Let the following grouped frequency dsitribution represent the markof 230 students out of 70.
CL 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Total
freq. 4 16 f3 f4 f5 6 4 230
Based on the above grouped frequency distribution, answer the following question by showing all neccessary steps.
a. Determine the missing frequencies if median and mode are 33.5 and 34.0 respectively

Based on a system of equations, the number of children (and adults) that attended the amusement park on that particular day is:

Children = 10,000

Adults = 20,000.

A system of equations is two or more equations solved concurrently or simultaneously.

A system of equations can be solved by graphing, matrix, elimination, and substitution methods.

The cost per child = $10

The cost per adult = #20

The total number of children and adults who attended on the da = 30,000

The total revenue generated by the park from tickets = $500,000

Let the number of children = x

Let the number of adults = y

x + y = 30,000 ... Equation 1

10x + 20y = 500,000 ... Equation 2

Multiply Equation 1 by 10:

10x + 10y = 300,000 ... Equation 3

Subtract Equation 3 from Equation 2:

10x + 20y = 500,000

-

10x + 10y = 300,000

10y = 200,000

y = 20,000

x = 30,000 - y

= 10,000

Check:

x + y = 30,000 ... Equation 1

10,000 + 20,000 = 30,000

10x + 20y = 500,000 ... Equation 2

100,000 + 400,000 = 500,000

Thus, using a system of equations, we can conclude that 10,000 children attended with 20,000 adults.

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The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

[tex]\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}[/tex]

[tex]\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]

[tex]\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.[/tex]

[tex]\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12[/tex]

[tex]\bold{Slope = 12}[/tex]

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

Step-by-step explanation:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13

Look at the first line on the table.

For 4 s'mores, 8 marshmallows are used.

8/4 = 2

2 marshmallows are used per s'more.

For 4 s'mores, 12 graham crackers are used.

12/4 = 3

3 graham crackers are used per s'more.

For 13 s'mores,

13 × 2 = 26

13 × 3 = 39

26 marshmallows and 39 graham crackers are needed.

Complete the table:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13                     26                              39

Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

Step-by-step explanation:

this is physics (not math per se).

the first moves to the left, because the distance to the positive charge on the left is shorter than the distance to the positive charge on the right.

the second moves to the right, because the positive charge is greater there and the distance to the positive charge is shorter too.

the third stays where it is. the -2 charge moves to the left until it hits the first +2 charge. there they neutralize each other, and nothing else is happening. also before -2 and +2 meet, they are neutralizing each other already for an outside observer (like the green ringed +2).

but - it depends how picky your teacher tries to be here.

because when you look at the very fine details, until -2 and the right +2 meet and really neutralize each other, there is a tiny little overhang of positive charges the green ringed +2 charge would "feel". simply because the +2 is a little bit closer than the -2.

and when we consider this, the green ringed +2 would move very little to the left (repelled by the other positive overhanging charge on the right) until -2 and +2 actually meet.

Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

24in^3

Step-by-step explanation:

this is a triangular prism and to find the volume of a right prism (a triangular prism in this case) we'll first find the area of cross-section which is basically the base area ( the triangle)

which is 1/2*4in*3in

this equals 6in^2

to find the volume we multiply it by the height of the prism which is 4 (the one on the top) so we multiply our previous answer with 4 to get 24in^3

Answer: Volume of the given shape is, 147 yards.

Step-by-step explanation:

Volume is the amount of space in a certain 3D object.

The given figure is a rectangular prism with a length of 7yd, width of 7yd, and height (depth) of 3 yd.

You can multiply those values L x W x H, to get the volume:

7yd x 7yd x 3yd = 147 yd

The volume of the sphere as shown in the diagram is 4186.67.

volume is the amount of space in a certain 3D object.

To calculate the volume of the sphere, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

When factoring x^2 + bx + c, we look for two binomial factors in the form (x + m)(x + n) that, when multiplied together, give the original quadratic expression. The coefficients b and c are directly used to determine the values of m and n.

Factoring a quadratic expression ax^2 + bx + c, where a ≠ 1, is different from factoring x^2 + bx + c due to the presence of the leading coefficient "a".

On the other hand, when factoring ax^2 + bx + c, where a ≠ 1, factoring becomes more complex because the leading coefficient "a" affects the factorization. To factor such a quadratic expression, we need to find two binomial factors in the form (px + m)(qx + n) that, when multiplied together, give the original quadratic expression.

Factoring quadratics with a leading coefficient of a requires finding two sets of factors for "a" and "c" that combine in different ways to give "b". This involves considering factors of "a" and "c", as well as their combinations, to determine the appropriate values for p, q, m, and n.

In summary, factoring ax^2 + bx + c, where a ≠ 1, involves additional considerations and calculations due to the presence of the leading coefficient "a", making the factorization process more intricate compared to factoring x^2 + bx + c.

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After graphing both equations, we can observe that they intersect at the points (±12, ±5). The answer is (±12, ±5).

To solve the system of equations by graphing, we need to plot the graphs of both equations on the same coordinate plane and find the points of intersection.

The first equation, 9x^2 - 48y^2 = 96, represents a hyperbola, while the second equation, x^2 + y^2 = 169, represents a circle.

Let's graph both equations:

For the first equation, we can rearrange it to the standard form:

9x^2/96 - 48y^2/96 = 1

x^2/32 - y^2/2 = 1

This hyperbola has its center at the origin (0,0), and its x-axis and y-axis intercepts are (±√32, 0) and (0, ±√2), respectively. We can sketch the hyperbola based on these points.

For the second equation, x^2 + y^2 = 169, we have a circle centered at the origin (0,0) with a radius of √169 = 13. We can plot this circle.

After graphing both equations, we can observe that they intersect at the points (±12, ±5).

Hence, the correct answer is (±12, ±5).

It's important to note that graphing is just one method of solving a system of equations. Other methods, such as substitution or elimination, can also be used to obtain the solution algebraically. However, in this case, graphing allows us to visualize the intersection points directly.

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Hello!

23x = 24

23x/23 = 24/23

x = 24/23

Hello !

Answer:

[tex]\Large \boxed{\sf x=\dfrac{24}{23} }[/tex]

Step-by-step explanation:

We want to find the value of x that verifies the following equation :

[tex]\sf 23x=24[/tex]

We want to isolate x.

Let's divide both sides by 23 :

[tex]\sf \dfrac{23x}{23} =\dfrac{24}{23}[/tex]

[tex]\boxed{\sf x=\dfrac{24}{23} }[/tex]

Have a nice day ;)

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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The expression 5⁶ ÷ 5⁴ rewritten using positive exponents is 5².

Given the expression in the question:

5⁶ ÷ 5⁴

To rewrite the expression 5⁶ ÷ 5⁴ using a single positive exponent, we can simply apply the exponent rule for division of like bases.

According to exponent rule for division of like bases, when dividing two numbers with similar bases, we can simply subtract the exponents.

That is:

zᵃ ÷ zᵇ = z⁽ᵃ ⁻ ᵇ⁾

Applying this rule: zᵃ ÷ zᵇ = z⁽ᵃ ⁻ ᵇ⁾

5⁶ ÷ 5⁴ = 5⁽ ⁶ ⁻ ⁴ ⁾

Subtract the exponents:

5²

Therefore, the simplified form is 5².

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The expression equivalent to (53−√4)12 is 5 to the power of 36.

To find the expression that is equivalent to (53−√4)12, we need to simplify the given expression:

(53−√4)12

First, let's simplify the expression inside the parentheses:

53−√4 = 53−2 = 125−2 = 123

Now, let's substitute this simplified expression back into the original expression:

(123)12

To simplify this expression further, we raise 123 to the power of 12:

(123)12 = 5312 = 5 to the power of (3 * 12) = 5 to the power of 36

Therefore, the expression equivalent to (53−√4)12 is 5 to the power of 36.

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Answer:

[tex]\LARGE\boxed{\sf 5^{\frac{3}{8}}}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\large\text{$\sf \left(\sqrt[4]{5^3}\right)^{\frac{1}{2}}$}[/tex]

To find the equivalent expression, apply exponent rules.

[tex]\textsf{Apply the exponent rule:} \quad \boxed{\sqrt[n]{a^m}=a^{\frac{m}{n}}}[/tex]

[tex]\implies \large\text{$\sf \left(5^{\frac{3}{4}}\right)^{\frac{1}{2}}$}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \boxed{(a^b)^c=a^{bc}}[/tex]

[tex]\implies \large\text{$\sf 5^{\frac{3}{4}\cdot \frac{1}{2}}$}[/tex]

[tex]\implies \large\text{$\sf 5^{\frac{3}{8}}$}[/tex]

Therefore, the equivalent expression to the given expression is:

[tex]\LARGE\boxed{\sf 5^{\frac{3}{8}}}[/tex]

The time it takes for a population to reach a certain size is given by:t = (ln(N/P₀)) / r Where:t = time in yearsN = target population size (1000 rabbits in this case)P₀ = initial population sizer = growth rate (expressed as a decimal)

To determine how long it will take for the population of rabbits to reach 1000 rabbits, we need to consider the growth rate of the rabbit population.

Let's assume that the rabbit population grows exponentially, meaning the growth rate is proportional to the current population. We can use the following exponential growth formula:

P(t) = P₀ * e^(r * t)

Where:

P(t) is the population at time t,

P₀ is the initial population,

e is the base of the natural logarithm (approximately 2.71828),

r is the growth rate,

t is the time in years.

In this case, we want to find the time it takes for the population to reach 1000 rabbits, so P(t) = 1000. Let's assume we know the initial population P₀ and the growth rate r. We can rearrange the equation and solve for t:

t = ln(1000 / P₀) / r

By plugging in the appropriate values for P₀ and r, you can calculate the time it will take for the rabbit population to reach 1000 rabbits, rounding the result to the nearest 0.01 years.

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(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.

Answer:

1.5926

Step-by-step explanation:

-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.

-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:

z = (x-mean) / standard deviation

-We would fill this out like this:

z = (74-69.7) / 2.7

-This equals = 1.592592593

-Rounded to 4 decimal places, this equals 1.5926

The equation of the blue graph, g(x) is g(x) = -x³ + 2

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

The functions f(x) and g(x)

In the graph, we can see that

The blue graph is reflected across the x-axis to get the red graph

This means that

g(x) = -f(x)

Recall that

f(x) = x³ - 2

So, we have

g(x) = -x³ + 2

This means that the equation of the blue graph is g(x) = -x³ + 2

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The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

Option D

Step-by-step explanation:

We have to find out the students who like both pepperoni and olives.

The part, which is in dark green, is the collection of students who like pepperoni and olive.

So, it is Maria and Zack

Answer:

See below

Step-by-step explanation:

When Margo places all 6 tiles in a row with sides touching, the length of the row is 4.8 inches.

Margo has 6 tiles of equal size, and each side of the tile measures 0.8 inches. To determine the length of the row when all the tiles are placed together with their sides touching, we need to calculate the total length covered by the tiles.

Since each tile has four sides, and all the sides are touching in a row, we can calculate the total length by multiplying the number of tiles by the length of each side. In this case, the number of tiles is 6, and the length of each side is 0.8 inches.

So, the total length covered by the tiles can be calculated as follows:

Total length = Number of tiles × Length of each side

Total length = 6 × 0.8 inches

Calculating the above expression, we find:

Total length = 4.8 inches

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