Area of Trapezoids and Other Figures quick check

ABCD is a parallelogram and ∠ BID is equal to ∠ BAI, which means that IA is a bisector of ∠BID.

An angle's bisector divides the angle into two identical segments. We must demonstrate that ∠BID equals ∠ BAI in order to demonstrate that IA is a bisector of ∠BID.

Since ABCD is a parallelogram, we have:

AB || CD, which means that ∠ABD is equal to ∠ADC.

BC || AD, which means that ∠ ABC is equal to ∠ DAC.

Adding these equal angles, we have:

∠ABD + ∠ ABC = ∠ ADC + ∠ DAC

∠BDA = ∠CDA

Also, since BM = DN, we have:

∠DBM = ∠ DNM (by vertical angles)

Adding these equal angles, we have:

∠ BDA + ∠ DBM = ∠CDA + ∠ DNM

∠ BID = ∠ BAI

Therefore, we have shown that ∠ BID is equal to ∠BAI, which means that IA is a bisector of ∠BID.

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The area of the base of the triangular prism is 3 inches square.

The figure above is a triangular prism. Therefore, the base of the triangular prism is a triangle.

Therefore, let's find the area of the base.

Hence,

area of the base = 1 / 2 bh

where

Therefore,

b = 5 inches

height = 1.2 inches

Hence,

area of the base = 1 / 2 × 5 × 1.2

area of the base = 6 / 2

Therefore,

area of the base = 3 inches²

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The median of the distribution is 6.

What is the median of the distribution?

The median of a distribution is the value that separates the data into two halves, such that half of the data is above the median and half is below the median. In a symmetrical distribution, the median is the same as the mean. In a skewed or non-symmetrical distribution, the median gives a better representation of the "typical" or "middle" value, as opposed to the mean, which may be influenced by extreme values.

So median means very middle, so mark off one side, then the other, then back and forth until you have 1 left

5                                       X

4                                       X  

3                           X          X

2              X           X    X   X    X

1          X   X    X    X    X   X    X   X

    1    2    3    4    5    6    7    8    9    10

The answer is 6 because it is in the very middle when finding the median

Hence, the median of the distribution is 6.

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In the given right triangle ,

Sin B = b / c .

When trigonometric functions are used in an expression or equation, trigonometric Identities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity is true. Certain trigonometric functions (such as sine, cosine, and tangent) of one or more angles are involved geometrically in these identities.

Now in the given question ,

We know that ,

Sin∅ = Perpendicular / hypotenuse

In the given right triangle ,

Sin B = AC / AB

Sin B = b / c

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The tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.

Tax refers to a compulsory financial charge or some other type of levy imposed upon a taxpayer (an individual or legal entity) by a governmental organization in order to fund various public expenditures. The tax amount is typically determined by the taxpayer's income or wealth and is used to fund various public services such as national defense, infrastructure, social services, and other government operations. Taxes can be direct, such as income tax, or indirect, such as sales tax. They are typically collected by the government through various tax collection agencies, and failing to pay taxes can result in penalties and legal consequences.

From the tax table, for a taxable income of $27,811 (which is greater than $27,450 and less than $27,500), the tax for a head-of-household taxpayer is $3,103.

Therefore, the tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.

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Step-by-step explanation:

The first term is, 3a2 its coefficient is 3 .

The middle term is, -10a its coefficient is -10 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 3 • 7 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -10 .

-21 + -1 = -22

-7 + -3 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -3

3a2 - 7a - 3a - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (3a-7)

Add up the last 2 terms, pulling out common factors :

1 • (3a-7)

Step-5 : Add up the four terms of step 4 :

(a-1) • (3a-7)

Which is the desired factorization

Equation at the end of step

2

:

(3a - 7) • (a - 1) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : 3a-7 = 0

Add 7 to both sides of the equation :

3a = 7

Divide both sides of the equation by 3:

a = 7/3 = 2.333

Solving a Single Variable Equation:

3.3 Solve : a-1 = 0

Add 1 to both sides of the equation :

a = 1

Supplement : Solving Quadratic Equation Directly

Solving 3a2-10a+7 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

4.1 Find the Vertex of y = 3a2-10a+7

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aa2+Ba+C,the a -coordinate of the vertex is given by -B/(2A) . In our case the a coordinate is 1.6667

Plugging into the parabola formula 1.6667 for a we can calculate the y -coordinate :

y = 3.0 * 1.67 * 1.67 - 10.0 * 1.67 + 7.0

4.2 Solving 3a2-10a+7 = 0 by Completing The Square .

Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :

a2-(10/3)a+(7/3) = 0

Subtract 7/3 from both side of the equation :

a2-(10/3)a = -7/3

Now the clever bit: Take the coefficient of a , which is 10/3 , divide by two, giving 5/3 , and finally square it giving 25/9

Add 25/9 to both sides of the equation :

On the right hand side we have :

-7/3 + 25/9 The common denominator of the two fractions is 9 Adding (-21/9)+(25/9) gives 4/9

So adding to both sides we finally get :

a2-(10/3)a+(25/9) = 4/9

Adding 25/9 has completed the left hand side into a perfect square :

a2-(10/3)a+(25/9) =

(a-(5/3)) • (a-(5/3)) =

(a-(5/3))2

Things which are equal to the same thing are also equal to one another. Since

a2-(10/3)a+(25/9) = 4/9 and

a2-(10/3)a+(25/9) = (a-(5/3))2

then, according to the law of transitivity,

(a-(5/3))2 = 4/9

We'll refer to this Equation as Eq. #4.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(a-(5/3))2 is

(a-(5/3))2/2 =

(a-(5/3))1 =

a-(5/3)

Now, applying the Square Root Principle to Eq. #4.2.1 we get:

a-(5/3) = √ 4/9

Add 5/3 to both sides to obtain:

a = 5/3 + √ 4/9

Since a square root has two values, one positive and the other negative

a2 - (10/3)a + (7/3) = 0

has two solutions:

a = 5/3 + √ 4/9

or

a = 5/3 - √ 4/9

Note that √ 4/9 can be written as

√ 4 / √ 9 which is 2 / 3

HOPE IT HELPS.

PLEASE MARKE AS BRAINLEST.

NOTE:IF THIS IS NOT WHAT YOU WANT,INFORM ME AND I WILL GOVE BETTER ANSWERS

The two amount of numbers are 11 and 135. 11 is a multiple of 11 and 135 is a multiple of 17. The sum of the two numbers is 146.

Step 1: One of the numbers is a multiple of 11

Let the number be 11x, where x is an integer

Step 2: The total of the two numbers is 146

Therefore, 11x + 17y = 146, where y is an integer

Step 3: Solve the equation

11x + 17y = 146

11x = 146 - 17y

x = (146 - 17y) / 11

Step 4: Find the two numbers

x = (146 - 17y) / 11

For y = 1, x = 11

Therefore, the two numbers are 11 and 17.

The two numbers that add up to 146 are 11 and 135. 11 is a multiple of 11, which means it is divisible by 11 without any remainder. 135 is a multiple of 17, which means it is divisible by 17 without any remainder. When these two numbers are added together, the sum is 146. This means that 11 and 135 are the two numbers that add up to 146. 11 is a multiple of 11 and 135 is a multiple of 17, which explains why the sum of the two numbers is 146. The two numbers together can be used to represent a variety of different mathematical equations, such as the addition of two integers or the multiplication of two fractions. Knowing the two numbers that add up to 146 can be useful in a variety of different scenarios, such as solving math problems or accounting for the total of two items.

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Answer:

(x + 6)(x + 4)

Step-by-step explanation:

x² + 10x + 24

= x²+ 6x + 4x + 24=0

= x(x + 6)+4(x + 6)

= (x + 6)(x + 4)

Answer:

(x + 6)(x +4)

Step-by-step explanation:

x² + 10x + 24

    Sum = 10

Product = 24

Factors = 6 , 4        

{When we multiply 6 and 4, we get 24  & when we add 6 and 4, we get 10}

x² + 10x + 24 = x² + 6x + 4x + 24    {Rewrite the middle term using the factors}

                    = x(x + 6) + 4 (x + 6)

{Group the first two terms and third & fourth term together. Then take out the common factors}

                   = (x + 6)(x + 4)

No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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Step-by-step explanation:

The circle as a whole is one.

So to find the shaded area find a common denominators for both first

1/4 = 7/28

2/7= 8/28

Add the two together

7/28 + 8/28 = 15/28

This is the area taken up the the white fractions areas

Now because the circle is one

28/28 - 15/28 = 13/28

So the area of the blue is

13/28

Hope this helped :)

We can write the following two linear equations to represent the distance each animal can travel in the race:

d1 = r1 * t

d2 = r2 * t

Let's call the distance that the first animal can travel in a certain amount of time "d1" and the distance that the second animal can travel in that same amount of time "d2". We can write the following two linear equations to represent the distance each animal can travel in the race:

d1 = r1 * t

d2 = r2 * t

where "r1" is the rate of the first animal, "r2" is the rate of the second animal, and "t" is the time that the race lasts. These two equations show how the distance each animal can travel is proportional to their rate and the time that the race lasts.

In this model, the variables are defined as follows:

d1 = distance traveled by the first animal

d2 = distance traveled by the second animal

r1 = rate of the first animal

r2 = rate of the second animal

t = time the race lasts

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The correct options are:

Oy=-x-2

2x + 5y = -10

2x - 5y = -10

What is the slope-intercept?

The slope-intercept form of a line is a linear equation that is written in the form of b

The equation of the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5,-4) can be found using the point-slope form of a line, where the slope of the line perpendicular to the original line will have a negative reciprocal slope.

The slope-intercept form of the original line is y = (5/2)x + b, where b can be found by substituting the point (5,-4) into the equation:

-4 = (5/2)(5) + b

-4 = 12.5 + b

-16.5 = b

So, the slope-intercept form of the original line is y = (5/2)x - 16.5. The slope of this line is 5/2. The negative reciprocal of this slope is -2/5.

Using the point-slope form, the equation of the line perpendicular to the original line and passing through the point (5,-4) is:

y - (-4) = -2/5 (x - 5)

y + 4 = -2/5 x + 10

Multiplying both sides by 5, we get:

5y + 20 = -2x + 50

Adding 2x to both sides, we get:

5y + 2x + 20 = 50

So, the equation of the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5,-4) is 5y + 2x + 20 = 50.

Thus, the correct options are:

Oy=-x-2

2x + 5y = -10

2x - 5y = -10

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Answer:

⅘

Step-by-step explanation:

We start by subtracting 11 from both sides of the equation:

√5x + 11 - 11 = 9 - 11

√5x = -2

Next, we square both sides of the equation:

(√5x)² = (-2)²

5x = 4

Finally, we divide both sides by 5:

x = 4/5.

Answer:

[tex]-\frac{3}{2} , -\frac{4}{9} , \frac{2}{11}, 0.7[/tex]

Step-by-step explanation:

Negative numbers are obviously smaller than positive numbers, hence, we have -4/9 and -3/2.

-3/2 is obviously have a smaller value than -4/9 as the mixed number for it is -1  1/2.    [In negative numbers, the larger the number, the smaller the value it holds.]

[tex]0.7= \frac{7}{10}[/tex]

We can turn the denominator of 2/11 and 7/10 to the same number, 110.

[tex]\frac{2}{11} = \frac{20}{110}[/tex]

[tex]\frac{7}{10} = \frac{77}{110}[/tex]

Hence, we know that 77 is larger than 20, so, the largest number is 0.7.

Answer:

Step-by-step explanation:

13

The coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Additionally, if we are aware of the ratio that the line segment connecting two places has produced, we can locate the point of division. The two can be accomplished using a section formula from coordinate geometry.

The coordinates of the points on the line are:

M = (-3, -3)

N = (4, 2)

m= 3

n = 2

Using the section formula we have:

M(x, y) = (mx2 + nx1 / m+n , my2 + ny1 /m + n)

M(x, y) = ((3)(4) + (2)(-3)) / (3 + 2) , (3)(2) + (2)(-3) / (3 + 2))

M (x, y) = (12 - 6 / 5 , 6. -6 / 5)

M (x, y) = (6/ 5 , 0)

Hence, the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).

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Answer:

Step-by-step explanation:

0.267

Answer:

D 588 miles

Step-by-step explanation:

We know

Leo is training for a marathon later this summer. He has run 42 miles over the last 3 days.

42 divided by 3 = 14 miles per day

So, he runs at a rate of 14 miles per day.

If he continues to run at the same rate, how many miles will he run over the next 6 weeks?

1 week = 7 days

1 week = 14 x 7 = 98 miles

6 weeks = 98 x 6 = 588 miles

So, he will run 588 miles over the next 6 weeks.

A. In this investigation, the mechanical engineer employed a 2-factor, 2-level factorial design experiment.

B. Factorial design assumptions: The parent population should have a regularly distributed distribution, The mistakes should be of the homoscedastic variety, Multicollinearity should not be present and The data should be of the continuous variables.

A. The mechanical engineer used a 2-factor, 2-level factorial design experiment in this study.

B. The population model that the engineer is using is the relationship between the thrust force (response variable) and the two factors, drill speed (A) and feed rate (B), that he suspects are the most important. The model can be expressed as:

Y = β0 + β1A + β2B + β12AB + ε

where Y is the thrust force, A and B are the two factors, AB is the interaction between the two factors, β0 is the intercept, β1, and β2 are the main effect coefficients for A and B, β12 is the interaction effect coefficient, and ε is the error term.

The set of assumptions for this experiment includes:

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The question is -

A mechanical engineer is studying the thrust force developed by a drill press. He suspects that the drilling speed and the feed rate of the material are the most important factors. He selects four-speed rates and uses a high and low drill speed chosen to represent the extreme operating conditions. He obtains the following results.

Feed rate (B)

Drill Speed (A) 0.015 0.030 0.045 0.060

125                          2.70   2.45   2.60 2.75

                                2.78          2.49   2.72       2.86

200                          2.83   2.85   2.86 2.94

                                2.86   2.80   2.87 2.88

A. What kind of design of experiment he used in this study?

B. Write down the population model and set of assumptions.

Answer: Let's use "x" to represent the number of electoral votes in Florida. Then, we can write the equation for North Carolina's number of electoral votes as "x - 12".

The equation can then be written as:

x + (x - 12) = total number of electoral votes

Solving for x, we get:

2x - 12 = total number of electoral votes

2x =total number of electoral votes + 12

2x = total number of electoral votes + 12

x = (total number of electoral votes + 12)/2

So, the number of electoral votes for Florida is (total number of electoral votes + 12)/2.

Note: The total number of electoral votes for both states needs to be known in order to solve for the number of electoral votes in Florida.

Step-by-step explanation:

The required radical form of the given expression [tex](x^2)^{4/3}[/tex] is ∛x⁸.

Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.

To rewrite [tex](x^2)^{4/3}[/tex]in radical form, you can simplify it by dividing the fractional part by the same number which will turn the fraction into a whole number. In this case, that number is 3.

So, you can simplify [tex](x^2)^{4/3}[/tex] as follows:

[tex](x^2)^{4/3}[/tex]

[tex]x^{2\times4/3}[/tex]

[tex]x^{8/3}[/tex]

[tex](x^8)^{1/3}[/tex]

∛x⁸

This is the radical form of [tex](x^2)^{4/3}[/tex].

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The distance between the golf balls is determined to be 14 feet.

Let's call the distance between the two golf balls "d".

Using the law of cosines, we can find the value of d by using the angles and the two distances to the hole:

d² = 8² + 13² - 2 * 8 * 13 * cos(64)

d² = 64 + 169 - 104 * cos(64)

d² = 233 - 104 * cos(64)

Next, we'll use a calculator to find the value of cos(64):

cos(64) = 0.37

So,

d² = 233 - 104 * 0.37 = 233 - 38.48

d² = 194.52

Finally, we'll take the square root of both sides to find the value of d:

d = √(194.52) = 14.0

So the distance between the golf balls is 14 feet.

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Answer:

a=4

b=18

c=30

d=46

e=60

Step-by-step explanation:

you first write the 4 and then add 14 i.e the next number on the frequency row. then you add the next number to the answer you get and so on

Answer:

0.000093

Step-by-step explanation:

0.000093.

To convert

9.3

x

10

−

5

to a standard notation we look at the exponent on the 10. Since this is a 5 we know we'll be moving the decimal place 5 spots. Since the number it -5 this means we move the decimal 5 places tot he left, filing the empty spaces in with zeros until we get to 0.000093

The appropriate test to see if neck size and number of teeth have a linear relationship in 18 randomly selected puppies is the t-test for slope of regression line.

A regression line is a line that best fits the data by minimizing the sum of the squared differences between the observed and predicted values. A t-test for slope of regression line tests the null hypothesis that the slope of the regression line is equal to zero, which would indicate that there is no linear relationship between the variables.

In this case, neck size and number of teeth are two continuous variables and we want to test if there is a linear relationship between them. A t-test for slope of regression line would provide information on the significance of the relationship and the direction of the relationship (positive or negative).

It is important to note that the test conditions such as independence, normality, and homoscedasticity must be met before conducting the test. If these conditions are not met, the results of the test may be biased and should be interpreted with caution.

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Complete Question: Comparing the neck circumference (in inches) and tooth count of 18 puppies chosen at random. Which statistical analysis should be performed to determine whether there is a linear relationship between neck size and tooth count? Assume that every test requirement is satisfied.

a. Z-test with two samples

b. T-test with two samples

c. Test of two proportions

d. T-Test for Regression Line Slope

e. Z-test for one proportion

The air conditioner is being sold for $673.20. The discount price is lower than the initial price of $680 because this is less. The air conditioner is therefore being sold for less than what it originally cost.

A singular tax known as GST is applied to the supply of products and services from the customer to the manufacturer. GST is basically a tax only on productivity improvement at each stage because credits of supply taxes paid at each step will be accessible in the following stage of value addition.

The first step is to calculate the GST that is added to the original price of the air conditioner:

GST = 10% of $680 = 0.1 x $680 = $68

So the total cost of the air conditioner including GST is:

Total cost = $680 + $68 = $748

Now, the air conditioner is sold at a 10% discount. To find the sale price, we need to subtract 10% of the total cost from the total cost:

Sale price = Total cost - 10% of Total cost

= $748 - 0.1 x $748

= $748 - $74.80

= $673.20

The sale price of the air conditioner is $673.20.

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The solution is, x= 50  &  y= 19.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

1.5x−y3=18

2x−3y=43

solving the equations in graph , we get,

x= 50

y= 19

Hence, The solution is, x= 50  &  y= 19.

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The cost of broccoli per ounce is $0.06.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

Given  2 pound bag of broccoli costs $1.92,

to find the cost per ounce

we know,

1 pound = 16 ounces

2 pound = 2*16 ounces

2 pound = 32 ounces

cost of 32 ounces = $1.92

cost per ounce = $1.92/32

cost per ounce = $0.06 per ounce

Hence per ounce, the cost is $0.06.

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The Price per ounce is $0.06.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A 2 pound bag of broccoli costs $1.92.

As, 1 pound = 16 ounce

So, the cost of 32 ounce of broccoli is 1.92.

Then, the price per ounce

= 1.92/ 32

= 0.06

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