how is the circumference of a circle related to the length of its diameter?

the answer is 14 strips of fabric.

In this question, measure of angle 4 is c. 60 degree. It has been calculated using properties of parallel lines.

It can be seen that in this question l and m are parallel lines and there is a transverse passing through it. We know through the properties of parallel lines that sum of ∠2 and ∠4 is 180° as they are consecutive interior angles and consecutive interior angles are supplementary meaning their sum is 180.

∠2 + ∠4 = 180° (consecutive interior angles)

120° + ∠4 = 180°

∠4 = 180 - 120

= 60°

Parallel lines are straight lines that never meet, no matter how far they are extended. Many pairs of angles are generated when two parallel lines are intersected by another line known as a transversal.

Some angles are congruent (equal), whereas others are supplementary (different).  Consecutive interior angles, also known as co-interior angles, develop on the inside of the transversal and are additional.

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Answer:

NO.

Step-by-step explanation:

The Professor's hypothesis:

An introductory course in Logic will affect college students with their other studies (will affect their Great Point Average - GPA).

25 students are used as the experimental group while the rest of the class are the control group.

The mean GPA in a sample size (SS) of 6 is = 2.58

The mean GPA in the full sample size of 25 would be = 10.75 by crossmultiplying.

This makes me believe the question was written wrongly. I assume SD (standard deviation) of 0.6 instead of SS (sample size) of 6.

Going by this, if standard deviation is 0.6 then the interval within which the GPA of the experimental group (the 25 students) falls is:

[2.58 - 0.6] to [2.58 + 0.6]

= 1.98 to 3.18

The rest of the graduating class (the control group) had a mean GPA of 2.33

Can the professor conclude that the GPA for the sample is significantly different from that of the control group?

The answer is NO because the GPA of the control group falls within the GPA interval of the experimental group!

This means that the population has doubled once more from 400 to 800 deer after 9 years.

The total population is the number of individuals who reside in a particular location. By assessing the population, we can determine the number of creatures and the best course of action. For instance, we can predict how many resources a city will require if we know its exact population.

In the model y = 100(2), y represents the population of deer, and 2 represents the growth factor, which is the factor by which the population is increasing.

If we plug in t = 3 (since the population is doubling every 3 years), we get:

y = 100(2¹) = 200

This means that the population has doubled from 100 to 200 deer after 3 years.

Similarly, if we plug in t = 6 (since the population doubles every 3 years), we get:

y = 100(2²) = 400

This means that the population has doubled again from 200 to 400 deer after 6 years.

And if we plug in t = 9, we get:

y = 100(2³) = 800

This means that the population has doubled once more from 400 to 800 deer after 9 years.

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The solution is,  the original number in the work force is 190.76.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A 35% decrease resulted in a new work force number of 124.

let, the original number in the work force is  x

then,

x - x*35% = 124

or, x - 0.35 x = 124

or, 0.65 x = 124

or, x = 190.76

Hence, The solution is,  the original number in the work force is 190.76.

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Answer:

\(Length =5\)

\(Width = 2\)

Step-by-step explanation:

Given

\(Length =x\)

\(Width = x -3\)

\(Area = 10\)

\(x(x-3) =10\)

See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

\(x(x-3) =10\)

Open bracket

\(x^2 -3x = 10\)

Equate to 0

\(x^2 -3x - 10 =0\)

Expand

\(x^2 + 2x - 5x - 10 = 0\)

Factorize

\(x(x + 2) - 5(x + 2) = 0\)

Factor out x + 2

\((x - 5)(x + 2) = 0\)

Solve for x

\(x - 5 = 0\) or \(x + 2 = 0\)

\(x = 5\) or \(x = -2\)

The value of x cannot be negative

So:

\(x = 5\)

Recall that:

\(Length = x\)

\(Width = x - 3\)

So:

\(Length =5\)

\(Width = 2\) ---- i.e. 5 - 3

Looks like the integral is

\(\displaystyle\int\frac{x^4-2x^2+4x+1}{x^3-x^2-x+1}\,\mathrm dx\)

First simplify the integrand by long division (or however you like):

\(\dfrac{x^4-2x^2+4x+1}{x^3-x^2-x+1}=x+1+\dfrac{4x}{x^3-x^2-x+1}\)

Also notice that

\(x^3-x^2-x+1=x^2(x-1)-(x-1)=(x^2-1)(x-1)=(x+1)(x-1)^2\)

Split the last term into partial fractions:

\(\dfrac{4x}{(x+1)(x-1)^2}=\dfrac a{x+1}+\dfrac b{x-1}+\dfrac c{(x-1)^2}\)

\(4x=a(x-1)^2+b(x+1)(x-1)+c(x+1)\)

\(4x=(a+b)x^2+(c-2a)x+a-b+c\)

\(\implies\begin{cases}a+b=0\\c-2a=4\\a-b+c=0\end{cases}\implies a=-1,b=1,c=2\)

So the integral is equivalent to

\(\displaystyle\int\left(x+1-\frac1{x+1}+\frac1{x-1}+\frac2{(x-1)^2}\right)\,\mathrm dx\)

\(=\displaystyle\frac{x^2}2+x-\ln|x+1|-\ln|x-1|-\frac2{x-1}+C\)

\(=\displaystyle\frac{x^2}2+x-\ln|x^2-1|-\frac2{x-1}+C\)

Given:

The vertices of ΔABC are A(-4,4), B(-2,5), and C(-5,2).

The triangle ABC is reflected across the line y-axis to produce the image ΔA'B'C'.

To find:

The coordinates of ΔA'B'C'.

Solution:

If a figure is reflected across the y-axis, then

\((x,y)\to (-x,y)\)

Using this rule, we get

\(A(-4,4)\to A'(4,4)\)

\(B(-2,5)\to B'(2,5)\)

\(C(-5,2)\to C'(5,2)\)

Therefore, the vertices of the ΔA'B'C' are A'(4,4), B'(2,5) and C'(5,2).

Answer:

2

Step-by-step explanation:

Plug in all of the values then solve using order of operations

y+(x^2)z

4+(-1^2)(-2)

4+1(-2)

4+(-2)

4-2=2

Answer:

x(12y+4)

2 0 l e t t e r s

After dividing 96 by 72 the value obtained in fraction will be equal to 4/3.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given data provided in the question,

Fraction after dividing 96 by 72

So,

96/72 = 4/3

Also, the value in decimal form is 1.33.

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Your complete question probably be:

What is 96 divided by 72 in a fraction?

Answer:

B

Step-by-step explanation:

right

have a good day, hope this helps

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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Given a random variable, x that arises from a binomial experiment and suppose that n = 10, and p = 0.81.

PART A:

The probability distribution for a binomial experiment is given as

where q =1-p

PART B

One way to illustrate the binomial distribution is with a histogram. A histogram shows the possible values of a probability distribution as a series of vertical bars. The height of each bar reflects the probability of each value occurring.

The histogram is given below:

PART C

The shape of the histogram shows it is skewed to the left.

PART D.

The mean of a binomial experiment is given below:

PART E

The variance of a binomial experiment is

PART F

The standard deviation is the square root of the variance.

Answer:

Continous distributions:

- A probability distribution showing the average number of days mothers spent in the hospital.

- A probability distribution showing the weights of newborns.

Step-by-step explanation:

A probability distribution showing the number of vaccines given to babies during their first year of life will have a discrete distribution as only a natural number can represent the number of vaccines (0, 1, 2 vaccines and so on).

A probability distribution showing the average number of days mothers spent in the hospital can be described as continous because we are averaging days and this average can be fractional, so it is not discrete.

A probability distribution showing the weights of newborns is continous, as the weights are a continous variable (physical measurement), not discrete.

A probability distribution showing the amount of births in a hospital in a month is a discrete distribution, as the number of births can only be represented by natural numbers.

The option that describes a continuous distribution include:

A continuous distribution simply means the probabilities of the values of a continuous random variable.

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Answer:

1. k≤ 26.11 hours

2. 5 ≤ x ≤ 6

Step-by-step explanation:

1.

38.76 + 2.69k ≤ 109

2.69k ≤ 70.24

k ≤ 26.11 hours

2.

19 ≤ 4 + 3x ≤ 22

15 ≤ 3x ≤ 18

5 ≤ x ≤ 6

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

2

y = -0.5x + 10.5

Step-by-step explanation:

put a negative sign and 1 on top of the number next to the x to get the line thats perpendicular

2

y = -0.5x + 10.5

I’m very sorry but I don’t understand

Step-by-step explanation:

Answer:

true by subtract ing 8 we solve it.

Answer:

True

Step-by-step explanation:

x + 8 = 32

x + 8 - 8 = 32 - 8

x = 24

Answer:

a+s=1650, 3.5a+2s=4650

Step-by-step explanation:

a=adult, s=student

a+s=1650 equation 1

3.5a+2s=4650 equation 2

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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x > 0: x < 50 (option C)

Slower than 50 miles per hour means he is at a speed less than 50 miles per hour

Speed cannot be negative. As a result his speed will be greater than 0 miles per hour

let his speed be x

We can say his speed would be greater than 0 but less than 50

Representing the above with mathematical symbol:

x > 0 but < 50

x > 0: x < 50 (option C)

Answer:

Ramona is walking 10,000 feet for a fundraiser. She walks at a rate of 270 feet per minute. This situation is modeled by the equation below, where d represents.

Step-by-step explanation:

Answer:

$4.50

Step-by-step explanation:

Use the mean formula: mean = sum of elements / number of elements

Let x represent the cost of the fifth book, and solve for x:

mean = sum of elements / number of elements

3.25 = (11.75 + x) / 5

16.25 = 11.75 + x

4.5 = x

So, the cost of the fifth book was $4.50