how is \( {1}^{4} \)differ from \( { {0.1}^{4} }^{} \)

Answer:

2.85714285714

Step-by-step explanation:

6x2 –14x ≥ –4

36 -14x ≥ -4

-14x ≥ -36-4

-14x ≥ -40

x ≥ -40/14

x \(\leq\) 2.85714285714

A

Step-by-step explanation:

did math

The statement is true. If a matrix B can be expressed as B = PDP^T, where P is an invertible matrix and D is a diagonal matrix, then B is a symmetric matrix.

This can be proven as follows:
First, let's take the transpose of B:

B^T = (PDP^T)^T = (P^T)^TD^T P^T

Since D is a diagonal matrix, its transpose is equal to itself:

D^T = D

Therefore, we can substitute D^T with D in the above equation:

B^T = PDP^T = B

Since B is equal to its transpose, it is a symmetric matrix.

In other words, if a matrix B can be diagonalized by an orthogonal matrix P, which means that P^T=P^-1, then B is a symmetric matrix. This is because orthogonal matrices preserve the dot product and the symmetry of a matrix. The diagonal matrix D represents the eigenvalues of B, which can be either positive, negative, or zero. Therefore, if all the eigenvalues of B are non-negative, then B is positive definite, and if they are non-positive, then B is negative definite. If some eigenvalues are positive and some are negative, then B is indefinite.

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The Probabilities are as follows

P(A) = 3/6 = 1/2

P(B) = 3/6 = 1/2

P(A and B) = 1/6

P(A or B) = 5/6

Sample Space (S) of the whole experiment: {1, 2, 3, 4, 5, 6}

Sample Space of Event A: {2, 4, 6}

Sample Space of Event B: {1, 2, 3}

A Venn diagram indicating two circles labeled A and B, and the overlap between the two circles labeled A and B]

Probabilities:

P(A) = |Event A| / |Sample Space| = 3/6 = 1/2

P(B) = |Event B| / |Sample Space| = 3/6 = 1/2

P(A and B) = |Event A and Event B| / |Sample Space| = 1/6

P(A or B) = 1 - P(Neither A nor B) = 1 - (6 - |Event A| - |Event B|) / |Sample Space| = 1 - (6 - 3 - 3) / 6 = 1 - (6 - 6) / 6 = 1/6 = 5/6

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The complete question goes thus:

Consider rolling a fair six-sided die once with the two possible events, Event A: roll an even number Event B: roll a number less than or equal to 3 • State the Sample Space of the whole experiment: State the Sample Space of the Event A: State the Sample Space of the Event B: Draw a Venn diagram: . Find the following probability: P(A)= P(B)= P (A and B) = P (A or B) =

l

Answer:

\( {x}^{2} + {(y - 139)}^{2} = {125}^{2} \)

The function h(x) = 1/x^6 can be written as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of inputs and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

This means that we are representing h(x) as the composition of two functions, g(x) and f(x), such that the output of g(x) is plugged into f(x) to give us h(x).

In this case, g(x) = (x^6) takes in x and returns x^6, while f(x) = 1/x takes in x^6 and returns 1/(x^6).

When we plug the output of g(x) into f(x), we get h(x) = 1/(x^6).

So, in essence, we have expressed h(x) = 1/x^6 as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

Hence, The function h(x) = 1/x^6 can be written as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

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The probability of pulling out a purple ball on the 101st try is 1/5.

The answer is A, 1 chance in 5.

The probability of any given event is given by the formula below:

The given data is as follows:

There are six balls in a hat. Each ball is a different color, but all are the same size, shape, and weight.

the number of expected outcomes (purple ball) = 20

the number of possible outcomes = 16 + 13 + 19 + 15 + 17 + 20

the number of possible outcomes = 100

The experimental probability of pulling out a purple ball is:

P(purple) = 20/100 = 1/5

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FOR THE GIVEN FUNCTION WE WILL HAVE TO CHECK DENOMINATOR PART BECAUSE IT IS THE ONE WITH THE GREATER EFFECT ON MAKING THE FUNCTION UNDEFINED.

THE FUNCTION WILL BE UNDEFINED ONLY IF x=0

THIS BRINGS US TO A CONCLUSION OF SAYING THE DOMAIN IS ALL REAL NUMBERS BUT X IS NOT EQUAL TO 0

Answer: true

Step-by-step explanation:

The good Samaritan law allows you to help people and not be liable for trying to do so.

Answer: So pretty much what you do is you put a dot on the positive 3 then move over one and put another on the 7 and you just keep doing that with all of them

Step-by-step explanation:

The total land area of Edgardo's property is 36,400 square meters.

The area is a measure of the amount of two-dimensional space that a flat surface or shape occupies. It is a fundamental concept in geometry and is expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Edgardo's original rectangular lot has an area of:

140 m x 120 m = 16,800 m²

The square lot he purchased has an area of:

140 m x 140 m = 19,600 m²

To find the total land area of Edgardo's property, we add the areas of the two lots:

16,800 m² + 19,600 m² = 36,400 m²

Therefore, the property owned by Edgardo has a total land size of 36,400 square meters.

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Answer:  choice F) m/26 = 12

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

Work Shown:

mpg = miles per gallon

mpg = miles/gallon

To find the mpg, we divide the number of miles driven over the number of gallons of gas used. For instance, if we can drive 100 miles on 5 gallons of gas, then we get 100/5 = 20 mpg

In this problem, we don't know how many miles we can travel. So m is the placeholder for that number. We know that we use 12 gallons of gas. So we have

mpg = miles/gallon

mpg = m/12

We're told Shannon gets 26 mpg, which allows us to say m/12 = 26

--------------------

Unfortunately m/12 = 26 doesn't match any of the answers. But we can do a bit of algebra to transform things.

Start off multiplying both sides by 12

m/12 = 26

12*(m/12) = 12*26

m = 12*26

Then divide both sides by 26

m = 12*26

m/26 = 12*26/26

m/26 = 12

which matches with choice F

Given:

The bases of a trapezoid lie on the lines

\(y=2x+7\)

\(y=2x-5\)

To find:

The equation that contains the midsegment of the trapezoid.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

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

On comparing \(y=2x+7\) with slope intercept form, we get

\(m_1=2,b_1=7\)

On comparing \(y=2x-5\) with slope intercept form, we get

\(m_2=2,b_2=-5\)

The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.

\(m=m_1=m_2=2\)

The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.

\(b=\dfrac{b_1+b_2}{2}\)

\(b=\dfrac{7-5}{2}\)

\(b=\dfrac{2}{2}\)

\(b=1\)

So, the y-intercept of the required line is 1.

Putting m=2 and b=1 in slope intercept form, we get

\(y=2x+1\)

Therefore, the equation of line that contains the midsegment of the trapezoid is \(y=2x+1\).

Answer:

Step-by-step explanation:

Let,

One of the siblings age be = x

So, the other siblings ages are = x+2, x+4 and x+6

Since,

Ashley is the oldest sibling so his age is x + 6

∴ By the problem,

=> x + (x+2) + (x+4) + (x+6) = 100

=> 4x + 12 = 100

=> 4x = 100 - 12

=> 4x = 88

=> x = 22

Now,

We got the age of the youngest one that is 22 years

As,

Ashley is the oldest sibling so his age is

= 22 + 6 = 28 years

Hence,

The age of Ashley is 28 years (Ans)

Answer:

28 years old

Step-by-step explanation:

100/4 = 25

The ages are consecutive even numbers,

so add 1 to and subtract 1 from 25.

Add 3 to and subtract 3 from 25.

Ages: 22, 24, 26, 28

Ashley is the oldest: 28 years old

The measure of each angle formed by the place where the median meets the vertex is 30 degrees

The median of an equilateral triangle divides the side and the angle into equal parts.

If the angle at the vertex is, the new angle would be

Angle = x/2

The angle at the vertex of an equilateral triangle is 60.

So, we have:

Angle = 60/2

Evaluate

Angle = 30

Hence, the measure of each angle formed by the place where the median meets the vertex is 30 degrees

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The value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

Let suppose that quadrilateral \(OABC\) is a parallelogram. Then, the following conditions must be fulfilled:

In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:

\(\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}\) (4)

If we know that \(\angle AOC = 142^{\circ}\), then the value of \(\angle ABC = y = 142^{\circ}\).

Based on all these finding, we conclude that the value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

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The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.

If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.

As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.

Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.

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This means that each input will result in one output, and (x) will satisfy the definition of a function. The value of (3) is 13. The solutions of (x) = 3 are x = -2 and x = 1.

A)  It is an example of a quadratic function and will have one y-value for each x-value that is input. This means that each input will result in one output, and (x) will satisfy the definition of a function.

B)The value of (3) can be found by substituting 3 for x in the expression.(3) = (3)^2 + 3 + 1= 9 + 3 + 1= 13Therefore, the value of (3) is 13.

C) Find the value(s) of x for which (x) = 3. Explain your result.We can solve the quadratic equation x² + x + 1 = 3 by subtracting 3 from both sides of the equation to obtain x² + x - 2 = 0. After that, we can factor the quadratic equation (x + 2)(x - 1) = 0, which can be used to find the values of x that satisfy the equation. x + 2 = 0 or x - 1 = 0 x = -2 or x = 1. Therefore, the solutions of (x) = 3 are x = -2 and x = 1.

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Answer:

3240°

Explanation:

The formula for calculating the sum of the interior angles of a polygon is (n-2)x180 where n refers to the number of sides. Because we know that the polygon has 20 sides, the equation would be (20-2)x180. The answer would be 3240°.

Answer:

28%

Step-by-step explanation:

32-25=7

7/25=0.28

0.28x100=28

28%

Answer:

To find 3.5% of 21, we can convert 3.5% to a decimal by dividing by 100:

3.5% = 3.5/100 = 0.035

Then, we can multiply 0.035 by 21 to find the answer:

0.035 * 21 = 0.735

Therefore, 3.5% of 21 is 0.735.

0.735

because o.31 percent of 21 is 0.735

Answer:

The first and the second equation is flipped... meaning you have to switch their places

Step-by-step explanation:

I think I did this before so good luck...

Answer:

The real solutions are:

x = -5, -3, 4, 8

number of adult ticket = x

number of child ticket = y

Total number of ticket = 16

Answer: It's C; Multiply her answer by -6 and see if the result is -108

Step-by-step explanation:

The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.

\(f(x) = cos(x) then f'(x) = -sin(x)\).

Let's proceed with the proof.  Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:

\(f(x) = cos(x) f(x + h) = cos(x + h)\)

Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)

We can then simplify the expression by using the trigonometric identity for the difference of two angles:

\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)

Applying this identity to the numerator of the difference quotient, we obtain:

\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)

We can then factor out a cos(x) term from the numerator:

\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)

We can then apply the limit laws to separate the limit into two limits:

\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)

The first limit can be evaluated using L'Hopital's rule:

\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)

Therefore, the first limit becomes zero:

\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)

Applying L'Hopital's rule to the second limit, we obtain:

\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)

Therefore, the second limit becomes 1:

\(f'(x) = -sin(x)\)

Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).

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Answer: 5w⁴ + w²

Step-by-step explanation: Pic is attached. Hope this helps. Sorry for bad handwriting, Im writing with a mouse.

The CNF representation in set notation is: {{P, A, Q, V}, {P, A, Q, R}}

The CNF representation in set notation is:{{P, V, Q}, {A}, {R}}

The CNF representation in set notation is:{{!P, H}, {Q}}

The CNF representation in set notation is:{{!S, P}, {!S, V}, {!S, Q}, {!S, V}, {!S, -R}}

The CNF representation in set notation is:{{R, S, -Q}, {R, S, -V}, {R, S, -P}}

To convert the formula (PAQVR) into CNF, we can break it down as follows:

Distribute the disjunction over the conjunction.

PAQVR = (PAQV) ∧ (PAQR)

Convert each clause into sets.

(PAQV) = {{P, A, Q, V}}

(PAQR) = {{P, A, Q, R}}

Combine the clauses using conjunction.

{{P, A, Q, V}} ∧ {{P, A, Q, R}}

The CNF representation in set notation is:

{{P, A, Q, V}, {P, A, Q, R}}

To convert the formula (-(PVQ) AR) into CNF, we can break it down as follows:

Remove the implication.

(-(PVQ) AR) = (!(-(PVQ)) ∨ A) ∧ R

Apply De Morgan's Law and distribute the disjunction over the conjunction.

(!(-(PVQ)) ∨ A) ∧ R = ((PVQ) ∨ A) ∧ R

Convert each clause into sets.

(PVQ) = {{P, V, Q}}

A = {{A}}

R = {{R}}

Combine the clauses using conjunction.

{{P, V, Q}, {A}} ∧ {{R}}

The CNF representation in set notation is:

{{P, V, Q}, {A}, {R}}

To convert the formula (PH-Q) into CNF, we can break it down as follows:

Convert the implication into disjunction and negation.

(PH-Q) = (!P ∨ H) ∨ Q

Convert each clause into sets.

!P = {{!P}}

H = {{H}}

Q = {{Q}}

Combine the clauses using conjunction.

{{!P, H}, {Q}}

The CNF representation in set notation is:

{{!P, H}, {Q}}

To convert the formula (-(S+ (-PVQV-R)) into CNF, we can break it down as follows:

Remove the double negation.

-(S+ (-PVQV-R)) = (!S ∨ (PVQV-R))

Distribute the disjunction over the conjunction.

(!S ∨ (PVQV-R)) = ((!S ∨ P) ∧ (!S ∨ V) ∧ (!S ∨ Q) ∧ (!S ∨ V) ∧ (!S ∨ -R))

Convert each clause into sets.

!S = {{!S}}

P = {{P}}

V = {{V}}

Q = {{Q}}

-R = {{-R}}

Combine the clauses using conjunction.

{{!S, P}, {!S, V}, {!S, Q}, {!S, V}, {!S, -R}}

The CNF representation in set notation is:

{{!S, P}, {!S, V}, {!S, Q}, {!S, V}, {!S, -R}}

To convert the formula ((RS) V-QV-P) into CNF, we can break it down as follows:

Distribute the disjunction over the conjunction.

((RS) V-QV-P) = ((RS ∨ -Q) ∧ (RS ∨ -V) ∧ (RS ∨ -P))

Convert each clause into sets.

RS = {{R, S}}

-Q = {{-Q}}

-V = {{-V}}

-P = {{-P}}

Combine the clauses using conjunction.

{{R, S, -Q}, {R, S, -V}, {R, S, -P}}

The CNF representation in set notation is:

{{R, S, -Q}, {R, S, -V}, {R, S, -P}}

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Answer:3x+2y=23

Step-by-step explanation:

Answer:

x/2-10=18

Step-by-step explanation:

An equation is formed of two equal expressions. The given statement The quotient of a number and -2, less 10, is -18 can be written as an equation as (x/-2)-10=-18.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number be represented by x. Therefore, the given statement can be written as,

(x/-2)-10=-18

Hence, the given statement The quotient of a number and -2, less 10, is -18 can be written as an equation as (x/-2)-10=-18.

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Answer:

\( \frac{44}{9} \)