Find the value of g (-2) if g(x) = x3 - x

The probability of each component failing must be 0.1 or less for the probability of the system functioning to be 0.99.

The formula for the probability of parallel events is as follows: P(A) + P(B) - P(A) * P(B)

For three parallelly connected events, the formula for the probability that none of the events will fail is as follows: Probability = P(A) * P(B) * P(C)

Therefore, the probability of failure for each of the parallel events = 1 - probability that it will function = 1 - p

Also, as the components are independent, we can say that the probability of the system functioning = the probability of all of the components functioning.

As a result, the following formula is used: P(system functions) = Probability(A) + Probability(B) + Probability(C) - Probability(A) * Probability(B) - Probability(B) * Probability(C) - Probability(A) * Probability(C) + Probability(A) * Probability(B) * Probability(C)

Given that P(system functions) = 0.99, we can write the following:

P(system functions) = 1 - P(At least one component fails)0.99 = 1 - (Probability(A) + Probability(B) + Probability(C) - Probability(A) * Probability(B) - Probability(B) * Probability(C) - Probability(A) * Probability(C) + Probability(A) * Probability(B) * Probability(C))

We substitute 1 - p for each of the probabilities in the formula because it is a parallel circuit with independent components.

We have: P(system functions) = 1 - (1 - p)(1 - p)(1 - p) = 0.99 ⇒ (1 - p)³ = 0.01⇒ 1 - p = ∛0.01⇒ 1 - p = 0.1⇒ p = 0.9

The probability of each component failing must be 0.1 or less for the probability of the system functioning to be 0.99.

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Answer:

x² - 4x - 9 = 29

x² - 4x - 9 - 29 = 0

x² - 4x - 38 = 0

Using the quadratic formula

\(x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \)

Where

a = 1 , b = -4 c = - 38

So we have

\(x = \frac{ - - 4± \sqrt{ { - 4}^{2} - 4(1)( - 38)} }{2(1)} \\ \\ x = \frac{4± \sqrt{16 +152 } }{2} \\ \\ x = \frac{4± \sqrt{168} }{ 2} \\ \\ x =2 ± \sqrt{42} \\ \\ \\ x = 2 + \sqrt{42} \: \: \: or \: \: \: x = 2 - \sqrt{42} \)

Hope this helps you

Answer:

1.89753

Step-by-step explanation:

22/11,594

         \(\frac{22}{11.594} * 1000 = \frac{22000}{11594}\)

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Respuesta: el deberá $8.43 de interés en un mes.

Explicación paso a paso:

Regla de 3

$562 -- 100%

x --- 18%

x = 101.16

$101.16 es la cantidad de intereses que deberá en un año, pero ¿en un mes?

Para saberlo solo lo dividimos entre la cantidad de meses en un año (12)

101.16 ÷ 12 = 8.43

Answer:

here is the required answer hope it help u

Step-by-step explanation:

−2(−5n+6)+5(2−7n)

10n-12+10-35n

-25n-2

Answer:

2/3 or 0.667

Step-by-step explanation:

5/9 ÷ 5/6

5/9 * 6/5

1/3 * 2/1 (after cancelling off)

= 2/3

Answer:

180

Step-by-step explanation:

There are 60 minutes in one hour. Multiply 3 x 60 = 180.

To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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Step-by-step explanation:

y = 6x

..................

area: 36 units²

\(\hookrightarrow \sf 9 \ * \ 4\)

\(\hookrightarrow \sf 36 \ units^2\)

Area:-

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

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Answer:

-2

Step-by-step explanation:

because it is on the -2 area

A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

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The height of the school is approximately 5.96 meters.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

The mirror and the triangles formed by the mirror, the top of the school, and the ground are similar. This means that the corresponding sides of the triangles are proportional.

Let x be the distance from the mirror to the top of the school. Then:

\(\dfrac{x} {7.95} = \dfrac{(x + h) }{ 2.3}\)

We can simplify this equation by cross-multiplying and solving for x:

2.3x = 7.95(x + h)

2.3x = 7.95x + 7.95h

5.65x = 7.95h

\(x = \dfrac{7.95h} { 5.65}\)

Now we can use the measurement of the distance from Ai Mi's eyes to the ground to find h. Let d be the distance from the mirror to Ai Mi's eyes. Then:

d = 1.15 meters

The triangles formed by Ai Mi's eye, the mirror, and the ground are similar, so:

\(\dfrac{h} { d} =\dfrac{ x} { (d + 2.3)}\)

We can substitute the value of x from earlier:

\(\dfrac{h} { 1.15} = \dfrac{(\dfrac{7.95h} { 5.65)}} { 3.45}\)

Simplifying:

\(h = \dfrac{(1.15 \times 7.95\times 3.45)}{ 5.65}\)

h = 5.96 meters

Therefore, the height of the school is approximately 5.96 meters. Rounded to the nearest hundredth of a meter, the answer is 5.96 meters.

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Answer:

c, b, c, a, b, c, c, a, b, a, b, d, c, d, d, b, c, a, d, b. i hope this will be all correct.

Answer:

Can I see the graph?

Step-by-step explanation:

The mistake that Shawn made in his definition of a reflection is that D. Shawn didn't make a mistake.

It should be noted that reflection simply means ten transformation of the shape of an object.

In this case, for any point R on the line of reflection L, the image R’ is at the same point as R. Furthermore, for any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.

Therefore, Shawn is right as no mistake was made.

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Answer:

PP' must be perpendicular to the line of reflection. Whatever the distance is between P and L, there are infinitely many points on the other side of L that are the same distance from L.

Step-by-step explanation:

Answer:

\(g(f(x)) = gof(x) =( x - 7)^{2} \\ = {x}^{2} - 14x + 49 \\ g(f(4) )\times g(f(4)) = (4^{2} - 14 \times 4 + 49 )\times( 4 ^{2} - 14 \times 4 + 49) \\ = 9 \times 9 \\ = 81\)

Answer:

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

It is assumed the provided numbers are the zero's of the polynomial function.

We know complex zero's come in pairs if function has rational constants.

So we should have zero's: 8, 3, -i and i.

Find the polynomial:

The surface area of the rectangular prism with the given dimensions is 540yd².

To find the surface area (sa) of the rectangular prism with the given dimensions, we need to calculate the area of each face and add them together.

The formula for the area of a rectangle is length multiplied by width (A = l x w).

Face 1 has a length of 5yd and a width of 37yd, so its area is 5 x 37 = 185yd².
Face 2 has a length of 5yd and a width of 20yd, so its area is 5 x 20 = 100yd².
Face 3 has a length of 5yd and a width of 51yd, so its area is 5 x 51 = 255yd².

To find the total surface area, we add the areas of all three faces:

sa = area of face 1 + area of face 2 + area of face 3
sa = 185yd² + 100yd² + 255yd²
sa = 540yd²

Therefore, the numerical value of the surface area of the rectangular prism with the given dimensions is 540yd².

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Given:

1 chocolate chip cookie recipe = 12 cup of chocolate chips per batch.

Alonzo wants to make 3 12 batches.

Lets's find the number of chocolate chips he will need.

Number of batches he wants to make is = 3 x 12 = 36 batches

SInce 1 chocolate chip cookie recipe calls for 12 cup of chocolate chips per batch, we have:

The Value of the double integral is 9/2.

To Evaluate the double integral ∫∫D x dA, we need to express the region D as a type I or type II region, and then integrate over that region.

For D enclosed by the lines y = x, y = 0, x = 3, we can see that the region is a right triangle with vertices at (0,0), (3,0), and (3,3), so it can be expressed as a type I region with:

a. D = {(x, y) | y ≤ x ≤ 3, 0 ≤ y ≤ x}

or as a type II region with:

b. D = {(x, y) | 0 ≤ y ≤ 3, y ≤ x ≤ 3}

To evaluate the double integral using either of these regions, we can use iterated integrals.

Using a type I region:

∫∫D x dA = ∫0³ ∫y³ x dy dx

= ∫0³ ∫0x x dy dx

= ∫0³ ½x² dx

= 9/2

Using a type II region:

∫∫D x dA = ∫0³ ∫0y y dx dy

= ∫0³ ½y² dy

= 9/2

.

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Answer:

A

Step-by-step explanation:

The solution that is not the same as the solutions to the system of equations is 2x - 2y = 5.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2x + 3y = 1 _____(1)

x - y = 5 _______(2)

From (1) and (2) we get,

x = 5 + y

2 (5 + y) + 3y = 1

10 + 2y + 3y = 1

10 + 5y = 1

5y = -9

y = -9/5

Now,

x = 5 - 9/5

x = (25 - 9)/5

x = 16/5

The solutions are x = 16/5 and y = -9/5.

Now,

(1) 3x + 2y=6

3 x (16/5) + 2 x (-9/5) = 6

48/5 - 18/5 = 6

30/5 = 6

6 = 6

(2) 5y = -9

5 x (-9/5) = -9

-9 = -9

(3) 2x - 2y = 5

2 x (16/5) - 2 x (-9/5) = 5

32/5 + 18/5 = 5

50/5 = 5

10 ≠ 5

(4) 4x + 6y = 2

4 x (16/5) + 6 x (-9/5) = 2

64/5 - 54/5 = 2

10/5 = 2

2 = 2

Thus,

3x+2y=6, 5y=-9, and 4x+6y=2 have the same solutions.

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Noon to 2:00 pm is 2 hours

3 degrees to -1 degree is a total of 4 degrees.

The temperature changed 4 degrees in 2 hours.

4/2 = 2

The temperature dropped 2 degrees per hour.

Answer:

$90

Step-by-step explanation:

The perimeter of the rectangle is (23.5y + 1) feet.

The perimeter of the rectangle formula:

The perimeter = the width + the length + the width + the length

The perimeter = 2 × (the width + the length)

The perimeter = 2 × ((4.25y - 7.5) + (7.5y + 8))

The perimeter = 2 × ((4.25y + 7.5y) + (- 7.5 + 8)

The perimeter = 2 × (11.75y + 0.5)

The perimeter = 23.5y + 1

So, the perimeter of the rectangle is (23.5y + 1) feet.

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By using what we know about right triangles, we will see that the height is 11.7 m.

We can view this as a right triangle, such that the wire is the hypotenuse of said triangle.

We know that the hypotenuse measures 14 m, and the angle between the ground and the wire si 57°. The height would be the opposite cathetus to that angle, so we can use the rule:

Sin(a) = (opposite cathetus)/hypotenuse

Replacing the values we get:

Sin(57°) = H/14m

Sin(57°)*14m = H = 11.7m

The height of the tower is 11.7 meters.

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the answer is (3,1)(1,-2)

To determine whether a quadrature formula is of the interpolatory type, we need to analyze the formula and check if it provides exact values for polynomials of degree less than or equal to a certain value.

a) Sf)dx*(2):

The notation Sf)dx*(2) represents a quadrature formula that approximates the integral of the function f(x) using a weighted sum of function evaluations.

However, without further information about the specific form of the quadrature weights and nodes, we cannot determine if this formula is of the interpolatory type.

Interpolatory quadrature formulas typically involve evaluating the function at specific interpolation nodes and using the values of the function at those nodes to construct the weights.

b) Sf(a)dx f(-1) + f(1)/2:

In this formula, the function f(x) is evaluated at two specific points, -1 and 1, and multiplied by specific weights, 1 and 1/2, respectively. This indicates that the formula is using the function values at these points to construct the weights. Therefore, this quadrature formula is of the interpolatory type because it directly interpolates the function at the points -1 and 1 to approximate the integral.

In summary:

a) Sf)dx*(2): Insufficient information to determine if it is of the interpolatory type.

b) Sf(a)dx f(-1) + f(1)/2: This quadrature formula is of the interpolatory type as it uses the function values at specific points (-1 and 1) to construct the weights.

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Answer:

Yes

Step-by-step explanation:

Answer:

no

Step-by-step explanation: