What is the slope of the line that passes through the points (-2, -1)
and (2, -3)? Write your answer in simplest form.

Answer:

Add m to both sides

Step-by-step explanation:

Add m to both sides

Niamh gets 16 pencils and Jack gets 32 pencils.

The ratio of 4:8 can be simplified to 1:2 by dividing both sides by 4. This means that for every one pencil Niamh gets, Jack gets two pencils.

To find out how many pencils each child gets, we need to divide the total number of pencils by the total number of parts in the ratio, which is 1 + 2 = 3.

So, each part of the ratio represents 48/3 = 16 pencils.

Therefore, Niamh gets 1 part, which is 16 pencils, and Jack gets 2 parts, which is 2 x 16 = 32 pencils.

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The given question is incomplete, the complete question is:

Ms. Adams shares out 48 pencils between Niamh and jack in the ratio 4:8, How many pencil does each child get ?

The Probability that no person is next to their partner is 104/105.

Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).

Permutations is defined as arrangement of elements/objects in a particular way.

According to the question ,

8 people can be arranged in 8! ways = 40320ways

First let us find the probability that person is next to their partner.

4 couples can be arranged in 4! ways

and the couple itself can be arranged in 2! ways

Since there are 4 couples ,

Number of arrangement = \(4!(2!)^{4}\)

=24x16

=384 ways

Probability that person is next to their partner = \(\frac{384}{40320} =\frac{1}{105}\)

and the probability that no person is next to their partner is \(1-\frac{1}{105} =\frac{104}{105}\).

Therefore , the probability that no person is next to their partner is \(\frac{104}{105}\).

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We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Answer:

\(5 \sqrt{3} \)

Step-by-step explanation:

Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.

Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

5√3

Decimal Form:

8.66025403…

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology.

He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

Product details

Publisher ‏ : ‎ Pearson; 4th edition (8 January 2018)

Language ‏ : ‎ English

Hardcover ‏ : ‎ 1224 pages

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Answer:

66%

bcz out of 3 stuff in 100% is 66%

Answer:

x=4 I hope this is helpful

Answer:

4x3(8+4)=24

Step-by-step explanation:

Answer:

the median of th given data is 243

Answer:

\(41^{\circ}\)

Step-by-step explanation:

\(~~~~~~\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \cos \theta = \dfrac{9}{12}\\\\\\\implies \theta = \cos^{-1} \left( \dfrac 9{12} \right)\\\\\\\implies \theta \approx 41^{\circ}\)

Answer:

41°

Step-by-step explanation:

Since the adjacent side and the hypotenuse are given, let's take the cosine ratio of the missing angle.

cos θ = adjacent side / hypotenuse

===========================================================

Given :

⇒ Adjacent side = 9

⇒ Hypotenuse = 12

===========================================================

Solving :

⇒ cos θ = 9/12

⇒ cos θ = 0.75

⇒ θ = cos⁻¹ (0.75)

⇒ θ = 41.4096221....

⇒ θ = 41° (to the nearest degree)

It is important to consider the limitations of case studies when interpreting the results.

The limitation of case studies is that it can be difficult to generalize from one person to the larger population. Case studies are a type of research method that is used to get a detailed understanding of an individual, group, or event. They are typically used when the researcher wants to answer questions about the ‘how’ and ‘why’ of phenomena, which cannot be answered using other methods such as surveys or experiments.

While case studies can be useful in providing an in-depth analysis of an individual or group, they have certain limitations that need to be taken into consideration. One of the primary limitations of case studies is that it is difficult to generalize from one person to the larger population.

This is because case studies are typically conducted on a single individual or a small group of individuals, which makes it difficult to make inferences about larger populations. This means that the findings of a case study cannot be applied to a broader population without further research.

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Answer:

feet

Step-by-step explanation:

The others measure liquid or weight.

Answer:

feet

Step-by-step explanation:

Both inches and feet could be used, but inches are so small that it would take much longer to measure the wall than it should. Feet are the appropriate unit to measure a wall.

The data from the college alumni organization should not be used to construct a confidence interval for the mean annual income of all recent graduates because the sample is not randomly selected to represent the students in the college.

This is because only 20% of the alumni responded to the survey, which means that the sample is not representative of the entire population of recent graduates. Additionally, the sample size is too small to accurately represent the entire population. It is also important to note that the population standard deviation is too small relative to the mean, which can affect the accuracy of the confidence interval. Overall, these factors make it difficult to accurately estimate the mean annual income of all recent graduates using the data from the college alumni organization.

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The absolute extrema of f(x) = 36/7 on the interval (-5, -3) does not exist as f(x) = 36/7 is a constant function.

Let's find the absolute maximum and minimum of the function.

The given function is f(x) = 36/7, which is a constant function. For a constant function, there is no variation in the values of the function for any value of x within the interval. Therefore, the function has no absolute maximum or minimum within the given interval (-5, -3).

To reiterate, for the function f(x) = 36/7 on the interval (-5, -3), there is no absolute maximum or absolute minimum, as it is a constant function.

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The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Therefore, we can create a postage amount of n using these stamps. This completes the induction step, so by the principle of strong induction, any postage amount greater than or equal to 1 can be created using these stamps.

Given that 3 and 8 cent stamps are available, we need to find out the postage that can be created using these stamps.To prove that a postage of n cents can be created using these stamps, we will use strong induction.Induction basis: We can create postage of 1, 2, 3, 4, 5, 6, 7, and 8 cents using these stamps.Because we have 3 and 8 cent stamps available to us, we can create any postage amount greater than or equal to 9 by adding a 3 cent stamp to a postage amount that we can create using these stamps.Induction hypothesis: For all n > 8, any postage amount less than n that is greater than or equal to 1 can be made using these stamps.Induction step: We must show that any postage amount greater than or equal to 9 can be created using these stamps.Suppose that a postage amount k can be created using these stamps for all 8 < k < n. Since we have 3 and 8 cent stamps, we can create a postage amount of n by adding a 3 cent stamp to a postage amount of (n - 3) that can be created using these stamps. Since (n - 3) is less than n and greater than or equal to 9, by the induction hypothesis, we know that a postage amount of (n - 3) can be created using these stamps. Therefore, we can create a postage amount of n using these stamps. This completes the induction step, so by the principle of strong induction, any postage amount greater than or equal to 1 can be created using these stamps.

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The distance between the pillar A(4, 6) and pillar B(18, 2) is approximately 14.56 m.

Given is the positions of three pillars, Cords connect Pillar A to Pillar B and Pillar B to Pillar C.  

We need to find the distance between the pillars A and B.

Using the distance formula,

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's determine the distance between points A (4, 6) and B (18, 2):

Here, (x₁, y₁) represents the coordinates of point A, and (x₂, y₂) represents the coordinates of point B.

Put the values,

Distance = √((18 - 4)² + (2 - 6)²)

= √(14² + (-4)²)

= √(196 + 16)

= √212

≈ 14.56

Therefore, the distance between point A(4, 6) and point B(18, 2) is approximately 14.56 units.

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The number of blue beads is; 90

If Carrie has 150 beads all together, and 3 times as many green beads as red beads, and twice as many blue beads as green beads. Then we can set up the following equation:

x + (3x) + (2(3x)) = 150

where x is the number of red beads.

Solving for x, we get:

x + 3x + 6x = 150

10x = 150

x = 15

So there are 15 red beads, 45 green beads (3 * 15), and 90 blue beads (2 * 45).

Therefore, the answer is 90 blue beads.

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Answer:

12x - 5

Step-by-step explanation:

3x + 9x - 5 can be easily simplified by combining like terms.

3x and 9x are like terms because they both contain the same variable and the same exponent (understood to be 1).

Therefore, because an addition sign separates the two terms, it is expected of you to add the two together. To do this, just add the terms together as you would any other terms.

3x + 9x = 12x

Because the 5 is the only constant in the equation, it cannot be combined with anything else.

The simplified expression is 12x - 5.

Heritability is a statistic that quantifies the proportion of observed variance in a group of individuals that can be attributed to genetic variance.

Heritability is a fundamental concept in genetics and behavioral sciences that helps understand the extent to which genetic factors contribute to observed variations in a particular trait within a population. It measures the proportion of phenotypic variation (differences in traits) that can be explained by genetic variation. Heritability estimates range from 0 to 1, where a value of 0 indicates that all observed variation is due to environmental factors, and a value of 1 suggests that all observed variation is due to genetic factors.

To calculate heritability, researchers typically study populations with varying degrees of genetic relatedness, such as twins or family members. By comparing the similarity of traits between individuals with known genetic relatedness, it is possible to estimate the contribution of genetic factors to the observed variance. Environmental factors that contribute to phenotypic variation are considered as part of the non-genetic or "environmental" component.

It is important to note that heritability estimates are population-specific and apply only to the particular group being studied. Additionally, heritability does not provide information about specific genes or the precise mechanisms by which genetic factors influence traits. Nonetheless, heritability serves as a valuable tool in understanding the relative importance of genetic and environmental factors in shaping individual differences within a population.

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Name all angles when there are two parallel lines cut by a transversal?

Alternate interior angles

Corresponding angles

Vertically opposite

From figure 1,

Since the angles marked with colour fulfil the vertically opposite angles properties ,so

(2x+35)° = (8x-49)°

⇒(2x-8x)=(-49-35)°

⇒-6x=-84

⇒x = 14°

Hence , x = 14°

From figure 2,

Since the angles marked are corresponding angles,therefore on equating both angles we get

(10x-18)°=(15x-48)°

⇒(10x-15x)=(-48+18)°

⇒-5x = -30°

⇒ x = 6°

From figure 3,

Since the given two angles are alternate interior angles ,so

(7x+5)°=(12x-75)°

⇒(7x-12x)=(-75-5)°

⇒-5x=-80°

⇒x = 16°

From figure 4 ,

Since the two angles lies in a straight line ,so sum is 180°

(27x-21)°+(10x-16)°=180°

⇒37x -37° = 0

⇒ x = 1°

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The decibel value of the noise is 50 db.

What is meaning of intensity of sound?

The quantity of energy going across a unit area in a unit time in a direction that is opposite to the direction of the sound waves.

The unit that used to calculate intensity of sound is decibel.

Given equation that represents the relation between intensity of sound and the ratio of the sound to the human hearing threshold is

db = 10 log i

Where i = the ratio of the sound to the human hearing threshold.

Putting i = 100,000 in the given equation:

db = 10 log 100,000

Replace 100,000 by 10⁵ :

db = 10 log 10⁵

Applying the formula of logarithm log 10^{a} = a:

db = 10 × 5

db = 50

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The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The pair of lines are shown in figure.

Now,

By figure, we see that;

The lines are perpendicular because they intersect at a right angle.

Thus, The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

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See picture for math work and answer.

Answer:

3

Step-by-step explanation:

2^3=8

11-8=3

If about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.

About 5% of americans have blue eyes

The probability of a person having blue eyes = 5% = 5/100

Eyes colour of a person is an indepedent event, which means the eye colour of one individual is independent of the other. The probability of one individual having blue eyes or not is independent of another person.

In case of independent event the probability of A intersection B = probability of A multiplied with probability of B

P(A∩B) = P(A) x P(B)

P(A∩B∩C) = P(A) x P(B) x P(C)

The probability that all 3 have blue eyes = 5/100 x 5/100 x 5/100

= 125/1000000

= 1/8000

Therefore, if about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.

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Answer:

66

Step-by-step explanation:

first layer is really

the area of the base that is 5 and 1/2 *3  

our unit is 1/2 so you could fit 2 cubes in 1 unit so the base area has

(2* 5 1/2) * ( 2* 3) = 11* 6 = 66 unit cubes

Answer:

A

Step-by-step explanation:

Think about it.

y = (0)x + b

this gives

y = b

therefore Y equals a single number regardless of the x value.

This behavior is shown in table A.

Step-by-step explanation:

a. They are alternate interior angles.

b. Line AC and Line DG

c.Line BE and Line BF

d. 45

e. 110

f. 65, triangle exterior theorem

f. 70, alternate interior angles