In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student chosen randomly from the class is a female?
Female Male
Has an A 5 2
Does not have an A 7 11

Answer:

The statement ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)) is false.

Let's start by understanding what "p" is. "p" is a function that takes in two arguments, x and y. It tells us whether the relationship between x and y is true or false.

Now, let's look at the statement

=>∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

This statement says that for every x, there exists a y and a z such that y is not equal to z and both p(x, y) and p(x, z) are true.

This statement is actually false.

Why? Imagine if p(x, y) only returned true when y was equal to x. Then, there would be no y and z such that y is not equal to z and both p(x, y) and p(x, z) are true.

Therefore, it is possible for the function "p" to return false for the statement

=> ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

It depends on the definition of the function. To determine if the statement is true or false, we need to know what the function "p" is.

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The process of creating a vector that ranges from 0 to π and contains 32 evenly spaced elements is illustrated below.

A vector is a mathematical concept that is used to represent a set of numbers in an ordered manner.

To create a vector that ranges from 0 to π and contains 32 evenly spaced elements, you first need to determine the step size.

This is done by dividing the range (π - 0) by the number of elements (32) and subtracting 1. In this case, the step size is

=> (π - 0) / (32 - 1) = π / 31.

Next, you will create a variable to represent the starting value of the vector, which is 0.

Finally, you can use the append function to add the elements of the vector to the list or array.

To ensure that the vector contains 32 evenly spaced elements, you can check the length of the vector using the len() function, and you can also check the spacing of the elements by printing the values of the vector.

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Perpendicular bisectors of a triangle's sides meet at the circumcenter. It is situated at the equator of a triangle.

The circumcenter is where the perpendicular bisectors of a triangle's sides meet. It is located in the middle of a triangle's perimeter. Draw the perpendicular bisectors of the sides and extend them to determine the circumcenter of any triangle. The circumcenter of the triangle will be determined by where the perpendiculars cross.

Here,

Given : (1, 10), (-5, 2), and (7, 2).

=> Perimeter of given triangle is:6

=> √(6)² + (8)² = √100 = 10

=>√(12)² = 12

=> √(6)² +(-8)² = 10

Perimeter = 10+ 12+ 10 = 32

The orthocenter is the location where the altitudes traced from a triangle's vertices intersect.

The place where the triangle's three elevations converge is known as the orthocenter. A line that goes through the triangle's vertices and is parallel to the other side is said to be an altitude. A triangle's orthocenter is the intersection of the perpendiculars that connect its vertices to its two sides.

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Answer: (0,-15/7)

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

7x + 14y = -30     re-arrange to get y = mx + b form    b is y -intercept

14y = - 7x - 30      divide by 14

   y = -1/2x - 30/14          then b = -30/14 = -  2 1/7      (or -15/7)

Answer:

$210

Step-by-step explanation:

42/2=21 5+3+2=10 21*10=210

The measure of ∠BDC = 79°

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of

2 x pi x r.

The area of a circle is given as:

We have,

∠BDC = (BC + AT) / 2

∠BDC = (95 + 63) / 2

∠BDC = 158 / 2 = 79°

Thus,

∠BDC = 79°

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The simplified expression is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[ 5/(x - 3) - 5/(x + 3) ] / 10/(x² - 9)

= [ {5(x + 3) - 5(x - 3)} / (x + 3)(x - 3) ] x (x² - 9)/10

 Using [ (a² - b²) = (a + b) (a - b) ]

= [(5x + 15 - 5x + 15) / (x + 3)(x - 3)] x [(x - 3)(x + 3) / 10]

= (5x + 15 - 5x + 15) / 10

= 30/10

= 3

Thus,

The value of the expression is 3.

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The values of {x} would be 38.1 units.

According to the Pythagoras theorem, we can write -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angled triangle JKL.

We can solve for {x} using the cosine function as -

cos(27) = 34/x

x = 34/cos(27)

x = 38.1 units

Therefore, the values of {x} would be 38.1 units.

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The volume of the cone is 600 cubic inches.

A cylinder has a volume of 600 inches.

We have to find the volume of a cone with the same radius and height as the cylinder.

Volume of cone: A cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.

Where,

‘r’ is the base radius of the cone

‘l’ is the slant height of a cone

‘h’ is the height  of the cone.

Volume of cylinder:  A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. Thus, the volume of the cylinder can be given by the product of the area of base and height.

Where,

‘r’ is the base radius of the cylinder.

‘h’ is the height of the cylinder.

Volume of cylinder=[tex]\pi r^{2} h[/tex]=600 cubic inches.

Volume of cone= [tex]\frac{1}{3}\pi r^{2} h[/tex].

=[tex]\frac{1}{3}*(600)=200[/tex] cubic inches.

Therefore, the volume of the cone is 600 cubic inches.

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The factorized form of the expression is 5(-2 + x).

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

We have an expression,

-10 + 5x.

To factorize the expression:

Simplifying,

-10 + 5x,

= 5(-2 + x)

Therefore, the required expression is  5(-2 + x).

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Salut/Hello!

Answer: 16,(6)% and it's a decrease

Step-by-step explanation:
/ - fraction line

initial records = 120
after selling = 100
=> records sold = 120 - 100 = 20

We know that:
100% = 120/100 => 1% = 1.2/100
120 - 100 = 20

So we can find: 20 : 1.2 = 16,(6)%
Because 5% = 6 and 6 : 1.2 = 5%

So by knowing the amount of records sold and the percentage per record we divide them and find out the percentage of records sold.

I hope it'll be useful! :]

Bill has a greater percentage of his math problems than kenji.

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

Given ,

During study hall, Kenji finished 2 out of 8 problems from his math homework. Bill did 1 out of 3 problems from his math homework.

SO,

Kenji percentage  =  2 / 8 * 100

= 1/4  * 100

= 25

Bill percentage = 1/3  * 100

= 33.33

so, the percentage of bill is more than Kenji.

Therefore, Bill has a greater percentage of his math problems than kenji.

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Answer: 0.48

Step-by-step explanation: To get your percentage multiplier, divide the desired percentage by one hundred. In this case, 48/100.

Answer: The percentage multiplier to decrease a price by 48% is 0.52. :)

Step-by-step explanation:

Answer: The probability is 50%.

Step-by-step explanation: The probability that both are girls if the older child is a girl can be calculated through probability. First, we know that there are two genders the child can be, male or female. When we have 2 possible outcomes, the probability of each outcome is 50%. We know the first child is a girl, and that the second child has a 50% chance of being a girl, so the probability is 50%.

Debemos tener la misma masa en ambos brazos del tubo, entonces veremos que la altura que alcanza la columna de aceite es 0.33m

La altura de la columna de aceite será de tal forma que la masa en ambos brazos sea igual.

Recordar que la masa es el producto entre la densidad y el volumen, para el caso de cilindros, el volumen es el producto entre la altura H y el area circular A.

Para que las masas sean iguales debemos tener que:

A*(0.30 m)* (1 g/cm^3) = A*(H)*(0.9 g/cm^3)

Podemos remover A de ambos lados para obtener:

(0.30 m)* (1 g/cm^3) = (H)*(0.9 g/cm^3)

Resolviendo esto para H obtendremos:

H = (0.30 m)* (1 g/cm^3)/(0.9 g/cm^3)

H = 0.33m

Esa es la altura que alcanza el aceite.

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Answer:

The missing number is 6.

Step-by-step explanation:

Answer:

Perpendicular

Step-by-step explanation:

They appear to be perpendicular when inputted on Desmos

Answer: neither

Step-by-step explanation: If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect. If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular

Answer:

Step-by-step explanation:

The shaded portion in the figure is a quarter-circle with a radius of half the side length of the square, or 10/2 = 5 units.

The area of a circle can be calculated using the formula:

A = πr^2

Where r is the radius and π is pi (approximately equal to 3.14).

So the area of a quarter-circle with a radius of 5 is:

A = (π * 5^2) / 4 = (π * 25) / 4 = 25π / 4

This is the area of the shaded portion in the figure.

Scatterplot provides a visual representation of the relationship between two variables and can be used to determine the strength and type of relationship between them.

The scatterplot is a useful tool for analyzing the relationship between two variables. In this scatterplot, each point represents a single data point (i.e. a grade for a student). The x-axis represents the discrete math course grade, and the y-axis represents the business calculus course grade.

From the scatterplot, it is possible to determine if there is a positive, negative, or no relationship between the two variables. A positive relationship means that as the value of x increases, the value of y also increases.

A negative relationship means that as the value of x increases, the value of y decreases. And no relationship means that there is no correlation between the two variables.

It is also possible to determine the strength of the relationship between the two variables by looking at the distribution of the points.

A tight cluster of points indicates a strong relationship, while a more dispersed scatter of points indicates a weaker relationship.

Complete Question:

The relationship between discrete math course grade x and business calculus course grade y I represented by the scatterplot

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The total number of hours Josh worked during the week is 44.7 hours.

We first need to calculate his regular pay by dividing his weekly gross earnings by his hourly rate:

$487.29 / $10.95 = 44.7 hours

Since the company pays time-and-a-half for any hours worked exceeding 40 in one week, we need to determine if Josh worked more than 40 hours during the week. If he did, we'll calculate his overtime pay by multiplying his regular pay by 1.5.

If Josh worked 44.7 hours, then he worked 44.7 - 40 = 4.7 hours of overtime.

His overtime pay would be 4.7 hours * $10.95 * 1.5 = $81.48

His regular pay would be 40 hours * $10.95 = $438.00

So his total weekly pay would be $438.00 + $81.48 = $519.48

The total number of hours Josh worked during the week is 44.7 hours.

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If slope of the line is 1/3,  then slope of the perpendicular line should be negative reciprocal, and so it is equal -3.

Lines that cross at a straight angle (90 degrees) are said to be perpendicular. Two geometric objects in basic geometry are perpendicular if they intersect at a right angle. The perpendicular sign,, is a graphic representation of the perpendicularity criterion.

Between two lines, between a line and a plane, or between two planes, it can be defined. slope, An evaluation of a line's inclination with respect to the horizontal using numbers.

The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line ("slope equals rise over run"). The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.

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The average rate of change of the function p(θ) over the interval [1,2] is 0.

The average rate of change of a function over an interval is given by the slope of the secant line that connects the two points on the function at the endpoints of the interval.

For the function p(θ)=θ^3−5θ^2 + 6θ and the interval [1,2], the average rate of change can be calculated as:

(p(2) - p(1)) / (2 - 1) = ((2^3 - 5 × 2^2 + 6 × 2) - (1^3 - 5 × 1^2 + 6 × 1)) / (2 - 1) = ((8 - 20 + 12) - (1 - 5 + 6)) / (2 - 1) = (0) / (1) = 0.

So, the average rate of change of the function p(θ) over the interval [1,2] is 0.

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For given triangle ABC, the measurement DC will be 90m.

With three sides and three vertices, triangles are a particular type of polygon in geometry. It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. The triangle can be categorised into six different types based on its sides and angle measurements.

Triangles can be divided into 3 categories according to their sides, including:

Triangle with scalene dimensions: Each side has a different size.

Triangle with an isosceles shape, in which two of the sides have the same length and the third side is shorter.

All three of a triangle's sides have the same length, or equilateral triangle.

Now for given triangle ABC,

ad² +bd² =ab²  by Pythagoras theorem

ab² =10² +30²

ab² =1000

ab=10√10

and

bc² =cd^2+bd²   by Pythagoras theorem

and also b² =ac² -ab²  by Pythagoras theorem

Therefore,

cd² +bd² =ac² -ab²

cd² +30² =(10+cd)² -1000

cd² +900+1000=100+cd² +20cd

20cd=1800

cd=90m

Hence, For given triangle ABC, DC will be 90m.

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Answer: 14

Step-by-step explanation:

Let's call the number of matches the team played "x".

We know that the team scored 36 goals in total, and if they had played five matches less, their goal average would have been exactly four goals per game. We can use this information to set up the following equation:

(36 goals) / (x - 5 matches) = 4 goals per match

To solve for x, we need to isolate x on one side of the equation. To do this, we can multiply both sides of the equation by (x - 5):

36 = 4(x - 5)

36 = 4x - 20

56 = 4x

Now we can divide both sides of the equation by 4:

x = 14

Therefore, the team played 14 matches in total.

Other points that are on line f will also be solutions to the linear system. Therefore, option 4 is the correct answer.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, graph lines f and g on the same coordinate plane and they intersect at point (4, 5).

When two lines intersect at (4, 5), then the point is the solution of system of  linear equations.

When substitute x=4 and y=5 in the system of equations, both the equations will be true.

Therefore, option 4 is the correct answer.

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The distance between the given pair of points (1,11) and (7,18) is √85.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given that;

Point 1 (1,11)

Point 2 (7,18)

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 7 - 1 )² + ( 18 - 11 )² )

D = √( ( 6 )² + ( 7 )² )

D = √( 36 + 49 )

D = √85

Therefore, the value of the distance is √85.

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Answer:

23.) x = 111

24.) x = 53

25.) x = 32

26.) x = 66

Step-by-step explanation:

The sum of the exterior angles of a polygon is 360°.

23.)

65 + 106 + 78 + x = 360

249 + x = 360

x = 111

24.)

50 + 48 + 59 + x + x + 58 + 39 = 360

254 + 2x = 360

2x = 106

x = 53

25.)

85 + 44 + 3x + 2x + 71 = 360

200 + 5x = 360

5x = 160

x = 32

26.)

40 + x + 77 + 2x + 45 = 360

162 + 3x = 360

3x = 198

x = 66