The output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier. Calculate the output voltage, in millivolts (mV), for a circuit if the input voltage is 45 mV and the gain is 30.

The solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.

2x² + 6 = - 36

2x² = - 36 - 6 { subtract 6 from both sides of the equation }

2x² = - 40

x² = -40/2 {divide through by the coefficient of x² which is 2}

x² = -20

we take the square root of both sides

x = ± √-20

√-20 = √20 x √-1 { -1 = I an imaginary number}

so;

x = √20i or x = -√20i

Therefore, the solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.

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Answer:

16.625 miles

Step-by-step explanation:

The time elapsed between 4:45 pm and 12 noon is 4 hours and 45 minutes

45 minutes is equivalent to 45/60 = 0.75 hour

Total elapsed time = 4.75 hours

At a speed of 3.5 mph the distance that can be covered

= 3.5 x 4.75 = 16.625 miles

The profit function is P ( x ) = 2x² + 5x - 12 and the number of months during which the company is not making a profit is x = 1.5 years = 18 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the profit function be represented as P ( x )

Let the cost function of the company be C ( x ) = 17 - 8x - 2x²

Let the revenue function of the company be R ( x ) = 5 - 3x

Now , Profit = Revenue - Costs

Substituting the values in the equation , we get

P ( x ) = R ( x ) = C ( x )

P ( x ) = 5 - 3x - ( 17 - 8x - 2x² )

On simplifying the equation , we get

P ( x ) = 2x² + 5x - 12

Now , when the profit of the company is 0

2x² + 5x - 12 = 0

On factorizing the equation , we get

2x² + 8x - 3x - 12 = 0

2x ( x + 4 ) - 3 ( x + 4 ) = 0

Taking the common factors of the equation , we get

( 2x - 3 ) ( x + 4 ) = 0

The value of x cannot be negative , so

2x - 3 = 0

Adding 3 on both sides of the equation , we get

2x = 3

Divide by 2 on both sides of the equation , we get

x = 3/2 years

Therefore , the number of months x = 18 months

Hence , the equation is solved

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Are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python

It is a branch of mathematics that deals with the occurrence of a random event.

Given that In a large IT company,

75% of programmers are male while 36% know Python.

27% of the programmers are male and know Python.

We need to find the probability that he knows Python

P(M)=0.75

P(P)=0.36

P(MUP)=0.27

The probability that he knows Python is 0.36-0.27=0.09

Independent events are those events whose occurrence is not dependent on any other event.

Hence, are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python

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Answer:

B.80

Step-by-step explanation:

use of pythagoras theorem.

a^2 + b^2 = c^2

where c is hypotenuse

Answer:

D

Step-by-step explanation:

first we can see from question is finding perimeter which means first step we need is  

                       24+24=48

second , we can know it from picture

ABD=[tex]\frac{1}{2}[/tex] times 60= 30, which means it is 1/2 marks

P=DB/BA

which we see DB=BE

so 2 time DB( or BE)=18 which is 18

so we just need use 24+24+18=66

Answer:

=$64.78

Step-by-step explanation:

If. 50 copies. = $2.05

than. 1,580 copies = ?

1580/50 × $2.05

=3239/50

=64.78

Therefore if the cost of 50 copies is $2.05 than the cost of 1,580 copies is $64.78.

Answer:

$64.78

Step-by-step explanation:

 Proportions:

 50 copies >>>> $2.05

1580 copies >>>> $C

C = 1580"2.05/504

C = 64.78

Shannon planted 6 - t trees.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

Shannon planted t fewer trees than toby.

Toby planted 6 trees.

Shannon planted.

= t - 6 trees.

Therefore, the result is 6 -t.

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Probability on cards.

(a) P(Jack or five or King) = 12/52 = 3/13

(b) P(heart or club or spade) = 39/52 = 3/4

(c) P(Ace or Queen or heart) = 19/52

(d) P(seven or Queen or heart or diamond) = 30/52 = 15/26

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

A single card is drawn from a standard 52-card deck. Find the probability that the card is either

a) a Jack, or a five, or a Jing?

b) a heart, or a club, or a spade?

c) an Ace, or a Queen, or a heart?

d) a seven, or a Queen, or a heart, or a diamond?

The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

The total number of events is n(S) = 52.

Let's count each number of favorable outcomes, then the probability of the event!

(a) The number of Jack is 4, five is 4, and King is 4. They are 12.

P(Jack or five or King) = 12/52 = 3/13

(b) The number of hearts is 13, clubs is 13, and spade is 13. They are 39.

P(heart or club or spade) = 39/52 = 3/4

(c) The number of hearts is 13, other Aces is 3, other Queens is 3. They are 19.

P(Ace or Queen or heart) = 19/52

(d) The number of diamonds is 13, hearts is 13, other seven is 2, other Queen is 2. They are 30.

P(seven or Queen or heart or diamond) = 30/52 = 15/26

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(a) New value = 0.81 * Old value

(b) New value = 0.81 * $388,000 = $313,480.

Max saves £5.50, which is 550p.

For every 50p Max saves, his mum gives him 20p, so for 550p, he gets 550/50 * 20p = 440p from his mum.

Altogether, Max has 550p + 440p = 990p, which is equivalent to £9.90.

Step-by-step explanation:

To find the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007, we need to add the two given polynomials.

The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 would be:

negative -19x^2+ 181x + 14,420 + 866x^2 – 78x + 10,190

Simplifying, we get:

847x^2 + 103x + 24,610

So the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is 847x^2 + 103x + 24,610.

Step-by-step explanation:

I'm not sure if there were answer choices, but the smallest possible positive integers for x/y=2 is x=2 and y=1

If we plug those in to the other equation

(x^2+y^2)=z

(2^2+1^2)=z

(4 + 1) = z

5=z

Indicating that any number less than 5 cannot equal Z

Step-by-step explanation:

The answer is do ur homework ur self

To calculate the probability of arrival of ten customer in one hour at a service station then use of option a. Poisson probability distribution is more applicable.

Therefore, the required probability for the given situation is Poisson probability distribution .

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The probability that all 3 selected guinea pigs are pregnant is 0.033.

Let's consider the event "A" as "3 guinea pigs selected are all pregnant". The number of ways to choose 3 guinea pigs from the 4 pregnant ones is C(4,3) = 4. The total number of ways to choose 3 guinea pigs from the 10 is

C(10,3) = 120.

The probability of event "A" is given by

P(A) = C(4,3) / C(10,3) = 4 / 120 = 1/30.

Therefore, the probability that all 3 guinea pigs selected are pregnant is 1/30 or 0.033 rounded to 3 decimal places.

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Answer: y-int = (0,7)

x-int= (-7,0)

Step-by-step explanation:

-x+2y=7

2y=x+7

y-int = (0,7)

x-int= (-7,0)

on the graph, (1,4) (2, 4.5) (3, 5) etc

a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

a. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.

In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:

pi = (2x1x2) / 2 = x1x2

By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:

dpi/dx i = x2 - xi = 0

Since xi is in the range [0,1], we have xi = x2.

Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b. Total Payoff: The total payoff of the project is given by:

pt = x1x2 + x1x2 = 2x1x2

By factoring the total payoff function, we get:

pt = 2x1x2 = 2x1x1 = 2x12

So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.

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Answer:

Below

Step-by-step explanation:

Circumf = pi * 2 r

Circumf/(2pi ) = r

area = pi r^2

       = pi * (circumf/2pi)^2    

        = circumf^2 / 4 pi =

                24^2 / (4 pi) = 45. 8  units^2  

Answer:

45.84 units^2

Answer:

Area is 438 Square Feet

Perimeter is 298

Step-by-step explanation:

Area is 438 Square Feet

Area= L x W

438 = L x 3

438 divided by 3 = 146

L=146

Perimeter is 2 (L x W)

2 (146x3)

Perimeter is 298

The number of days you will need to work in order to earn R3500,00 given the ratio of amount earned in 5 days is 20 days

If in 5 working days, you earn R87,500

Then, you will earn R350,000 in x working days

The task content can be solved using the concept of equivalent ratio;

Number of days : amount earned

5 : 87,500 = x : 350,000

5/87500 = x / 350,000

cross product

5 × 350,000 = x × 87500

1,750,000 = 87,500x

divide both sides by 87,500

x = 1,750,000 / 87,500

x = 20

Hence, you need to work for 20 days in order to earn R350,000

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There are indefinitely many solutions to the system.

[x(1), x(2), x(3)] = [-t, 0, t]

The matrix is:

[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]

The system of equations' equivalent augmented matrix is

[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]

The following matrix has been reduced and transformed into a set of equations.

x(1) + x(3) = 0

Subtract x(3) on both side, we get

x(1) = -x(3)

x(1) = -t

x(2) = 0

Let x(3) = t

[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]

There are indefinitely many solutions to the system.

[x(1), x(2), x(3)] = [-t, 0, t]

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The complete question is:

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)

[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]

(x1, x2, x3) =

Answer: We can set up an equation to represent the given information:

4.563 = 4B + 127

where B is the number of residents in Town B.

To solve for B, we can first subtract 127 from both sides:

4.563 - 127 = 4B

Then divide both sides by 4:

B = (4.563 - 127) / 4

B = 1.140775

So Town B has approximately 1.140775 residents.

Step-by-step explanation:

Answer:

(a) The number of tiles Jon will use to cover the worktop is 6 * 15 = 90 tiles.

(b) To find the length of the worktop, we first need to find the length of each tile, which is 20 cm = 0.2 m.

The length of the worktop is then 0.2 m * 6 tiles = 1.2 m.

The width of the worktop is 0.2 m * 15 tiles = 3 m.

So, the length of the worktop is 1.2 m and the width is 3 m.

In the given case- An inverse of a Laplace transform, which is the sum of two distinct components, is the sum of the inverse transforms of each term separately.

What does inverse Laplace transform refer to?

A Laplace transform that is the sum of two different terms has an inverse that is the sum of the inverse transforms of each term taken separately. A Laplace transform, which also has an inverse of the constant multiplied by the inverse of the function, is produced when a constant is multiplied by a function.

A given derivative function with a real variable (t) is transformed into a complex function with a variable (s) by the Laplace transform, which is an integral transformation. Assuming that f(t) complies with a number of later-explained conditions,

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Answer:

To find 26% of an amount, you would use the percentage multiplier of 0.26.

Step-by-step explanation:

To use the multiplier, you would simply multiply the amount by 0.26.

For example:

26% of $100 = $100 x 0.26 = $26.

Alternatively, you can also express the percentage as a decimal by moving the decimal point two places to the left. In this case 26% is equal to 0.26

So, to find 26% of an amount you would multiply the amount by 0.26

For example:

26% of $100 = $100 x 0.26 = $26.

Answer: 24.35333333

Step-by-step explanation:

Answer:

  ±320

Step-by-step explanation:

You want the 4th term of the geometric progression that has first and third terms 5 and 80.

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

for first term a1 and common ratio r.

We are given the 1st and 3rd terms, so we can find the common ratio from ...

  80 = 5·r^(3-1) . . . . . use a3 = 80, a1 = 5, n = 3

  16 = r^2 . . . . . . divide by 5

  ±4 = r . . . . . . . . take the square root

The 4th term will be the product of the 3rd term and the common ratio:

  a4 = a3·(±4) = 80·(±4) = ±320

The fourth term is -320 or +320.