On the coordinate plane, A(–1,5) and B(2,8) are vertices of equilateral triangle ABC. Find the perimeter of ABC.

The probability that the marble drawn is not red is 8/10 or 4/5

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total possible outcome. If the probability that an event happen is 'x'. Then the probability that it does not happen is 1-x

Similarly the probability that a red marble is drawn is 2/10 , therefore the probability that a red marble is not drawn will be ;

1 - 2/10

= (10-2)/10

= 8/10 = 4/5

therefore the probability that a red marble is not drawn is 4/5

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Answer:

Is there a full question??

Step-by-step explanation:

Answer: 4.00?

Step-by-step explanation:

a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

18. a. If B is any echelon form of A, then the pivot columns of B form a basis for the column space of A.

This statement is true. An echelon form of a matrix is obtained by performing row operations on the original matrix to transform it into a specific triangular form. In this form, the pivot columns correspond to the columns containing the leading entries in each row. The pivot columns of an echelon form of matrix A will also be pivot columns of matrix A itself.

The column space of a matrix is the span of its column vectors. Since the pivot columns of B are a subset of the column vectors of A, they will also span the column space of A. Therefore, the pivot columns of B form a basis for the column space of A.

b. Row operations preserve the linear dependence relations among the rows of A.

This statement is true. When we perform row operations on a matrix, such as multiplying a row by a scalar, adding rows together, or swapping rows, the resulting matrix will have the same row space as the original matrix. This means that the linear dependence relations among the rows of the original matrix will be preserved in the transformed matrix.

c. The dimension of the null space of A is the number of columns of A that are not pivot columns.

This statement is false. The dimension of the null space of A, also known as the nullity of A, is the number of free variables in the reduced row echelon form of A. It is equal to the number of columns of A minus the number of pivot columns. Therefore, the dimension of the null space of A is the number of columns of A minus the number of pivot columns, rather than the other way around.

To summarize:
a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

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The number of  α-helix and the number of β-pleated sheet are part of the secondary structure of proteins.

The secondary structure of proteins consists of recurring patterns of amino acids, such as the number of α-helix and the β-pleated sheet, which form the backbone of the protein. The α-helix is a spiral structure which is formed when the amino acids hydrogen-bond with one another. The β-pleated sheet is a flat structure which is formed when the amino acids form hydrogen bonds with one another in an alternating pattern. Together, the α-helix and the β-pleated sheet form the secondary structure of proteins.

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The total number of protons and neutrons in an atom exists directed as the mass number. The atomic mass number of an atom with 10p and 10 n exists 20.

The total number of protons and neutrons in an atom's nucleus is known as the mass number. Protons plus neutrons equal mass number.

The neon atom has 10 protons and 10 neutrons with the atomic number 10. It has 10 protons and neutrons inside of its nucleus, along with ten electrons outside, due to its atomic weight of 20.179.

Ne is an inert, colorless noble gas that is also the second-lightest of the noble gases. Due to its distinctive reddish glow, it is frequently utilized in lamps and signs.

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The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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The diameter of the sphere is 4.2 inches.

Since it takes 111.3 cubic inches of rubber to make 3 equally sized balls, the volume of one ball is calculated as;

111.3 / 3 = 37.1

The diameter of the sphere is calculated as follows;

V = (4/3)πr³

where;

\(r = (3V/4\pi)^{1/3}\)

\(r = (3(37.1) / (4\pie))^{1/3}\)

r = 2.1 inches

The diameter of the sphere is calculated as follows;

d = 2r

d = 2 x  2.1 inches

d = 4.2 inches

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the probability of experiencing neither side effect is 0.37 or 37%.let's denote the probability of experiencing nausea by P(n) and the probability of experiencing decreased sexual drive by P(d). We know that:

P(n) = 0.23
P(d) = 0.52
P(n ∩ d) = 0.12

We want to find the probability of experiencing neither side effect, which can be denoted by P(~n ∩ ~d), where ~n and ~d represent the complements of nausea and decreased sexual drive, respectively.

We can use the formula for the probability of the union of two events to find P(~n ∪ ~d):

P(~n ∪ ~d) = 1 - P(n ∪ d)

We know that P(n ∪ d) = P(n) + P(d) - P(n ∩ d), so we can substitute the given values to get:

P(n ∪ d) = 0.23 + 0.52 - 0.12 = 0.63

Therefore,

P(~n ∪ ~d) = 1 - 0.63 = 0.37

So the probability of experiencing neither side effect is 0.37 or 37%.

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The information about the metal object that would be most useful in determining if Vivienne's hypothesis is correct is its density. Therefore, the correct option is D.

This is because density is a measure of an object's mass relative to its volume. Since density is an intrinsic property of the material from which the object is made, it can help determine what type of metal the object is. Furthermore, since copper has a relatively high density, knowing the density of the metal object can help determine whether or not it is made of copper.

Density is a physical property that describes the mass per unit volume of a substance. The term density is used to describe the mass of an object per unit volume. The formula for calculating density is:

Density = mass/volume

Therefore, to determine whether the object is a copper penny that was run over by a train, we need to determine its density. Hence, the correct answer is option D.

Note: The question is incomplete. The complete question probably is: Vivienne noticed a metal object lying by the railroad tracks. She believes the object may have originally been a copper penny that was run over by a train. What information about the metal object would be most useful in determining if her hypothesis is correct? A. its mass B. its texture C. its volume D. its density.

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The 10th score should be 9.5 for the mean to be 5.

The mean value is the average value of the given data.

According to the given question  the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.

The total average score for 9 games is

= ( 9 × 4.5 )

= 40.5.

The total average score for the mean to be 5 in 10 games is

= ( 10 × 5 )

= 50.

∴ The 10th score must be ( 50 - 40.5 ) which is

= 9.5.

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Answer:

x = 32

Step-by-step explanation:

2x+1 + x-7 = 90

3x - 6 = 90

3x = 96

x = 32

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

Hi there!

Here is your answer...

The Area of the Parallelogram is:

The Perimeter of the Parallelogram is:

\(64ft\)

Step-by-step explanation:

To find the Area of a Parallelogram you must first identify the Base and Height. In this instance the Base would be the top and bottom which we know are 17ft in length. The Height would be the dotted line that we know it 12ft tall. The next step would be to Multiply the Base by the Height. That would give us 204. After we add the correct units we have \(204ft^{2}\).

To find the Perimeter we would simply add together all side lengths. We know that the top and bottom are equal to 17ft and the left and right are equal to 15 feet. This gives us 17+17+15+15. Which would equal 64, add the units and it becomes \(64ft\).

Area=base x height

Perimeter = base + base + angle +angle

(angle is the side length.)

The sοlutiοn οf the given prοblem οf quadrilateral cοmes οut tο be DC  = 12 .

In mathematics, a rectangle is a fοur-sided οbject with fοur cοrners. Either "quad" οr "array οf inventive ideas" are Latin terms that were used tο cοin the phrase (meaning "side"). Fοur cοrners, fοur areas, and fοur cοrners are the three cοmpοnents οf a rectangle. Cοnvex and cοncave are the twο primary varieties οf cοnvex and cοncave fοrms. Cοnvex quadrilaterals alsο include the subdivisiοns οf trapezοids, geοmetric shapes, angles, rhοmbuses, and squares.

Here,

Assuming that ABCD is a trapezοid with parallel sides AB and CD, we can use the knοwledge that the perimeter οf a trapezοid is equal tο the sum οf its οppοsite sides tο cοnstruct the fοllοwing equatiοn:

=> AB = 52 + CD = BC + AD

Assuming AB = 13 and BC = 15, the equatiοn can be simplified as fοllοws:

=>  13 + CD + 15 + AD = 52

=>  CD + AD = 24

=> DC  = 12

Hοwever, we are unable tο determine the length οf DC οr AD withοut additiοnal details regarding the angles οr side lengths οf the trapezοid. As a result, there is nο clear sοlutiοn.

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Complete question:

Answer:

he get 12 an hour

Step-by-step explanation:

The work done in stretching the spring from its natural length to 0.9 feet beyond its natural length is 3 foot-pounds.

This can be calculated using the equation W = F * d, where W is the work done, F is the force applied, and d is the distance the spring is stretched. In this case, F is 6 pounds and d is 0.5 feet (0.9 feet - 0.4 feet). Thus, W = 6 * 0.5 = 3 foot-pounds.

Force is a concept in physics that describes the influence that can change the motion of an object. Work done is the amount of energy transferred to or from an object when a force acts on it and causes it to move through a distance.

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Correct question:

A force of 6 pounds is required to hold a spring stretched 0.4 feet beyond its natural length.

How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?

The set of vectors S={(−2,1,1),(0,3,1),(0,1,0)} does not form a basis for R^3.

A basis for a vector space is a set of vectors that spans the space and is linearly independent. The set S spans R^3, because any vector in R^3 can be written as a linear combination of the vectors in S.

However, the set S is not linearly independent, because the vector (0,3,1) is a linear combination of the vectors (0,1,0) and (−2,1,1).

To see this, we can write (0,3,1) as follows:

(0,3,1) = 3(0,1,0) + (-2,1,1)

Therefore, the set S is not linearly independent, and so it does not form a basis for R^3.

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The set of vectors S={(−2,1,1),(0,3,1),(0,1,0)} does not form a basis for R^3. So, The set of vectors  S={(−2,1,1),(0,3,1),(0,1,0)} is not forming the basis for R^{3} .

A basis for a vector space is a set of vectors that spans the space and is linearly independent. The set S spans R^3, because any vector in R^3 can be written as a linear combination of the vectors in S.

However, the set S is not linearly independent, because the vector (0,3,1) is a linear combination of the vectors (0,1,0) and (−2,1,1).

To see this, we can write (0,3,1) as follows:

(0,3,1) = 3(0,1,0) + (-2,1,1)

Therefore, the set S is not linearly independent, and so it does not form a basis for R^3.

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60% decrease

15 is 60% of 25

What is 60% of 25?

Y is 60% of 25

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 60% * 25

Converting percent to decimal:

p = 60%/100 = 0.6

Y = 0.6 * 25

Y = 15

Answer:

It decreased by 71%

Step-by-step explanation:

25 divided by 35

The 90th percentile of the mean number of cups per day for a sample of 30 men is 4.472 cups.

There are different types of percentiles including the 25th percentile, 50th percentile, and 75th percentile which are commonly known as the first quartile (Q1), median, and third quartile (Q3) respectively. In order to find the 90th percentile of the mean number of cups per day for a sample of 30 men, we will first use the formula for calculating the standard error of the mean (SEM) which is calculated as SEM = s / sqrt(n), where s is the standard deviation and n is the sample size. Next, we will use the z-score formula which is given by z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean. We will use the z-table to find the z-score for the 90th percentile, which is approximately 1.28. Finally, we will use the formula x = z * SEM + μ to find the 90th percentile of the mean number of cups per day for a sample of 30 men.

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The equation represents the relationship between x and y is y = x + 5. The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The table represents a linear relationship between x and y, where y increases by 5 for every increase of 5 in x. This means that the slope of the line is 5/5 or 1, and the y-intercept is 5. Using this information, we can write the equation of the line in slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept. Substituting the values we found, we get:

y = 1x + 5

or

y = x + 5

Therefore, the equation that represents the relationship between x and y is y = x + 5.

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There are 7,941,658,620 different ways to divide up the prizes so that either Alice or Bob, or both, win.

To count the number of ways to distribute the prizes such that Alice and/or Bob receive a prize, we will use the principle of inclusion-exclusion.

Let A be the event that Alice receives a prize and B be the event that Bob receives a prize. Then, we want to count the number of outcomes in the event A∪B (that is, the number of ways in which either Alice or Bob or both receive a prize).

By the principle of inclusion-exclusion, we have:

|A∪B| = |A| + |B| - |A∩B|

where |A| is the number of outcomes in event A, |B| is the number of outcomes in event B, and |A∩B| is the number of outcomes in the intersection of events A and B.

To count these values, we consider the following cases:

Case 1: Alice and Bob both receive a prize.

In this case, we have 8 prizes left to distribute to the remaining 98 students. The number of ways to distribute these prizes is:

98\(c_{8}\)

Case 2: Alice receives a prize but Bob does not.

In this case, we have 1 prize that must be given to Alice, and 9 prizes left to distribute to the remaining 98 students. The number of ways to distribute these prizes is:

98\(C_{9}\)

Case 3: Bob receives a prize but Alice does not.

This is the same as Case 2, so the number of ways is also 98\(C_{9}\)

Adding up the number of outcomes from each case gives us:

|A∪B| = 98\(c_{8}\) + 2{98\(C_{9}\)}

Plugging in the values, we get:

|A∪B| = 7,941,658,620

Therefore, there are 7,941,658,620 ways to distribute the prizes such that either Alice or Bob or both receive a prize.

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Answer: 50-50

Step-by-step explanation:

The rank of a matrix is the number of linearly independent columns or rows in the matrix.

If the columns of an n × n matrix A are linearly independent as vectors in ℝn, then the rank of A is n. This is because linearly independent vectors are not multiples of each other, and therefore do not reduce to a smaller set of linearly independent vectors when the matrix is put in reduced row echelon form. As a result, the rank of the matrix is equal to the number of columns, which is n. Therefore, the rank of A is n.

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The area of the wetland that will be covered in purple loosestrife 7 years from now is modeled by this expression 500(1.2)^7

The exponential expression to calculate the area covered by purple loosestrife seven years from now will be:

= 500 × 1.2^7

After evaluating the expression, the model predicts that approximately 1,792 acres of the wetland will be covered in purple loosestrife 7 years from now.

This is not a valid prediction because the total area of the wetland is only 1,240 acres. Therefore, a constraint on the model is that the value of the expression 500(1.2)^t must be less than or equal to 1,240.

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