There are 3 roles and they are assigned randomly to 3 people ( Alice, Bob and Charlie ): Truth teller ( Always tells the truth ) Liar ( Always lies ) Spy ( Can tell truths and lies ) - Alice says she is not the truth teller - Bob says he is not the spy - Charlie says he is not a liar Deduce who has what role?

The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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Answer:

c=0.59p+2

Step-by-step explanation:

In the parallelogram ABCD the triangles that are similar to ΔAEX is -

Option 1: ΔCFX, Option 2: ΔADC, and Option 5: ΔCBA

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

The parallelogram ABCD is given.

AC is the diagonal of the parallelogram and EF is a line segment parallel to AB and CD in the parallelogram.

In ΔAEX and ΔADC -

m ∠AEX ≅ m ∠ADC, since they are corresponding angles.

m ∠A ≅ m ∠A, since they are reflexive angles.

So, ΔAEX ~ m ∠ADC, by AA similarity.

Similarly, in ΔAEX and ΔCFX -

m ∠EAX ≅ m ∠XCF, since they are alternate interior angles.

m ∠AXE ≅ m ∠CXF, since they are vertical angles.

So, ΔAEX ~ m ∠CFX, by AA similarity.

Now, in ΔAEX and ΔCBA -

Since, EF is parallel to AB then AEFB is also a parallelogram because ABCD is a parallelogram.

Then m ∠E ≅ m ∠B, since they are opposite angles of parallelogram AEFB.

m ∠EAX ≅ m ∠ACB, since they are alternate interior angles.

So, ΔAEX ~ m ∠CBA, by AA similarity.

Therefore, the similar triangles are ΔADC, ΔCFX, ΔCBA.

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The present ages are the Boy is 17 years old and his sister's age is 14 years old.

Since the ratio of ages is 4: 3 take them as 4x and 3x and form an equation as given in the problem. Solve the resultant equation for the values of 'x'. And calculate the ages 5 years ago and add 5 to get the present ages.

Here we have

A boy is older than his sister by 3 years  

Then the difference is both ages = 3

Given that five years ago the ratio of ages = 4: 3  

Let 4x and 3x be the age of a boy and his sister five years

As we know the difference between them = 3 years

=> 4x - 3x = 3

=> x = 3 years

=> 4x = 4(3) = 12

Boy's age after '5' years = 12 + 5 = 17 years

His sister's age = 17 - 3 = 14 years

Therefore,

The present ages the Boy is 17 years old and his sister's age is 14 years old.

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Complete Question:

A boy is older than his sister by 3 years, five years ago the ratio was 4:3. Find his present age.

An online calculator of simplifying fractions is a tool that can be used to reduce a fraction to its simplest form or lowest terms.

These calculators are easily accessible on the internet and are designed to make it easy for users to simplify fractions quickly and accurately. To use the calculator, users simply input the numerator and denominator of the fraction they wish to simplify.

The calculator then performs the necessary calculations to find the greatest common factor of the numerator and denominator and divides both by this factor to provide the simplified fraction. These calculators can be especially helpful for students and professionals who need to simplify a large number of fractions or who are learning how to simplify fractions for the first time.

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2.75 can be written as a fraction in lowest terms as 11/4.

To convert a decimal like 2.75 to a fraction, we can follow these steps:

Step 1: Write the decimal as a fraction with the decimal as the numerator and 1 as the denominator.

In this case, we can write 2.75 as a fraction with a denominator of 1:

= 2.75/1

Step 2: Multiply the numerator and denominator of the fraction by 10 until the decimal is gone.

We can remove the decimal by multiplying both the numerator and denominator by 100 (since there are two decimal places):

2.75/1 x 100/100 = 275/100

Step 3: Simplify the fraction.

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case:

275/100 ÷ 25/25 = 11/4

Therefore, the fraction is 11/4

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Answer:

0 triangles can be formed

Step-by-step explanation:

In order to determine the number of distinct triangles that can be formed with the given information, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's start by drawing a rough sketch of the triangle:

     Z

     |\

     | \

     |   \ x

     |     \

     |       \

     X-----Y

      y=2

We know that mZX = 51°, so we can label that angle on our diagram:

     Z

     |\

     | \

     |   \ x

     |     \

     |51°  \

     X-----Y

      y=2

We can use the sine law to find the length of side XY:

sin(51°) = XY / 5

XY = 5 * sin(51°)

XY ≈ 3.95

Now we need to check whether XY is less than the sum of the other two sides, XZ and YZ:

XZ + YZ > XY

2 + √(x² - XY²) > XY

2 + √(5² - 3.95²) > 3.95

2.86 > 3.95 (false)

Since XY is greater than the sum of the other two sides, it is not possible to form a triangle with the given measurements. Therefore, the number of distinct triangles that can be formed is 0.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

68 kilograms is approximately equal to 149.91416 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

It is currently defined based on the fixed numerical value of the Planck constant, h,

Which is equal to 6.62607015 × 10-34 in the units of J·s.

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms.

To convert 68 kilograms to pounds,

We need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

68 kilograms multiplied by 2.20462 gives us:

68 kg x 2.20462 = 149.91416 pounds

(rounded to five decimal places)

So, 68 kilograms is approximately equal to 149.91416 pounds.

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Answer:

unit rate = $ 10 per km.

y = 10x

Step-by-step explanation:

Unit rate:

    Cost of travelling 1 km is $ 10. So, unit rate is $10

Equation:

       If 'x' km distance is travelled, then cost 'y',

              y = x * unit rate

               y = x * 10

               y = 10x

iv or IV is actually a roman numeral. By the mathematics roman numeral system we can figure out that IV is 4 in normal number system.

Roman numerals are a system of numbers that were first utilized in ancient Rome and were widely used throughout Europe well into the Late Middle Ages. Numbers are represented by Latin letter combinations with fixed integer values.

Roman numerals continued to be used for a very long time after the fall of the Roman Empire. Beginning in the 14th century, Roman numerals began to be gradually replaced by Arabic numerals, but some applications continue to use Roman numerals today.

In ancient Rome, usage was extremely diverse, and in medieval Europe, it was completely disorganized. Variant forms are even defended by some contemporary writers as providing improved "flexibility," despite the post-renaissance restoration of a largely "classical" notation failing to produce total consistency.

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The cost of the top of the table, to the nearest naira, is 7678.

Area of circle can be defined as the product of pi and square of radius of circle.

The area of the circular table top can be found using the formula for the area of a circle:

[tex]A = pi*r*r[/tex]

where r is the radius of the entire circle.

[tex]A = π(1m)^2 = π m^2[/tex]

The area of the inner glass section can also be found using the same formula, but with the radius of the glass section:

A_glass =[tex]π(0.75m)^2 = 0.5625π m^2[/tex]

The area of the outer wooden section can be found by subtracting the area of the inner glass section from the area of the entire circle:

A_wood = A - A_glass = [tex]π m^2 - 0.5625π m^2 = 0.4375π m^2[/tex]

The cost of the glass section is 2500 per m², so the cost of the glass section can be found by multiplying the area of the glass section by the cost per square meter:

Cost_glass = [tex]0.5625π m^2 × 2500/m² ≈ 4418.60[/tex]

Similarly, the cost of the wooden section can be found by multiplying the area of the wooden section by the cost per square meter:

Cost_wood [tex]= 0.4375π m^2 × 1500/m² ≈ 3259.68[/tex]

The total cost of the table top is the sum of the cost of the glass section and the cost of the wooden section:

Total cost = Cost_glass + Cost_wood ≈ 7678.28

Therefore, the cost of the top of the table, to the nearest naira, is 7678.

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Answer:

Step-by-step explanation:

first step you want round that into decimal

The length of the side AC of the right-angled triangle is equal to 24cm by comparison using the trigonometric ratio of sine of angle B.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangles ABC and DBC, we shall evaluate for the length AC using the trigonometric ratio of sine for the angle B° to derive an equation as follows:

For ∆ABC;

sin B = AC/BC {opposite/hypotenuse}

For ∆DBC;

sin B = 24cm/BC {opposite/hypotenuse}

thus;

AC/BC = 24cm/BC

Therefore, by comparison using the trigonometric ratio of sine for the angle B, we have the length of AC equal to 24cm.

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The scale factor of the dilation that takes P to Q is,

⇒ 4/5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

⇒ Quadrilateral P and Q are similar.

Hence, The scale factor of the dilation that takes P to Q is,

⇒ 2 / 2.5

⇒ 20 / 25

⇒ 4/5

Thus, The scale factor of the dilation that takes P to Q is, 4/5.

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The conversion of 24 mm into inches is 0.94488 inches.

Millimeter (mm) and inch are both units of length or distance, but they are used in different parts of the world.

A millimeter is a metric unit of length used in most countries outside the United States. It is equal to one-thousandth of a meter (1/1000 of a meter), or approximately 0.03937 inches.

To convert millimeters (mm) to inches, you can use the conversion factor of 1 mm = 0.03937 inches.

So, to convert 24 mm to inches, you can multiply 24 by 0.03937:

24 mm * 0.03937 inches/mm = 0.94488 inches

Therefore, 24 millimeters is approximately equal to 0.94488 inches.

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The lengths of the missing sides are: y = 7.0 * sqrt(2) and x = 7.0 * sqrt(2)

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

According to the 45-45-90 triangle theorem, the two legs of a 45-45-90 triangle are congruent and the hypotenuse is the square root of 2 times the length of the legs. Therefore, if the side opposite the 45-degree angle is 7, then the other leg is also 7.

Let's label the hypotenuse as h. We know that h is the side opposite the right angle, so h = x. Using the Pythagorean theorem, we can find the length of x:

[tex]x^2 = 7^2 + 7^2x^2 = 98x = sqrt(98) = 7.0 * sqrt(2)[/tex]

So the length of the hypotenuse is 7.0 * sqrt(2).

Now let's find the length of the side opposite the other 45-degree angle, which we'll label as y. Since the two legs are congruent, y is also equal to 7.0 * sqrt(2).

Therefore, the lengths of the missing sides are: y = 7.0 * sqrt(2) and x = 7.0 * sqrt(2)

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Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)

The dividend divided by the price is the Dividend yield. The ratio of a company's annual dividend to its stock price.

Dividend Yield:

Dividend yield is expressed as a percentage and is a financial ratio (dividend/price) that indicates how much a company pays in annual dividends as a share price. The reciprocal of the dividend yield is total dividends/net income, which is the dividend payout ratio.

The dividend yield is an estimate of the dividend yield of a stock investment. Assuming dividends don't rise or fall, yields rise when stock prices fall. Conversely, when stock prices rise, they fall. Dividend yields vary with share price, so stocks that are rapidly declining in value may seem unusually high dividend yields.

The formula for dividend yield is as follows:

Dividend Yield = Annual Dividends Per Share/ Price Per Share

​The dividend yield can be calculated based on the financial statements for the past year. This is permitted during the first few months after the company's annual report is issued. However, the more time has passed since the release of the annual report, the less relevant this data is to investors. Alternatively, investors may add the last 4 quarter dividends to reflect dividend data for the last 12 months. It is acceptable to use the dividend numbers that follow, but yields may be too high or too low if the dividend has been recently cut or raised.

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​

Answer: To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

Step-by-step explanation:

When x = 6 and y = -4, the value of of the expression 50-3(x²-y²)+x is -4.

An algebraic expression is when we use numbers and words in solving a particular mathematical question.  The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Substitute x=6 and y=-4 into the expression 50-3(x²-y²)+x:

50 - 3(6² - (-4)²) + 6

= 50 - 3(36 - 16) + 6

= 50 - 3(20) + 6

= 50 - 60 + 6

= -4

Hence, when x = 6 and y = -4, the value of 50-3(x²-y²)+x is -4.

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The demand curve under monopoly is less elastic than under monopolistic competition because there are no close substitutes under monopoly.

Monopoly:

A monopoly is a business characterized by no competition in the market and no substitute for a product. A monopoly can dictate price fluctuations and create barriers for competitors to enter the market.

A company controls the entire supply chain from production to sales through vertical integration, or becomes a monopoly by acquiring competitors in the market through horizontal integration to become a monopolistic producer.

Monopolistic Competition:

Monopolistic competition exists when many companies offer competing products or services that are similar but not perfect substitutes.

Barriers to entry into monopolistic competition industries are low, and decisions by one company do not directly affect competitors. Competitive companies vary in their pricing and marketing decisions.

The demand curve for monopolistic firm less elastic because the demand curve under monopoly is less elastic than under monopolistic competition because there are no close substitutes under monopoly. The demand curve under monopolistic competition is similar to the monopoly curve. However, the key difference between monopoly and monopolistic competition is that it is monopolistic competition. The demand curve is more elastic. This means that the quantity demanded changes more as the price changes. This is because in monopolistically competitive markets there are substitutes that are close to goods, and in monopolistic markets there are no close substitutes.

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An algebra over a field F is a vector space over F equipped with a bilinear operation called multiplication.

Let F be a field and let A be a vector space over F. An algebra over F is a triple (A, ×, 1) where × is a bilinear operation A x A -> A, and 1 is an element of A such that:

a × (b × c) = (a × b) × c for all a,b,c in A (associativity)

There exists an element 1 in A such that a × 1 = a = 1 × a for all a in A (existence of identity)

a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) for all a,b,c in A (distributivity)

a × b = b × a for all a,b in A if and only if A is commutative

The operation × is usually referred to as multiplication and the element 1 as the unit or identity element.

Examples of algebras over a field F include the set of n x n matrices over F, the polynomial ring F[x], and the complex numbers C, which can be viewed as an algebra over the field of real numbers R.

Therefore, the algebra over a field F has been explained

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In Python, the term "hitters data" refers to a dataset that details the hitting statistics of Major League Baseball (MLB) players.

It is a well-known dataset in the area of sports analytics and is frequently utilized in applications for data analysis and machine learning.

The player name, team, and different statistics like hits, runs, home runs and batting averages are often variables in the Hitters dataset. To examine player performance and spot trends or patterns in the data, the dataset may be employed.

The Hitters dataset may be imported and worked with in Python using a variety of tools, including Pandas, NumPy, and Scikit-learn. Based on Hitter's data, these libraries enable data cleansing, exploratory analysis, and the construction of predictive models.

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Answer: 50.27

Step-by-step explanation:

AB=πr2=π·42≈50.26548

Answer:

Number of $5 notes = 18

Number of $10 notes = 15

Step-by-step explanation:

Let the number of $5 notes be 'x' and the number of $10 notes be 'y'.

      Total number of notes = 33

                  x + y = 33 -------------------(I)

       The value of $5 notes = 5*x = 5x

       The value of $10 notes = 10 *y = 10y

          Total amount = $240

          5x + 10y = 240

Divide the entire equation by 5,

             [tex]\sf \dfrac{5}{5}x+\dfrac{10}{5}y=\dfrac{240}{5}\\\\[/tex]

                x + 2y = 48 -----------------------(II)

Multiply the equation (I) by (-1) and then add to equation(I) and so the x will be eliminated, and we can find the value of 'y'.

(I)* (-1)                -x -   y  = -33

(II)                      x + 2y = 48  {Now add}

                               y     = 15

                             [tex]\boxed{\bf y = 15}[/tex]

Substitute y = 15 in equation(I)

              x + 15 = 33

                      x = 33 - 15

                      x = 18

                          [tex]\boxed{\bf x = 18}[/tex]

Number of $5 notes = 18

Number of $10 notes = 15

The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

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The length of w is 33.8 inches.

What is Sines law?

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is also known as the sine rule.

What are opposite angles ?

If two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°. And the angle adjacent to angle X will be equal to 180 – 45 = 135°. When two lines meet at a point in a plane, they are known as intersecting lines.

This is a law of sines problem since the triangle that contains side WY has all the angle measures & one of side measures.

a/sin a = b/sin b

7.3/sin 39 = YW/sin 8

YW = 7.3sin 8/sin 39 = 33.8

Hence , the length of w is 33.8 inches.

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Answer:

200 * 25/100 --> 25% of 200

200 * 15/100 --> 15% of 200

100 * 35/100 --> 35% of 100

Step-by-step explanation:

Percentages are always out of 100 ( e.g 60% is equivalent to 60/100) and whole numbers have a denominator of 1 meaning you could simply solve this sort of problem if you set it up right.

For example) 25% of 200

25/ 100  *  200/1

25 * 200 is 5000 and 100 * 1 is 100

So the answer would be 5000/100 (which you would simplify to get the right answer but that's just an example)

Hope you have a great day :)

The expected temperature on February 15 would be 77.72 °F.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness.

Given is that the average daily temperature in Peoria, Illinois, can be predicted using the formula T = 50 - 28cos[2π(x−31)365], where {x} is the number of the day in the year.

The value of {x} for February 15 would be -

{x} = 46

So, we can write the temperature as -

T{46} = 50 - 28 cos[2π(46−31)365]

T{46} = 50 - 28 cos[2π x 15 x 365]

T{46} = 50 - 28 cos[2π x 15 x 365]

T{46} = 50 - 28 cos[34383]

T{46} = 50 - 28 x -0.99

T{46} = 77.72

Therefore, the expected temperature on February 15 would be 77.72 °F.

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