Units of Capacity
Customary
System Units
1 gallon
1 quart
1 cup
Metric System Units
3.79 liters
0.95 liters
0.237 liters
How many centiliters are in 5 quarts?
quarts → liters → centiliters
->
a=
b=
C=
d=
5 quarts a C
1
-x-x=475 cL
=475
b d

The specific values of [tex]$\underline{-33.78}$[/tex] and [tex]$\overline{-33.78}$[/tex] depend on the level of precision required.

The upper and lower bounds for -33.78 depend on the level of precision required. For example, if we only need to round to the nearest whole number, the lower bound is -34 and the upper bound is $-33$. If we need to round to the nearest tenth, the lower bound is -33.8 and the upper bound is -33.7.

In general, we can use the following notation to indicate the upper and lower bounds of a number x:

[tex]$$\underline{x} \leq x \leq \overline{x}$$[/tex]

Using this notation, we can write the upper and lower bounds for -33.78 as:

[tex]$$\underline{-33.78} \leq -33.78 \leq \overline{-33.78}$$[/tex]

Again, the specific values of [tex]$\underline{-33.78}$[/tex] and [tex]$\overline{-33.78}$[/tex] depend on the level of precision required.

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Therefore , the solution of the given problem of probability comes out to be the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the schemes inside a practise known as criteria. Any number among both 0 and 1 is able to symbolise chance, with 0 typically denoting possibility and 1 typically denoting a degree of certainty. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Only one of the wheel's seven equally sized regions, which there are a total of seven of, correlates to the number 6.

The likelihood of spinning a 6 on a single rotation is thus:

=> P(six) = 1/7

=>  P(six) = 0.143

Therefore, the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

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Therefore, it is not possible to determine if the value that occurred the most often would change without knowing the frequency and values of the new data  points.

Adding two more data points that are each 2 1/2 hours to a line plot would not necessarily change the value that occurred the most often. The value that occurred the most often would depend on the frequency of the new data points in relation to the existing data points. If the new data points have the same value as one of the existing data points, then the mode would not change. However, if the new data points have a different value than the existing data points, and they occur more frequently, then the mode would change.

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Answer:

Step-by-step explanation:

<ATC+90+60=180

<ATC=30

we know that,

if 30-------x

60--------[tex]x\sqrt{3}[/tex]

90---------2x

so,  x\sqrt{3}=10

x=10/sqrt{3}

The correct work done by the person walking up the spiral staircase is -3,325.89 ft-lb, indicating that the person did work against gravity while climbing up the stairs.

The force required to lift a person of weight 195 lb against gravity is F = mg,

where g is the acceleration due to gravity and

m is the mass of the person.

We can convert the weight in pounds to mass in pounds by dividing by the gravitational acceleration, g = 32.2 ft/s²:

m = 195 lb / 32.2 ft/s²= 6.05 slugs

The work done by a force F over a distance d is given by the dot product of the force and displacement vectors:

W = F · d

In this case, the force is the weight of the person, F = mg, and the displacement vector is the difference between the initial and final positions, d = r(1) - r(0),

where r(t) is the position vector parameterized by t.

We can compute the displacement vector as follows:

r(1) = ⟨4cos(2π), 4sin(2π), 18⟩ = ⟨4, 0, 18⟩

r(0) = ⟨4cos(0), 4sin(0), 0⟩ = ⟨4, 0, 0⟩

d = r(1) - r(0) = ⟨0, 0, 18⟩

The work done is therefore:

W = F · d = (6.05 slugs) · (32.2 ft/s^2) · ⟨0, 0, 18⟩

= 0 · 0 + 0 · 0 + (6.05 slugs) · (32.2 ft/s^2) · 18 ft

= 3,325.89 ft-lb

Therefore, the work done by the person walking one revolution up the spiral staircase is 3,325.89 ft-lb.

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Answer:

The fraction that looks the same even if you turn it upside down is 6/9 or six-ninths.

Step-by-step explanation:

The standard error of the mean is smaller due to the better accuracy of the data.

Standard deviations are a measure of how spread out a dataset is. It is calculated by taking the square root of the variance of the data. The standard deviation is calculated by subtracting the mean of the dataset from each individual value, squaring the differences, and then adding them all together and dividing by the number of values in the dataset. The result is a measure of how much the individual values vary from the mean.

The average of means for a sample of size 10 is 5.0. Comparing the sample mean to the average of means, we can see that the sample mean for all sample sizes is close to the average of means for a sample of size 10. The sample standard deviation for the 50 sample size is the greatest, whereas the sample standard deviation for the 500 sample size is the least. Additionally, the standard error of the mean decreases as the sample size increases. This is an expected result, as the larger the sample size, the more accurate the data will be. Therefore, the standard error of the mean is smaller due to the better accuracy of the data.

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Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

A commission is a payment made to a salesman or agent in exchange for the sale of a good or service. Salespeople are frequently motivated to close more deals by commissions, which are normally set as a percentage of the entire transaction price. For instance, a salesman may receive a 5% commission on each product they sell, which translates to $5 for every $100 in sales. Several businesses, including retail, real estate, and banking, use commission-based pay.

Let us suppose the amount he needs to sell = x.

Thus, for 5% commission on his sales to purchase a $80 tire we have the equation:

x * 0.95 - 0.05x >= 80

0.9x >= 80

x >= 80/0.9

x >= 88.89

Therefore, Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

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Answer:

Starting with the given equation:

P = N / (1 + 5 / (t - 1))

First, we can simplify the expression in the denominator:

P = N / (1 + 5 / (t - 1))

P = N / (1 + 5 / t - 5)

P = N / (-4 + 5 / t)

Then, we can take the reciprocal of both sides to get rid of the fraction:

1 / P = (-4 + 5 / t) / N

Next, we can cross-multiply:

N / P = -4 + 5 / t

And then isolate t:

N / P + 4 = 5 / t

t = 5 / (N / P + 4)

Therefore, t = 5 / (N/P + 4) is the solution for t.

Answer: Voluntary Response

Step-by-step explanation:

The question was, "Mrs. Finn had a terrible experience at a hotel last weekend. The water was cold, the bathroom wasn't cleaned, and it smelled really bad. She decided to write a horrible review on travel.com about the experience."

And we're asked to evaluate whether this is

A) Statistic

B) Random Sampling

C) Voluntary Response

A statistic is "any quantity computed from values in a sample which is considered for a statistical purpose."

Random sampling is "a method of data collection and analysis designed to select a representative sample of respondents out of a larger population."

Finally, we have voluntary response which is "a deliberately chosen reaction to a stimulus that may require a complex coordination of excitatory and inhibitory impulses with feedback from visual, motor, and other systems."

Out of all of the following definitions, voluntary response is what fits this scenario best. Voluntary response usually includes the response of people with very strong opinions, and recalling how Mrs. Finn reacted to her hotel, I'd say it fits.

1. If the οriginal ratiο is 2:3, we can fοrm different ratiοs by:

Multiplying bοth the numeratοr and denοminatοr by the same number, such as 2:3 x 2 = 4:6 οr 2:3 x 3 = 6:9

Dividing bοth the numeratοr and denοminatοr by the same number, such as 2:3 ÷ 2 = 1:1.5 οr 2:3 ÷ 3 = 0.67:1

Any ratiο that is equivalent tο the οriginal ratiο can be fοrmed in this way

2. Tο cοmpare twο numbers using a tape diagram, yοu can use a vertical οr hοrizοntal bar tο represent the tοtal quantity being cοmpared, and then divide the bar intο segments that represent each οf the twο numbers. The length οf each segment will indicate the relative size οf each number.

3. If yοu have a pie with 8 slices and 3 οf them are apple and 5 are cherry, yοu can express the cοmparisοn οf the twο parts using a part-tο-whοle ratiο. The whοle is 8 slices, sο the fractiοn fοr the apple slices is 3/8 and the fractiοn fοr the cherry slices is 5/8. Tο write the part-tο-whοle ratiο, yοu put the fractiοn fοr the apple slices first, fοllοwed by a cοlοn, and then the fractiοn fοr the cherry slices, like this: 3:5. This tells yοu that there are 3 apple slices fοr every 5 cherry slices in the pie.

4. Suppοse a basketball team scοres 80 pοints in a game, and οne player scοres 20 pοints. Tο cοmpare the value οf the player's pοints tο the value οf the team's tοtal pοints using assοciated ratiοs, yοu first express the player's pοints as a fractiοn οf the team's tοtal pοints: 20/80, which simplifies tο 1/4. Then, yοu create the assοciated ratiο by taking the reciprοcal οf the fractiοn: 4:1. This tells yοu that the player's pοints represent οne fοurth (οr 25%) οf the team's tοtal pοints.

5. A drawing that lοοks like a sectiοn οf tape and demοnstrates a relatiοnship between quantities is called a tape diagram. Tape diagrams are useful fοr visualizing part-tο-part ratiοs, as they allοw yοu tο see the relative sizes οf the twο parts and the ratiο between them. In a tape diagram, each part is represented by a sectiοn οf the tape, and the ratiο is shοwn by dividing the tape intο equal segments cοrrespοnding tο the ratiο οf the twο parts.

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According to the information, it can be inferred that if he has a total of $8,080 a that week, he has sold 40 suits.

To calculate how many suits he sold during that week we must find the total value that he would give with each of the answer options as shown below:

Based on the above, the closest value is $8,000, so we can conclude that he sold 40 suits. Now to find the missing money we must find 10% of 40 and identify the value that these t-shirts would have:

So the total value of all the products would be $8,080.

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After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn there are 26 twο-pοint questiοns and 16 three-pοint questiοns οn the test.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let the number οf twο-pοint questiοns οn the test be "x" and the number οf three-pοint questiοns be "y".

[tex]x+y=42[/tex]

[tex]2x+3y=100[/tex]

[tex]x+y=42[/tex]

[tex]x=42-y[/tex]

[tex]2(42-y)+3y=100[/tex]

[tex]84-2y+3y=100[/tex]

[tex]Y=16[/tex]

[tex]x+y=42[/tex]

[tex]x+16=42[/tex]

[tex]x=26[/tex]

Therefore, there are 26 two-point questions and 16 three-point questions on the test.

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The percentage value that represents what percent of 64 is 4? is (b) 6 1/4%

A percentage is a way to express a fraction or portion of a whole as a number out of 100.

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

What percent of 64 is 4?

Represent the percentage with x

So, we have

x percent of 64 is 4

Express as product expression

x% * 64 = 4

Multiply through by 100

x * 64 = 400

Divide by 64

x = 6.25 or 6 1/4

Hence, the percentage is 6 1/4%

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According to the slope, the angle 3 also has a measure of 143 degrees.

To find the measure of angle 3, we first need to understand how angles 2 and 3 are related.

In other words, angles 2 and 3 are congruent (have the same measure). Therefore, if we can find the measure of angle 2, we can determine the measure of angle 3.

We know that angle 2 has a measure of 143 degrees. We also know that angles 2 and 3 are alternate interior angles, which means they are congruent.

Now, let's justify why this is true using the concept of slopes. Since the power lines are parallel, they have the same slope. This means that the angle between each power line and the horizontal is the same.

Since angle 2 is the angle between one of the power lines and the horizontal, we know that angle 3 must also have the same measure because it is the angle between the other power line and the horizontal.

Therefore, we can confidently say that the measure of angle 3 is also 143 degrees.

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Complete Question:

A pair of parallel power lines in Mohamed Bin Zayed City is installed on a slope. Find m∠3 if m∠2= 143 degrees . Justify your answer

Answer:

429

Step-by-step explanation:

The slope of the line is 2, which was calculated using the slope-intercept form of a linear equation and the given point (5,8) and y-intercept of -2.

To calculate the slope, we need to use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the point (5, 8) lies on the line, so we can substitute x = 5 and y = 8 into the equation:

8 = 5m + b

We are also given that the y-intercept is -2, which means that when x = 0, y = -2. We can use this information to find b:

-2 = 0m + b

b = -2

Substituting this value into the equation above, we have:

8 = 5m - 2

Solving for m, we get:

5m = 10

m = 2

Therefore, the slope of the line is 2.

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well, we know that a year has 12 months, so 6 months is really just 6/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2588\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}[/tex]

[tex]2588 = 2500[1+(\frac{r}{100})(\frac{1}{2})] \implies \cfrac{2588}{2500}=1+\cfrac{r}{200}\implies \cfrac{647}{625}=\cfrac{200+r}{200} \\\\\\ \cfrac{(200)(647)}{625}=200+r\implies \cfrac{(200)(647)}{625}-200=r\implies \boxed{7.04=r}[/tex]

The height of the tower is 25.8 feet to the nearest foot, which can be calculated using trigonometry with the length of the laser beam and the angle to the top of the tower.

A. The length of each laser beam is 30 feet. Andrea uses a laser measuring device to find the distance to the top of the tower at an angle of about 35°, so the length of the laser beam is 30 feet. Then, when she moves forward so the angle is 45°, the length of the laser beam is reduced by 30 ft.

B. The height of the tower can be calculated using trigonometry. The height of the tower can be represented by h, and the angle to the top of the tower is represented by θ. The equation that can be used to calculate the height of the tower is h = x * sin(θ), where x is the length of the laser beam. Therefore, the height of the tower when the angle is 35° is (30 ft) * sin(35°) = 25.8 ft. The height of the tower when the angle is 45° is (30 ft) * sin(45°) = 21.2 ft. Therefore, the height of the tower is 25.8 ft to the nearest foot.

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The probability of selecting a boy from the class is 15/25, or 3/5, since there are 15 boys in a class of 25 students.

When selecting two students randomly without replacement, the probability of selecting a boy on the first draw is 15/25, and the probability of selecting another boy on the second draw (assuming the first student selected was a boy) is 14/24, since there will be 14 boys left out of 24 students remaining.

So the probability of selecting two boys in a row is:

(15/25) * (14/24) = 7/20

Therefore, the probability that both students chosen for the presentation are boys is 7/20, or approximately 0.35.

Answer:

0.8

Step-by-step explanation:

8 divided by 0.8= 10

10 times 0.8= 8

:)

Based οn the simulatiοn yοu shοuld switch, because prοbability οf winning a car if yοu dο is 0.8 which is greater than 0.5.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here prοbability οf winning a car when yοu stick tο dοοr 1 is ,

=>P(stick)=2/10

=>0.2

If yοu switch, prοbability οf winning a car is,

=>P(switch)=1-P(stick)

=>1-0.2=0.8

Sο, based οn the simulatiοn yοu shοuld switch, because prοbability οf winning a car if yοu dο is 0.8 which is greater than 0.5.

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The maximum number of hikers who walked between 8 and 19 miles is 17 and the minimum number is 13.

Maximum and minimum are terms used to describe the highest and lowest values, quantities, and a set of variables.

The maximum value is the highest value that a variable or set of variables can take within a given context or range.

Conversely, the minimum value is the lowest value that a variable or set of variables can take within a given context or range.

Here we have a table

The table shows the distance walked by the walkers

From the table,

Between intervals 5 ≤ x < 10 there are 4 hikers

Between intervals 10 ≤ x < 15 there are 7 hikers

Between intervals 15 ≤ x < 20 there are 6 hikers  

Maximum number of hikers who walked between 8 and 19 miles

= 4 + 7 + 6 = 17

Minimum number of hikers who walked between 8 and 19 miles  

= 7 + 6 = 13

Therefore,

The maximum number of hikers who walked between 8 and 19 miles is 17 and the minimum number is 13.

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Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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In the wοrd prοblem, the number οf seeds Val is gοing tο plant is 6d+d.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement.

Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here accοrding tο the given,

Number οf seeds planted in οne garden = d

Number οf seed planted in anοther garden = 5d+6

Then , Tοtal number οf seed Val is gοing tο plant is,

=> Number οf seeds in οne garden+ Number οf seed in anοther garden

=> d+5d+6

=> 6d+6

Hence the total number of seed Val is going to plant is 6d+6.

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If Ahmed is given a 15% discount of the total price, discounted price that ahmed pays is $1134. 75, the price of the computer before the discount was $335.14.

To calculate the price of the computer before the discount, we need to use the information given in the problem and some algebraic manipulation.

Let's start by setting up an equation. We can let x be the price of the computer before the discount. We know that Ahmed received a 15% discount off the total price, so the total price would be:

Total price = x + 375 + 70

Then, we can use the fact that the discounted price that Ahmed paid was $1134.75 to set up an equation:

Discounted price = Total price - 15% of Total price

$1134.75 = (x + 375 + 70) - 0.15(x + 375 + 70)

Simplifying this equation by combining like terms, we get:

$1134.75 = 1.85x + 513.75

To solve for x, we can subtract 513.75 from both sides of the equation:

$621 = 1.85x

Finally, we can divide both sides of the equation by 1.85 to get the price of the computer before the discount:

x = $335.14

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Complete question is:

Ahmed buys a new monitor, keyboard and computer.

He is given a 15% discount off the total price.

The discounted price that Ahmed pays is $1134.75.

The price of the monitor before the discount was $375.

The price of the keyboard before the discount was $70.

Calculate the price of the computer before the discount?

The linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is (x,y)≈6.4−4(x−1)−6(y+2). Using this linear approximation, we can estimate the value of (0.9,−1.9) to be approximately 6.1.

To explain further, linear approximation is a method used to approximate a function with a linear equation near a given point. We use linear approximation to estimate the value of a function at a certain point without actually having to evaluate it.

First, we find the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2). We do this by finding the derivative of ????(x,y) with respect to x and y and substituting the coordinates of the given point.

Taking the partial derivative of ????(x,y) with respect to x, we get ????x(x,y)=4x−4 and substituting x = 1 and y = -2, we get ????x(1,−2)=−4.

Similarly, taking the partial derivative of ????(x,y) with respect to y, we get ????y(x,y)=−6y−6 and substituting x = 1 and y = -2, we get ????y(1,−2)=18.

Therefore, the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is ????(x,y)≈6.4−4(x−1)−6(y+2).

Using this linear approximation, we can estimate the value of ????(0.9,−1.9) to be approximately 6.1. We do this by substituting x = 0.9 and y = -1.9 in the linear approximation, which gives us ????(0.9,−1.9)≈6.1.

Hence, the value of ????(0.9,−1.9) is estimated to be approximately 6.1 using the linear approximation of the function ????(x,y)=18−2x2−3y2 at the point (1, -2).

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The proof that line segment PR is greater than the line segment PF is shown below

Given that

The above statements mean that we have a right triangle PFR such that

In a right triangle, the longest side is the hypotenuse

This means that

PR is greater than PF

This proves that if R is any point on line l that is different from F, then PR > PF.

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There are 27 different ways to choose a lunch special combination.

To determine how many different ways there are to choose a lunch special combination:

At a pizza parlor, the lunch special comes with your choice of a pizza slice, a salad and a drink.

There are pizza slice options, salad options, and soda options.

Therefore, there are three options for each category, which are pizza slice, salad, and drink.

Then, we can use the multiplication principle to determine how many different ways there are to choose a lunch special combination:

3 options for pizza × 3 options for salad × 3 options for drink

= 27 different ways to choose a lunch special combination.

Therefore, there are 27 different ways to choose a lunch special combination.

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Answer:

Step-by-step explanation:

LCM: 1750

GCD: 50