which statement best describes the value of square root of 8?

a. the value of 8 is 2
b. the value of 8 is 4
c. the value of 8 is between 2 and 3.
d. the value of 8 is between 7 and 9.

The area of the semicircle is 39.275 square cm

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

Diameter = 10 cm

Start by calculating the radius of the semicircle

So, we have the following representation

radius = Diameter/2

This gives

radius = 10/2

Evaluate

radius = 5

The area of the semicircle is then calculated as

Area = πr²/2

So, we have

Area = 3.142 * 5²/2

Evaluate

Area = 39.275

Hence, the area is 39.275 square cm

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Answer:

x=b

Step-by-step explanation:

Answer:

X = 30

Your answer is B.)30

Step-by-step explanation:

Answer:

É necessário dividir por 3 para calcular a média simples das 3 notas.

Média = 7.

Step-by-step explanation:

O resultado deve ser dividido por três porque três notas com pesos iguais (projeto, prova e trabalho em grupo) foram somadas, portanto para calcular a média bimestral de Laura, a soma das três notas deve ser dividida por 3. A média de Laura é:

\(M=\frac{5,0+6,5+9,5}{3}\\ M=7\)

Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the formulas 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" between them.

Here,

If two lines have the same slope, they are considered to be parallel.

This will allow us to determine the equation for the line that is perpendicular to the graphed line and goes through the points (4, 1): y = -2*x + 9.

Let's try to locate the line as follows:

Finding the graphed line's slope is the first step towards locating the line.

Keep in mind that a generic statement is anything like:

y = a*x + b

where a represents the slope and b the y-intercept

If the line does indeed travel through the points (x1, y1) and (x2, y2), then the slope of that line can be expressed as follows:

\(m=\frac{y_{2}- y_{1}}{x_{2} -x_{1} }\)

As seen below, the graphed line crosses (-3, 3) and (-2, 1). The slope will therefore be:

\(m=\frac{1- 3}{2 -(-3) }\)

Since the parallel line's slope is likewise 2, it will look somewhat like this:

y = -2*x + c

Using the knowledge that this line passes through, we may determine the value of c. (4, 1).

Thus, y = 1 must exist when x = 4.

When we swap these out in the line equation, we get:

-2*4 + c = 1

-8 + c = 1

1 + 8 = c = 9

Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9

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Answer:

4 and 20

Step-by-step explanation:

let one number be x then the other number is 5x , so

x + 5x = 24

6x = 24 ( divide both sides by 6 )

x = 4 and 5x = 5 × 4 = 20

The 2 numbers are 4 and 20

The net asset value (NAV) per share of the Fidelity Active Equity fund is $46.43.

To calculate the net asset value (NAV) per share of the Fidelity Active Equity fund, we need to subtract the liabilities from the total assets and then divide the result by the number of outstanding shares.

The total assets of the fund are $330 million, and its liabilities are $5 million, so its net assets are

= $330 million - $5 million

Substract the numbers

= $325 million

The fund has sold 7 million shares, so the NAV per share is

= $325 million / 7 million shares

Divide the numbers

= $46.43 per share

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The properties used to simplify the problem are associative property of addition, additive inverse, and additive identity.

Consider the given problem;

( 38 + 677 ) + ( - 38 )

The associative properties can be represented as:

( A + B ) + C = A + ( B + C )

Now, we need to check all the options to determine the properties used:

( 38 + 677 ) + ( - 38 ) = 38 + ( 677 - 38 )

( A + B ) + C = A + ( B + C )

Therefore, this is the associative property.

Now,

677 + 0 = 677

A + 0 = A

Thus, this is the additive identity.

Similarly,

677 + [ 38 + ( -38 ) ]

Here, 38 + ( -3 8 ) represents,

A + ( - A ) = 0.

Therefore, this is the additive inverse.

Thus, the properties used to simplify the problem are the associative property of addition, additive identity, and additive inverse properties.

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The integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

To solve the given integral ∫(3x^4 + x - 2 + √x^3) * x, we can break it down into separate terms and integrate each term individually.

In the first term, 3x^4 * x, we can simplify it by multiplying the exponents: 3x^5. We apply the power rule for integration, which states that the integral of x^n is (x^(n+1))/(n+1). Applying this rule to our first term, we get (3/6)x^6 = x^6/2.

Moving on to the second term, x * x, we simply have x^2. Again, applying the power rule, the integral of x^2 is (x^3)/3.

In the third term, -2 * x, we have a constant multiple of x, which can be integrated as -(2/2)x^2 = -x^2.

Lastly, in the fourth term, √x^3 * x, we can simplify √x^3 as 3/x^2. Therefore, the term becomes (3/x^2) * x = 3/x.

Combining all the integrated terms, the final result of the integral is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C is the constant of integration.

In summary, the integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

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The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Ted's calculation for the number of teams is incorrect because it fails to consider the restrictions of having at least one dwarf and at least one goblin in the team. The correct number of teams with these restrictions can be computed using a combinatorial approach.

Ted's calculation of 5⋅7⋅C(10,3) assumes that any dwarf can be paired with any goblin and then any three members can be chosen from the remaining 10 adventurers. However, this calculation does not take into account the requirement of having at least one dwarf and at least one goblin in each team.

To compute the number of teams with at least one dwarf and at least one goblin, we can use the principle of inclusion-exclusion. We start by finding the total number of teams without any restrictions, which is C(12,5) since we need to choose 5 members from a pool of 12 adventurers.

Next, we subtract the number of teams that don't include a dwarf, which is C(11,5) since we have 11 adventurers remaining after excluding all the dwarfs. Similarly, we subtract the number of teams without a goblin, which is C(10,5) considering the remaining adventurers after excluding all the goblins.

However, we need to add back the number of teams that don't have both a dwarf and a goblin since they were subtracted twice. This number is C(9,5) since we have 9 adventurers left after excluding both the dwarfs and goblins.

Therefore, the number of teams with at least one dwarf and at least one goblin can be computed as C(12,5) - C(11,5) - C(10,5) + C(9,5), resulting in the correct value.

The combinatorial argument for the formula C(2n,2) = 2C(n,2) + n^2 can be demonstrated using the village scenario mentioned in the hint. Considering a village with n men and n women, we need to select two people from the total 2n individuals to count the spikes on the sleeping dragon.

The left side of the equation, C(2n,2), represents the total number of ways to choose two people from the 2n individuals.

On the right side, 2C(n,2) represents the number of ways to choose two people when both are selected from either the men or the women in the village. There are 2 options for selecting either men or women, and C(n,2) represents the number of ways to choose two people from each group.

The term n^2 accounts for the possibility of selecting one man and one woman as the two chosen individuals. There are n choices for selecting a man and n choices for selecting a woman, resulting in n^2 combinations.

By considering these cases and adding them up, we can see that both sides of the equation are equal, demonstrating the combinatorial relationship C(2n,2) = 2C(n,2) + n^2.

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Answer:

x(x - 6)(x + 4)

Step-by-step explanation:

x³ - 2x² - 24x ← factor out x from each term

= x(x² - 2x - 24) ← factor the quadratic

consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)

the factors are - 6 and + 4 , then

x² - 2x - 24 = (x - 6)(x + 4)

then

x³ - 2x² - 24x = x(x - 6)(x + 4)

(a). We need to select at least 5 balls to guarantee at least three balls of the same color have been chosen. (b). We need to select at least 13 balls to guarantee at least three balls of the red color have been selected.

A bowl contains 10 red balls and 10 blue balls. you select balls at random without looking at them.

Using Pigeonhole Principle,

We can apply the pigeonhole principle to ensure that at least three balls of the same color have been selected. Given that we have two colors, we must take the worst-case option—choosing alternating colors—into account. Two balls, one red and one blue, might be chosen. We might have two red and two blue balls if we choose four balls.

She must choose a ball so that the ceiling(X/2) =3

So X = 2*(3-1) +1 = 5 OR

⇒2(red)+2(blue)+1 (either blue or red)=5

Therefore, we need to select at least 5 balls to guarantee at least three balls of the same color have been chosen.

(b). There is a possibility that the first 10 balls that we select are all red. Then to have at least 3 blue balls she has to pick three balls from the rest of the 10 balls. As all of them are blue only 3 picks are needed for that.

⇒She has to select at least 13 balls to ensure the color.

⇒10(red)+2(blue)+1(blue)=13

Therefore, we need to select at least 13 balls to guarantee at least three balls of the red color have been selected.

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Let N' be a set of all positive even numbers and a set of all positive odd numbers arranged in ascending order. Let us denote the positive even numbers as {0,2,4,6,..} and the positive odd numbers as {1,3,5,7,...}.Let a, b, and c be three arbitrary elements of N'.

The following three cases can arise: Case 1: a < b Let us consider the condition given in the problem, i.e. "a <' b if a Answer. The set N' consists of all positive even numbers and positive odd numbers arranged in ascending order. So, the set N' can be expressed as{0, 1, 2, 3, 4, 5, 6, 7, ....} In the given set N', there are three arbitrary elements a, b, and c. Now, let us consider the three cases that can arise: Case 1: a < b In this case, we have to show that a <' b if a< b.

Here, a and b are two arbitrary elements of N' such that a is even and b is odd. For two elements a and b of N', the relation a <' b holds if either a is even and b is odd or a is even and b is even or a is odd and b is odd. Let us consider the first condition, i.e. a is even and b is odd. So, we have a = 2p and b = 2q + 1, where p and q are positive integers. Now, we have to show that a <' b if a< b. a <' b if a is even and b is odd a <' b if 2p < 2q + 1a <' b if p < q + 1/2 (Equation 1) Now, since p and q are positive integers, q + 1/2 is not an integer. Therefore, we can write Equation 1 as

p < q or p <= q This implies that a <' b if a< b for a and b satisfying the condition a is even and b is odd.

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Answer:

(i) 4.1

(ii)  67.24

Step-by-step explanation:

multiply 288 by 3 which is 864. divide 864 by 4π which is 68.7, cube root 68.7, that gives you 4.09/ 4.1

Answer:

wrong

Step-by-step explanation:

(a+b)^2=(a+b)(a+b)

=a(a+b)b(a+b)

=a^2+ab+ab+b^2

=a^2+2ab+b^2

i hope it helps you

The additional information that could be used to prove congruence using AAS or ASA is: Angle A ≅ Angle T and AC (ASA) Angle A ≅ Angle T and BC ≅ PQ (ASA).

To prove that two triangles are congruent using the Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA) criteria, we need specific information about the angles and sides of the triangles.

In this case, we are given three options, and we need to determine which combination of angles and sides would be sufficient to prove congruence using AAS or ASA.

To prove congruence using AAS, we need to show that two angles and the side between them in one triangle are congruent to the corresponding angles and side in the other triangle.

For the given options:

Angle B ≅ Angle P and BC ≅ PQ: This information alone is not sufficient to prove congruence using AAS or ASA. We need additional information about another angle or side in order to establish congruence.

Angle A ≅ Angle T and AC: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.

To determine the third option, we need to consider the remaining combinations of angles and sides:

Angle A ≅ Angle T and BC ≅ PQ: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.

In summary, the additional information that could be used to prove congruence using AAS or ASA is:

Angle A ≅ Angle T and AC (ASA)

Angle A ≅ Angle T and BC ≅ PQ (ASA)

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The total cost paid by Matt if he joins for 6 months is found as 320.

For the stated query:

The joining cost of gym = 200

The month cost = 20.

Let the number of month be 'x'.

Let the total cost be 'c'.

Then , linear equation forms be.

c = 200 + 20x

For 6 months, put x = 6.

c = 200 + 20*6

c = 200 + 120

c = 320

Thus, the total cost paid by Matt if he joins for 6 months is found as 320.

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The complete question is-

Matt joins a gym the cost includes a one time fee of 200 plus a monthly fee of 20. Find the total cost paid by Matt if he joins for 6 months.

Answer:

there is only 1 natural number between n2 and (n+1)2

Step-by-step explanation:

expand/open brackets of (n+1)2

(2×n)+(2×1) = 2n+2 can also be written as n2+2

the questions asks for the numbers between so the number between is n2+ 1. we should not count the n2 and n2+2

this is the "closure" property of natural numbers

Answer:

1

Step-by-step explanation:

The probability of including k specified members in a random sample of size n without replacement from a population of size N can be calculated using the hypergeometric distribution.

The hypergeometric probability mass function is given by:

\(\[P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N-K}{n-k}}}{{\binom{N}{n}}}\]\)

where:

- K is the number of specified members in the population.

- n is the size of the sample.

- k is the number of specified members in the sample.

- N is the total population size.

In this case, we want to find the probability that k specified members are included in the sample, so the probability can be calculated using the hypergeometric distribution formula.

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Answer:

y is 12 degrees

x is 30 degrees

Step-by-step explanation:

If angle ABC is equal to angle MNC, that means 5y equals to 60 degrees. 60 divided by 5 equals 12. So, y equals 12 degrees

2x and 4x equals 180 degrees. So, 180 divided by 6 equals to 30. So x equals 30 degrees

Answer:

x = 30, y = 12

Step-by-step explanation:

2 similar equilateral triangles, each corner is 60 degrees.

2x = 60 degrees

divide by 2

x = 30 degrees

5y = 60 degrees

divide by 5

y = 12 degrees

This can be verified by checking 4x + 2x which gives you 180 degrees forming that straight line angle.

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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The value x in the formula represents the value of each observation of the data-set.

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The value of tan V as a fraction in simplest terms is 4/3

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

The triangle

From the triangle, we have the following readings

Opposite of V = √(35² - 21²) = 28

Adjacent of V = 21

The formula for tan V is then calculated as

tan V = Opposite /Adjacent

Substitute the known values in the above equation, so, we have the following representation

tan V = 28/21

Simplify

tan V = 4/3

Hence, the solution is 4/3

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Answer:

19

Step-by-step explanation:

37/3= 12. something

12+7+19

Main answer: The majority of respondents who favored the legalization of marijuana identified as liberal or very liberal.

Supporting explanation: The table shows that out of the 486 respondents who favored the legalization of marijuana, 296 identified as liberal and 120 identified as very liberal. This means that 616 out of the 826 respondents who answered both questions identified as liberal or very liberal. On the other hand, only 60 respondents who favored the legalization of marijuana identified as conservative or very conservative. This suggests that there is a correlation between political leaning and views on the legalization of marijuana, with those on the left end of the political spectrum more likely to support it.

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Answer:

X=4 Y= -5

Step-by-step explanation:

There are 625 possible combinations.

According to the multiplication principle, if an event A can happen in x different ways and an event B can happen in y different ways, then there are x y possibilities for both events to happen at once.

To determine the number of combinations possible with 4 cards and a spinner with 5 numbers, we can use the concept of the multiplication principle.

For the spinner, we have 5 possible numbers that can be selected.

For the 4 cards, each card can have any one of the 5 possible numbers from the spinner.

Using the multiplication principle, we multiply the number of choices for each item together to find the total number of combinations.

Number of combinations = Number of choices for the spinner × Number of choices for each card

                       = 5 × 5 × 5 × 5

                       = 625

Therefore, there are 625 possible combinations.

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Answer:

\(x = -4\)

Step-by-step explanation:

\(~~~~~~f(x) = -1\\\\\implies 2x +7 = -1\\\\\implies 2x = -1 - 7\\\\\implies 2x = -8 \\\\\implies x = -\dfrac 82 \\\\\implies x = -4\)