Jorge compró 4/12 Kg de azúcar en enero, en febrero compró 5/12 Kg de azúcar y en marzo compró 2/12 Kg de azúcar, ¿cuántos Kg de azúcar, ¿cuántos Kg de azúcar compró en total? *

The required given expression are categorized on perfect cube and square.

A number is said to be a perfect cube if it can be multiplied by itself three times. X must equal Y3 if it is a perfect cube of Y. As a result, a natural integer, not a fraction, is obtained when we take the cube root of a perfect cube. Therefore, 3x Equals y. For instance, the number 8 is a perfect cube as 38 = 2.

1) x³ + 125

= x³ + (5)³

It is perfect cube.

2) 8p³ - 27

= (2p)³ - (3)³

It is difference of perfect cube.

3) 12x³ - 9

We can not make perfect cube of this expression.

4) a² - 100

= a² - 10²

It is a difference of Perfect square.

5) 4m² + 25

= (2m)² + 5²

it is a sum of Perfect square.

6) 16x² - 9

= (4x)² - 3²

It is difference of perfect square.

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The exact area of the circle is 17π.  To determine the coordinates of the center of the circle, we need to rewrite the equation of the circle in the standard form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r represents the radius.

Given equation: x^2 + 2x + y^2 - 4y = 12

To complete the square for x, we add (2/2)^2 = 1 to both sides of the equation:

x^2 + 2x + 1 + y^2 - 4y = 12 + 1

(x + 1)^2 + y^2 - 4y = 13

To complete the square for y, we add (-4/2)^2 = 4 to both sides of the equation:

(x + 1)^2 + y^2 - 4y + 4 = 13 + 4

(x + 1)^2 + (y - 2)^2 = 17

Comparing this with the standard form, we can see that the center of the circle is (-1, 2).

The area of the circle can be calculated using the formula A = πr^2, where r is the radius. In this case, the radius can be found by taking the square root of the right side of the equation in standard form:

r = √17

Therefore, the exact area of the circle in terms of π is:

A = π(√17)^2 = 17π.

Hence, the exact area of the circle is 17π.

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Answer: B: 11

Step-by-step explanation:

Just to the quiz for it

An equation is formed of two equal expressions. The number of players going to the tournament is 11.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Since the cost of the van is fixed, therefore, 231. Thus, the two equations can be written as,

Solving the above two equations we will get,

Px + 3P - 4.50x -13.5 = 231

3P - 4.50x - 13.5 = 0

3P - 4.50x = 13.5

3(231/x) - (4.50x) = 13.5

693 - 4.50x² = 13.5x

-4.50x² - 13.5x + 693 = 0

x² + 3x - 154 = 0

x = -14, 11

Since the number of members can not be negative, the number of players going to the tournament is 11.

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The speed of the airplane is the ratio of the distance to the time

The initial average speed of the airplane is approximately 110.8 mph

Reason:

Given parameters are;

The distance between Portland Oregon and Seattle Washington = 145 miles

The decrease in travel time when the speed is increase by 20 mph =  minutes

The initial speed of the airplane, v = Required;

Solution;

\(t = \dfrac{145}{v}\)

\(t - \dfrac{12}{60} = \dfrac{145}{v + 20}\)

Therefore;

\(\dfrac{145}{v} - \dfrac{12}{60} = \dfrac{145}{v + 20}\)

Which gives;

\(\dfrac{145}{v + 20} - \dfrac{145}{v} + \dfrac{12}{60} = 0\)

Therefore

0.2·v² + 4·v - 2,900 = 0

v ≈ ±110.8 mph

The initial average speed of the airplane, v≈ ± 110.8 mph

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Answer:

5

Step-by-step explanation:

EF = 47 - 7x = 1/2 BC = 1/2 * (14+4x)

solve for x

x=6

so EF = 47-7*6 =  5

The answer is 2(x+3)

hope it helps!

Answer:

2x + 6

Step-by-step explanation:

2(x +3)

2x +6

multiply x by 2=2x

multiply 3×2=6

2x +6

Explanation:

The ratio we want to find can be thought of in the form in:out

We list the number of "in-state" people first followed by the "out-of-state" people next. A colon separates the two values. So we have the initial ratio of 108:63

Divide both parts by the GCF 9

The ratio 108:63 fully reduces to 12:7 meaning there are 12 in-state students for every 7 out-of-state students. The order is important because 7:12 would be incorrect and imply we had 7 in-state vs 12 out-of-state.

Answer:

i bleive that it is 261 havent done this in a wile tho

Step-by-step explanation:

15×12=180 ( did not divide because there are two of the same triangle) and 9×9=81 add them together and you get 216

Answer:

\(( \frac{1}{2} \times \frac{1}{3} ) + ( \frac{1}{2} \times \frac{1}{4} ) = \)

\( \frac{1}{2} ( \frac{1}{3} + \frac{1}{4} ) = \frac{1}{2} ( \frac{4}{12} + \frac{3}{12}) = \)

\( \frac{1}{2} \times \frac{7}{12} = \frac{7}{24} \)

The relative frequency for the 55 - 60 class is equal to 0.022.

In a frequency distribution table, a class width simply refers to the difference between the maximum) and minimum boundaries of any class in a data set.

This ultimately implies that, all classes must all have the same width in a frequency distribution table.

First of all, we would determine the total frequency as follows:

Total frequency = 8 + 10 + 6 + 7 + 15

Total frequency = 46.

Mathematically, the relative frequency of a class width can be calculated by using this formula:

Relative frequency = class frequency/total frequency

Relative frequency = 1/46

Relative frequency = 0.022

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

There are no specific ways of calculating the areas of a shaded region. Several questions may require different approaches.

I've added as an attachment, the missing figures.

Figure A

The figure can be divided into 2 by separating the top and the bottom. The resulting figures will be

The area of the rectangle is:

\(A_1 = 6cm \times (6 - 2)cm\)

\(A_1 = 6cm \times 4cm\)

\(A_1 = 24cm^2\)

The area of the square is:

\(A_2 = 2cm \times 2cm\)

\(A_2 = 4cm^2\)

So, the area of the shaded region is:

\(Area = A_1 +A_2\)

\(Area = 24cm^2 + 4cm^2\)

\(Area = 28cm^2\)

Hence, the area of the shaded region is \(28cm^2\)

Figure B

First, calculate the area of the big rectangle (8cm by 5cm)

The area of the rectangle is:

\(A_1 = 8cm \times 5cm\)

\(A_1 = 40cm^2\)

Next, calculate the area of the small rectangle (3cm by 2cm):

The area of the square is:

\(A_2 = 3cm \times 2cm\)

\(A_2 = 6cm^2\)

So, the area of the shaded region is:

\(Area= A_1 - A_2\)

\(Area= 40cm^2 - 6cm^2\)

\(Area= 34cm^2\)

Hence, the area of the shaded region is \(34cm^2\)

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The COGS margin percentage must be 40%, and the gross profit must be $17,250.

What is COGS margin?

Net sales less cost of goods sold equals gross margin (COGS). In other words, it is the amount of money a company keeps after deducting the direct costs of producing the goods and services it sells.

The income statement is missing, so the given information was:

Revenue =  100,000

COGS =  40,000

Gross Profit = 60,000

Salaries

Marketing

Rent

Earnings Before Tax 23,000

Income Tax 25%

We have to find the net income.

Since COGS are $40,000 and total sales are $100,000, the COGS margin percentage = 40,000 / 100,000 = 40%

Then earnings before taxes are $23,000 and taxes are 25%, then net income = $23,000 x (1 - 25%) = $23,000 x 75% = $17,250

Hence, the COGS margin percentage must be 40%, and the gross profit must be $17,250.

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Answer:

0.52

Step-by-step explanation:

250 females out of 479 total

250/479 = 0.5219206681

Rounded

0.52

Answer:

Step-by-step explanation:

Given:

Work:

Hence, the area of square is 25x⁶.

Hoped this helped.

\(BrainiacUser1357\)

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer:

149 inches squared

Step-by-step explanation:

top rectangle: 25 * 7 = 175

second rectangle: 8 * (25 - 17) = 8^2 = 64

triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10

175 + 64 + 10 = 149 sq in

hopefully got this right!

The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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The total volume of fluid that the patient takes in is:

V = 1284.13 mL

We need to add the total volume of liquid that the patient consumes.

First, we need to rewrite both volumes in mL, remember that:

1 pint = 568.26 mL

Then for the 1/2-pint of apple juice:

1/2 pint = (1/2)*568.26 mL = 284.13 mL

And:

1L = 1000L

For the liter we have:

1 L = 1000ml

Then the total volume of fluid that the patient takes in is:

V = 284.13 mL + 1000ml = 1284.13 mL

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Answer and Explanation:

The circumference of a circle is defined as:

\(C = 2\pi r\)

If we use 3.14 for π, then the formula becomes:

\(C = 2(3.14)r\)

\(C = 6.28r\)

A regular polygon with 40 sides that is the same size as a circle will have a perimeter closer to the circumference of the circle than a polygon with 20 sides.

We can think of a circle as having infinite tiny sides, so the more sides a regular polygon has, the closer its circumference gets to a circle.

We can plug the given radius (\(r\)) value into the above formula.

\(C = 6.28(9 \text{ cm})\)

\(C \approx \boxed{56.6 \text{ cm}}\)

It's the same process as for problem 2.

\(C = 6.28(9 \text{ in})\)

\(C \approx \boxed{150.7 \text{ in}}\)

This time, we can take the original formula:  \(C = 2(3.14)r\)  and notice that \(2r = d\), so we can substitute the given diameter (\(d\)) value for \(2r\) in that formula.

\(C = 3.14d\)

\(C = 3.14(14.22 \text{ mm})\)

\(C \approx \boxed{44.7 \text{ mm}}\)

This problem is the same as problems 1 and 2, but it's in word problem format. We can keep plugging into the circumference formula.

\(C = 6.28(9 \text{ in})\)

\(C \approx \boxed{56.5 \text{ in}}\)

These are equivalent to problem 4, but in word problem format. Keep plugging into the formula \(C = 3.14d\).

__________

The area of a circle is defined as:

\(A = \pi r^2\)

But we can plug in 3.14 for π:

\(A = 3.14r^2\)

__________

We can plug the given radius value into the above area formula.

\(A = 3.14(7 \text{ yd})\)

\(A \approx \boxed{21.98 \text{ yd}}\)

These are the same type of problem as 8, but since we are given the diameter (\(d\)), we have to divide it by 2 to plug it in for the radius (\(r\)).

\(r = \dfrac{d}{2}\)

Answer:

x = 12

Step-by-step explanation:

Because the two sides are parallel as shown, the two triangles are similar.

The lengths of corresponding sides of similar triangles are proportional.

Look at the large triangle first.

The upper side of the large triangle measures x + x + 6 = 2x + 6.

The lower side of the large triangle measures 8 + 12 = 20.

Now look at the small triangle at the right.

The upper side measures x + 6.

The lower side measures 12.

The corresponding sides of the large triangle to the small triangle are:

2x + 6 corresponds to x + 6.

20 corresponds to 12.

Since the lengths of the corresponding sides are proportional, we set up a proportion.

\( \dfrac{2x + 6}{x + 6} = \dfrac{20}{12} \)

Cross multiply.

\( 12(2x + 6) = 20(x + 6) \)

Divide both sides by 4.

\( 3(2x + 6) = 5(x + 6) \)

\( 6x + 18 = 5x + 30 \)

Subtract 5x from both sides. Subtract 18 from both sides.

\( 6x - 5x + 18 - 18 = 5x - 5x + 30 - 18\)

\( x = 12 \)

Answer:

(-8, -4) U (0, 4)

Step-by-step explanation:

Answer:

not answered this question

Kajal's expected value of playing this game is -$1

The given parameters are:

There are 26 black cards in a standard 52 card decks.

So, we have:

P(Black) = 26/52

There are 6 face cards that are not black in a standard 52 card decks.

So, we have:

P(Face card and not black) = 6/52

There are 20 other cards not in the above categories.

So, we have:

P(Others) = 20/52

The expected value is then calculated as:

\(E(x) = \sum x * P(x)\)

This gives

E(x) = 5 * 26/52 + 3 * 6/52 -  10 * 20/52

Evaluate the products

E(x) = 130/52 + 18/52 -  200/52

Evaluate the sum and difference

E(x) = (130 + 18 -  200)/52

This gives

E(x) = -52/52

Evaluate

E(x) = -1

Hence, Kajal's expected value of playing this game is -$1

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Rotation is the type of rigid transformation which is equivalent of two reflections across intersecting lines.

Define rigid transformation

A rigid  transformation is a transformation that persists the original size or shape of a given figure. Examples of rigid transformations are rotation, reflection etc;  

In mathematics a rigid transformation is also known as Euclidean Isometry or Euclidean transformation. Euclidean Isometry deals mainly with transformation of any figure. But, doesn't changes the length, shape or size of a given figure.

The concept of of two reflections across intersecting lines is equivalent to single rotation transformation of the original figure.  

Therefore the rigid transformation or Euclidean  isometry which is similar to two reflections across intersecting lines is rotation.  

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Answer:

\(= x^{2} -4x + 4\)

Step-by-step explanation:

A trinomial is an expression with three terms. tri = 3

\((x-2)^{2}\\ = (x-2)(x-2)\\= (x*x )+(-2*x)( -2*x)+(-2 * -2)\\= x^{2} -4x + 4\)

The answers are as follows:

1 Angle Bisector Theorem

2 Sum of Adjacent Angles

3 Co-interior angle property

4 Additive law

Given:

Note: Diagram for Question is attached

1. Angle Bisector Theorem

The angle bisector is BD. Bisection entails splitting into two equal pieces. Angles 3 and 4 are therefore equal.

2. Sum of Adjacent Angles

To determine the greater angle that is created by the two adjacent angles, add the two angles together.

3. Co-interior angle property

According to the co-interior property, the sum of interior angles (on the same side) formed when a single line crosses two parallel lines is equal to 180.

4. Additive law

By applying the additive law, we can take a value away from both sides of the equation without throwing the equation out of balance. Therefore, we may take 110 out of both sides of the equation to get the final result of 70.

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Answer:

5 students out of each of the 4 homeroom classes

Step-by-step explanation:

The most random sample is 5 students out of each of the 4 homeroom classes.

Thus, option (C) is correct.

Selecting 5 students from each of the 4 homeroom classes ensures that the sample represents a diverse range of students from different classes.

This approach helps to minimize bias and increase the randomness of the sample.

The other options, such as selecting the first 20 students who arrive at school or the last 20 people in line for breakfast, may introduce some bias based on the specific circumstances or characteristics of those groups. Selecting all 20 boys on the swim team would also not provide a representative sample of the overall student population.

Thus, option (C) is correct.

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The probability that the person has a tattoo is 230 out of 995.

We randomly select a person who responded to this survey. The calculation that gives the probability that the person has a tattoo is 230 out of 995.

Probability is a measure of the likelihood of a particular event occurring, typically expressed as a fraction or percentage.

The probability of an event occurring is calculated by dividing the number of favorable outcomes by the number of possible outcomes.

Therefore, the calculation that gives the probability that the person has a tattoo is 230 out of 995.

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