write the product USING EXPONENTS ​

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Answer:

1.28571

Step-by-step explanation:

is the answer

Answer:

368,181

Step-by-step explanation:

You subtract 373,558 and 5,377

373,558-5,377 and you get 368,181

Answer:

if its 6² it means 6×6 =36

Answer:

36

Step-by-step explanation:

6² = 6 × 6 = 36

Note any number squared, raised to the power of 2 is the number multiplied by itself.

No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

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Answer:0.48

Step-by-step equation:

An example of a second-order non-homogeneous linear differential equation that cannot be solved by the method of undetermined coefficients is y'' - 2xy' + y = e^x.

The method of undetermined coefficients is a technique used to solve non-homogeneous linear differential equations by assuming a particular form for the solution based on the form of the non-homogeneous term. However, there are cases where this method fails to provide a solution.

In the example equation y'' - 2xy' + y = e^x, the non-homogeneous term is e^x. When applying the method of undetermined coefficients, we would assume a particular solution of the form y_p = Ae^x, where A is a constant to be determined. However, when we substitute this solution into the differential equation, we find that the terms involving x and its derivatives do not cancel out.

The presence of the term -2xy' in the equation causes the method of undetermined coefficients to fail. This term introduces a higher order polynomial in x, which cannot be expressed in the assumed form Ae^x. Therefore, alternative methods, such as the method of variation of parameters or the method of annihilators, need to be employed to find the solution to this particular non-homogeneous linear differential equation.

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(a) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−8)²+(y−2)² = 16 oriented counterclockwise, we need to parametrize the curve C. The parametric equations for a circle of radius 4 centered at (8, 2) can be written as x = 8 + 4cos(t) and y = 2 + 4sin(t), where t ranges from 0 to 2π.

Substituting these expressions into the integrand and evaluating the dot product, we have:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))dx + 5((2 + 4sin(t))² + (8 + 4cos(t)))dy.

Using the parametric equations and differentiating with respect to t, we can express dx and dy in terms of dt:

dx = -4sin(t)dt,

dy = 4cos(t)dt.

Substituting these expressions into the integral, we get:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))(-4sin(t))dt + 5((2 + 4sin(t))² + (8 + 4cos(t)))(4cos(t))dt.

Integrating with respect to t over the range 0 to 2π, we can evaluate the integral to obtain the final answer.

(b) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−a)²+(y−b)² = r² in the xy-plane oriented counterclockwise, we need the specific values for a, b, and r. Please provide the values for a, b, and r in order to proceed with the calculation.

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We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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the base-ten representation for 19! = 121,6T5,100,40M,832,000 then

H+M+T =12

19! has three 5s so it will end with three 0s.

Hence H = 0

19! = 121,6T5,100,40M,832,000 = 121,6T5,100,40M,832 * 1000

19! has many 2s. So M832 will be divisible by 16 (last 4 digits).

So M000 + 832 is divisible by 16. 832 is completely divisible by 16. Since 16*5 = 80, 8000 must be divisible by 16.

M = 8

19! = 121,6T5,100,408,832,000

Since 19! is divisible by 9, sum of all digits must be divisible by 9.

1+2+1+6+T+5+1+4+8+8+3+2 = T + 41

To make this divisible by 9, T must be 4.

H+M+T = 0 + 8 + 4 = 12

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Center = (-1,0)   Radius= 1

when you complete the square your equation should look something like

(x²+2x+1) (y²+0) = 1.The 1 on the left side coming from (b/2)² which is (2/2)² which equals 1 and whatever you add to one side, you have to add to the other so when you add 0+1 you get the 1 on the right side. Then factor or use the (b/2) from earlier without the ² so you should get (x²+1) + (y²+0) = 1. Flip the sign so you have negative 1 and 0. For the radius, square the right side and of course, \(\sqrt{1}\) is simply 1 so your radius is 1. A lot of 1's huh? lol at least it makes the operations nice and simple :)

Answer:

less than 1, smaller than 1

Step-by-step explanation:

I do not agree that the line y = -2x + 3 is perpendicular to the line x + 2y = 8.

Perpendicular lines are lines that form right angles at the point of intersection. The equation of the lines that are in perpendicular with each other have slopes that are negative reciprocal with one another.

If slope of A = a/b, and B is perpendicular to A, then slope of B = -b/a.

To check if the two given equation of the line is perpendicular with each other, get their slopes and see if they're negative reciprocal of one another.

Line 1 : y = -2x + 3

m = -2

slope of perpendicular line to line 1 = 1/2

Line 2 : x + 2y = 8 ⇒ 2y = -x + 8 ⇒ y = -1/2 x + 4

m = -1/2

1/2 ≠ -1/2

Since the negative reciprocal of the slope of the first line is not equal to the slope of the second line, then they are not perpendicular with each other.

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uh i did this wrong so uh just ignore what i said

Answer:

82°

Step-by-step explanation:

Angle C and B equal the measure of angle A so,

143 - 61 = 82

Angle B is 82°

Answer:

he correct answer is D. 12 adult tickets, 4 child ticket

Step-by-step explanation:

To find the equation for the plane passing through point P₀(-3,-9,2) and perpendicular to the given line, we can use the point-normal form of the equation of a plane.

The normal vector of the plane is parallel to the direction vector of the line. We can determine the direction vector of the line from the given parametric equations. Then, using the normal vector and the coordinates of P₀, we can write the equation of the plane.

The parametric equations of the line are:

x = -3 + t

y = -9 + 3t

z = -2t

The direction vector of the line is given by <1, 3, -2>.

A plane perpendicular to a line will have a normal vector parallel to the direction vector of the line. So, the normal vector of the plane is also <1, 3, -2>.

Using the point-normal form of the equation of a plane, where (x, y, z) represents a point on the plane and (a, b, c) is the normal vector, we have:

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

Substituting the coordinates of P₀(-3, -9, 2) and the values of a, b, and c from the normal vector, we get:

(1)(x + 3) + (3)(y + 9) + (-2)(z - 2) = 0

Simplifying the equation, we have:

x + 3 + 3y + 27 - 2z + 4 = 0

x + 3y - 2z + 34 = 0

Therefore, the equation of the plane passing through P₀(-3, -9, 2) and perpendicular to the given line is x + 3y - 2z + 34 = 0.

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Answer:

You find the surface area with:

10*2+10*2+4*2+4*2+2*2+2*2+4*7+4*7+4*4+4*4 or in short 152 in^2.

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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Answer:

2,301,384

Step-by-step explanation:

The following logarithmic equation is equivalent to the given exponential equation,

\(log_{4}(256) = c\)

Computing the Equivalent Logarithmic Equation

The given exponential equation is,

\((4)^{c} = 256\)

As per the fundamental properties of exponentiation, the logarithmic equivalent equation of any exponential equation has the same base as that in the corresponding exponential equation. Exponentiation refers to the act of raising a number to the power of another number.

In the exponential equation, \((4)^{c} = 256\), $ is the base. So, the base in its equivalent logarithmic equation will also be 4.

The result of the exponential expression becomes the operand for the log.

Terms in a Logarithmic Equation

For the logarithmic equation, \(log_{4}(256) = c\),

4 is called the base of the log. The variable  'c' is the logarithm of 256 to base 'a'.

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Refer to the attachment

The area of the square bedroom given that the side length is 6pa has a value of 36a²p²

The dimensions and the shape of the bedroom from the question are given as

Shape = square

Length = 6pa

By definition, the area of a square shape is

Area = Length x Length

When the known values are substituted, we have

Area = 6pa x 6pa

Evaluating the product, we have

Area = 36a²p²

Hence, the area is 36a²p²

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Answer:

80%

Step-by-step explanation:

How to get that answer:

We have 6 red out of 5+6+2 = 13 total.

The fraction 6/13 represents the probability of selecting red at random.

Because the marble is replaced, the probability does not change on the next selection.

The probability of getting two reds in a row is (6/13)*(6/13) = 36/169

Answer:

3×0+1=1

Step-by-step explanation:

i hope that helps

The constant term of the polynomial \(2x^3 - 8x^2+ 3x -7\\\) is -7

What is a polynomial?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division sign.

A mathematical expression of the form \(a_0 + a_1x + a_2x^2 + .... + a_nx^n, (a_n \neq 0)\) is called a polynomial of degree n

Here the polynomial is

\(2x^3 - 8x^2+ 3x -7\\\)

There is no variable associated with the term -7

So the constant in this polynomial is -7

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Correct Question

What is the constant of this polynomial?

\(2x^3 - 8x^2+ 3x -7\\\)

Answer:

Step-by-step explanation:

Dookie

When you ask for the square root of a positive number a : √a you ask to find a number c such that c × c = a

For example, take a = 4. Then as you know, √4 = √(2×2) because 4 = 2×2

And so you finally got this number c, such that c × c = 4 it is c = 2

Now the cubic root of a number a is the same principle, the only difference is we are looking for a (positive) number c, such that c × c × c = a, this number c will be the cubic root of ∛a

But we already know that 8 = 2 × 2 × 2

So we found that number c, such that c × c × c = 8, it is c = 2

Conclusion : -∛8 = - ∛(2×2×2) = - 2

Good Luck !

a.yes

Step-by-step explanation:

a.angle BCD =b because angle BCD is alternate angle of angle ABC

b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line