There are 24 students in the class 3/6
of the students are boys how many students are boys

The required line is y = -(3/2)x - 6 which is perpendicular and shifted down 8 units.

Perpendicular lines are two lines that cross one other and create a 90-degree angle. Two lines are perpendicular if the product of their slopes is -1.

The slope-intercept form of a line is y = (2/3)x + 2.

To find the slope of the perpendicular line, we simply need to negate the reciprocal of the original line's slope.

The slope of the original line is 2/3. The slope of the perpendicular line is therefore -3/2.

To shift the line down 8 units, we simply need to subtract 8 from the y-intercept.

The slope-intercept form of the line perpendicular to y = (2/3)x + 2 and shifted down 8 units is:

y = -(3/2)x + 2 - 8 = -(3/2)x - 6

So the line that is perpendicular and shifted down 8 units is y = -(3/2)x - 6.

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Answers:

B ' (6, 4)

C ' (2, 3)

D ' (3, -1)

E ' (7, 0)

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

Explanation:

The y-axis reflection rule is:

[tex](\text{x},\text{y})\to (-\text{x},\text{y})[/tex]

The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.

So for example, the point B(-6,4) moves to B ' (6, 4).

You can use a graphing tool like GeoGebra to confirm the answers are correct.

In mathematical terms, if T is injective, then for any vectors u and v in the domain V, T(u) = T(v) only if u = v. This property is also known as one-to-one correspondence.

One important property of linear operators is their infectivity, which means that the function maps distinct vectors in the domain to distinct vectors in the codomain.

To prove that {Tvi} is also linearly independent, we need to show that if a1T(v1) + a2T(v2) + ... + akT(vk) = 0, then the only solution is a1 = a2 = ... = ak = 0. We can do this by assuming that there exist scalars a1, a2, ..., ak that are not all zero, and show that this leads to a contradiction.

Suppose that

=> a1T(v1) + a2T(v2) + ... + akT(vk) = 0,

where not all of the ai's are zero. Then, we can write this as

=> T(a1v1 + a2v2 + ... + akvk) = 0.

Since T is injective, this implies that a1v1 + a2v2 + ... + akvk = 0.

Now, let's move on to the second part of the problem statement, which deals with the surjectivity of the linear operator T.

In other words, if T is surjective, then for any vector w in the codomain V, there exists a vector v in the domain V such that T(v) = w.

If {vi} spans V, then every vector in V can be expressed as a linear combination of the {vi}'s. In other words, for any vector u in V, there exist scalars c1, c2, ..., ck such that

=> u = c1v1 + c2v2 + ... + ckvk.

To prove that {Tvi} also spans V, we need to show that every vector w in V can be expressed as a linear combination of the T(vi)'s.

Then, we can express v as a linear combination of the {vi}'s:

=> v = c1v1 + c2v2 + ... + ckvk.

Applying T to both sides, we get:

w = T(v) = T(c1v1 + c2v2 + ... + ck

W = c1T(v1) + c2T(v2) + ... + ckT(vk)

This shows that w can be expressed as a linear combination of the T(vi)'s, which means that {Tvi} also spans V.

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I'm sorry, there is no image or diagram provided to identify the shaded region. Could you please provide more information or a visual aid for me?

The area of the shaded region is 0.725746882.

The probability distribution of random variables is described using the cumulative distribution function. The probability for a discrete, continuous, or mixed variable may be described using it. The cumulative probability for a random variable is calculated by adding the probability density function.

Given:

The graph depicts the IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 91.

From the diagram,

the critical value is 91.

The formula to calculate the z-score is,

z = (x - u) / s,

Substituting the given values to the formula,

the given values are;

x = critical value = 91

u = mean = 100

s = standard deviation = 15

Thus,

z = (x - u) / s

z = -0.6

P(z > -0.6 ) = 0.725746882

Therefore, the area is 0.725746882.

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The probability that a defective part made at this factory was made on the first assembly line is 0.299 or 29.9%,

This issue can be resolved using Bayes' theorem. Let L1, L2, and L3 represent the events that the component was produced on the first, second, and third assembly lines, respectively, and let D represent the event that a defective part is produced. Next, given that the part is defective, we want to determine P(L1 | D), which is the likelihood that the component was made on the first production line.

We can determine P(D), the overall likelihood of creating a defective part, using the rule of total probability:

P(D) = P(D | L1) P(L1) + P(D | L2) P(L2) + P(D | L3) P(L3)

= 0.02 × 0.29 + 0.04 × 0.27 + 0.01 × 0.44

= 0.0195

next, we can determine P(L1 | D) using Bayes' theorem:

P(L1 | D) = P(D | L1) P(L1) / P(D)

= 0.02 × 0.29 / 0.0195

= 0.299

As a result, there is a 29.9% chance that a defective component produced at this factory was made on the first assembly line, or about 0.299 of a chance.

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Answer: The store paid $84 to purchase the skateboard

Step-by-step explanation:

If the selling price of the skateboard is $147 and the markup is 75%, we can find the cost of the skateboard by working backwards from the selling price.

Let's start by calculating the original cost of the skateboard before the markup was applied. We can do this by dividing the selling price by 1 plus the markup percentage as a decimal:

original cost = selling price / (1 + markup percentage)

Converting the markup percentage to a decimal:

markup percentage = 75% = 0.75

original cost = 147 / (1 + 0.75)

original cost = 147 / 1.75

original cost = 84

Brandon have a total of $32 originally

From the question, we have the following parameters that can be used in our computation:

When he spends $24, he has 3/4 of the original amount left

Using the above as a guide, we have the following:

24 = Original * 3/4

Make "Original" the subject of the formula

So, we have the following representation

Original = 24/(3/4)

Evaluate the expression

Original = 32

Hence, the amount is $32

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[tex]A =\left[\begin{array}{ccc}3&0\\-2&1\\\end{array}\right][/tex] , [tex]B =\left[\begin{array}{ccc}-2&0\\2&0\\\end{array}\right][/tex] so that A,B are non-invertible matrices and  A+B is invertible.

An invertible matrix is a matrix in given square matrix A of order n × n is called invertible if there exists another n × n square matrix B such that, AB = BA = Iₙ, where Iₙ is an identity matrix of order n × n.

A non-invertible matrix is a matrix that does not have an inverse, i.e. non-invertible matrices do not satisfy the requisite condition to be invertible.

We have to find non-invertible matrices A,B such that A+B is invertible

so, A =[tex]\left[\begin{array}{ccc}3&0\\-2&1\\\end{array}\right][/tex]

and B =[tex]\left[\begin{array}{ccc}-2&0\\2&0\\\end{array}\right][/tex]

AB = [tex]\left[\begin{array}{ccc}-6&0\\6&0\\\end{array}\right][/tex]  

Therefore A and B matrix are non- invertible

A + B = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

A square matrix in which every element except the principal diagonal elements is zero is called a Diagonal Matrix.

so, A,B neither is a diagonal matrix and A,B are not scalar multiples of each other.

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(a) Glen Cove's current population is 5,000.

In order to determine Glen Cove's current population, we must calculate P(0) because P(t) provides the population (in thousands) for t years in the future. In other words,

P(0) = (35(0)2 + 125(0) + 200) / (02 + 4(0) + 40)

      = 200 / 40

      = 5.

Since P(t) yields the population in thousands, Glen Cove's current population is 5,000.

(b) The population in the long run (as t approaches infinity) is 35,000.

As t approaches infinity, we must discover the limit of P(t) in order to determine the population over the long term. To do this, we can divide the function's numerator and denominator by t2, which results in the formula: P(t) = (35 + 125/t + 200/t2) / (1 + 4/t + 40/t2).

The terms 125/t and 200/t2 get smaller and smaller as t increases, so we can ignore them in the numerator. We can therefore disregard the terms 4/t and 40/t2 because they also degenerate in the denominator to lower and smaller values. Thus, we are left with:

P(t) ≈ 35/1 \s = 35

Since P(t) represents the population in thousands, the population in the long run (as t approaches infinity) is 35,000.

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The actual dimensions of the rectangular garden are 17.5 cm by 12.5 cm

From the question, we have the following parameters that can be used in our computation:

Scale: 1.6 cm = 2 cm

A scale is the ratio of the size of the drawing to the size of the actual object.

Given that the dimension is

14 cm by 10 cm

Using the above as a guide, we have the following equation

Actual = 14 * 2/1.6 cm by 10 * 2/1.6 cm

Evaluate

So, we have the following representation

Actual = 17.5 cm by 12.5 cm

Hence, the actual is 17.5 cm by 12.5 cm

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Answer:

Step-by-step explanation:

if we simplify both of them,

5/10=1/2

and

6/12=1/2

then it means they are equal

The simplest way to calculate the surface area of a polyhedron, though, remains to simply sum the areas of the polygons that make up its faces. The surface area of a sphere has a very interesting formula. It depends solely on the radius of the sphere. The surface area of a sphere is equal to 4Π times the square of the radius of the sphere: 4Πr2.

Step-by-step explanation:

To find the greatest common factor (GCF) of the expression (8 + 12), we need to first simplify the expression by finding the sum, which is 20. Therefore, the GCF of (8 + 12) is simply the GCF of 20, which is 20.

To rewrite the expression as a multiple of a sum of two whole numbers with no common factor, we can factor out the GCF of 4 from both 8 and 12, giving us:

(8 + 12) = 4(2 + 3)

The expression (8 + 12) is thus a multiple of the sum of the whole numbers 2 and 3, which have no common factor.

Answer:

Equivalent fractions.

Step-by-step explanation:

[tex]\dfrac{1}{2}\\\\\dfrac{2}{4}=\dfrac{2 \div 2}{4 \div 2}=\dfrac{1}{2}\\\\\\\dfrac{4}{8}=\dfrac{4 \div 4}{8 \div 4}=\dfrac{1}{2}[/tex]

So, they are equivalent fractions. Equivalent fractions are fractions with different denominators and numerators representing the same part of a whole.

Answer:

thet are equivalent fractions

Step-by-step explanation:

1/2*2/2=2/4,

2/4*2/2=4/8 or

The range of the given data is 15, the sum is 110, variance is 37.

The sample variance is a value that measures the variability of values in the data set and how much the observed values deviate from the value of the mean or central value of the data set.

X=[23,17,15,30,25]

(a)

The value of the range is the difference between the maximum value and minimum value:

range=30-15=15

(b)

Sum(x)= 23+17+15+30+25=110

the sum of x2 = [tex]23^2+17^2+15^2+30^2+25^2=2568[/tex]

(c)

from part (b)

[tex]s^2=\sum x_i-nX^2]/[n-1]\\\\=[2568-5(22)^2][5-1]\\\\=37[/tex]

(d)

Using the definition of the variance, first we calculate the mean,

u=110/5=22

u=22

[tex]v^2=\frac{1}{n-1}\sum (x_i-u)^2\\\\=148/4\\=29.6\\s=6.083.[/tex]

e)

The value of population variance is v =5.44

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i. The assumptions required to use Theorem 7.4 are that the daily downtimes are independent and identically distributed with a mean of 4 hours and a standard deviation of .8 hour.

ii. The approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is about 0.998.

b. The approximate probability that the total downtime for a period of 30 days is less than 115 hours is about 0.03.

a) i) The assumptions that must be true to use the result of Theorem 7.4 (Central Limit Theorem) are:

The daily downtime observations must be independent.

The number of daily downtime observations, n = 30, must be large enough such that the normal approximation is valid. A general guideline is n >= 30, but for this specific case, n = 30 is sufficient.

The individual daily downtime observations must have the same mean and standard deviation, with mean μ = 4 hours and standard deviation σ = 0.8 hours.

ii) Under these assumptions, we can use the Central Limit Theorem to approximate the distribution of the average daily downtime as normal with mean μ = 4 hours and standard deviation σ/√n = 0.8/√30 = 0.17 hours.

Using a standard normal table or calculator, we can find that the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is:

P(1 < μ_bar < 5) = P( (1-4)/0.17 < Z < (5-4)/0.17 ) = P(-23.53 < Z < 2.94) = 0.998

So, the answer is approximately 0.998 or 99.8%.

b) Under the same assumptions, the total downtime for a period of 30 days is a sum of 30 independent daily downtime observations, and we can use the central limit theorem to approximate its distribution as normal with mean 30*4 = 120 hours and standard deviation 0.8 * sqrt(30) = 2.7 hours.

Using a standard normal table or calculator, we can find that the approximate probability that the total downtime for a period of 30 days is less than 115 hours is:

P(X < 115) = P((115-120)/2.7 < Z) = P(-1.85 < Z) = 0.03

So, the answer is approximately 0.03 or 3%.

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Answer:

Below

Step-by-step explanation:

You have ONE equation and TWO unknowns, so there is infinite solutions for a and c......you cannot solve for a specific a and c unless you have another equation relating the two or a definition of one of them.

 You can Solve for a

  20a + 15 c = 340

     20 a = 340-15c

        a = ( 340 -15c) / 20 = 17 - 3/4 c

Similarly:

   20 a + 15 c = 340

  15c = 340 - 20 a

c = (340-20a)/15

For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.

In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.

A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).

To graph the piecewise function f(x), we will graph each part of the function separately.

For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.

For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.

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It would be 20 because of the numbers

Answer:

B , 0.75 grams/cm3

Step-by-step explanation:

Crispin's mass measurement (202 grams) has three significant figures, but his volume measurement (270 cm3) only has two significant figures. So when one of these factors is divided by the other, the factor with the lowest number of significant figures takes precedence. This means that the density calculation can only have two significant figures.

The density of an object is its mass divided by its volume:

So, 202 grams ÷ 270 cm3 = 0.75 grams/cm3

(I also did this on study island and the other person made me get it wrong so i got the answer)

The point-slope form of data contained in this table is y - 15 = 8.3(x - 7.2).

The slope-intercept form of data contained in this table is y = 8.3x - 10.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (7.2, 15), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 15 = (35 - 15)/(4.8 - 7.2)(x - 7.2)

y - 15 = 8.3(x - 7.2)

y - 15 = 8.3x - 25

y = 8.3x - 10

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One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.

To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.

Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.

First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.

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The probability of at most 2 phone calls received in a given day is roughly 0.021.

Since we are asked for the likelihood of a specific number of phone calls in a given day and are provided the average daily rate of phone calls, we must use the Poisson distribution to solve this problem.

Let represent the average daily call volume, which is provided as = 8.6. Following that, the likelihood of getting no more than two phone conversations in a day is:

P(X ≤ 2) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!)

= e^(-8.6) * (8.6^0/0!) + e^(-8.6) * (8.6^1/1!) + e^(-8.6) * (8.6^2/2!)

≈ 0.021

Therefore, the probability of receiving no more than 2 phone calls in a given day is roughly 0.021.

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The probability that a randomly selected person will have a z-score less than 2.00 is about 97.72%. (option closest: 0.9750)

To utilize the experimental rule, we want to know the z-score comparing to a given likelihood. The z-score addresses the quantity of standard deviations an information point is from the mean.

Utilizing the mean and standard deviation given, we can switch the crude score of somebody's pay over completely to a z-score utilizing the recipe:

z = (x - μ)/σ

z = (64,000 - 64,000) / 12,000 = 0

where x is the crude score (family pay), μ is the mean, and σ is the standard deviation.

To find the likelihood that somebody chose indiscriminately will have a z-score under 2.00, we can utilize a standard typical dispersion table or number cruncher to track down the region under the bend to one side of 2.00. This relates to the likelihood of a haphazardly chosen individual having a pay under 2 standard deviations over the mean.

The exact decide states that for an ordinary dissemination with a symmetric recurrence conveyance, around 68% of the information falls inside one standard deviation of the mean, around 95% falls inside two standard deviations of the mean, and around 99.7% falls inside three standard deviations of the mean.

Since we are searching for the likelihood of a z-score under 2.00, which is inside two standard deviations of the mean, we can utilize the experimental decide and gauge that the likelihood is around 95%.

Nonetheless, on the off chance that we need a more exact response, we can utilize a standard typical dissemination table or mini-computer to track down the region under the bend to one side of 2.00. The region under the standard typical dispersion bend to one side of 2.00 is 0.9772, which relates to a likelihood of 0.9772 or 97.72%. Accordingly, the right response is roughly 0.9772 or 97.72%.

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Answer: It is D.

Step-by-step explanation:

Jack may not be obligated to pay Sam the $100 reward because he revoked the offer before Sam found the wallet.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

The amount of reward= $100

Now,

An offer can be revoked at any time before acceptance, and the revocation must be communicated to the offeree. In this case, Jack placed a second ad in the same newspaper revoking his offer before Sam found the wallet. Therefore, Sam did not accept the offer before it was revoked.

Additionally, Sam may not have provided consideration for the reward. Consideration is something of value given in exchange for a promise. In this case, Sam found the wallet before the reward was offered, so he did not provide consideration for the reward when he returned the wallet.

since the offer was revoked before acceptance and Sam did not provide consideration for the reward,

Therefore, by unitary method Jack may not be obligated to pay Sam the $100.

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The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.

By the face of the pyramid that lies in a base of the prism and the face of the pyramid, h2 = 108°

Let B and C be the vertices adjacent to A on the same base as A, and let D be the last vertex of the triangular pyramid. Then angle CAB = 120. Let x be the foot of the altitude from A to line BC. Then since triangle ABX is a 30-60-90 triangle, AX=6. Since the dihedral angle between triangle ABC  and triangle BCD is 60 degree, triangle AXD is a 30-60-90 triangle and 

[tex]AD = 6 \sqrt{3} = h[/tex]

Therefore,

[tex] {h}^{2} = 108[/tex]

A triangular prism is a three-sided prism that has three faces joining the corresponding sides of its triangular base, translated copy, and polyhedron construction. If the sides of a right triangular prism are not rectangular, the prism is oblique. Having square sides and equilateral bases, a uniform triangular prism is a right triangle.

It is, in essence, a polyhedron with three faces, all of whose surface normals are in the same plane (which need not be parallel to the base planes), and two of whose faces are parallel. It is a parallelogram that has these three faces. The same triangle can be seen in all cross-sections that are perpendicular to the base faces.

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