A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:





How many students are in the class?

The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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Answer:

1.5 litres

Step-by-step explanation:

1/2 of the punch in a 3 litre bottle is found by dividing 3 by 2, splitting it in half. 3÷2=1.5, or 1 and a half litres

Answer:

Step-by-step explanation:

Its 4.51

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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we can conclude that 2/3 is not equal to 4/5.

To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.

To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

For 2/3 and 4/5, we have:

2 * 5 = 10

3 * 4 = 12

Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.

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The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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There are 56 numbers of schedules that are possible for Hannah.

Basically, A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given Hannah, a roller coaster enthusiast has decided to ride 2 of the world's 8 most famous roller coasters this year.

total roller coasters = 8

since Hannah wants to ride 2 roller coasters,

that can be completed in a certain manner, after completing the first one she will go for the next,

total number of possibilities is calculated by permutation,

ⁿPₓ = n!/(n - x)!

n = 8,  x = 2

⁸P₂ = 8!/(8 - 2)!

⁸P₂ = 8*7*6!/6!

⁸P₂ = 56

Hence there are 56 different schedules are possible.

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Answer:

percentage flim rated very good = 54/80*100%

                                                      = 67.5%

Step-by-step explanation:

Answer:

k = 4/25 or 0.16

Step-by-step explanation:

Given the following data;

y = 4/5

x = 5

To find the variation constant, k;

y is directly proportional to x

Mathematically, y = kx

Substituting into the formula, we have;

4/5 = k5

Cross-multiplying, we have;

4 = 25k

k = 4/25

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

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Answer:

B

Makes the most sense for the question and answer

The correct proof of sin(90-theta)=cos theta is given below.

We have given that

Malia tried to prove that cos(theta) = sin (90 - theta)

The formula for sin(a-b) is sin(a)cos(b)-cos(a)sin(b)

\(Sin(90-\theta)=cos\theta\)

\(sin(90-\theta)=sin(90)cos(\theta)-cos(90)sin(\theta)\\We \ know\\ sin(90)=1 and cos(90)=0\\=(1)cos(\theta)-(0)sin(\theta)\\=cos(\theta)\)

Therefore we get sin(90-theta)=cos theta.

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\((4x)^{2} (6x)^{5} \\4^{2} x^{2} (6x)^{5} \\16x^{2} (6x)^{5} \\16x^{2} *6^{5} x^{5} \\16x^{2} *7776x^{5} \\(16*7776)x^{2} x^{5} \\124416x^{2} x^{5} \\124416x^{2+5} \\124416x^{7}\)

Answer:

Step-by-step explanation:

Your choice is correct

Answer:

C

Step-by-step explanation:

On each linear pair, there is one of the Vertical angles and an angle shared between the two angles. This means we can use the fact that supplements of the same angle are congruent.

The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

In the provided figure.

∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)

∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)

According to transitive property, if a = b and b = c then a = c

Therefore,

∠1 + ∠2 = ∠1 + ∠4...(iii)

⇒∠2 = ∠4

Similarly, we can prove that

∠1 = ∠3

Therefore, we conclude that vertically opposite angles are always equal.

Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Thus, statement c is correct.

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Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer:

0.0078

Step-by-step explanation:

What is 0.00784 rounded to 2 significant figures?

Because 0's to the right of the decimal are not significant your first two significant figures are 7 and 8. So rounded to two significant figures:

0.0078

The number 0.00784 rounded to 2 significant figures is 0.0078.

Significant figures of a given number are the numbers or digits which are significant and it conveys the accurate meaning of the digit.

Given decimal number is 0.00784.

We have to round the number to 2 significant figures.

For that, look at the first non zero digit from the left.

It is the number 7.

Since the number must be in 2 significant figures, look at the next number, it is 8.

Since the number next to 8 is 4, which is less than 5, leave 8 as such.

So the number rounded is 0.0078.

Hence the required number rounded to is 0.0078.

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total number of students = 25

number of stdents tthat play tennis = 13

number of students that play volleyball = 14

number of students that doesn't play tennis nor volleyball = 1

(a) to look for number of students that plays both tennis and volleyball

Let the number of students that play both games be x

25 = (13-+x) + x + x + (14-x) + 1

25 = 13 - x + x + 14 - x + 1

25 = 28 - x

x = 3

so probability that the student plays both volleyball and tennes = 3/25

(b) probability that the student plays atleast one of the the two sports

to get the probability that the student plays one of the two sports = 1 - probability that neither plays

probability that neither plays = 1/25

probability that the student plays atleast one = 1 - 1/25

= 24/25

(c) Play volleyball given that he or she does not play tennis

Number of students that play volleyball = 14 - 3

= 11

Therefore, the probability that the student only play volleyball = 11/25

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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Answer:

70 percent?

Step-by-step explanation:

I hope this helps:)

Answer:

3) Because the run go by 4 and the rise go up by 2

Step-by-step explanation:

Answer:

1. 1,605

2. -605

3. 21,575

Step-by-step explanation:

Answer:

1.1,605

2.-605

3.21,575

Answer:

x ≈ 30,37

y ≈ 29,00

Step-by-step explanation:

Use trigonometry:

\( \sin(38°) = \frac{9}{x} \)

Now, use the property of the proportion to find x:

\(x = \frac{9}{ \sin(38°) } ≈30.37\)

Do the same thing to find y:

\( \tan(38°) = \frac{9}{y} \)

\(y = \frac{9}{ \tan(38°) } ≈29.00\)

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

Step-by-step explanation:

NOT 5.

_____________________

Firstly note that the radius of the circle is 13 ( centre to D )

Thus the distance from B to the centre is 13

Thus B → E → centre is a right triangle and distance from centre to E (x) can be calculated using Pythagoras' identity, that is

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x =  = 5

The distance from the centre to C ( the radius ) is 13, thus

x + EC = 13, that is

5 + EC = 13 ( subtract 5 from both sides )

EC = 8

Answer:

The answer is 8

Step-by-step explanation:

Answer:

14 miles

Step-by-step explanation:

Since we know that the distance of the paths from Cedarburg to Allenville is 22 and 13/16 miles, and we know the distance from Cedarburg to Lakeside is 8 and 13/16 miles.

We know that the total distance is made up of the distance from C to L and L to A.

So 22 and 13/16 = 8 and 13/16 + L to A

We can subtract 22 and 13/16 by 8 and 13/16 to get 14 miles.

Hope this helps.

Answer:

iTS UPside dOWn

But you were supposed to multiply so your answer is 476

aka the last one

HOPE THIS HELPS!

The misleading about the data shown on the figure is the clas width

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

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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Answer:

(0.5, 4.5)

Step-by-step explanation:

midpoint formula:

((sum of the two x values)/2, (sum of the two y values)/2)

= ((5+(-4))/2 , (6+3)/2)

= (0.5, 4.5)

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Step-by-step explanation:

here is your answer, this is how you do it

Answer:

\(\boxed{\bf G. \: x = {25}^{o}} \)

\(\boxed{\bf H. \: x = {20}^{o} }\)

Step-by-step explanation:

In the given figure, the linear pairs are supplementary angles, meaning they should add up to 180°.

G)

H)

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