a population of women has 40% with dark eyes. if a sample of 20 women are selected from this population, what is the probability that exactly ten of the women have dark eyes?

Answer:

$1,625

Step-by-step explanation:

a) class interval that contains the median is: 2 ≤ h ≤ 3

b) An estimate for the mean numbers of hours: 23

In statistics, the median is the value that, when placed in order, falls in the centre of the supplied collection of data. Either descending or ascending order can be used to arrange the data or observations. The median of 2,3,4, for instance, is 3. The median is a form of average that is used to determine the center value in mathematics. The middle pair must be identified, added, then divided by two in order to calculate the median value in a list of even integers.

To find median class calculating cumulative freq. (cf) of less than type first:

Number of hours(h)        frequency(f)           cf

0 ≤ h ≤ 1                               4                         4

1 ≤ h ≤ 2                               8                         12

2 ≤ h ≤ 3                              11                         23

3 ≤ h ≤ 4                               7                         30

N/2 = 30/2

Where, N = ∑f

N = 15 ∑cf > N/2

so, median class is 2 ≤ h ≤ 3 since cf 23 is corresponding to this class.

Therefore class interval that contains the median is: 2 ≤ h ≤ 3.

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Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.

Since that it has three sections and two vertices, a triangular qualifies as a polygon. It corresponds to the essential geometric patterns. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. Because when three principles are not linearly related, a unique plane composite triangle in Geometric shapes are discovered. Triangles are polygons because they have three sections and three corners. The points where it three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

m∠ELG = 124°

m∠ELD = 2x

Thus:

m∠ELG + m∠ELD = 180° (linear pair)

Substitute

124 + 2x = 180

2x = 180 - 124

2x = 56

x = 56/2

x = 18

Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.

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The exponential growth factor of the given function is 7.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

The slope of the line that represents a linear relationship is equal to the growth factor. When the relationship is shown as an equation in the form y = mx + b, the growth factor is also equal to the value of m.

Given exponential function is

y = 4 * 5⁷.

Now compare the given function with y = P₀e^k

P₀ = 4

e = 5

k = 7

The growth factor is 7.

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As per the concept of permutation,  there are 362,880 possible arrangements of the letters of "sociological."

In mathematics and combinatorics, the number of arrangements of a set of objects is calculated using a formula called permutation.

When it comes to the word "sociological," there are 9 letters, and we want to calculate the number of arrangements that can be made using all 9 letters.

To find the number of arrangements, we can use the formula for permutation.

In this case, it would be

=> 9!

which is equal to

=> 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =  362,880

Complete Question:

How many arrangements are there of all the letters of word "sociological" calculate it by using the permutation method?

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For the given data, probability of union of A and B (A U B) is 0.95, intersection P(A n B) = 0.75.

Set theory terms like the union and intersection are used to describe the connection between two or more sets.

The set containing all items that are a part of either set A, set B, or both sets is the union of the two sets A and B. The symbol for it is A U B.

The set containing all elements that are a part of both sets A and B is the intersection of the two sets A and B. It has the symbols A and B.

a) We may apply the formula for the union of two events to determine P(A U B), or the likelihood that either A or B will occur:

P(A U B) = P(A) + P(B) - P(A n B)

Plugging in the given values:

P(A U B) = 0.9 + 0.8 - 0.75 = 0.95

b) P(A n B), the probability of both A and B happening, is already given as 0.75. So, P(A n B) = 0.75.

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The length of any side of the square basket would be 6 feet.

What are Square roots and length?

In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.

The word "length" refers to the size of an object or the separation between two points. For instance, the length of a ruler is indicated below and indicates how long the ruler is.

You can find this by finding the square root of 36, which is 6.

The length of any side of the square basket would be 6 feet.

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The equivalent expression to ( x - 3 )² is  x² - 6x + 9.

Given the expression in the question;

( x - 3 )²

To simplify, first write ( x - 3 )² as;

( x - 3 )( x - 3 )

Now, expand using FOIL Method

x( x - 3 ) -3( x - 3 )

x×x + x×-3 - 3×x - 3×-3

x² - 3x -3x + 9

Collect and add like terms

Add -3x and -3x

x² - 6x + 9

Therefore, the simplified form is x² - 6x + 9.

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Answer:

  b = c = 2, z = 5

Step-by-step explanation:

You want the solution to the equations ...

A number of methods are available for solving this system of equations. We like the matrix method using a calculator, as shown in the attachment.

Since 'c' and 'z' appear with coefficients of 1, writing expressions for those that can be substituted into the other equations is pretty easy:

  z = 11 -(2b +c) . . . . . . . using the first equation for an expression for z

  3b +4c +(11 -2b -c) = 19   ⇒   b +3c = 8 . . . . . sub for z in 2nd equation

  3b +6c +5(11 -2b -c) = 43   ⇒   -7b +c = -12 . . . . sub for z in 3rd equation

  -7(8 -3c) +c = -12   ⇒   22c = 44   ⇒   c = 2 . . . . sub (8-3c) for b in 3rd eqn

  b = 8 -3(2) = 2

  z = 11 -(2(2) +2) = 5

The solution is (b, c, z) = (2, 2, 5).

Sanchez made more money by 3.93$

Corey ran 131.69 meters around a rectangular soccer field.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Corey ran around a rectangular soccer field that measures 38.50 meters by 27.345 meters.

Corey ran = Perimeter of rectangle =2 (38.50 + 27.345)

Corey ran = 131.69 meters.

Therefore, Corey ran 131.69 meters.

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The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.

The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants can be represented by the following formula:

Final Cost = Sweatshirt Cost + (2 x T Shirt Cost) + Pants Cost

For example, if the cost of a sweatshirt is $20, the cost of a T shirt is $10, and the cost of a pair of pants is $30, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be:

Final Cost = $20 + (2 x $10) + $30

Final Cost = $20 + $20 + $30

Final Cost = $70

Therefore, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.

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Complete question:

What is the Final Cost of 1 Sweatshirt, 2 T-Shirts, and 1 Pair of Pants?

The result of the second run is equal to (x + 4) * 25 + 20.

The computer is programmed to accept a number, add 4 to it, and then multiply the sum by 5. Let represents the number first fed into the machine, and the result of the first run is then fed back into the computer.

Let's call the result of the first run "y". So, y = (x + 4) * 5.

If we then feed y back into the computer, the result of the second run will be:

z = (y + 4) * 5 = ((x + 4) * 5 + 4) * 5.

Expanding the parentheses, we have:

z = ((x + 4) * 5 + 4) * 5 = (x + 4) * 25 + 4 * 5 = (x + 4) * 25 + 20.

So, the result of the second run is equal to (x + 4) * 25 + 20, where x is the original number fed into the computer.

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Answer:

D. :

x y

−2 0

−1 2

0 1

2 0

5 2

Step-by-step explanation:

That should do it.

The expected number of men who will be colorblind is 36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

5. About 8% of males are colorblind. A researcher has a list of 12 men who have volunteered to be tested.

Here, 8% of 12

= 8/100 ×12

= 0.08×12

= 0.96

Exactly 1 of the 12 men is colorblind.

6. About 8% of males are colorblind. The researcher test 450 volunteers, hoping to find many colorblind men for their study.

Now, 8% of 450

= 8/100 ×450

= 0.08×450

= 36

The expected number of men who will be colorblind is 36.

Therefore, the expected number of men who will be colorblind is 36.

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Answer: To write the equation of a parabolic function in vertex form, we need to know its vertex. The vertex of a parabolic function can be found by taking the average of the x-coordinates of two given points and using the midpoint formula.

The midpoint formula for the vertex of a parabolic function is:

Vertex = (x1 + x2, y1 + y2) / 2

where (x1, y1) and (x2, y2) are two points on the parabolic function.

Using the midpoint formula, the vertex of the parabolic function that goes through the points (5,3) and (8,13) is:

Vertex = (5 + 8, 3 + 13) / 2 = (13, 8).

Now that we have the vertex of the parabolic function, we can write its equation in vertex form. The vertex form of a parabolic function is:

y = a(x - h)^2 + k

Where (h, k) is the vertex, and a is the coefficient that determines the direction and width of the parabolic function. To find the value of a, we can use one of the given points and substitute it into the equation:

y = a(x - h)^2 + k

3 = a(5 - 13)^2 + 8

Expanding and simplifying the right side of the equation:

3 = a(-8)^2 + 8

3 = 64a + 8

56 = 64a

a = 7/8.

Finally, substitute the values for the vertex and an into the equation:

y = a(x - h)^2 + k

y = 7/8(x - 13)^2 + 8

So, the equation of the parabolic function that goes through the points (5,3) and (8,13) in vertex form is y = 7/8(x - 13)^2 + 8.

Step-by-step explanation:

The adult male foot length of 24.2 cm is significantly low as it falls outside of the range of 26.10 cm to 28.72 cm.

The range is just the difference between the greatest and smallest data points in a set.

The square root of the variance is the standard deviation.

The standard deviation measures how far apart the data is from the mean.

The range is a less useful measure of variance than the standard deviation.

The range of data is a measure of variance that indicates the difference between the dataset's maximum and least observation.

It is based only on two observations, the maximum and minimum.

The range rule of thumb states that approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% of the data falls within two standard deviations of the mean.

So, the lower limit separating significantly low values will be:

27.41 - 1.31 = 26.10 cm

And the upper limit separating significantly high values will be:

27.41 + 1.31 = 28.72 cm.

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Since the statistical survey was done with 5108 randomly selected households it can be concluded that the sample is 5108 randomly selected households.

In order to draw conclusions about the population as a whole a sample of data can be chosen.
A sample is a subset of a larger population that represents the larger population that is chosen for analysis.

In this instance, the sample consists of 5108 homes that were chosen at random for the survey to determine the proportion of homes with televisions tuned to the Super Bowl.

In order to accurately represent the number of households that watched the Super Bowl, a sample size of 5108 was used.

It should be also noted that Nielsen Media Research is a market research company that specializes in measuring media audiences, including television viewership.

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Answer:

42-13 =28 so there are 28

Generally, if the solution is composed of more ions than molecules, δsol will be positive. If the solution is composed of more molecules than ions, δsol will be negative.

The sign of δsol is dependent on the properties of the solution. δsol is a measure of the concentration of ions in the solution, and is calculated by subtracting the molar concentration of ions from the molar concentration of molecules. If the solution contains a higher molar concentration of ions than molecules, then the difference will be positive, and δsol will be positive. Conversely, if the solution contains a higher molar concentration of molecules than ions, then the difference will be negative, and δsol will be negative. It is important to note that the sign of δsol can be affected by the type of molecules and ions present in the solution. For example, if the solution contains anionic molecules, such as anions from acid-base reactions, then δsol will be negative. Conversely, if the solution contains cations, such as those from acid-base reactions, then δsol will be positive.  It is also important to note that the sign of δsol can be affected by the temperature of the solution. As the temperature increases, the solubility of the ions in the solution increases, resulting in a higher molar concentration of ions and a resulting positive.

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Answer:

25 cents

Step-by-step explanation:

Sand sells at 8.5 cents per pound, an hundred-pound bag of this price would total $8.50 (8.5 * 100).

This is 25 cents more than buying a hundred-pound bag for 8.25, meaning you would save [25 cents]

Answer:

A rational number is any number that can be expressed as a whole number, a fraction, or as a non repeating decimal. Otherwise, it is an irrational number.

19/5: it is a rational number because it is in fraction form

√12: this is an irrational number

√49: this is a rational number because when you simplify this you will get the answer 7, that is a whole number.

0.3425563758:  This is a decimal, hence, this is rational.

4/25 :  it is a fraction so it is a rational number.

√1/8: this is an irrational number

√0.6¯: this is an irrational number

For a real-valued function f, it is said that the interval's value increases for every x and y where f (x) f (y) (x). and the interval is referred to as declining if its value is f (x) f (y) for every x y.

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The point P(12,−2) is not on ⨀C which has a centre at (9, -7) and radius √13

The equation for a circle has the generic form: x² + y² + 2gx + 2fy + c = 0. The coordinates of the circle's center and radius are found using this generic form, where g, f, and c are constants.

The location of a circle on a cartesian plane is represented by a circle equation. If the center and radius of a circle are known, it may be sketched on paper. Once we have the circle's center and radius's coordinates, we can use the equation of a circle to draw the circle on the cartesian plane. The equation of a circle can be represented in several ways, including

General form

Standard form

Parametric form

Polar form

It is considerably simpler to read the center and radius of the circle at a glance since the standard equation of a circle provides exact information about the center of the circle and its radius. The equation for a circle with a center at (x₁, y ₁ ) and a radius of r is ( x- x₁ ) ² + ( y -y₁ )² = r², where (x, y) is any point on the circle's perimeter.

The centre of the cirle is (9, -7) and one point on circumference is (6, -5)

The radius of the circle √{(9 - 6)² + (-7 + 5)²} = √{3² + (-2)²} = √{9+4} = √13

The equation of the circle will be

(x - 9)² + (y + 7)² = 13

Now for P(12, -2)

(12-9)² + (-2 + 7)² = 3² + 5² = 34 ≠ 13

So, the point does not lie on the circle.

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The complete points of each x for the given linear function are:

Please refer to the attached graph for the graph of the function.

From the question, we have a linear function of:

y = x + 4

x points given are:

Let's try to find the output of y and the (x,y) point for each given x-point:

x = -2

y = (-2) + 4

y = 2 --> (-2, 2)

x = 0

y = (0) + 4

y = 4 --> (0, 4)

x = 2

y = (2) + 4

y = 6 --> (2, 6)

x = 6

y = (6) + 4

y = 10 --> (6, 10)

x = 8

y = (8) + 4

y = 12 --> (8, 12)

Those points are used to make a graph as attached below.

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The type of function represented in the table is exponential.

The table shows an exponential function, which is a function that increases or decreases by a constant rate over a period of time. The table shows a relationship between the x-values and the y-values, where the y-values increase or decrease by a constant factor as the x-values increase. In this particular table, the y-values increase by a factor of two as the x-values increase by one. This type of function is common in mathematics and can be used to model a variety of real-world phenomena, such as population growth, compound interest, and radioactive decay.

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Answer:

The Mathman guy is wrong, the answer is actually 15.

Step-by-step explanation:

because from the equation that you gave, nicole started with $5 and added $15 every week
thus let y represent the total money and x represent the number of week after x week
nicole save: 15x
because at the beginning he has $5
so, y = 15x + 15
y = mx+c m is the slope c is the y intercept
so slope = 15
so we reach to the conclusion that the rate of change is 15

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

What is slope ?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

he equation of the position y (in meters) of a submarine after x minutes can be represented as:

y = -8x - 12

Where x is the time in minutes and y is the position in meters. To solve for y, we can substitute a specific value of x and calculate the corresponding value of y.

For example, if we substitute x = 0, we can find the initial position of the submarine:

y = -8 * 0 - 12

y = -12

So, the initial position of the submarine is -12 meters.

In general, the slope of the line represented by this equation is -8, meaning that for every one unit increase in x (i.e., one minute), the position of the submarine decreases by 8 meters.

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

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The position y (8 meters per minute) of a submarine after x minutes is y = -8x - 12,

given that:

The position y (in meters) of a submarine after x minutes is y = -8x - 12

The slope of the equation y = -8x - 12 represents the rate of change of the position of the submarine. It tells us the amount by which the position of the submarine changes for each unit change in time that is (minutes).

In this case, the slope is -8, which means that for each 1-minute increase in time, the position of the submarine decreases by 8 meters. This indicates that the submarine is descending at a rate of 8 meters per minute. Hence our result is 8 meters per minute.

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The solution is of the function 3f(x) +2g(x) is:

=> -5x-2  

Now, According to the question:

Algebra of  functions:

Algebra of functions means the operations of the functions, specifically the arithmetic operations. Algebra of functions mainly deals with the following four arithmetic operations of functions:

The function given as:

f(x) = -3x, g(x) = 2x-1 are the two functions

then by the algebra of two functions(adding two functions) we can find the value of 3f(x) + 2g(x)

Now find

3f(x) = 3(-3x) = -9x            -----------(i)

2g(x) = 2(2x-1)

         = 2(2x)-2(1)                        

2g(x) = 4x-2                     ----------(ii)

Now, add the above two equation (i) and (ii)

3f(x) + 2g(x) = -9x + 4x - 2

                   = -5x-2  

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The given question is incomplete, complete question is:

Let f(x) = -3x and g(x) = 2x-1

Find the following: 3f(x) +2g(x)

0 6x +4

0 -5x - 2

O There is no correct answer given.

O 8x -8

O 5x+1