Help pls!
Simplify arctan 5 + arctan 6
(round to the nearest degree).

a. 21°
b. 159°
c. 201°

The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.

The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.

First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.

Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.

Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.

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Graph of g(x) will be wider than f(x) is false.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The graph of f(x)=x² was transformed to create g(x)=2/3x².

The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.

This means that the graph of g(x) will be narrower than the graph of f(x), not wider.

Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).

Hence,  graph of g(x) will be wider than f(x) is false.

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The value of the variable x for the similar triangles is equal to 3

The triangles PTQ and STR are similar, this implies that the length ST of the smaller triangle is similar to the length PT of the larger triangle

and the length RT of the smaller triangle is similar to the length QT of the larger triangle

so;

5/(2x + 9) = 7/(3x + 12)

5(3x + 12) = 7(2x + 9) {cross multiplication}

15x + 60 = 14x + 63

15x - 14x = 63 - 60 {collect like terms}

x = 3.

Therefore, the value of the variable x for the similar triangles is equal to 3

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a) The confidence interval of a 95% confidence interval for the proportion of returns at the store in Maniou province is exactly between 0.3718 and 0.4282

b) Do not reject the null hypothesis. The correct answer is option C.

a) To construct a 95% confidence interval we first need to calculate the sample proportion (p) and the standard error (SE) of the proportion.

p = 12/80 = 0.15
SE = sqrt[(p*(1-p))/n] = sqrt[(0.15*0.85)/80] = 0.0347

Using the Z-score for a 95% confidence interval (1.96), we can calculate the lower and upper bounds of the interval:

Lower bound = p - 1.96*SE = 0.15 - 1.96*0.0347 = 0.083
Upper bound = p + 1.96*SE = 0.15 + 1.96*0.0347 = 0.217

Therefore, the 95% confidence interval for the proportion of returns at the store in Maniou province is between 0.083 and 0.217.

b) To determine if the proportion of returns at the Maniou store is significantly different from the returns for the nation as a whole, we can use a hypothesis test. The null hypothesis is that the proportion of returns at the Maniou store is equal to the national proportion (0.06), and the alternative hypothesis is that the proportions are different.

Using the sample proportion (p) and standard error (SE) calculated above, we can calculate the Z-score:

Z = (p - 0.06)/SE = (0.15 - 0.06)/0.0347 = 2.59

Using a Z-table, we can find the p-value for this Z-score. The p-value is 0.0096, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that the proportion of returns at the Maniou store is significantly different from the returns for the nation as a whole.

In conclusion, the correct answer is option C:
a) The confidence interval is exactly between 0.083 and 0.217
b) Reject the null hypothesis

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Answer:

Yes, the ratios 3:6 and 2:4 are equivalent because they represent the same proportion. To confirm, we can simplify both ratios to their simplest form:

3:6 can be simplified by dividing both terms by 3: 3/3 : 6/3 -> 1:2

2:4 can be simplified by dividing both terms by 2: 2/2 : 4/2 -> 1:2

Since both ratios simplify to the same ratio, 1:2, they are equivalent.

Answer: yes !!

Step-by-step explanation: 3:6 and 2:4 are equivalent b/c of their common factors.

Answer: g(g(1)) = 4 and g(g(g(1))) = 5 1/2

Step-by-step explanation:

We will first find g(1). To do so, we plug 1 in for x.

g(1) = (1) + 3/2 = 5/2 = 2 1/2

To find g(g(1)) we will plug in 5/2 for x.

g(g(1)) = (5/2) + 3/2 = 8/2 = 4

To find g(g(g(1))) we will plug in 4 for x.

g(g(g(1))) = (4) + 3/2 = 11/2 = 5 1/2

Hope this helps!

We have saved approximately 15% of the total cost.

What is the process to calculate the percentage saved in a sale?

When items are on sale, they are usually offered at a discounted price. The percentage saved is a measure of the amount that a buyer has saved on the original price of the item. The process to calculate the percentage saved in a sale involves determining the original price, the discounted price, and then using a formula to find the percentage saved.

The formula for the percentage saved is:

Percentage saved = (Amount saved / Original price) x 100%

Calculation of  the total amount saved and the percentage saved :

For the paperbacks, the original price is $9 each and we bought four of them, so the total original price is:

$9/book × 4 books = $36

With a 10% discount, the discounted price of each paperback is:

$9/book × 0.10 = $0.90 discount

$9/book - $0.90 discount = $8.10 discounted price

So, the total discounted price for the four paperbacks is:

$8.10/book × 4 books = $32.40

Therefore, we saved:

$36 - $32.40 = $3.60

For the hardbacks, the original price is $20 each and we bought two of them, so the total original price is:

$20/book × 2 books = $40

With a 20% discount, the discounted price of each hardback is:

$20/book × 0.20 = $4 discount

$20/book - $4 discount = $16 discounted price

So, the total discounted price for the two hardbacks is:

$16/book × 2 books = $32

Therefore, we saved:

$40 - $32 = $8

The total original price of all the books is:

$36 + $40 = $76

The total discounted price of all the books is:

$32.40 + $32 = $64.40

Therefore, we saved:

$76 - $64.40 = $11.60

Plugging in the values , we get:

percentage saved = ($11.60 / $76) × 100%

percentage saved ≈ 15%

Therefore, we have saved approximately 15% of the total cost.

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The given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.

As per the given data:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

Simplifying to evaluate the expression:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

[tex]= 2x+6 = 5(4x -3)\\= 2x + 6 = 20x - 15\\= 18x = 21\\= x = \frac{21}{18}\\\\= x = \frac76[/tex]

Hence, the given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

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The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.

The given expression is:

[tex]y^6 * y^3[/tex]

We can simplify this expression by adding the exponents of y:

[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]

Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

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Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.

Let's use algebra to solve the problem.

If 19,700 employees represent 22.9% of the company's total number of employees, we can write:

0.229 = 19,700 / Total number of employees

To find the total number of employees, we can isolate the variable on one side of the equation:

Total number of employees = 19,700 / 0.229

Using a calculator, we get:

Total number of employees = 86,026.2

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

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The polygons are classified as :-

1.CONVEX

2.CONCAVE

3.CONCAVE

4.REGULAR

5.CONCAVE

6.IRREGULAR

A polygon is a geometrical figure, with finite sides and angles, they can be regular and irregular.

Regular Polygon

A regular polygon is that which has all its sides and angles equal, for example an equilateral triangle and a square.

Irregular Polygon

A irregular polygon is that which has all its sides and angles unequal,

For example, a scalene triangle, a rectangle, a kite, etc.

Convex Polygon

A Convex polygon is that which has all its angles less than 180 degrees,

Concave Polygon

A Concave polygon is that which has its angles greater than 180 degrees,

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The complete question attached

The probability when analyst performed a two-tailed test for the given one tailed probability is equal to 0.2.

Mean = 500

Standard deviation = 100

Number of applicants in art college = 100

Mean of the art college = 510

t-statistic = 1.70

One tailed probability = 0.4

Analyst performed a two-tailed test,

⇒ Probability value = 2(one-tailed probability value)

In a two-tailed test, deviations from the mean in both directions.

Probability of observing values are both higher and lower than the mean.

⇒ Probability for two-tailed test = Probability value for one-tailed test / 2

⇒Probability for two-tailed test = 0.4 / 2

⇒Probability for two-tailed test = 0.2

Therefore, the probability for a two-tailed test is equal to 0.2.

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Step-by-step explanation:

for % questions always find 100% and/or 1%.

everything else can be easily calculated out of these 2.

the original price of $210 = 100%, as we want to know how many % the new price is different from that.

100% = $210

1% = 100%/100 = 210/100 = $2.10

the new price is $300.

the difference is 300 - 210 = $90

how many % are $90 compared to the original price ?

well, as many as the times 2.1 (1%) fits into 90 :

90/2.1 = 42.85714286...%

that increase from $210 to $300 was 42.85714286...%.

an additional $50 baggage fee ?

we have to add this to the $300 and get $350 as new price.

that difference is now 350 - 210 = $140.

how many % are $140 compared to the original price ?

140/2.1 = 66.66666666...%

that increase from $210 to $350 was 66.66666666...%.

Answer:

x would be 8 and y is 10

so (8,10)

Step-by-step explanation:

hope it helps

The solution is, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of the given line is,

y=3x-3 ....1

We have to find the equation of a line parallel to y=3x-3 and passing through the point (x1, y1)=(3,2).

The general equation of a line is,

y = mx+c ....2

Here, m is the slope of the line.

Comparing equations (1) and (2), we find that the slope of the line

y=3x-3 is m=3.

The slope of two parallel lines are always equal.

Hence, the slope of a line parallel to the line y=3x-3 is also m=3.

Now, the formula for the point slope form of the equation of a line can be written as,

y - y1 = m (x - x1)

Substitute m=3, x1=3 and y1=2 in the above equation to find the equation of a line parallel to y=3x-3 and passing through point (3,2) is,

y-2 = 3(x - 3)

Therefore, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

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Answer:

The distributive property is used when finding the product of two polynomials by distributing one polynomial to each term of the other polynomial. For example, if we wanted to multiply (3x - 4)(2x + 5), we would use the distributive property by first multiplying 3x(-4) and 2x(5) and then adding the results together.

Polynomials are closed under multiplication, meaning that when two polynomials are multiplied together, the result is always another polynomial. This is true because a polynomial is a combination of constants and variables raised to non-negative integer powers, and when two polynomials are multiplied, the result is a combination of constants and variables raised to non-negative integer powers, which is a polynomial.

The mass of the P₂O₅ formed from 3.4 moles of O₂ gas is equal to 386.1 g.

A mole can be described as a unit for measurement of a huge number of quantities of atoms, molecules, ions, or other particles. The atomic mass can be expressed as the one mole of any element.

The number of particles present in one mole was to be equal to 6.023 × 10 ²³ which is Avogadro’s constant.

Given, the number of moles of O₂ gas = 3.4 moles

The balanced chemical reaction of phosphorous and oxygen gas can be given as:

4 P  +  5 O₂   →   2 P₂O₅

5 mol of Oxygen reacts with moles of P₂O₅ = 2 mol

3.4 mol of O₂ gas reacts with moles of P₂O₅ = (2/5) × 3.4 = 1.36 mol

The mass of the 1.36 mol of P₂O₅ = 1.36 × 283.89 = 386.1 g

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The cost of 5 pounds of bananas in 1939 would have been $2.709.

According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.

Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb

Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb

Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709

Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.

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After 3 years and 9 months, the copier is worth $30,750. After 5 years, the salvage value of the copier is $35,000. The domain of the function is 0 <= t <= 5.

a. To find the value of the copier after 3 years and 9 months, we need to plug in the value of t into the function V(t). Since 3 years and 9 months is equivalent to 3.75 years, we plug in 3.75 for t:
V(3.75) = 3400(3.75) + 18000
V(3.75) = 12750 + 18000
V(3.75) = 30750
Therefore, the copier is worth $30,750 after 3 years and 9 months.

b. To find the salvage value of the copier after 5 years, we need to plug in 5 for t into the function V(t):
V(5) = 3400(5) + 18000
V(5) = 17000 + 18000
V(5) = 35000
Therefore, after 5 years, the salvage value of the copier is $35,000.

c. The domain of this function is the set of all possible values of t. Since the function is defined for the first 5 years of use, the domain is 0 <= t <= 5.

d. To sketch the graph of this function, we can plot a few points and connect them with a line. For example, we can plot the points (0, 18000), (1, 21400), (2, 24800), (3, 28200), (4, 31600), and (5, 35000). The graph will be a straight line with a positive slope, starting at (0, 18000) and ending at (5, 35000).

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ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).

First, we can find the prime factorization of 144:

[tex]144 = 2^4 * 3^2[/tex]

Using the property above, we can rewrite ln(144) as:

[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]

Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):

ln(144) = 4 ln(2) + 2 ln(3)

Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

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Percentage error is 17.30%, it can be said that the answer given by student is correct.

The percent error is the distinction between the estimated value and the actual value in relation to the actual value.

Estimated number of balls in each bag = 86

Real number of balls in the bag = 104

Percentage error = | ( estimated value - real value / real value ) | * 100

Percentage error = | ( 86 - 104 / 104 ) | * 100

Percentage error = | ( -18 / 104 ) | * 100

Percentage error = | - 17.30 | * 100

Percentage error = 17.30%

Thus, it can be said that the answer given by student is correct.

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The zeros of the function are: x = 1, x = -3, and the other two zeros may be irrational or complex.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

Using the Rational Root Theorem, the possible rational roots of the polynomial function F(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:

±1, ±3, ±5, ±15

Using synthetic division, we can find that x = 1 and x = -3 are zeros of the function. Therefore, the zeros of the function are:

x = 1, x = -3, and the other two zeros may be irrational or complex.

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The possible values of x are 2 and 17

The complete question is added as an attachment

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

Similar triangles

In the triangles, we have the following possible equations

15/18 = 10/(10 + x)

10/18 = 15/(10 + x)

Solving the equations, we have

15/18 = 10/(10 + x)

150 + 15x = 180

15x = 30

x = 2

10/18 = 15/(10 + x)

100 + 10x = 270

10x = 170

x =17

Hence, the values of x are 2 and 17

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Complete Question

The two triangles in the diagram are similar there are 2 possible values for x

See attachment for image of the triangle

The fraction of all the sandwiches that are ham sandwiches on rye bread is 4⁄15.

To find the fraction of all the sandwiches that are ham sandwiches on rye bread, we need to multiply the fraction of sandwiches that use rye bread by the fraction of those that are ham sandwiches.

Here's how we can do that:

1. Start with the fraction of sandwiches that use rye bread: (4)/(5)
2. Multiply that by the fraction of those that are ham sandwiches: (1)/(3)
3. Multiply the numerators together: 4 x 1 = 4
4. Multiply the denominators together: 5 x 3 = 15
5. Put the new numerator and denominator together to get the fraction: (4)/(15)

So, the fraction of all the sandwiches that are ham sandwiches on rye bread is (4)/(15).

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The base and height of the parallelogram is B = 16 cm and H = 48 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be represented as A

Now , area of parallelogram A = bh

And , base of a parallelogram is one third its height

So , B = ( 1/3 )H

And , area of parallelogram is A = 768 cm²

On simplifying , we get

768 = ( 1/3 )H²

Multiply by 3 on both sides , we get

H² = 2304

Taking square roots on both sides , we get

H = 48 cm

So , the height of the parallelogram is 48 cm

And , the base of the parallelogram is 16 cm

Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively

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The probability a firm will have a stock price of at least $40 is 0.1112. There should be 40.50 stock price have to be to put a firm in the top 10%.  The correct answer is e) None of the answers are correct.

(i) To find the probability that a firm will have a stock price of at least $40, we need to find the z-score for $40 and use the standard normal table to find the corresponding probability. The z-score is calculated as (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

In this case, the z-score for $40 is (40 - 30)/8.20 = 1.22. Using the standard normal table, we find that the probability of a z-score less than 1.22 is 0.8888. Therefore, the probability of a stock price of at least $40 is 1 - 0.8888 = 0.1112.

(ii) To find the stock price that puts a firm in the top 10%, we need to find the z-score that corresponds to the 90th percentile in the standard normal table. The z-score for the 90th percentile is 1.28. We can then use the formula x = μ + zσ to find the stock price that corresponds to this z-score. In this case, the stock price is 30 + 1.28(8.20) = 40.50.

Therefore, the correct answer is (i) 0.1112 and (ii) 40.50.

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The perimeter of a regular octagon, we use the expression 8s, where s represents side length. The perimeter of a regular octagon with side length 1.5 feet is equals to the 12 feet.

Regular octagon is a polygon with eight sides. The perimeter of a polygon is equals to the sum of all its sides. All eight sides of regular octagon are same measure. So, in other words the perimeter of Regular octagon is equal to eight times the length its side. Here,

Side length of a regular octagon

= 1.5 feet

=> Perimeter = 8 × 1.5 feet [An octagon has 8 sides]

=> Perimeter = 12 feet

Hence, required perimeter is 12 feet.

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The linear dependence between the vectors is -3[10 02] + 1[21 3−1] + 2[11 3−3] = 0.

The linear dependence between the following vectors in Mat 2×2 (R) [10 02],[21 3−1],[11 3−3] can be found by solving the equation a[10 02] + b[21 3−1] + c[11 3−3] = 0 for a, b, and c. This gives us the following system of equations:10a + 21b + 11c = 02a + 3b + 3c = 02b - c = 0Solving this system of equations, we get a = -3, b = 1, and c = 2. Therefore, the linear dependence between the vectors is -3[10 02] + 1[21 3−1] + 2[11 3−3] = 0. This means that the vectors are linearly dependent and can be written as a linear combination of each other.

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David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.

Each bottle holds 3/4 of a quart, and his measuring cup holds 1/4 of a quart.

David will have to fill his measuring cup 3 times in order to fill 1 bottle of capacity 3/4 quarts.

For 5 bottles, it will be 3*5 times which results in 15 times.

Thus, David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

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By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:

64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.

So Kendra's water bottle holds 64 fluid ounces.

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