Use the drawing tools to form the corect answer on the provided dot plots.
For nine full months of the school year, two teachers recorded the number of students who were late to their first class of the day. Their monthly
totals are presented in these data sets.
Ms. Cleary: 3. 4. 8. 6, 5, 4, 2, 3. 3
Mr. Tram: 2, 7, 4, 5, 1, 8, 7, 4, 4
Construct a dot plot for each set of data
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23 456
Ms. Cleary
0
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234567
Mr. Tram

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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Answer:

26) 1.32

27) 90

28) 0.00845

29) 2.56x10^-1

30) 9.5x10^-3

31) 7.8x10

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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Answer:

parallelogram kite kite trapazoid

216.25 square feet

……….

The price of the emerald ring after marked down by 64% is equal to $1.908.

Original price of the emerald ring = $5,300

Let us consider the price of the ring after marked down be 'x'.

Marked down percent at the time of clearance = 64%

Calculate 64% of the original price and then subtract that amount from the original price,

64% of $5,300

= 0.64 x $5,300

= $3,392

So, the amount of the markdown is $3,392.

The price of the ring now is equal to,

Price of the ring now 'x'  = Original price - Markdown

⇒ Price of the ring now 'x' = $5,300 - $3,392

⇒ Price of the ring now 'x' = $1,908

Therefore, now the price of the ring is equal to $1,908.

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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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Answer:

the answer of the question is

104+8x

Since angles A and B are vertical angles, the value of x is equal to 9.

In Mathematics and Geometry, the vertical angles theorem is sometimes referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following congruent angles:

m∠A = m∠B

(4x - 19)° = (5x - 28)°

5x - 4x = 28 - 19

x = 9

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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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Yes, based on the given sample data provide convincing evidence that more than 84% of teenagers think highly of their mother.

Percentage of teenagers think highly of their mother = 84%

Sample data = 150

Number of teenagers think highly of their mother = 135

To check convincing evidence that the true proportion of teens who think highly of their mother is greater than 0.84,

Use a hypothesis testing ,

Let p be the true proportion of teenagers who think highly of their mother.

The null hypothesis is that p = 0.84,

and the alternative hypothesis is that p > 0.84.

Use a one-tailed z-test for proportions to test this hypothesis.

The test statistic is calculated as,

z = (p₁ - p) / √(p(1-p)/n)

where p₁ is the sample proportion,

n is the sample size,

and p is the null hypothesis value.

Here,

p₁ = 135/150

   = 0.9

p = 0.84

n = 150

The test statistic is,

z = (0.9 - 0.84) / √(0.84×(1-0.84)/150)

  ≈ 2.006

Using a significance level of 0.05,

The critical value for a one-tailed test is 1.645.

Since our test statistic 2.006 is greater than the critical value (1.645).

Reject the null hypothesis.

And conclude that there is sufficient evidence.

Therefore, the true proportion of teenagers of given sample data who think highly of their mother is greater than 0.84 is showing convincing evidence .

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Step-by-step explanation:

yes,because of SAS side angle side are equal.

The underlying distribution for the independent groups t-test is the sampling distribution of the difference between means, assuming it's approximately normally distributed. The correct answer is C).

The underlying distribution for the independent groups t-test is the sampling distribution of the difference between means. The independent groups t-test is used to compare the means of two independent groups, and it assumes that the sampling distribution of the difference between the means is approximately normally distributed.

The t-test uses the sample means and sample standard deviations to estimate the population means and population standard deviations, and it tests the null hypothesis that the difference between the population means is zero. The correct option is C).

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Answer:

$12405.40

Step-by-step explanation:

We Know

She has $1240.54 right now

Miss Western is setting a goal to earn 10 times her savings account to buy a new car.

What is her goal?

We Take

1240.54 x 10 = $12405.40

So, her goal is $12405.40

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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Step-by-step explanation:

this is to calculate the area of a rectangle. you really need help with that ?

the area is

8 × 22 = 176 ft²

the wallpaper costs $3 per ft².

so, the total costs will be

176 × 3 = $528.-

The wallpaper will cost Jacob $528 to cover his entire wall.

This is a simple mathematics problem that can be solved using mensuration.

Firstly we need to find the area of the wall. Since the wall is rectangular in shape, we will use the formula of the area of a rectangle to find the area of the wall.

Area of the wall (rectangle) = length x breadth

Area of the wall (rectangle) = 22 x 8

Area of the wall (rectangle) = 176 square feet

Now we have been given that the rate per square foot of wallpaper is $3. So we need to multiply the area of the wall by the rate per square foot of the wallpaper to get our answer.

Cost of wallpaper = Area of wall x Rate per square foot of wallpaper

Cost of wallpaper = 176 x 3

Cost of wallpaper = 528

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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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On a normal curve, the center of the range of scores is represented by the mean

In a normal distribution, the center of the range of scores is represented by the mean or average of the scores. The normal distribution is a symmetrical bell-shaped curve, with the mean in the center, and the standard deviation determining the width of the curve. The mean is also the point of highest frequency, where the curve is highest.

The normal distribution is widely used in statistics and is a fundamental concept in many fields. It is used to describe real-world phenomena, such as heights or weights of people, test scores, and many other variables. Understanding the normal distribution is crucial in statistical analysis and decision making.

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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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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.

The function represents exponential decay, meaning that the population is decreasing over time.

Exponential growth and decay are mathematical concepts that describe the increase or decrease of a quantity over time.  

Exponential decay occurs when the rate of decrease of a quantity is proportional to the current value of the quantity.

The formula for exponential decay is given:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the decay rate, and t is the time.

Here we have

The population of a country is modeled by the function

f(x) = 375(1 − 0.002)x.

The given function is f(x) = 375(1 − 0.002)x,

which can be written in form f(x) = a(1 + r)x,

where a = 375 and r = -0.002.

The formula a(1 + r)x represents exponential growth if r is positive and exponential decay if r is negative.

In this case, r = -0.002, which is negative.

Therefore,

The function represents exponential decay, meaning that the population is decreasing over time.

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Answer:

Step-by-step explanation:

The answer would be D. exponential decay

The given function is f(x)=375(1-0.002)^x

It's being raised to a power making it exponential and it's a decay because the function has a -0.002 and not +0.002

The value of digit 4 to the left of the decimal point (400) is much greater than the value of the digit 4 to the right of the decimal point (0.004).

What is the decimal point?

The decimal point is a punctuation mark represented by a dot (.) or a comma (,) used to separate the whole number part from the fractional part in decimal notation. It is placed between the units and the tenth places and separates the integer part of a number from its fractional part.

The digit 4 to the left of the decimal point is in the hundreds place, and has a value of 4 x 100 = 400.

The digit 4 to the right of the decimal point is in the thousandth place, and has a value of 4 x 0.001 = 0.004.

Therefore, the value of digit 4 to the left of the decimal point (400) is much greater than the value of the digit 4 to the right of the decimal point (0.004).

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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:4/3

Step-by-step explanation:start by converting the mixed numbers to improper fractions to make the subtraction easier:

5⅔ cups of cereal = 17/3 cups of cereal

4⅓ cups of marshmallows = 13/3 cups of marshmallows

Now subtract the amount of marshmal ows from the amount of cereal: 4/3 of a cup

Answer:

1  1/3

Step-by-step explanation:

so first you must take the 5 2/3 and subtract if from the 4 1/3 which gives:

1  1/3

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 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 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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Dan did a total of 27/20 loads of laundry.

What is fraction?

A fraction is a numerical representation of a part of a whole or a ratio between two numbers, expressed as one number divided by another number and typically written with a horizontal line between the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole or the total number of items being compared.

From the information given, we know that Dan did three loads of laundry on different days, with the following breakdown of the first load: 2/5 colored clothes.

To find out how many loads of laundry Dan did in total, we need to add up the number of loads he did on each day,

3/11 + 3/4 + 3/10

To add these fractions, we need to find a common denominator. In this case, the lowest common denominator is 220,

3/11 = 60/220

3/4 = 165/220

3/10 = 66/220

Now we can add the fractions,

60/220 + 165/220 + 66/220 = 291/220

This means that Dan did a total of 291/220 loads of laundry. However, this is not a practical or meaningful way to express the answer. We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 11,

291/220 = (291 ÷ 11) / (220 ÷ 11) = 27/20

Therefore, Dan did a total of 27/20 loads of laundry.

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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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