what is the difference between relative frequency and cumlative relative frequency

The homogeneity of variance assumption in the independent measures t-test assumes that option (c) the variances of the two populations from which the samples are drawn are equal.

In mathematical terms, the t-test assumes that the two populations from which the samples are drawn have equal variances. The homogeneity of variance assumption is important because it affects the calculation of the t-statistic.

When the variances of the two populations are equal, the t-test uses a pooled estimate of the variance to calculate the standard error of the difference between the two sample means.

If the homogeneity of variance assumption is violated, meaning the variances of the two populations are not equal, the t-test may produce inaccurate results.

In this case, an alternative test such as Welch's t-test may be used. Welch's t-test does not assume equal variances and is therefore more robust when the homogeneity of variance assumption is violated.

Therefore, the right choice is option (c).

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In C programming, an integer array is a collection of integer values identified by a unique index within the array.

In C programming language, a whole number exhibit is an information structure that holds a grouping of number qualities. A cluster is an assortment of components of similar information type, where every component is recognized by a one of a kind record or position inside the exhibit. Number exhibits in C are proclaimed utilizing a particular language structure, which incorporates the information type and the size of the exhibit. For instance, to pronounce a number cluster with ten components, you can utilize the accompanying linguistic structure:

int myArray[10];

Once announced, you can get to individual components of the cluster utilizing their record, what begins from 0. For instance, to dole out a worth of 5 to the main component of the exhibit, you can utilize the accompanying sentence structure:

myArray[0] = 5;

In general, whole number exhibits are a helpful device in C programming for putting away and controlling assortments of number qualities.

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The depth of Elk River on Day 3 can be estimated by looking at data from previous days.

You can look at the average depth of the river during different times of day, or research historical data to get an idea of what the depth may be.

Additionally, local weather forecasts can be consulted to determine if there are any expected changes in the water level of the river.

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The conversion factor for changing centimetres to feet is 0.032. Thus, the conversion of 150 centimetres in feet is equals to the 4.92 feet.

A conversion factor is a number used to convert one set of units into another set of units by multiplication or division. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So,150 meters

= 150 × 3.28 feet

= 492 feet --(1)

But we need to convert 150 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 150 meters = 15000 centimeters --(2). Now from equations (1) and (2),

15000 centimeters = 492 feet,

Divide both parts by 100,

=> 150 centimetres = (492/100 ) feet

= 4.92 feet

Hence required value is 4.92 feet.

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There are various online tools available to calculate the slope and y-intercept of a linear equation given two points or a slope and one point.

To calculate the slope and y-intercept, enter the necessary input data into the online calculator and click the "calculate" button. The output will provide you with the values of the slope and y-intercept of the line, as well as an equation of the form

where m is the slope and b is the y-intercept. This can be a useful tool for quickly finding the equation of a line or checking your own work.

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The mural has a height equal to 10 feet.

In this problem we find the case of a square mural, whose area is already known. The following conditions associated with the statement of the problem are described below:

A = 100 ft²

A = l²

Where:

Then, the height of the mural is equal to:

100 ft² = l²

l = 10 ft

The height of the mural is 10 feet.

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The mathematical formula v = 1/3 πr²h is the formula for calculating the volume of a cone.

The volume of a cone is the amount of space or the capacity of the cone.

The formula for determining the volume of a cone is:

Volume, v = ¹/₃ πr²h

where

For example:

Calculate the volume of a cone if r= 2 cm and h= 5 cm.

V= ¹/₃ × 22/7 × 2² × 5

V = 20.95 cm³

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We know that Angle-side-angle is one of the criterias to find congruent triangles, then with the given information we can make only one unique triangle.

Here we know two of the angles of a triangles and the length of the side between these two angles.

This can be written as an: Angle-Side-Angle.

Remember that this is one of the conditions for congruent triangles.

This means that A-S-A defines completely a single triangle, thus, there is only one triangle that we can make with that information.

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The volumes of the given cube and rectangular prisms in cubic centimeters are:

1) Cube with a side length of 2/5 cm: 8/125 cm^3

2) Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm respectively: 36/125 cm^3

3) Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3.5 cm respectively: 6/125 cm^3

4) Cube with a side length of 1/5 cm: 1/125 cm^3

To find the volume of a cube or rectangular prism, you need to use the formula:

Volume = length x width x height

The length, width, and height represent the three dimensions of the object, which are measured in units such as centimeters, meters, or inches. To find the volume in cubic centimeters, you would use centimeters as your unit of measurement.

For example, let's say we have a cube with a side length of 2/5 cm. To find the volume, we would use the formula:

Volume = length x width x height

Volume = 2/5 cm x 2/5 cm x 2/5 cm

Volume = 8/125 cm^3

So the volume of this cube is 8/125 cubic centimeters.

Similarly, for the other pairs:

Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm respectively:

Volume = length x width x height

Volume = 3/5 cm x 4/5 cm x 3/5 cm

Volume = 36/125 cm^3

Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3.5 cm respectively:

Volume = length x width x height

Volume = 1/5 cm x 2/5 cm x 3.5 cm

Volume = 6/125 cm^3

Cube with a side length of 1/5 cm:

Volume = length x width x height

Volume = 1/5 cm x 1/5 cm x 1/5 cm

Volume = 1/125 cm^3

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The given question is incomplete, the complete question is :

D rag the tiles to the correct boxes to complete the pairs. Find the volume of the cubes or rectangular prisms in cubic centimeter's answers: 6/125 cm^3, 36/125 cm^3, 8/125 cm^3, 1/125 cm^3.the pairing questions are :cube with a side length of 2/5 cm,,,, rectangular prism with a length width and height of 3/5 cm 4/5 cm and 3/5 cm respectively.,,, rectangular prism with a length width and height of 1/5 cm, 2/5 cm, and 3,5 cm respectively and cube with a side length of 1/5cm.

Answer:

1

Step-by-step explanation:

To predict the number of students who will receive historical fiction novels for free reading time, we need to use the concept of probability. Probability is the likelihood of an event occurring, and is expressed as a number between 0 and 1.

In this case, there are a total of 10 + 2 + 8 = 20 books in Miss Nestor's basket. Of these, 2 are historical fiction novels. Therefore, the probability of a student randomly selecting a historical fiction novel from the basket is:

P(historical fiction) = number of historical fiction novels / total number of books

P(historical fiction) = 2/20 = 0.1

This means that there is a 10% chance that a student will randomly select a historical fiction novel from the basket. To predict the number of students who will receive historical fiction novels, we can multiply the probability by the total number of students:

Number of students receiving historical fiction = Probability of historical fiction * Total number of students

Number of students receiving historical fiction = 0.1 * 10

Number of students receiving historical fiction = 1

Therefore, the best prediction of the number of students who will receive historical fiction novels for free reading time is 1.

꧁༒αηѕωєяє∂ ву gσ∂кєу༒꧂

Answer:

1.07 x 10^8

Step-by-step explanation:

Hence, 10(5 + 3) is the equation that represents 50 + 30 written as the product of two elements.

It is able to multiply, divide, add, or deduct in mathematics. The follows is how an utterance is put together: Number, expression, and mathematical operator The components of a linear equation include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast terms and phrases. An expression, usually known as an algebraic expression, is there any mathematical statement that contains variables, quantities, and an arithmetic function between them. For instance, the word m in the given equation is distinguished from the words 4m and 5 by the arithmetic symbol +, just like the variable m in the statement 4m + 5.

given

Check each choice.

(A) 5(10 + 7)

= 5(10) + 5(7) (7)

= 50 + 35

(B)5(10+ 3)

= 5(10) + 5(3) (3)

= 50 + 15

(C)10(5+ 2)

= 10(5) + 10(2) (2)

= 50 + 20

(D) 10(5 + 3)

= 10(5) + 10(3) (3)

= 50 + 30

Hence, 10(5 + 3) is the equation that represents 50 + 30 written as the product of two elements.

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Number of people were invited on Friday is 2^3 = 8 and  the value of the power is 3

Let's track the number of invitations over the course of the week:

Monday: 2 invitations

Tuesday: Each of the 2 friends invited 2 more friends, for a total of 2 x 2 = 4 invitations

Friday: Each of the 4 friends invited 2 more friends, for a total of 4 x 2 = 8 invitations

So on Friday, there were a total of 8 invitations. We can write this as 2^3, since we started with 2 invitations and multiplied by 2 three times (once for each round of invitations). Therefore, the value of the power is 3.

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The standard deviation of the content weight distribution is historically 0.04 fluid ounces. a mean setting of 12 ounces will result in 50% of the bottles having less than the advertised weight. This statement is false.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Since the weight of the contents in the bottles follows a normal distribution, we can use the standard normal distribution to calculate the proportion of bottles that have contents below the advertised weight.

Let's define the random variable X as the weight of the contents in a bottle.

Then, we can standardize X by subtracting the mean weight (12 fluid ounces) & dividing by the standard deviation (0.04 fluid ounces):

Z = (X - μ) / σ

where μ = 12 and σ = 0.04.

We want to find the proportion of bottles that have contents below 12 fluid ounces, which is equivalent to finding the probability that Z is less than 0 -

P(Z < 0) = 0.5

This means that 50% of the bottles will have contents below the advertised weight if the mean setting is 12 ounces.

However, the problem states that state law requires that no more than 0.3% of the bottles can have contents below the advertised weight.

This means that we need to find the probability that Z is less than some value such that the area under the standard normal distribution to the left of that value is 0.003.

We can find this value using a standard normal distribution table or calculator -

P(Z < z) = 0.003  

z ≈ -2.88

Therefore, the mean setting needs to be adjusted such that the mean weight of the contents is at least 12 + (-2.88) x 0.04 = 11.856 fluid ounces to ensure that no more than 0.3% of the bottles have contents below 12 fluid ounces.

Therefore, the statement in false.

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Answer:

Both have 4 points, and sides.  

Squares have 4 even sides

Rectangles have 2 short sides and 2 long sides.

If we have an angle equal to 175.5°, then its supplementary angle is equal to 4.5°.

To solve this problem we must know that an angle and its supplementary add up to 180º, that is, the following equality must be satisfied:

β + α = 180º

The measure of a supplementary angle is the difference between 180° and the given angle. In this case, the given angle is 175.5°. To find the measure of the supplementary angle, we will subtract 175.5° from 180°.
α = 180° - 175.5° = 4.5°

Therefore, the measure of the supplementary angle is 4.5°.

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The lateral surface area of the pyramid is 108 square feet.

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Given:
The shape is a square pyramid.

To find the lateral surface area of the square pyramid:
Use the formula,

the lateral surface area of the pyramid = 1/2 x (perimeter of the base x slant height)

Here, we have,

Slant height = 9 feet.

The side of the square = 6 feet.

So, the lateral surface area of the pyramid = 1/2 x (4 x 6 x 9)

= 108 square feet.

Therefore, the area is 108 square feet.

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The cook still needs 24 kilograms of beans to complete the recipe. The cook has a total of 2 bags of beans, each containing 7 kilograms of beans.

Therefore, the total weight of the beans he has is 2 * 7 = 14 kilograms.

To find out how many more kilograms of beans he needs, we can subtract the weight of the beans he has from the total amount he needs. Therefore:

Amount of beans the cook needs - Amount of beans the cook has = Amount of beans he still needs

Substituting the values we get:

38 - 14 = 24

Therefore, the cook still needs 24 kilograms of beans to complete the recipe.

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Answer:

In order for f

to have an inverse, it must be a bijection. That is, it must be an injection and a surjection. So we must restrict the domain and codomain appropriately. It is standard that the square root operation returns positive values, so we use that as the basis for our restriction.

The answers to each type of quadrilateral given below.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given:

A quadrilateral with a pair of opposite sides parallel but not congruent is a Trapezium.

A quadrilateral with a pair of opposite sides congruent not parallel

is isosceles trapezoid.

A quadrilateral with 2 pairs of congruent angles is a parallelogram.

A quadrilateral with one right angle is right quadrilateral. .

A quadrilateral with two consecutive congruent sides is Kite.

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Answer: 41.3386

Step-by-step explanation:

We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.

Summary of Result:

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:

Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).

SST = ΣΣ(yij - ȳ)^2 = 359.2

where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.

SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2

where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.

SSE = SST - SSTR = 241.0

Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.

df(Total) = N - 1 = 14

where N is the total number of observations.

df(Treatment) = k - 1 = 2

where k is the number of treatment levels.

df(Error) = df(Total) - df(Treatment) = 12

Step 3: Calculate the mean square (MS) for SSTR and SSE.

MS(Treatment) = SSTR / df(Treatment) = 59.1

MS(Error) = SSE / df(Error) = 20.1

Step 4: Calculate the F-statistic.

F = MS(Treatment) / MS(Error) = 2.94

Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.

From a table of F-distributions, the critical value of F is 3.89.

Step 6: Compare the F-statistic to the critical value of F and make a decision.

Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.

Step 7: Summarize the results in an ANOVA table.

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.

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Answer:

The number of terms in the series is (n-m+3)/3, where n is the last term in the series.

From the above question we conclude that when [tex]\sqrt[x]{5} + \sqrt[4x]{5}[/tex] simplifies to

[tex]\sqrt[5x]{5}[/tex].

What is the simplifying expressions involving square roots?

In this case, we combined like terms by adding x√5 and 4x√5, which resulted in (x + 4x)√5 = 5x√5. This involves the distributive property of multiplication over addition, and simplification of expressions involving radicals.

We can simplify the given expression as follows:

[tex]\sqrt[x]{5} + \sqrt[4x]{5}[/tex]

= [tex]\sqrt[(x+4x)]{5}[/tex]

=[tex]\sqrt[5x]{5}[/tex]

Hence,  [tex]\sqrt[x]{5} + \sqrt[4x]{5}[/tex] simplifies to [tex]\sqrt[5x]{5}[/tex].

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Answer:

Angle 6 is 130 degrees

Vertical angles are 1 and 4, 2 and 3

Alt angles are 3 and 6, 4 and 5

Alt Exterior angles are 2 and 7, 8 and 1

Corresponding angles are 2 and 6, 1 and 5

Step-by-step explanation:

[tex]{\qquad \qquad \huge \rm \underline { \underline{ Répondre}}}[/tex]

Standard equation of an ellipse is :

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {(x - h)}^{2} }{ {a}^{2} } + \dfrac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

If b is smaller than a, then it will be a horizontal ellipse, and if b is greater than a, it will be a vertical ellipse. and shifting depends upon coordinates of its centre.

Now, our given equation is :

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ 15 } + \dfrac{ {y }^{2} }{ {10} } = 1[/tex]

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ {(\sqrt{15})}^{2} } + \dfrac{ {y}^{2} }{ {(\sqrt{10}) {}^{2} } } = 1[/tex]

[ here, b = root 10 and a = root 15, hence a is greater than b here, which means : its a horizontal ellipse.

And since it is a horizontal ellipse with center at origin, it's major axis will lie on x - axis.

Now we can solve for x by simplifying and isolating x on one side of the equation:

3x - x = 7 - 1

2x = 6

x = 3

Therefore, the value of x is 3.

In order to determine whether two lines are parallel, we must compare their slopes. Two lines are only considered parallel if and only if their slopes are equal. The conventional version of the equation is 2x - 3y = 4. Line q must have a slope of -2/-3 = 2/3 as a line with the equation Ax + By = C frequently has a slope of -A/B.

Since <1 and <2 are corresponding angles formed by two parallel lines and a traversal, they are congruent.

m<1 = m<2

(3x-7)* = (x-1)*

We can remove the asterisks on both sides of the equation since they represent the same unit of measurement for the angles.

3x - 7 = x - 1

Now we can solve for x by simplifying and isolating x on one side of the equation:

3x - x = 7 - 1

2x = 6

x = 3

Therefore, the value of x is 3.

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Answer: An increase in demand or a reduction in supply will increase the equilibrium wage. A reduction in demand or an increase in supply will reduce the equilibrium wage.

Step-by-step explanation:

Wages in a competitive market are determined by demand and supply. An increase in demand or a reduction in supply will increase the equilibrium wage. A reduction in demand or an increase in supply will reduce the equilibrium wage.

The weight 132 Kg is approximately equivalent to  291 pounds (lbs) .

Both the units Pounds (lbs) and Kilogram (kg) are both the units of measurement of weights or mass .

We know that , 1 Kilogram is approximately equal to 2.2046 pounds (lbs) .

So , the conversion factor to convert the given weight becomes 2.2046  ;

We multiply the given weight with the conversion factor ,

We can write  ;

⇒ 132 Kg = 132 × 2.2046

⇒ 132 Kg = 291.0072 lbs ≈ 291 lbs .

Therefore , 132 Kg is approximately equal to 291 lbs .

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