Everybody's blood pressure varies over the course of the day. In a certain individual the resting diastolic blood pressure at time t is given by
B(t) = 90 + 9 sin(t/12),
where t is measured in hours since midnight and B(t) in mmHg (millimeters of mercury). Find this person's diastolic blood pressure at the following times. (Round your answers to one decimal place.)

The percentage error of the student's estimated mass is 2.15%.

The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.

The estimated mass of the student = 82.0 kg

The actual mass of the student = 83.8 kg

Absolute error = Actual Value - Estimated Value

= 1.8 kg (83.8 - 82.0)

Percentage error = Actual Value - Estimated Value /Actual Value x 100

= 2.15% (1.8/83.8 x 100)

Thus, we can conclude that the student's estimate contains a 2.15% error.

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Answer:

A. Image shows the two circles

B. he ordered point(2, 0) will go to the ordered pair [tex]\mbox{\large \left(\boxed{1}, \boxed{0}\right)}[/tex]'

C. The small circle is a [tex]\boxed{\textsf{copy}}[/tex] of the larger one using the origin as a center and a scale factor of [tex]\boxed{\dfrac{1}{2}}[/tex]

*** I am guessing what word goes into the first box. It should be something that is close to the word copy. The words replica or duplicate could be other choices If you are unable to come up with a choice, post the answer choices as a comment and I can be more specific ***

Step-by-step explanation:

A. Image shows the two circles

B. The larger circle x² + y² = 4 is dilated by a factor of 1/2

The ordered point(2, 0) will go to the ordered pair (2/2, 0/2) = (1,0)

C. What do you notice about the two circles?
They are concentric circles with origin(0, 0) as the center

The small circle is a copy of the larger one using the origin as a center and a scale factor of 1/2

* I do not know what your answer choices are. I have just filled in a term which indicates the relationship.

Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:

D = R * T = 20 km/h * 1.6 h = 32 km

Therefore, the bicyclist traveled a total distance of 32 kilometers.

Step-by-step explanation:

The area of the triangle DEF shown in the coordinate plane is 6 units².

Area of a triangle is defined as the total region bounded by the shape of the triangle.

The formula to calculate the area of a triangle if the base length and height is given is,

Area = [tex]\frac{1}{2}[/tex] × base × height

Given is a triangle in a coordinate plane.

Base of the triangle is the side DE.

Length of DE is the length of the points (1, 1) t0 (1, 4), which is 3 units apart.

Length of base = 3 units

Height of the triangle is the perpendicular length from the vertex opposite base to the base.

That is, the distance from F(-3, 3) to (1, 3), which are 4 units apart.

Height = 4 units.

Area of triangle DEF = [tex]\frac{1}{2}[/tex] × 3 × 4

                                  = 6 units²

Hence the area of the triangle is 6 units².

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The fractional equivalent of the repeating decimal is 15/99

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

n = 0.1515...-------(1)

multiply n by 100 =10²

The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.

100n=15.15......--------(2)

Subtract (1) from (2)

100n=15.15...

n = 0.1515....

___________

99n=15

=> n=15/99

The fractional equivalent of the repeating decimal is 15/99

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Answer:

Step-by-step explanation: To calculate the total amount of money Jamal made in six months, we need to multiply the number of paintings sold by the price of each painting, and then add the results for the large and small paintings:

7 large paintings * $45.99/large painting = $321.93

4 small paintings * $28.99/small painting = $115.96

Total amount made = $321.93 + $115.96 = $437.89

Therefore, Jamal made $437.89 in six months by selling seven large paintings and four small ones.

Inputting the values provided yields:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

A + B = 5 - sqrt (34)after simplifying and solving for a + b. 

As a result, we have established that a + b=  0.27.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.

Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:

[tex]CH^2 = CB^2 - BH^2[/tex]

Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:

[tex]CH^2 = AC^2 - x^2[/tex]

We can also use the given values of x and h to find AC:

[tex]AC^2 = x^2 + h^2[/tex]

Substituting this into the equation for [tex]CH^2[/tex], we get:

[tex]CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2[/tex]

Taking the square root of both sides, we get:

CH = h = 4

Therefore, we have found that CH = 4.

Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:

Area = (1/2) * CH * AB

Area = (1/2) * AC * BC

Setting these two expressions equal to each other and substituting the given values, we get:

(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5

Simplifying and solving for y, we get:

2x + 8 = 15 - 5/2 * y

2x + 13/2 = 5/2 * y

y = 2x + 13/5

Using the given value of x, we can find y:

y = 2(3) + 13/5 = 6.6

Therefore, we have found that y + h = 6.6 + 4 = 10.6.

Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:

[tex]AC^2 + BC^2 = AB^2[/tex]

Substituting the given values, we get:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

Simplifying and solving for a + b, we get:

a + b = 5 - sqrt(34)

Therefore, we have found that a + b ≈ 0.27.

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Answer:

1. volume= 135

2. prism volume in cubic feet is: 21

3. surface area is 294 ft^2

4. surface area is 430 ft^2

We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.

According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.

As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.

To figure this out, we can use the formula below:

Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.

Estimated number of influenza patients = 0.04 times 25

Expected number of influenza patients is one.

Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.

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Answer:

See below

Step-by-step explanation:

The linear function is to be expressed in slope-intercept form:

y = mx + c

where:              

                           m = slope

                               = [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

           Select a pair of x and y coordinates of two points along this graph

e.g (0,1) and (5,0):

                          m = [tex]\frac{(0 - 1)Percent InDecimal}{(5 - 0) hour}[/tex]

                              = [tex]\frac{-1}{5}[/tex]

       ∴ slope = [tex]-\frac{1}{5}[/tex] = [tex]-0.2\frac{PercentInDecimal}{hour}[/tex]

  which means 0.2 × 100%= 20%

∴The slope indicates that the power decreases by 20% per hour

                          c = y-intercept:

   It is the y-value AT which the graph cuts or meets the y-axis. Its corresponding x-coordinate is 0. The y-intercept can be either read directly from the graph or calculated mathematically

       ∴y-intercept = 1

In this scenario, the y-intercept indicates the initial value or the value present in the beginning.
which means 1.0 × 100% = 100%
∴The y-intercept indicates that the battery is at 100% when you turn on the laptop.

∴Linear function relating y to x:

Substituting the values of m and c into the above stated equation:

     [tex]y = -\frac{1}{5}x + 1[/tex]

The x-intercept is the x-value at which the graph crosses or intersects the x-axis. It’s corresponding y-coordinate is zero.

     x-intercept = 5

In this scenario, the x-intercept indicates the point at which the final value is reached or achieved.

∴ The x-intercept indicates that the battery lasts 5 hours.

The battery power is at 75% = [tex]\frac{75}{100}[/tex] = 0.75 (expressed in decimal form. This means y = 0.75, which is to be substituted into the above derived linear function to solve for the corresponding value of x:

[tex]0.75 = -\frac{1}{5}(x) + 1[/tex]

Rearrange the equation to isolate x and make it the subject of the equation:

[tex]\frac{1}{5}x = 1 - 0.75[/tex]

[tex]\frac{1}{5}x = 0.25[/tex]

Cross-multiplication is applied:

[tex](1)(x) = (5)(0.25)[/tex]

x = 1.25 hours

∴The battery power is at 75% after 1.25 hours

The measures in the parallelogram are given as follows:

In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.

The angles of 12x + 3 and 7x - 13 are consecutive, meaning that the value of x is given as follows:

12x + 3 + 7x - 13 = 180

19x = 190

x = 190/19

x = 10.

Then the angle measures are given as follows:

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Answer:

Step-by-step explanation:

You want to know how long Hoang and Bill have worked at the hospital if Hoang has worked there 5 years longer, and 5 years ago that was twice as long as her friend Bill.

Hoang's longevity will be twice Bills when Bill's is equal to the difference. That is, 5 years ago, Bill had been there 5 years and Hoang had been there 10 years.

Now, each has been there 5 years longer, so ...

If h represents Hoang's time at the hospital, 5 years ago it was (h-5). Currently, Bill's time at the hospital is (h-5), and 5 years ago it was (h-10). The relation between the times 5 years ago is ...

  (h -5) = 2(h -10)

  15 = h . . . . . . . . . . add 20-h to both sides

  h-5 = 15 -5 = 10 . . . . Bill's time at the hospital

Hoang and Bill have been at the hospital 15 years and 10 years, respectively.

Answer:

The slope of the line that passes through (7,-4) and (11 -4) is 0, since it is a horizontal line.

To find the slope when given two points, use the formula:

y2-y1/x2-x1=m(-4- -4)/(11-7)=0/4=0

So the slope is 0 because 0 is the numerator. If 0 is the denominator, the slope will be undefined.

Hope this helped!

Answer:

Account B will have the most after 10 years. It will be worth $21760

Step-by-step explanation:

Hope it helps! =D

The solution of the equations are

x^2 - 36 = 0

x = 6, -6

The equation x2 + 12x + 36 = 0

x = -6, -6

The equation x^2 - 36 = 0 is solved as follows

x^2 - 36 = 0

x = ±√36

x = 6 or -6

The quadratic equation x^2 + 12x + 36 = 0 is solved as follows

x^2 + 6x + 6x + 36 = 0

x(x + 6) + 6(x + 6) = 0

(x + 6)(x + 6) = 0

hence

x = -6 and -6

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Answer:

Step-by-step explanation:

Here is a more detailed explanation:

We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:

x   f(x)   g(x)

1    3      5

4    9      20

To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.

For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

So the equation of f(x) is y = 2x + 1.

Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x

So the equation of g(x) is y = 5x.

To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:

2x + 1 = 5x

3x = 1

x = 1/3

Substituting this value of x back into either equation, we can find the corresponding value of y:

y = 2(1/3) + 1 = 7/3

So the point of intersection is (1/3, 7/3).

Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.

The area of the triangular sail in the sail model is 42 square inches.

The area of a triangular sail is given by the formula:

Area = (1/2)bh

where b is the length of the base and h is the height.

Substituting b = 12 inches and h = 7 inches, we get:

Area = (1/2)(12 inches)(7 inches) = 42 square inches

Therefore, the area of the triangular sail in the sail model is 42 square inches.

The area of a triangle is given by the formula:

Area = (1/2) * base * height

where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.

To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.

Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.

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Answer:

24

Step-by-step explanation:

N/A

Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

Answer:

the perimeter of the rectangle is 26 meters.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:

width = area / length = 36 / 9 = 4 meters

Now we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

Substituting the given values, we get:

perimeter = 2(9 + 4) = 2(13) = 26 meters

Therefore, the perimeter of the rectangle is 26 meters.

Answer:

2026 to maximize the present value function.

Step-by-step explanation:

To find the year in which the timber should be harvested to maximize the present value function, we need to find the time t that maximizes the present value function A(t). We can begin by finding A(t):

A(t) = V(t)e^(-0.09t)

A(t) = 140,000e^(0.72√t) * e^(-0.09t)

A(t) = 140,000e^(0.72√t - 0.09t)

To maximize A(t), we need to find the critical points of A(t). We can do this by taking the derivative of A(t) and setting it equal to zero:

A'(t) = 140,000(0.36/√t - 0.09)e^(0.72√t - 0.09t) = 0

Simplifying this equation, we get:

0.36/√t - 0.09 = 0

0.36/√t = 0.09

√t = 4

t = 16

Therefore, the critical point of A(t) occurs at t = 16 years.

We can check that this is a maximum by taking the second derivative of A(t) and evaluating it at t = 16:

A''(t) = 140,000(-0.648/t^3 - 0.243/√t + 0.081)e^(0.72√t - 0.09t)

A''(16) = 140,000(-0.648/16^3 - 0.243/4√16 + 0.081)e^(0.72√16 - 0.09(16))

A''(16) ≈ -4,980.4

Since the second derivative is negative, we can conclude that t = 16 years corresponds to a maximum for the present value function A(t).

Therefore, the timber should be harvested in the year 2010 + 16 = 2026 to maximize the present value function.

Answer:

Step-by-step explanation:

whatb you need

Answer:

I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.

Step-by-step explanation:

The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.

Answer:

According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.

Step-by-step explanation:

The equation given is:

y = 20x + 0

where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:

y = 20(20) + 0

y = 400

Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.

The least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:

Length = 24 feet + 6 inches = 24.5 feet

Width = 4 feet + 6 inches = 4.5 feet

Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)

The volume of the sidewalk is then:

Volume = Length x Width x Depth

= 24.5 feet x 4.5 feet x 1/3 feet

= 3.25 cubic feet

Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:

Number of bags = Volume of sidewalk / Volume per bag

= 3.25 cubic feet / 0.6 cubic feet per bag

= 5.42 bags

Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

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Answer:

The width of the patio is 15 feet

Step-by-step explanation:

We can start by using the formula for the area of a rectangle:

Area = length x width

In this case, we know that the area of the patio is given by:

16x^2 + 20x square feet

And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:

16x^2 + 20x = (x + 5) x width

Simplifying the right-hand side by multiplying x + 5 by width, we get:

16x^2 + 20x = width x^2 + 5x

To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:

width x^2 - 16x^2 + 20x - 5x = 0

Simplifying the left-hand side by combining like terms, we get:

width x^2 - 16x^2 + 15x = 0

Factoring out x, we get:

x (width x - 16x + 15) = 0

Now we can solve for the width by setting each factor equal to zero and solving for x:

x = 0 or width x - 16x + 15 = 0

Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:

width x - 16x + 15 = 0

We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:

(width x - 1)(x - 15) = 0

Setting each factor equal to zero and solving for x, we get:

width x - 1 = 0 or x - 15 = 0

width x = 1 or x = 15

Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:

width x = 1, x = 15, so we choose x = 15

width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet

Therefore, the width of the patio is 15 feet.

a. The angle generated by P in time t is pi radians.

b. The distance traveled by P along the circle in time t is 16pi cm.

c. The linear speed of P is 2pi cm/sec.

What is angular speed ?

Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second and is denoted by the symbol "ω" (omega).

Angular speed is calculated as the change in angle (measured in radians) divided by the time it takes to make that change. In other words, it is the rate at which the angle is changing over time.

Angular speed is an important concept in physics and engineering, as it is used to describe the motion of rotating objects such as wheels, gears, and turbines. It is also used to calculate other important parameters such as linear speed, centripetal force, and torque.

The problem involves finding the properties of a point P that is rotating around a circle with a given radius r and angular speed omega. The problem provides the values of r, omega, and t and asks to find the angle generated by P in time t, the distance traveled by P along the circle in time t, and the linear speed of P.

(a) To find the angle generated by P in time t, we use the formula for angular displacement:

theta = omega * t

Here, omega is given as pi/8 radians per second and t is given as 8 seconds. We substitute these values to get:

theta = (pi/8) * 8 = pi radians

Therefore, the angle generated by P in time t is pi radians.

(b) To find the distance traveled by P along the circle in time t, we use the formula for arc length:

s = r * theta

Here, r is given as 16 cm and theta is calculated in part (a) as pi radians. We substitute these values to get:

s = 16 * pi = 16pi cm

Therefore, the distance traveled by P along the circle in time t is 16pi cm.

(c) To find the linear speed of P, we use the formula for tangential velocity:

v = r * omega

Here, r is given as 16 cm and omega is given as pi/8 radians per second. We substitute these values to get:

v = 16 * (pi/8) = 2pi cm/sec

Therefore, the linear speed of P is 2pi cm/sec.

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.

The values are Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and range  IQR ≈ 0.5250 months.

The IQR for the average first-time walking age for groups of 33 people can be found as follows:

The standard deviation of the sample mean is given by:

σM = σ/√n = 2.2/√33 ≈ 0.3839

Using the standard normal distribution, the z-scores for the first and third quartiles are:

zQ1 = invNorm(0.25) ≈ -0.6745

zQ3 = invNorm(0.75) ≈ 0.6745

The corresponding sample means can be found using:

M = μ ± z(σM)

Where μ = 12, the population mean.

M1 = 12 - 0.6745(0.3839) ≈ 11.7375

M3 = 12 + 0.6745(0.3839) ≈ 12.2625

Therefore, the first quartile Q1 is approximately equal to 11.7375 months and the third quartile Q3 is approximately equal to 12.2625 months.

The IQR is given by:

IQR = Q3 - Q1 = 12.2625 - 11.7375 ≈ 0.5250 months.

Rounding to 4 decimal places gives Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and IQR ≈ 0.5250 months.

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The maximum possible value of the result is 8.

How to solve Linear Equations?

We are given the linear equation;

4x - x = 0

From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;

The first step to solving the equation is to; C. add x to both sides

The second step  to solving the equation is to; C. cube both sides

Solving the equation for x initially yields; C. two possible values

Checking the solutions shows that; D. none are valid solutions

4x - x + x = 0 + x

4x = x

Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;

(4x)³ = x³

4³x = x³

64x = x³

Divide both sides by x to get;

x² = 64

Take square root of both sides to get;

x = ±√64

x = ±8

Hence, The maximum possible value of the result is 8.

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Answer:

Step-by-step explanation:

rational

Sara need 9/4 ounces of chopped nuts

Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces

The recipe feeds 6 people

The number of ounces of chopped nuts that Sara needs can be calculated as follows

13 1/2

= 27/2 ÷ 6

= 27/2 × 1/6

= 27/12

= 9/4

Hence Sara needs 9/4 ounces of chopped nuts for one serving

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