-2x^2+6x+7=2x-3 by quadratic formula

\(5.51134751094269\times10^8\) transistors could fit on a microchip \(19\) years later.

Moore's law predicts that the number of transistors that can be fit on a microchip will increase 40% every year.

So the expected increment every year \(40\%\).

Microchips from a given year could hold about \(922,200\) transistors.

We have to find ow many transistors could fit on a microchip \(19\) years later.

From the question total years are \(19\).

Since the number of transistors is increased every year so number of transistors of previous year added. So we can see that  the number of transistors that can be fit on a microchip is increased compound. We can find the total number of transistors by multiplying number of transistors with the rate assembled by one. So we can use the formula

So the number of transistors could fit on a microchip 19 years later.

Number of transistor = Microchips from a given year could hold about transistors(1 + increment rate)^total years

Number of transistor \(=922,200(1+\frac{40}{100})^{19}\)

Number of transistor \(=922,200(1+\frac{2}{5})^{19}\)

Number of transistor \(=922,200(\frac{5+2}{5})^{19}\)

Number of transistor \(=922,200(\frac{7}{5})^{19}\)

After evaluating the expression using the calculator we get

Number of transistor \(=551134751.094269\)

Number of transistor \(=5.51134751094269\times10^8\)

Hence, \(5.51134751094269\times10^8\) transistors could fit on a microchip \(19\) years later.

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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The surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

To evaluate the surface integral of f over the unit sphere, we need to use the formula:

∫∫S f · dS = ∫∫R f(φ,θ) · ||r(φ,θ)|| sin(φ) dφdθ

Where S is the surface of the unit sphere, R is the region in the parameter domain (φ,θ) that corresponds to S, ||r(φ,θ)|| is the magnitude of the partial derivative of the position vector r(φ,θ), and sin(φ) is the Jacobian factor.

For the unit sphere, we have:

x = sin(φ) cos(θ)
y = sin(φ) sin(θ)
z = cos(φ)

So, we can find the partial derivatives:

r_φ = cos(φ) cos(θ) i + cos(φ) sin(θ) j - sin(φ) k
r_θ = -sin(φ) sin(θ) i + sin(φ) cos(θ) j

Then, we can compute the magnitude:

||r_φ x r_θ|| = ||sin(φ) cos(φ) cos(θ) j + sin(φ) cos(φ) sin(θ) (-i) + sin^2(φ) k|| = sin(φ)

Now, we can substitute into the formula and evaluate the integral:

∫∫S f · dS = ∫0^π ∫0^2π (sin^3(φ) cos^3(θ) i + sin^3(φ) sin^3(θ) j + sin^3(φ) cos^3(φ) k) · sin(φ) dφdθ
= ∫0^π ∫0^2π sin^4(φ) (cos^3(θ) i + sin^3(θ) j + cos^3(φ) k) dφdθ

To integrate over θ, we can use the fact that cos^3(θ) and sin^3(θ) are odd functions, so their integral over a full period is zero. Thus, we get:

∫∫S f · dS = ∫0^π (1/5) sin^5(φ) (3 cos^3(φ) k + 2 sin^3(φ) i + 2 cos^3(φ) j) dφ
= (4π/15) (3 k)

Therefore, the surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

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Answer:

17.83 ft

Step-by-step explanation:

Pedro will lose 11 pencils.

What is an average?

Calculating the outcome of multiplying the total of numerous quantities by the number of quantities, then dividing this result.

Here, we have

Pedro has twelve more pencils than Peter.

Peter has nine more pencils than Paul

Then,

The three quantities of pencils are x, x - 12, and x - 21.

The average of this is (x - 33)/3 = x - 11.

Hence, Pedro will lose 11 pencils.

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the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]] provides a general formula for calculating the probability of event A based on the given partition B1, B2, ..., Bt of the sample space.

(a) To prove the equation Pr[A] = Σ[Pr[A | Bx] Pr[Bx]], we start by using the law of total probability. The law of total probability states that for any event A and a partition B1, B2, ..., Bt of the sample space, we have Pr[A] = Σ[Pr[A | Bi] Pr[Bi]], where Pr[A | Bi] is the conditional probability of A given Bi.

By rearranging the terms, we get Pr[A] = Σ[Pr[A | Bi] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bi] / Pr[Bk] Pr[Bk]], where Pr[Bk] is the probability of the event Bk.

Next, we multiply and divide Pr[A | Bi] by Pr[Bk], giving us Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]].

Since the summands have the same denominator Pr[Bk] Pr[Bi], we can write Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bk] Pr[Bi]].

Finally, by canceling out the common factor Pr[Bk], we obtain Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], which proves the equation.

(b) From the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], we can see that Pr[A] can be expressed as a sum of terms involving the conditional probabilities Pr[A | Bi] and the probabilities of the partition sets Pr[Bi]. This equation allows us to compute the probability of A by considering the conditional probabilities and the probabilities of the partition sets.

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Answer:

I think the answers would be :

a . 4/3

b. 1/5

c . - 5/4

hope it helps u ^^

To find a subset of vectors that forms a basis for the subspace of R4 spanned by S, we need to determine which vectors in S are linearly independent.

Let's write the vectors in S as columns of a matrix:

S = [2, 3, 3, -8; V2, V3, -5, 25; -1, 26, 2, -8; -6, 0, 0, 0]

To find the linearly independent vectors, we can perform row reduction on the matrix to obtain its row-echelon form.

After performing row reduction, we get:

[1, 0, 0, -2; 0, 1, 0, 5; 0, 0, 1, 1; 0, 0, 0, 0]

The row-echelon form shows that the first three rows are linearly independent, while the last row is a zero row. Therefore, the corresponding vectors in S form a basis for the subspace of R4 spanned by S.

The subset that forms a basis for the subspace is: { [2, 3, 3, -8], [V2, V3, -5, 25], [-1, 26, 2, -8] }

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We can express an inequality that describes this situation like this:

From the statement of the question, we are told that Mr. Hall has $216, then he can spend no more than this amount, then we can express:

spent money ≤ available money

spent money ≤ 216

Now, from the given information, we know that the money is spent buying a bookshelf and some books, then the spent money would be the cost of the bookshelf plus the total cost of all the books.

spent money ≤ 216

Bookshelf cost + books cost ≤ 216

From the statement of the question, we know that the bookshelf cost equals $81 and that each book costs $3, the total books cost equals the cost per book times the number of books x, then we rewrite the expression like this:

Bookshelf cost + books cost ≤ 216

81 + 3*x ≤ 216

From this inequality, if we solve for x, we get:

81 - 81 +3x ≤ 216 - 81

3x ≤ 135

3x/3 ≤ 135/3

x ≤ 27

Then, the answer is x ≤ 27

Answer:

11

Step-by-step explanation:

11 + 8 + 14 + v + 8 + 14

==================   = 11             Combine Terms

6

(55 + v) / 6 = 11                               Multiply by 6

55 + v = 11 * 6                                 Combine the right

55 + v = 66                                     Subtract 55

55-55+v = 66- 55

v = 11

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

it would be d

Step-by-step explanation:

I hope that helps

The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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(C) "historians should conduct research in the areas in which they have expertise"

The author attempted to exploit her ignorance of Black women's history as an excuse for not complying with Herd's request. The idea that historians should only work in their fields of competence is implicit in this conduct.

The answer is not (A). The author makes no implication that her lack of academic experience in an understudied field is embarrassing. (B) is the wrong answer. The author did not suggest that she had believed it would be difficult to obtain primary materials, even though she had not researched any primary sources prior to accepting Herd's request.

The answer is not (D). Since she had never "thought about Black women as historical subjects," the author claims she had never done so. The answer is not (E). Nothing in this statement implies that Black women's history was seen as a popular topic.

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Answer:

t=+4.06

Step-by-step explanation:

when the baseball hits the ground, the height will be 0.

h=0we are given that h=−16t2+64t+4.

this means that the height is 0 when −16t2+64t+4=0.−16t2+64t+4=0divide both sides by 4:−4t2+16t+1=04=0−4t2+16t+1=0 can be solved using the quadratic formula:t=−b±√b2−4ac2a, where at2+bt+c=0.at2+bt+c=−4t2+16t+1a=−4,b=16,c=1t=−b+√b2−4ac2aor−b−√b2−4ac2a−b+√b2−4ac2a=−16+√272−8=−0.06..−b−√b2−4ac2a=−16−√272−8=4.06 (3s.f.)we have 2 values for t:−0.06 and 4.06.

since time cannot be negative, only the positive value can be taken.

this is 4.06, to 3 significant figures.the time taken is 4.06 seconds.

We have the following:

The first thing is to calculate the ratio between both paintings.

After finding the ratios, it can be calculated for any value using a proportionality rule.

for example, for 5 cups of blue paint, should be for yellow paint:

therefore, should be 25 cups of yellow paint

Answer:

A. 1

B. -1

C. Proportional

D. y=x-1

Answer:

  1

Step-by-step explanation:

You want the standard deviation of a normal distribution.

The "standard normal distribution" is defined to have a mean of 0 and a standard deviation of 1.

__

Additional comment

The standard distribution is often shifted and scaled to have some other particular mean and standard deviation. The computation of a "Z-score" is a way to relate a value in the scaled distribution back to the characteristics of the standard normal distribution. The Z-score is the number of standard deviations a value is from the mean.

Answer:

t > 3

Step-by-step explanation:

1 hour = 194

582 / 194 = 3

She needs to ride for 3 hours to burn 582 calories

She needs to ride for more than 3 hours to burn more than 582 calories

Answer:

D

Step-by-step explanation:

Angle V is correspondent to angle w

The form factor of a standard Parallel connector is DB-25.

A Parallel connector is a type of interface commonly used for connecting devices such as printers, scanners, and external storage devices to a computer. It allows for the simultaneous transmission of multiple bits of data through separate data lines. The form factor refers to the physical shape and configuration of the connector.

Option A, DB-9, is incorrect because DB-9 connectors are commonly used for serial communication, not parallel communication. They have 9 pins arranged in two rows and are typically used for applications such as RS-232 serial ports.

Option B, DB-15, is also incorrect as DB-15 connectors are commonly used for video graphics (VGA) connections, not parallel communication. They have 15 pins arranged in three rows and are commonly found on older computer monitors.

Option D, DIN-6, is also not the correct form factor for a standard Parallel connector. DIN-6 connectors are typically used for MIDI (Musical Instrument Digital Interface) connections or other audio applications. They have 6 pins arranged in a circular configuration.

The correct option is C, DB-25. The DB-25 connector, also known as a "D-sub 25" or "D-subminiature 25," is a type of connector commonly used for parallel communication interfaces. It has 25 pins arranged in two rows, with the pins surrounded by a D-shaped metal shield. The DB-25 connector is typically used for printer ports, parallel ports, and other parallel communication applications.

Therefore, the form factor of a standard Parallel connector is DB-25.

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Answer:

BC ≈ 4.0

Step-by-step explanation:

∠ DCA = 180° - 70° = 110° ( adjacent angles )

∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle

∠ DAC = 180° - 140° = 40°

Using the Sine rule in Δ ACD to find common side AC

\(\frac{AC}{sin30}\) = \(\frac{15}{sin40}\) ( cross- multiply )

AC × sin40° = 15 × sin30° ( divide both sides by sin40° )

AC = \(\frac{15sin30}{sin40}\) ≈ 11.668

Using the cosine ratio in right triangle ABC

cos70° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{BC}{11.668}\) ( multiply both sides by 11.668 )

11.668 × cos70° = BC , then

BC ≈ 4.0 ( to the nearest tenth )

Answer:

X = 3

Y = all real numbers

Step-by-step explanation:

x is the input

y is the output

The equation would be x = 3

Answer:

The perimeter of the drawing: 18 inches

The perimeter of the actual flower bed: 540 inches

If they were multiplied by 24 instead the actual perimeter of the flower bed would be 432 inches. The effect is that it decreases by 108 inches.

Step-by-step explanation:

Taking the 4 inches and 5 inches and multiplying them by 30 gets 120 by 150. If its a rectangle we will add together all 4 sides to get the perimeter of the actual one.

Answer:

b, and c

Step-by-step explanation:

The exact solutions of the equation 6cos²(x)+5cos(x)-4=0 in the interval [0,2π) are x= π/3, 5π/3.

To find the exact solutions of the equation 6cos²(x)+5cos(x)-4=0 in the interval [0,2π), we can use a quadratic equation.

Let's substitute u=cos(x) to simplify the equation: 6u²+5u−4=0.

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring is not straightforward, so we can use the quadratic formula: u= {-b±√(b²-4ac)}/2a

​For our equation, the coefficients are a=6, b=5, and c=−4.

Substituting these values into the quadratic formula, we have:

u= {-5±√(5²-4(6) (-4))}/2(6)

Simplifying further: u= {-5±√121}/12

⇒u= {-5±11}/12

We have two possible solutions:

u₁= {-5+11}/12=1/3

u₂= {-5-11}/12=-2

Since the cosine function is defined within the range [−1,1], we discard the second solution (u₂ =−2).

To find x, we can use the inverse cosine function:

x=cos⁻¹(u₁)

Evaluating this expression, we find:

⁡x=cos⁻¹(1/3)

Using a calculator or reference table, we obtain

x= π/3.

Since the cosine function has a period of 2π, we can add 2π to the solution to find all the solutions within the interval [0,2π). Adding 2π to

π/3, we get 5π/3.

Therefore, the exact solutions of the equation 6cos²(x)+5cos(x)-4=0 in the interval [0,2π) are x= π/3, 5π/3.

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Answer:

3

Step-by-step explanation:

3³=27

Answer: 3

Step-by-step explanation:

A. For hand rubbers, the interval that contains about 95% of the bacterial counts is [0, 134].b. For hand washers, the interval that contains about 95% of the bacterial counts is [0, 202].

a) For hand rubbers, an interval that contains about 95% of the bacterial counts is given byLower limit=mean-2 standard deviation=62-2*36=62-72=-10 (since bacterial count cannot be negative, the lower limit is 0)

Upper limit=mean+2 standard deviation=62+2*36=62+72=134

The interval that contains about 95% of the bacterial counts for hand rubbers is [0, 134].

b) For hand washers, an interval that contains about 95% of the bacterial counts is given byLower limit=mean-2 standard deviation=92-2*55=92-110=-18 (since bacterial count cannot be negative, the lower limit is 0)

Upper limit=mean+2 standard deviation=92+2*55=92+110=202

The interval that contains about 95% of the bacterial counts for hand washers is [0, 202].

Hence, the answer to the given question is:

a. For hand rubbers, the interval that contains about 95% of the bacterial counts is [0, 134].b. For hand washers, the interval that contains about 95% of the bacterial counts is [0, 202].

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Here is ur perfect answer

Answer:

x = 207

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(\(\sqrt{x}\) )² + 7² = 16²

x + 49 = 256 ( subtract 49 from both sides )

x = 207