that the sign alternates between positive and negative.

The denominator is given by 6n + 5.

Putting it all together, the formula for the nth term, an, is:

an = (-1)ⁿ⁺¹ * n² / (6n + 5).

This formula will give you the value of each term in the sequence based on the position of n.

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Answer:

\(|x-8|=6\)

Step-by-step explanation:

Let's begin by finding the midpoint of 2 and 14. To do this, we'll add the numbers and then divide by 2.

2+14=16

16/2=8

The number that is the same distance between 2 and 14 is 8.

Now, let's find how far away each number is from 8.

8-2=6

14-8=6

2 and 14 are 6 away from 8.

Let's set up the absolute value equation using these two values.

Since 8 is the midpoint, this will be what the absolute value expression is equal to.

Since each number is 6 away from 8, this is the number (6) we will be taking away from 2 and 14.

Remember that absolute value is just distance.

In other words, 2 is 6 away from 8, and 14 is also 6 away from 8.

Or, the distance between a number x and 8 is 6.

Using this knowledge, we have:

\(|x-8|=6\)

Answer:

|x-8|=6

Step-by-step explanation:

i checked rsm its correct :3

The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

that does not make sense

Step-by-step explanation:

The greatest common factor of the polynomial is 4y².

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

-12\(y^4\) + 8y³ - 4y²

Now,

Taking out the common factors.

4y² (-3y² + 2y - 1)

Now,

4y² is the common factor in the given polynomial.

Thus,

The greatest common factor of the polynomial is 4y².

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Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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In the given recipe, a total of 17/24 cup of sugar mixture is used to make the cake. The remaining 11/24 cup is the measurement used in making the cake.

To determine the amount of sugar mixture used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

Given:

Brown sugar = 3/8 cup

White sugar = 1/3 cup

Set aside for crumb topping = 1/4 cup

To find the amount used for the cake:

Total sugar mixture = Brown sugar + White sugar

Total sugar mixture = 3/8 + 1/3

                  = 9/24 + 8/24

                  = 17/24 cup

Amount used for the cake = Total sugar mixture - Set aside for crumb topping

Amount used for the cake = 17/24 - 1/4

                        = (17/24) - (6/24)

                        = 11/24 cup

Therefore, 11/24 cup of the sugar mixture is used to make the cake.

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The probability that an observation on flow rate when pressure drop is 10 in. will exceed an observation on flow rate made when pressure drop is 11 in. is .7602.

a. The expected change in flow rate associated with a 1-in. increase in pressure drop is the slope of the regression line, which is .095 m3/min per in. of water. This means that for each additional inch of pressure drop, we can expect the flow rate to increase by an average of .095 m3/min.

b. When pressure drop decreases by 5 in., we can expect the flow rate to decrease by an average of .095 * (-5) = -.475 m3/min.

c. For a pressure drop of 10 in., the expected flow rate can be calculated by plugging x = 10 into the regression line equation: y = -.12 + .095(10) = .838 m3/min.

d. To find the probabilities, we need to standardize the flow rate values using the formula z = (y - μ) / σ, where μ is the mean flow rate and σ is the standard deviation. For a pressure drop of 10 in., the expected flow rate is .838 m3/min, so

P(Y > .835) = P(Z > (.835 - .838) / .025) = P(Z > -.12) = .4522

P(Y > .840) = P(Z > (.840 - .838) / .025) = P(Z > .08) = .4681

where Z is a standard normal random variable.

e. We need to find the probability that an observation on flow rate when pressure drop is 10 in. will exceed an observation on flow rate made when pressure drop is 11 in. This can be done by subtracting the mean flow rate for each pressure drop from their respective observations, and then finding the probability that the difference is positive. Let Y_10 and Y_11 denote the flow rates for pressure drops of 10 in. and 11 in., respectively. Then the probability of interest is:

P(Y_10 - Y_11 > 0) = P((Y_10 - μ_10) - (Y_11 - μ_11) > -(μ_11 - μ_10))

where μ_10 and μ_11 are the mean flow rates for pressure drops of 10 in. and 11 in., respectively. Since the regression line is linear, we can find the mean flow rate for any given pressure drop x using the equation μ = -.12 + .095x. Therefore,

μ_10 = -.12 + .095(10) = .758 m3/min

μ_11 = -.12 + .095(11) = .853 m3/min

Substituting these values into the probability expression gives:

P(Y_10 - Y_11 > 0) = P((Y_10 - .758) - (Y_11 - .853) > -.095)

We know from part (a) that the standard deviation of the flow rate is σ = .095 m3/min per in. of water. Therefore, the standard deviation of the difference Y_10 - Y_11 is

σ_diff = sqrt(σ^2 + σ^2) = sqrt(2)*σ = .134 m3/min

Using the formula for a standardized normal variable, we have:

P((Y_10 - .758) - (Y_11 - .853) > -.095) = P(Z > (-.095 / .134)) = P(Z > -.71) = .7602

where Z is a standard normal random variable. Therefore, the probability that an observation on flow rate when pressure drop is 10 in. will exceed an observation on flow rate made when pressure drop is 11 in. is .7602.

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The number of batches Nathaniel can make is 16.5 batches.

Nathaniel plans to make use of less than 40 cups of flour and he has already used 6 cups of flour. In order to determine how many batches he can make, we have to determine the number of cups of flour he can use. The cups of flour would be divided by the amount of flour that can be used to make a batch of muffins.

Maximum amount of flour Nathaniel can use = 39 - 6 = 33

Number of batches he can make = 33 / 2 = 16.5 batches

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