Mrs. Greenthumb is planning to build a rectangular planter for her garden. She wants the length to be twice as long as the width plus one foot and the total area is 300ft^2
a- What quadratic equation will represent this situation?
b- What are the dimensions of Mrs. Greenthumb's garden?

The probability that the flight will leave on time when it is not raining is approximately 0.83.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).

According to the given information:

To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).

Let:

P(rain) = 0.07 (probability of rain)

P(delayed) = 0.17 (probability of delay)

P(rain and delayed) = 0.02 (probability of rain and delay)

We can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we want to find P(on time | not raining), which can be expressed as:

P(on time | not raining) = P(on time and not raining) / P(not raining)

Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:

P(on time | not raining) = P(on time) / (1 - P(rain))

We can now substitute the given probabilities to calculate the required probability:

P(on time | not raining) = P(on time) / (1 - P(rain))

P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))

P(on time | not raining) = (1 - 0.17) / (1 - 0.07)

P(on time | not raining) = 0.83

So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).

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Answer: 9 study all three subjects

Step-by-step explanation:

The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

What is equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.

This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.

It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.

Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

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The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.

To solve the equation (4)/(x) + (1)/(2) = (5)/(x):

Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.

Multiply the left side of the equation by 2/2 to get:

(8)/(2x) + (1)/(2) = (5)/(x)

Combine the two fractions on the left side of the equation:

(8+1)/(2x) = (9)/(2x)

Set the left side of the equation equal to the right side:

(9)/(2x) = (5)/(x)

Cross-multiply:

9x = 10x

Simplify:

x = 0

Therefore, the solution to the equation is x = 0.

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Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

To minimize the cost of materials, we need to find the dimensions of the crate that will minimize the surface area of the crate. Let's call the height, width, and length of the crate "h", "w", and "l", respectively.

We know that the volume of the crate is 16 ft3, so we can write:

lwh = 16

We want to minimize the cost of materials, which is determined by the surface area of the crate. The surface area consists of the top, bottom, front, back, left, and right sides of the crate. The cost of the materials for the base is twice the cost of the materials for the sides, and the cost of the materials for the top is half the cost of the materials for the sides. Let's call the cost of the materials for the sides "c".

The surface area of the crate can be written as:

2lw + 2lh + 2wh

We can use the volume equation to solve for one of the variables, say "h":

[tex]h = \frac{16}{(lw)}[/tex]

Now we can substitute this expression for "h" into the surface area equation:

[tex]2lw + 2l(\frac{16}{(lw))} + 2wh[/tex]

Simplifying this expression gives:

[tex]2lw + 32/l + 2wh[/tex]
To find the dimensions that minimize this expression, we need to take the partial derivatives with respect to "l" and "w" and set them equal to zero:
[tex]\frac{d}{dl} (2lw + 32/l + 2wh) = 2w - \frac{32}{l^2} = 0\\[/tex]

[tex]\frac{d}{dw} (2lw + 32/l + 2wh) = 2l + 2h = 2l + 2(16/(lw)) = 2l + 32/(lw) = 0[/tex]
Solving these equations for "l" and "w" gives:

[tex]l = 2^{(1/3)}\\w = 2^{(2/3)}[/tex]

Substituting these values into the equation for "h" gives:

[tex]h = 8/(2^{(2/3)})[/tex]

Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

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The dimensions of the box that minimize the cost of materials are approximate:

x ≈ 2.52 ft

y ≈ 3.55 ft

z ≈ 2.52 ft

Let's denote the length, width, and height of the box as x, y, and z,

respectively. We are given the volume of the box is [tex]16 ft^3[/tex], so we

have:

x × y × z = 16

We are also given that the material used to make the base costs twice as

much (per square foot) as the material in the sides.

Let's denote the cost of the material for the sides as c, so the cost of the

material for the base is 2c.

The area of the base is xy, so the cost of the material for the base is

2cxy.

Similarly, the material used to make the top costs half as much (per

square foot) as the material in the sides.

Let's denote the cost of the material for the top as 0.5c.

The area of the top is also xy, so the cost of the material for the top is 0.5cxy.

The cost of the material for the four sides is simply 4cz.

Therefore, the total cost of materials is:

C(x, y, z) = 2cxy + 4cz + 0.5cxy

Simplifying, we have:

C(x, y, z) = (2.5c)xy + 4cz

We want to minimize this function subject to the constraint that the volume of the box is [tex]16 ft^3[/tex]:

x × y × z = 16

We can use the method of Lagrange multipliers to solve this constrained optimization problem:

L(x, y, z, λ) = (2.5c)xy + 4cz - λ(xyz - 16)

Taking partial derivatives with respect to x, y, z, and λ, we get:

dL/dx = 2.5cy - λyz = 0

dL/dy = 2.5cx - λxz = 0

dL/dz = 4c - λxy = 0

dL/dλ = xyz - 16 = 0

From the first two equations, we can solve for λ:

λ = 2.5cy/yz = 2.5cx/xz

Setting these two expressions equal to each other and simplifying, we get:

y/x = z/y

This implies that x:y:z = 1:√2:1, since we know that the dimensions of the box must be in proportion to each other.

Substituting this into the constraint x × y × z = 16, we get:

x = 2∛2

y = 2∛4

z = 2∛2

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The more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

Let us denote the expected number of times the variable bmax gets updated by E.

We can start by computing the probability that the ith agent updates bmax. This is equal to the probability that agent i has the highest bid among the first i bids. Since all bids are distinct and the order of the agents is chosen uniformly at random, the probability of this event is 1/i.

Therefore, the expected number of updates to bmax is:

E = ∑i=1 to n P(agent i updates bmax)

E = ∑i=1 to n 1/i

This is the harmonic series, which diverges as n approaches infinity. Therefore, as the number of bidding agents increases, the expected number of updates to bmax increases without bound.

In practical terms, this means that the more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

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The expanded form of the given expression (h² − h) + (5h + 6)-(3h² +4h - 9) is -2h² + 15.

Given the expression in the question;

(h² − h) + (5h + 6) - (3h² + 4h - 9)

Expanding an algebraic expression means to remove any parentheses and simplify the expression as much as possible.

In the given expression, we have three sets of parentheses:

(h² − h)

(5h + 6)

(3h² +4h - 9)

To expand the expression, we will remove the parentheses and simplify the resulting terms.

(h² − h) becomes h² - h

(5h + 6) remains the same

(3h² +4h - 9) becomes 3h² + 4h - 9

Putting all the terms together, we get:

h² - h + 5h + 6 - (3h² + 4h - 9)

Now, we will distribute the negative sign to all the terms inside the parentheses:

h² - h + 5h + 6 - 3h² - 4h + 9

Simplifying further by combining like terms, we get:

h² - 3h² - h + 5h - 4h + 6  + 9

-2h² + 15

Therefore, the expanded form is -2h² + 15.

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The guy wire must be about 55 feet long and the slope of the guy wire, expressed as a fraction is 25/11.

We can use the Pythagorean Theorem to find the length of the guy wire. Let's call the length of the guy wire "g".

g^2 = 50^2 + 22^2

g^2 = 2500 + 484

g^2 = 2984

g ≈ 54.65

So the guy wire must be about 55 feet long.

The slope of the guy wire is the ratio of the vertical distance it covers to the horizontal distance it covers. In this case, the vertical distance is 50 feet (the height of the pole) and the horizontal distance is 22 feet. So the slope is

50/22 = 25/11

Therefore, the slope of the guy wire is 25/11.

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The length of the rectangular prism given the volume, width and height is 19 yd.

Volume of a rectangular prism = length × width × height

Volume of the prism = 2,280 yd³

Width of the prism = 20 yd

Height of the prism = 6 yd

Length of the prism = x

So,

Volume of a rectangular prism = length × width × height

2,280 = x × 20 × 6

2,280 = 120x

divide both sides by 120

x = 2,280 / 120

x = 19 yd

Therefore, the length is 19 yd

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Therefore, both functions have the same axis of symmetry equation, which is x = -3.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are one of the central objects of study in mathematics and have many applications in various fields such as physics, economics, engineering, and computer science. A function is typically represented using a mathematical expression or equation, and it can be analyzed and manipulated using a variety of mathematical techniques.

Here,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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Step-by-step explanation:

yes,because of SAS side angle side are equal.

0.5 is used as a conservative estimate of p in determining the minimum sample size for a proportion confidence interval to account for maximum uncertainty.

In statistical hypothesis testing and estimation, we often need to make inferences about population parameters based on a sample. One of the parameters of interest is the proportion of successes in a population.

When we construct a confidence interval for a proportion, we need to specify the desired level of confidence and the desired margin of error. The margin of error depends on the sample size and the standard error of the sample proportion.

The standard error of the sample proportion is estimated using the population proportion, p, which is unknown. Since we don't know the true value of p, we typically use the sample proportion, p-hat, as an estimate. However, using p-hat alone can lead to an overly optimistic estimate of the standard error and, therefore, an overly narrow confidence interval.

To account for this uncertainty, we use a conservative estimate of the standard error that assumes a worst-case scenario for p. The worst-case scenario is when p is 0.5, which corresponds to maximum uncertainty or variability in the estimate of the proportion. This is why 0.5 is often used as a conservative estimate of p when determining the minimum sample size necessary for a proportion confidence interval. By assuming p = 0.5, we ensure that our sample size is large enough to account for the worst-case scenario and provide a reliable estimate of the proportion.

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Answer:

the answer of the question is

104+8x

216.25 square feet

……….

The equation is solved as x = −89.5. The correct option is 1.

What is a mathematical equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

To solve the equation −0.18x − 13.7 = 2.41 for x, we need to isolate x on one side of the equation by adding 13.7 to both sides and then dividing by −0.18:

−0.18x − 13.7 = 2.41

−0.18x = 2.41 + 13.7

−0.18x = 16.11

x = 16.11 / (−0.18)

x = −89.5

Therefore, the solution to the equation is x = −89.5. the correct option is 1.

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The probability of accepting the whole shipment is 0.384, or about 38.4%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial probability problem, where the probability of a defect (or non-conformance) is p=0.11 and the sample size is n=27. We want to find the probability of having at most one defect in a sample of 27 tablets.

Let X be the number of defects in the sample. Then X follows a binomial distribution with parameters n=27 and p=0.11. We want to find P(X ≤ 1), which is the probability of having 0 or 1 defects in the sample.

Using the binomial distribution formula, we have:

P(X ≤ 1) = P(X = 0) + P(X = 1)

= (27 choose 0) * [tex](0.11)^{0}[/tex] * [tex](0.89)^{27}[/tex] + (27 choose 1) * [tex](0.11)^{1}[/tex] * [tex](0.89)^{26}[/tex]

= (1) * (1) * [tex](0.89)^{27}[/tex] + (27) * (0.11) * [tex](0.89)^{26}[/tex]

= 0.384

Therefore, the probability of accepting the whole shipment is 0.384, or about 38.4%.

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The value of c in increasing order which satisfy the Rolle's theorem for a given function is equal to  c = 1/4 and c = 3/4.

Function f(x) = 7sin(2πx) ,

Interval = [0, 1]

To apply Rolle's Theorem, check the following conditions,

f(x) must be continuous on the closed interval [a, b].

Here, the interval is [0,1].

f(x) must be differentiable on the open interval (a, b).

f(a) = f(b)

Function f(x) = 7sin(2πx).

f(x) is continuous on the interval [0, 1].

f(x) is differentiable on the interval (0, 1), and its derivative is,

f'(x) = 14π cos(2πx)

The derivative is continuous on the interval (0, 1).

f(0) = 7sin(0)

     = 0

f(1) = 7sin(2π)

     = 0

Since f(0) = f(1) = 0,

⇒ As per Rolle's Theorem there exists at least one number c in the interval (0, 1) .

Such that f'(c) = 0.

Values of c that satisfy this conclusion,

Solve the equation

f'(c) = 14π cos(2πc)

⇒14π cos(2πc) = 0

⇒ cos(2πc) = 0

This equation has solutions at c = 1/4 and c = 3/4,

As

cos(2π(1/4))

= cos(π/2)

= 0

and

cos(2π(3/4))

= cos(3π/2)

= 0.

Therefore, the values of c that satisfy the conclusion of Rolle's Theorem for the given function are c = 1/4 and c = 3/4, and they are already in increasing order.

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The above question is incomplete, the complete question is:

Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function 7sin(2pix) and interval [0, 1 ]. Enter the values in increasing order and enter N in any blanks you don't need to use.

We have confirmed that the sum of the series is 28/3. Therefore, the correct answer is option (b) 28/3.

A geometric series is a series of numbers where each term is a fixed multiple of the preceding term. Specifically, a geometric series has the form:

a+ar+ar²+ar³+.....

The given series is a geometric series with first term (a) = 14 and common ratio (r) = -1/2.

Consider sum of series be S, So-

S = a/(1 - r) = 14/(1 - (-1/2)) = 28/3

To see why this is the correct answer, we can also write out the first few terms of the series:

14-7+7/2-7/4+7/8-.....

It is evident that each term is produced by multiplying the one before it by -1/2.

So, the second term is obtained by multiplying the first term by -1/2, the third term is obtained by multiplying the second term by -1/2, and so on.

We can also notice that the sum of the first two terms is 7, the sum of the first three terms is 21/2, and the sum of the first four terms is 28/3. This suggests that the sum of the first n terms of the series might be given by the formula Sn = a(1 - rⁿ)/(1 - r).

We can verify that this is true by using the formula to find the sum of the first four terms:

S4 = 14(1 - (-1/2)⁴)/(1 - (-1/2)) = 28/3

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Some reasons why John and Mary should buy a house could be investment, control and stability. The reasons why they should rent could be flexibility, maintenance costs and lower upfront.

When considering whether to rent or buy a home, there are many factors to take into account, including financial considerations, lifestyle preferences, and personal circumstances.

Therefore, the decision to rent or buy a home is a complex one that involves many factors. By carefully considering these factors and weighing the pros and cons of each option, John and Mary can make an informed decision that is best for their needs and goals.

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The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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Answer:  (x + 3) (x - 3) (x^2 + 9) (x^2 - 9)

Step-by-step explanation: We can use the difference of squares formula to factor x^4 - 81 as (x^2 + 9)(x^2 - 9).

Then, we can use the difference of squares formula again to factor x^2 - 9 as (x + 3)(x - 3).

Therefore, the complete factorization of x^4 - 81 is (x + 3)(x - 3)(x^2 + 9)(x^2 - 9).

Answer: We can begin by factoring the quadratic expression in the numerator and denominator of the left-hand side of the inequality:

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

x^2 + 5x + 4 = (x + 1)(x + 4)

Substituting these expressions into the inequality, we get:

(x + 1)(x - 1)/(x + 1)(x + 4) ≤ 0

We can simplify this expression by canceling out the common factor of (x + 1) from both the numerator and the denominator:

(x - 1)/(x + 4) ≤ 0

To solve this inequality, we can use a sign chart or test values. Here's a sign chart:

x x - 1 x + 4 (x - 1)/(x + 4)

-4 -5 0 +

-1 -2 3 -

1 0 5 0

4 3 8 +

The inequality is satisfied when (x - 1)/(x + 4) is less than or equal to 0, which occurs when x is between -4 and -1, or when x is equal to 1. Therefore, the solution to the inequality is:

-4 ≤ x < -1 or x = 1

Step-by-step explanation:

Thus, the area of the actual bridge deck is found as 1750 square feet.

A scale factor refers to the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.

Given dimension-

Length l = 24 inches

width w = 4 1/5 = 21/5 inches

Convert inches to feet:

1 foot = 12 inches.

Scaled length = 24 inches ÷ 12 inches/foot = 2 feet

Scaled width =21/5 inches ÷ 12 inches/foot = 21 / 5*12 = 0.35 feet

Now, scale factor = 50.: 1

Actual length = Scaled length × Scale factor

Actual length = 2 feet × 50 = 100 feet

Actual width = Scaled width × Scale factor

Actual width = 0.35 feet × 50 = 17.5 feet

Area of actual bridge deck:

Area = Actual length × Actual width

Area = 100 feet × 17.5 feet

Area = 1750 square feet

Thus, the area of the actual bridge deck is found as 1750 square feet.

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The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].

Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).

Given:

[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]

Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.

We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:

The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50

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The thing that would be needed to be congruent to show that APQR = ASTU by ASA is A. <Q ≡ <T

To prove the congruence of triangles ΔPQR and ΔSTQ, we need to establish that the angle Q in ΔPQR is congruent to the angle T in ΔSTQ, in addition to the given conditions that PQ = ST and ∠P = ∠S.

This is because the ASA (angle-side-angle) congruence postulate states that if two triangles have two pairs of corresponding angles and a corresponding side between them equal, then the triangles are congruent.

Therefore, establishing the congruence of the angles Q and T, along with the given conditions, satisfies the requirements of the ASA postulate, and proves the congruence of ΔPQR and ΔSTQ.

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Answer:

26) 1.32

27) 90

28) 0.00845

29) 2.56x10^-1

30) 9.5x10^-3

31) 7.8x10

The base area, the lateral area and the surface area of the prism are 124.8 cm², 288 cm² and 412.8 cm², respectively.

In this problem we need to compute three kinds of areas in a prism with a triangular base. The base area, that is, the sum of the areas of the two triangles, the lateral area, that is, the sum of the areas of the three rectangles and the surface area, that is, the sum of the base and lateral areas.

The area formulas of the triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine each kind of area:

Base area

A = 2 · 0.5 · (12 cm) · (10.4 cm)

A = 124.8 cm²

Lateral area

A = 3 · (8 cm) · (12 cm)

A = 288 cm²

Surface area

A = 124.8 cm² + 288 cm²

A = 412.8 cm²

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The total cups of milk orange juice Enrique has in refrigerator is equal to  18 cups.

Gallons of milk Enrique has in his refrigerator = 1 gallon

Pint of orange juice Enrique has in his refrigerator = 1 pint

Convert gallons to cups and pint to cups .

There are ,

16 cups = 1 gallon of milk

And 2 cups = 1 pint of orange juice

Enrique has 16 cups of milk

and 2 cups of orange juice.

Total cups of milk and orange juice in refrigerator

=16 cups of milk + 2 cups of orange juice

= 18 cups of milk and orange juice

Therefore, in total Enrique has  18 cups of liquid in his refrigerator.

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Answer: 4 milimeters

Step-by-step explanation:

1 centimeters = 10 millimeters

0.4 centimeters= 4 miliimeters

Answer:

parallelogram kite kite trapazoid