Evaluate 16 to the power of 1/2 x 2 to the power of -3


Give your answer as a fraction in its simplest form.


If you get it right then i will give you 5 stars 1 thank you and mark you Brainallist

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

2s +9

———

3r ÷ s

(If r = -14 and s = 6)

\( \large \boxed{\mathfrak{Answer \: with \:Explanation} \downarrow}\)

\( \sf\frac{2s + 9}{3r \div s} \\ \)

Substitute the values of r & s with -14 & 6 respectively.

\( \sf\frac { 2 ( 6 ) + 9 } { 3 ( - 14 ) \div ( 6 ) } \\ \)

Multiply 2 and 6 to get 12.

\( \sf\frac{12+9}{\frac{3\left(-14\right)}{6}} \\ \)

Add 12 and 9 to get 21.

\( \sf\frac{21}{\frac{3\left(-14\right)}{6}} \\ \)

Multiply 3 and -14 to get -42.

\( \sf\frac{21}{\frac{-42}{6}} \\ \)

Divide -42 by 6 to get -7.

\( \sf\frac{21}{-7} \\ \)

Divide 21 by -7 to get -3.

\( = \boxed{ \boxed{\bf \: - 3}}\)

Answer:

25+9

--------

3r÷5

=2×6+9

----------

3×(-14)÷6

=12+9

---------

(-42)÷6

=21

----

-7

=_3

Answer:

8

Step-by-step explanation:

It is going up by 5, so you have to subtract 13-5 to get the number before 13.

Answer:

A

Step-by-step explanation:

Answer:

22/33,2/3 and 6/9=0.66666666666666666 or 0.6(bar) as asked in question

3/5 is equal to 0.6 not 0.66666666

Pls mark as brainliest

If you only have $10 and the book costs $20, No, you cannot buy the book. However, if you have $25, Yes, you can afford the book and still have $5 left after the purchase.

In scenario A, where you have $10 and the book costs $20, you cannot buy the book. The cost of the book exceeds the amount of money you have, leaving you $10 short. In this case, you would need to find an additional $10 in order to afford the book.

In scenario B, where you have $25 and the book costs $20, you can buy the book. With $25, you have enough funds to cover the full price of the book. After purchasing the book, the remaining amount found by subtraction of the cost of the book from the amount you have (ie) the remaining amount = the amount you have - the cost of the book = $25 - $20 = $5

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The given question is

You want to read a certain book.

A. This book costs $ 20. If you only have$ 10, can you buy the book?

B. If you have $ 25, can you buy the book?

Answer:

The answer is 0 because the minimum is 5

Step-by-step explanation:

Use the formula  

x  =  −  b /2 a

to find the maximum and minimum.

( 0 , 5 )

The set H, consisting of matrices of the form [ab0d], is not a subspace of M2×2 because it fails to satisfy closure under addition and does not contain the zero vector.

To determine if the set H of all matrices of the form [ab0d] is a subspace of M2×2, we need to check if it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector. Closure under addition means that if we take any two matrices from H, their sum should also be in H. Let's consider two matrices A and B in H:

A = [a1 b1 0 d1]

B = [a2 b2 0 d2]

Now, let's add A and B:

A + B = [a1 + a2, b1 + b2, 0, d1 + d2]

The sum A + B does not have the form [ab0d] since it contains non-zero elements in the third position. Therefore, H is not closed under addition. Next, closure under scalar multiplication means that if we multiply a matrix from H by a scalar, the result should also be in H. Let's consider a matrix A in H and a scalar k:

A = [a b 0 d]

Now, let's multiply A by k:

kA = [ka kb 0 kd]

The product kA still has the form [ab0d], so H is closed under scalar multiplication. Lastly, a subspace must contain the zero vector, which is the matrix [0 0 0 0]. Since the zero vector can be represented as [00 00], it does not have the form [ab0d]. Therefore, H does not contain the zero vector. Since H fails to satisfy the closure under addition and containing the zero vector, it is not a subspace of M2×2.

In summary, the set H of matrices of the form [ab0d] is not a subspace of M2×2 because it does not satisfy closure under addition and does not contain the zero vector.

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Answer:

Rs 750 .

Step-by-step explanation:

We need to find 16 ⅔ % of Rs 45,00 .

So , we can write 16 ⅔ % as 50/3 %.

= \(\dfrac{50}{\cancel3}\times Rs ,\cancel{ 4500 }^{1500}\times\dfrac{1}{100}\)

=\(\red{ Rs 750 }\)

The molar volume of ethane at 300 K and 200 atm, calculated using the Van der Waals equation of state, is approximately 0.109 L/mol.

To calculate the molar volume, we need to solve the cubic equation obtained from the expanded Van der Waals equation of state:

V^3 - (b + pRT)V^2 + (pa)V - pab = 0

Given the values of a = 5.5088 L^2 atm mol^(-2) and b = 0.065144 L mol^(-1) for ethane gas, and the temperature T = 300 K and pressure p = 200 atm, we can substitute these values into the cubic equation.

Substituting the values into the equation, we have:

V^3 - (0.065144 + (200)(0.0821)(300))V^2 + (5.5088)(200)V - (200)(0.065144)(5.5088) = 0

Solving this cubic equation, we find that one of the roots corresponds to the molar volume of ethane at the given conditions, which is approximately 0.109 L/mol.

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Answer:

here ,

\( \sqrt[3]{x {}^{3} y {}^{3} } \)

\( = (x {}^{3} y {}^{3} ) {}^{ \frac{1}{3} } \)

therefore the anwer is xy.

was it hellful plz let me know..

Answer:

Solution,

\( \sqrt[3]{ {x}^{3} {y}^{3} } \\ = {x}^{ \frac{3}{3} } {y}^{ \frac{3}{3} } \\ = xy\)

It is a root law of indices.

For example:

\( \: if \: {a}^{ \frac{m}{n} } \)

is an algebraic term, where m and n are the positive integers, then :

\( {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } \)

Hope this helps...

Good luck on your assignment...

Answer:

=1

Step-by-step explanation:

i hope this helps :)

Answer:

Option (3)

Step-by-step explanation:

Given expression is,

\(\frac{2^3\times 125^\frac{2}{3}\times 81^\frac{3}{4}}{8^\frac{1}{3}\times 9\times 5^2}\)

To solve the given expression we will apply the law of exponents,

\(\frac{2^3\times 125^\frac{2}{3}\times 81^\frac{3}{4}}{8^\frac{1}{3}\times 9\times 5^2}=\frac{2^3\times (5^3)^\frac{2}{3}\times (3^4)^\frac{3}{4}}{(2^3)^\frac{1}{3}\times (3^2)\times 5^2}\)

                    \(=\frac{2^3\times (5^{3\times \frac{2}{3}})\times (3^{4\times \frac{3}{4}})}{(2^{3\times \frac{1}{3}})\times (3^2)\times 5^2}\)

                    \(=\frac{2^3\times 5^2\times 3^3}{2\times 3^2\times 5^2}\)

                    \(=\frac{2^3}{2}\times (\frac{5^2}{5^2})\times (\frac{3^3}{3^2})\)

                    \(=2^{3-1}\times (1)\times 3^{3-2}\)

                    \(=2^2\times 1\times 3\)

                    \(=12\)

Therefore, Option (3) will be the correct option.

Answer:

15, 25, 45, 75, 115, 165.

Step-by-step explanation:

pattern. So then you just stick the 5s back on 15, 25, 45, 75, 115, 165.

Answer:

$240

Step-by-step explanation:

this would be solved using simultaneous equation

let c = cost of cds

d = cost of dvds

two equatiions can be derived from the question

5d + 9c = 285 eqn 1

5d + 5c = 225 equation 2

subtract equation 2 from 1

4c = 60

c = 15

substitute for c in eqn 1

5d + 9(15) = 285

5d = 150

d = 30

5(30) + 6(15) = 240

The minimum possible value of the sum $xyz$ occurs when $x$, $y$, and $z$ are as close to each other as possible.

To find the minimum possible value of the sum $xyz$, we need to consider the factors of 2004 and distribute them as evenly as possible among $x$, $y$, and $z$. Since we want the sum to be minimum, we try to minimize the differences between the values of $x$, $y$, and $z$.

The prime factorization of 2004 is $2^2 \times 3 \times 167$. To minimize the sum, we allocate the prime factors evenly: $x = 2$, $y = 2 \times 3 = 6$, and $z = 167$. Therefore, the minimum value of the sum $xyz$ is $2 \times 6 \times 167 = 2004$.

In this case, $x$, $y$, and $z$ are as close to each other as possible, resulting in the minimum value of the sum. Any other allocation of factors would increase the sum, making this the optimal solution.

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Answer:

\(f(t) = 4100( {2}^{ \frac{t}{2} }) \)

The total number of ways to achieve a Straight is 10,240.

The total number of ways to achieve a Flush is 5148.

The total number of ways to achieve a Full House is 312.

The total number of ways to achieve a Straight Flush is 40.

What is number of ways?

The term "number of ways" refers to the total count of possible arrangements or combinations of a set of objects or events. It is often used in combinatorics, which is the branch of mathematics concerned with counting and arranging objects.

a) A Straight: There are 10 possible sequences of 5 cards of sequential rank (e.g., 2, 3, 4, 5, 6 or 10, J, Q, K, A), and for each sequence, there are \(4^5\) = 1024 ways to choose the suits of the cards. Therefore, the total number of ways to achieve a Straight is 10 * 1024 = 10,240.

b) A Flush: There are 4 suits in the deck, and for each suit, there are (13 choose 5) ways to choose 5 cards of that suit. Therefore, the total number of ways to achieve a Flush is 4 * (13 choose 5) = 5148.

c) A Full House: There are 13 ranks in the deck, and for the 3 cards of one rank, there are (4 choose 3) = 4 ways to choose the suits, and for the 2 cards of another rank, there are (4 choose 2) = 6 ways to choose the suits. Therefore, the total number of ways to achieve a Full House is 13 * 4 * 6 = 312.

d) A Straight Flush: There are 10 possible sequences of 5 cards of sequential rank (as in part a)), and for each sequence, there are 4 ways to choose the suit of the cards. Therefore, the total number of ways to achieve a Straight Flush is 10 * 4 = 40.

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The angle measures, in order from least to greatest, of the dilated image  45°,55° and 80°.

A dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.

Euclidean space, In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.

Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still 45 °, 55 °, and 80 °.

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Answer:45,55,80

Step-by-step explanation:  dilations preserve angles measures regardless of the scale factor. Therefore the angle measures of the image will be the same of that of the pre-image ,so our answer is still 4545,5555,8080 .

The measurement of AB is given as follows:

AB = 16.23.

The three trigonometric ratios are defined as follows:

For the angle of 52º, we have that:

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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Answer:

5x+18

Have a great day :)

Answer:

The answer in this picture :)

The given statement "A and B are n x n matrices. The determinant of A is the product of the diagonal entries in A" is False because the product of the diagonal entries in A for n x n matrix will not be equal to determinant of A.

The determinant of a matrix is a scalar value that can be calculated using a specific formula. The formula for finding the determinant of an n x n matrix involves finding the sum of products of the elements in certain combinations of rows and columns.

The product of the diagonal entries is only one element in the calculation of the determinant of a matrix, and it is not equal to the determinant unless the matrix has all zeros except on the diagonal.

For example, consider the following 2x2 matrices:

A = [2 3; 4 5]

B = [1 0; 0 1]

The determinant of A is (25) - (34) = -2

The product of the diagonal entries in A is 2*5 = 10, which is not equal to the determinant.

The determinant of B is (11) - (00) = 1

The product of the diagonal entries in B is 1*1 = 1, which is equal to the determinant.

Therefore, the statement "The determinant of A is the product of the diagonal entries in A" is false in general, and the determinant of a matrix is typically calculated using a more involved formula that takes into account all the elements in the matrix.

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

3. True

Step-by-step explanation:

Y = (2, - 1) and Y’ = (4, - 2)

2x = 4

x = 4/2 = 2

-1x = -2

X = -2/-1

X = 2

Answer: 3 true, Y = (2, - 1) and Y’ = (4, - 2)2x = 4x = 4/2 = 2-1x = -2X = -2/-1X = 2

Step-by-step explanation: hope this helps<3

Answer:

i didn't understand what your question is

Answer:

\(\pm\frac{2}{3}\)

Step-by-step explanation:

\(\sqrt{\frac{45}{20}}=\sqrt{\frac{5*9}{5*4}}=\sqrt{\frac{9}{4}}=\pm\frac{2}{3}\)

Answer:

-3y

Step-by-step explanation:

Whether y is smaller than 0 or not, the square root of y^2 is y, a positive quantity.

Thus, -√(9y²) = -3y

Answer

It's actually 3y instead of -3y.

BTW, anybody from RSM

Answer:

J' (- 10, - 8 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

J (10, - 8 ) → J' (- 10, - 8 )

Answer:

(-10, -8)

Step-by-step explanation:

The rule for a reflection over the y -axis is (x, y)→(−x, y) .

so J(10, -8) becomes J'(-10, -8)

Given a pseudorandom generator (PRG) g with an expansion factor l(n) > 2n, we need to determine whether g' is necessarily a PRG in each of the following cases.

To answer this question, let's consider each case separately:

Case 1: If l(n) = 2n+1
In this case, the expansion factor l(n) is greater than 2n. Therefore, g' is necessarily a PRG. This can be proven as follows:

Proof:
Since l(n) = 2n+1 > 2n, it means that the length of the output of g is larger than 2n.

By definition, a PRG expands the length of the seed and produces a longer pseudorandom output. Since g is a PRG, it means that for any input seed of length n, g produces an output of length greater than 2n.

Now, let's consider g', which is defined as g'(x) = g(x) || 0, where || denotes concatenation and 0 is a constant bit.

For any input seed x of length n, g' produces an output of length greater than 2n+1 (since g outputs length is greater than 2n and we append one extra bit 0).

Therefore, g' is a PRG as its output length exceeds the expansion factor of 2n+1.

Case 2: If l(n) = 2n
In this case, the expansion factor l(n) is exactly 2n. We need to show a counterexample where g' is not necessarily a PRG.

Counterexample:
Let's assume g is a PRG with a seed of length n and an output of length 2n. Now, consider g' defined as g'(x) = g(x) || 0, where || denotes concatenation and 0 is a constant bit.

In this counterexample, g' is not a PRG.

The reason is that the expansion factor of g' is exactly 2n, which is equal to the length of its output. Thus, g' fails to expand the length of the seed. The last bit 0 that is appended to the output of g does not contribute to expanding the length.

Therefore, g' is not a PRG in this case.

In conclusion, for the case where l(n) = 2n+1, g' is necessarily a PRG, as its output length exceeds the expansion factor. However, for the case where l(n) = 2n, g' is not necessarily a PRG, as it fails to expand the length of the seed.

- For l(n) = 2n+1, g' is necessarily a PRG.
- For l(n) = 2n, g' is not necessarily a PRG.

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Answer:

The distance measure is 4.2 ft

Step-by-step explanation:

Here, we want to get the distance from the bottom of the ladder to the side of the house

To get this, we can see that what we have is a right-angled triangle

We need to apply the appropriate trigonometric identity to get the value of what we want

Let us call the measure we want to calculate x

Mathematically;

Tan 72 = 13/x

x = 13/tan 72

x = 4.2 ft