How to find volume in a 3 dimensional shape?

Step-by-step explanation:

(a) To count the number of paths of length 2 in G, we need to consider all possible pairs of vertices that are connected by a path of length 2. There are three types of pairs:

1. Pairs of vertices in A that are adjacent in the cycle: There are n such pairs, since there are n vertices in the cycle and each vertex has two neighbors in the cycle.

2. Pairs of vertices in A that are not adjacent in the cycle: There are n(n-3) such pairs, since we can choose any two vertices in A that are not adjacent, and there are n-3 non-adjacent pairs of vertices in a cycle.

3. Pairs of a vertex in A and c: There are n such pairs, since there are n vertices in A and c is connected to each of them.

Therefore, the total number of paths of length 2 in G is:

n + n(n-3) + n = n^2 - 2n

(b) To count the number of cycles in G, we need to consider all possible cycles that can be formed. There are two types of cycles:

1. Cycles that only include vertices in A: There are (n-1)! such cycles, since we can choose any vertex in A as the starting point, and then traverse the cycle in (n-1) ways.

2. Cycles that include c: There is only one such cycle, which is the cycle c-a1-a2-...-an-c.

Therefore, the total number of cycles in G is:

(n-1)! + 1.

Answer:

\(y_1 = -2\) and \(y_2 = 4\)

Step-by-step explanation:

\( \sqrt{10y + 24} - 3 = y + 1\)

Move the constant to the right-hand side and change their sign.

\( \sqrt{10y + 24} = y + 1 + 3 \)

combine like terms

\( \sqrt{10y + 24} - 3 = y + 4\)

Square both side to remove square brackets.

10y + 24 - 3 = y²+ 8y + 16

Move the expression to the left-hand side and change its sign.

10y + 24 - y² - 8y - 16 = 0

Combine like terms

10y - 8y + 24 - 16 - y² = 0

2y + 8 - y² = 0

Use commutative property to reorder the terms.

-y² + 2y + 8 = 0

Change the sign of expression.

y² -2y -8 = 0

split -2y

y² + 2y - 4y - 8 = 0

Factor out y from the first pair and -4 from the second equation.

y ( y + 2 ) - 4 ( y + 2 ) = 0

Factor out y+2 from the expression.

( y + 2 ) ( y - 4)

When the products and factors equals 0, at least one factor is 0.

y + 2 = 0

y - 4 = 0

Solve for y

y = -2

y = 4

When we plug the both solution as y we found that both is true solution of this equation.

This equation has two solutions which are -2 and 4.

Answer:

Solution given:

\( \sqrt{10y + 24} - 3 = y + 1\)

keep the constant term in one side

\( \sqrt{10y + 24} =y+1+3\)

solve possible one

\(\sqrt{10y+24}=y+4\)

now

squaring both side

\((\sqrt{10y+24})²=(y+4)²\)

10y+24=y²+8y+16

taking all term on one side

10y+24-y²-8y-16=0

solve like terms

8+2y-y²=0

doing middle term factorisation

8+4y-2y-y²=0

4(2+y)-y(2+y)=0

(2+y)(4-y)=0

either

y=-2

or

y=4

y=-2,4

Answer:

x<12

Step-by-step explanation:

Step 1: Simplify both sides

-1/4x > -3

Step 2: Multiply both sides by 4/-1

(4/-1) * (-1/4) > (4/-1) * (-3)

Final Conclusion: [x < 12]

Answer:

330

Step-by-step explanation:

The prism is a triangular prism

9 * (12 + 5 + 13) + (2 * 30)= 330

30 being the base area

Answer:

330

Step-by-step explanation:

We can break each surface area into it pieces.

For the squares:

9x13=117

9x5=45

9x12=108

For the triangles:

12x5÷2=30

12x5÷2=30

Add all of those together to get the total square area, which is

330

Answer:

1 x 3 x 1 = 3

Step-by-step explanation:

In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

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Answer:  x-intercept 5 and y-intercept 8.

Step-by-step explanation:  As you work through it, you will discover that algebra, geometry, and trigonometry ... AB. For each of the following, find coordinates for the midpoint of AB: ... Given that 2x − 3y = 17 and 4x + 3y = 7, using mental math (that is, without using ... Find a and b so that ax + by = 1 has x-intercept 5 and y-intercept 8.

Answer:

3/4

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

sub in 2 fo the x and 3 for the y

2(2) + 3(3) = 13

13 does not equal 6 so it is not true

Answer:

0.4285

Step-by-step explanation: That’s what Siri told me✊✊✊‍♂️

The total number of ways in which elements from set-1 can be arranged in a line is given by the permutation of 10 elements, denoted by P(10), which is 10!. So, the total number of ways to arrange 10 elements in a line is 10! = 3,628,800.

If set-1 consists of 10 elements, the total number of ways in which elements from s1 can be arranged in a line is given by the permutation of 10 elements, denoted by P(10), which is:

P(10) = 10!

This means that there are 10 ways to choose the first element, 9 ways to choose the second element (since one element has already been chosen), 8 ways to choose the third element (since two elements have already been chosen), and so on, until there is only 1 way to choose the last element.

Therefore, the total number of ways to arrange 10 elements in a line is 10! = 3,628,800.

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The general term of the given sequence aₙ can be shown as, aₙ = (-8)(-2/3)ⁿ⁻¹.

In the question, we are asked to find a formula for the general term aₙ of the sequence, assuming that the pattern of the first few terms continues. (assume that n begins with 1.) −8, 16/3, − 32/9, 64/27, − 128/81, ...

The given sequence is a geometric progression, where every term is the product of the previous term and a common ratio, which can be calculated as: r = a₂/a₁ = (16/3)/(-8) = -2/3.

The formula for the general term of a geometric sequence is given as, aₙ = arⁿ⁻¹, where a = a₁, the first term of the geometric sequence.

Substituting the values, we get:

aₙ = (-8)(-2/3)ⁿ⁻¹.

Thus, the general term of the given sequence aₙ can be shown as, aₙ = (-8)(-2/3)ⁿ⁻¹.

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The provided question is incomplete. The complete question is:

"Find a formula for the general term aₙ of the sequence, assuming that the pattern of the first few terms continues. (assume that n begins with 1.) −8, 16/3, − 32/9, 64/27, − 128/81, ..."

Answer:

5(12 : 3) -8

Step-by-step explanation

when you solve the first half of the equation you get 1.

so 9-1 is 8.

Answer:

4y - x = 20

Step-by-step explanation:

y-y1 = m (x-x1)

y - 6 = 1/4 (x - 4)

4y - 24 = x - 4

4y - x = 20

If the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

The selling price = $90

The rate of sales tax = 3%

The amount of sale tax = The selling price × The rate of sales tax

Substitute the values in the equation

The amount of sale tax = 90 × (3/100)

= 90 × 0.03

= $2.7

The total price = The selling price + The amount of sale tax

Substitute the values in the equation

The selling price  = 90 + 2.7

= $92.7

Hence, if the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

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At the 0.10 significance level, first year salaries are higher at the recruiter's company.

We will conduct a one-sided hypothesis test to determine if the first year salaries at the recruiter's company are higher than the average reported by the university newsletter ($46,580).

H₀: μ = 46,580

Ha: μ > 46,580

The null and alternative hypothesis have been set up, with the level of significance set at 0.10.

Here,

The sample mean is X = (52,450+48,620+44,800+56,200+46,770+49,335+43,900+58,090+49,780+53,820)/10

= 503765/10.

= 50376.5

We can calculate the sample standard deviation using the formula s = √((∑(x - X)²)/(n−1)), where x is the individual salaries, X is the sample mean, and n is the sample size.

Substituting the values, s = √((∑(x - 49,833)²)/(10−1)) = 3,451.

Now, we will compute the test statistic. We will use the t-test as the population standard deviation is unknown.

The t-test statistic is t = (X - μ₀)/(s/√n)

Substituting the values, t = (50376.5- 46,580)/(3,451/√10)

= 3796.5/1091.3

= 3.478

To find the p-value, we need to use a t-table to find the corresponding p-value for a one-tailed t-test with 9 degrees of freedom and a two-tailed significance level of 0.10.

The critical t-score from the t-table is 1.833.

Since our t-statistic of 3.478 is greater than 1.833, the p-value is less than 0.10. This means that we can reject the null hypothesis and conclude that, at the 0.10 significance level, first year salaries are higher at the recruiter's company.

Therefore, at the 0.10 significance level, first year salaries are higher at the recruiter's company.

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"Your question is incomplete, probably the complete question/missing part is:"

A university newsletter reported that on average college graduates earned $46,580 their first year after graduation. A major corporation recruiter claims that, at his company, first years' salaries are higher. The recruiter found the starting salaries for 10 first year graduates at his company listed below. Can the recruiter conclude, at the 0.10 significance level, that the first year salaries are higher? 52,450 48,620 44,800 56,200 46,770 49,335 43,900 58,090 49,780 53,820

A linear transformation t defined by a square matrix a is an isomorphism if and only if a is nonsingular.

To prove this statement, we first recall that an isomorphism is a linear transformation that is both injective (one-to-one) and surjective (onto). If t is an isomorphism, then it is invertible, which means that there exists another linear transformation t^-1 such that t(t^-1(x)) = x and t^-1(t(x)) = x for all vectors x in the domain of t. In matrix notation, this means that aa^-1 = a^-1a = I, where I is the identity matrix.

Now suppose that a is nonsingular, which means that its determinant det(a) is nonzero. This implies that a^-1 exists and is also a square matrix. If we can show that t is injective and surjective, then we can conclude that t is an isomorphism. To prove injectivity, suppose that t(x) = t(y) for some vectors x and y. Then ax = ay, which implies that a(x - y) = 0. Since det(a) is nonzero, it follows that x - y = 0, which means that x = y. Thus, t is injective. To prove surjectivity, let z be an arbitrary vector in the range of t. Then there exists a vector y such that t(y) = z.

This implies that ay = z, which means that y = a^-1z. Thus, every vector in the range of t can be written as t(a^-1z), which shows that t is surjective. Therefore, we can conclude that t is an isomorphism if a is nonsingular. Conversely, if t is an isomorphism, then it must be invertible, which implies that a must be nonsingular, as we showed earlier. Thus, t is an isomorphism if and only if a is nonsingular.

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1. To find the center of mass of a rod with varying linear density, we integrate the product of the linear density and the position along the rod over its length.

2. To find the mass of a rod with linear density varying linearly, we integrate the linear density function over the length of the rod.

3. To find the largest value of linear density for a rod with density varying quadratically, we determine the point where the derivative of the linear density function is maximum.

4. To find the value of m for the given particles, we use the formula for the center of mass and solve for m.

5. To find the centroid of the region bounded by two curves, we calculate the coordinates of the centroid using the formulas for the x-coordinate and y-coordinate.

1. For the rod with varying linear density, we integrate (4x+1) over the length of the rod and divide by the total mass.

2. For the rod with linearly varying density, we integrate the linear density function (a linear equation) from the left end to the right end to find the mass.

3. For the rod with density varying quadratically, we take the derivative of the linear density function, set it equal to zero to find the critical point, and determine the maximum value of the linear density.

4. Using the center of mass formula, we calculate the x-coordinate of the center of mass using the given masses and coordinates and solve for m.

5. To find the centroid of the region, we calculate the area under the curves y=x^3 and y=4x in the first quadrant, find the coordinates of the centroid using the formulas, and represent the answer as (x-coordinate, y-coordinate).

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Answer:

288 that's it answer you can multiply

Answer:

i say 252

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Measure of one arc = 90°

-> Measure of other arc = 360°- 90° = 270°

x° = 1/2 (270° - 90°)

-> x° = 1/2 * 180°

-> x° = 90°

-> x° = 90°

-> x = 90

Answer:

( 3, 7)

Step-by-step explanation:

x= 3 Y = 7. The origin is (0, 0)

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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ANSWER

D. y = -5x + 3

EXPLANATION

The equation of a line in slope-intercept form is,

Where m is the slope and b is the y-intercept.

In this graph, we can see that the y-intercept - which is the value of y where the line intersects the y-axis, is 3,

To find the slope, we will use the second point shown in the graph above. The formula to find the slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,

Using the points (0, 3) and (1, -2),

Hence, the equation of the line is y = -5x + 3.

Step-by-step explanation:

i hope it helped U

The given equation can be written as:

u² - 17u + 16 = 0

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

You probably are interested in expressing the given equation as a quadratic equation in u, as it will make it easy to find the solutions.

Let u = x²

So,

u² = x⁴

So, the given equation can be written as:

u² - 17u + 16 = 0

Now the equation is quadratic in u and the solutions can be calculated using quadratic formula or factorization.

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Answer:

8! or 456 ways

Step-by-step explanation:

8 x 7 x 6 x 5 x 4 x 3 x 2 = 456

The graph of the function f(x) = x - 2 is a straight line that passes through the origin and has a slope of 1.

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.

This means that for every unit increase in x, the value of f(x) increases by 1 unit. Therefore, when x is equal to 0, the value of f(x) is equal to -2. When x is equal to 1, the value of f(x) is equal to -1. When x is equal to 2, the value of f(x) is equal to 0. When x is equal to 16, the value of f(x) is equal to 14. As you can see, for every increase in x, the value of f(x) increases by 2 units.  This is the reason why the line drawn from the value of x to the corresponding value of f(x) increases by 2 units when x is increased by 1 unit.

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In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
In this example, the function f(x) = x-2 is being represented by a line that connects each value of x to the corresponding value of f(x).

When x = 4,

then f(x) = 4-2

f(x) = 2,

so the line extends from (4, 2) to the origin (0, 0).

Similarly, when x = 0,

then f(x) = 0-2

f(x) = -2,

so the line extends from (0, -2) to (4, 2).

When x = 1,

then f(x) = 1-2

f(x) = -1,

so the line extends from (1, -1) to (4, 2).

Finally,

when x = 2,

then f(x) is undefined.

In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

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One way to find the general solution of x' = Ax is to use the exponential matrix method. The general solution is given by x(t) = e^(At)x(0), where e^(At) is the matrix exponential of A.

Another way to find the general solution is to solve the system of differential equations directly using the method of undetermined coefficients. Let x(t) = (x1(t), x2(t), ..., xn(t)) be the solution of x' = Ax. Then we have

x1'(t) = a11x1(t) + a12x2(t) + ... + a1nxn(t)

x2'(t) = a21x1(t) + a22x2(t) + ... + a2nxn(t)

...

xn'(t) = an1x1(t) + an2x2(t) + ... + annxn(t)

This is a system of n linear homogeneous first-order differential equations. We can solve it by assuming that each xi(t) has the form e^(rt), where r is a constant. Substituting this into the system, we get

r e^(rt) = a11 e^(rt) x1(0) + a12 e^(rt) x2(0) + ... + a1n e^(rt) xn(0)

r e^(rt) = a21 e^(rt) x1(0) + a22 e^(rt) x2(0) + ... + a2n e^(rt) xn(0)

...

r e^(rt) = an1 e^(rt) x1(0) + an2 e^(rt) x2(0) + ... + ann e^(rt) xn(0)

Dividing by e^(rt) (which is nonzero for all t) and rearranging, we obtain the system

r x1(0) + a12 x2(0) + ... + a1n xn(0) = a11 r x1(0)

a21 x1(0) + r x2(0) + ... + a2n xn(0) = a22 r x2(0)

...

an1 x1(0) + an2 x2(0) + ... + r xn(0) = ann r xn(0)

or, in matrix form,

(rI - A) x(0) = 0,

where I is the identity matrix and x(0) = (x1(0), x2(0), ..., xn(0)). Since x(0) is nonzero, the matrix (rI - A) must be singular. Therefore, we must have det(rI - A) = 0. This gives us the characteristic equation of A:

det(rI - A) = (r - λ1)(r - λ2)...(r - λn) = 0,

where λ1, λ2, ..., λn are the eigenvalues of A. The roots of this equation are the values of r for which the system has nonzero solutions.

For each eigenvalue λ of A, we can find a corresponding eigenvector v such that Av = λv. Then the solution of the system is given by

x(t) = c1 e^(λ1t) v1 + c2 e^(λ2t) v2 + ... + cn e^(λnt) vn,

where c1, c2, ..., cn are constants determined by the initial conditions.

To verify that the two methods give the same answer, we can compute the matrix exponential of A using the formula

e^(At) = ∑(k=0 to ∞) (At)^k /

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