Which expression best estimates 6 3/4 ÷ 1 2/3


7 ÷ 2
6 ÷ 1
8 ÷ 3
3 ÷ 2​

The frequency-domain equivalent circuit equation obtained using phasor methods can be used to analyze the behavior of the circuit at different frequencies, and to predict the performance of the circuit under various operating conditions.  

To transform a circuit from the time domain to the frequency domain using phasor methods, follow these steps:

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The given tableau represents a linear program being solved using the M-Method. It depicts the current solution and the values of the decision variables x1 and x2, along with their respective costs.

The tableau provided is a representation of the simplex method in solving a linear program. The decision variables x1 and x2 are shown along with their respective costs in the "Solution" row. The "Basic" row indicates which variables are currently in the basis.

To find the optimal solution, we need to ensure that all the coefficients in the bottom row (excluding the last column) are non-negative. If any negative values exist, we would perform row operations to pivot and select a different basic variable.

In this specific case, the coefficients in the bottom row are 1, -¹/4, -¹/4, and 0. Since the coefficient of -¹/4 is negative, we can select that column to perform the pivot operation. This would involve dividing the corresponding row (a3) by -¹/4, resulting in 3 + 4M in the pivot position.

The tableau will be adjusted accordingly, and the process would continue iteratively until an optimal solution is obtained. The objective is to maximize the solution value in the "Solution" row while ensuring non-negativity in the bottom row coefficients.

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Answer:

C

Step-by-step explanation:

I believe it's C because it barely touches the circle-

The following statement is true: strong winds occur where isobars are closely spaced.

Isobars are lines on a weather map that connect points of equal atmospheric pressure. The spacing between isobars provides information about the pressure gradient, which is the change in pressure over a given distance. When isobars are closely spaced, it indicates a steep pressure gradient, which in turn leads to strong winds.

This is because air moves from areas of high pressure to areas of low pressure, and the greater the pressure difference, the faster the air will flow. Therefore, when isobars are closely spaced, it suggests a rapid change in pressure over a short distance, creating strong winds.

Regarding the other options:

- Isobars on a surface map are not necessarily drawn at 8mb intervals. The spacing between isobars can vary depending on the map and the purpose for which it is created.

- Atmospheric pressure increases towards the center of a high-pressure system, not a low-pressure system. In a high-pressure system, air descends and compresses near the surface, leading to higher pressure at the center.

- Atmospheric pressure decreases towards the center of a low-pressure system. In a low-pressure system, air rises and expands, causing lower pressure at the center.

Therefore, the true statement is that strong winds occur where isobars are closely spaced.

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The height of the building is approximately 125 feet to the nearest foot.

What is angle of incidence?

The angle of incidence is the angle formed by a ray of light or other wave as it approaches a surface, and a line perpendicular to that surface (known as the normal). It is the angle between the incident ray and the normal

We can use trigonometry to solve this problem. Let's assume the height of the building "h".

First, we need to find the distance between the man's eye level and the ground. We can use tangent function:

tan(85°) = h / 20

Solving for h, we get:

h = 20 * tan(85°)

h ≈ 125.36 feet

Therefore, the height of the building is approximately 125 feet to the nearest foot.

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

As seen on the picture, all the steps A to D are correct.

Note:

The ratio of used books to all books is 7 : 13 and  the ratio of new books to used books is 6 : 7

If there are 13 books on a shelf. 6 of these books are new.

(a) The ratio of used books to all books

Number of all books = 13

Number of used books = total no. of books - no. of new books

                                       =  13 - 6

                                       = 7

So, ratio of used books to all books

= no. of all books : no. of total books

= 7 : 13

Thus, the ratio of used books to all books = 7 : 13

(b) The ratio of new books to used books

Number of new books = 6

Number of used books = 7

So, the ratio of new books to used books

= no. of new books : no. of used books

= 6 : 7

Thus, the ratio of new books to used books = 6 : 7

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Answer:

Between 8 and 9

Step-by-step explanation:

The square root of 75 is about 8.6

Therefore the answer is between the number 8 and 9.

Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

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

The characteristics of normal distributions are as follows: Bell-like in its symmetry.

The distribution's mean and median, which are both at its center, are equal.

68 percent of the data, or approximately, falls within one standard deviation of the mean.

So, the formula is used to determine the Z score for a data point x in a normal distribution:

Z = z - mean/standard deviation

Now, use the formula to calculate the z value as follows:

Z = z - mean/standard deviation

Z = 25 - 16/6

Z = 9/6

Z = 3/2

Z = 1.5

Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

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a. The probability that the amount of collagen is greater than 60 grams per mililiter is 0.5398

b. The probability that the amount of collagen is less than 90 grams per mililiter is 0.9985.

c. Approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.

a. To find the probability that the amount of collagen is greater than 60 grams per milliliter, we'll use the z-score formula:
z = (X - μ) / σ
where X is the value we're interested in, μ is the mean, and σ is the standard deviation.
z = (60 - 61) / 9.8 ≈ -0.1
Now, we'll use a z-table or calculator to find the probability corresponding to this z-score.

A z-score of -0.1 corresponds to a probability of approximately 0.4602.

Since we're looking for the probability that the amount of collagen is greater than 60 grams per milliliter, we need to find the area to the right of this z-score:
P(X > 60) = 1 - P(X ≤ 60) = 1 - 0.4602 ≈ 0.5398
b. To find the probability that the amount of collagen is less than 90 grams per milliliter, we'll again use the z-score formula:
z = (90 - 61) / 9.8 ≈ 2.96
A z-score of 2.96 corresponds to a probability of approximately 0.9985.

Since we're looking for the probability that the amount of collagen is less than 90 grams per milliliter, we'll use this probability directly:
P(X < 90) ≈ 0.9985
c. To find the percentage of compounds formed from the extract of this plant that fall within 1 standard deviation of the mean, we'll use the empirical rule (68-95-99.7 rule), which states that approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.

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Answer:

Hey there!

When reflecting across both axis, we switch up the signs but keep the order of the coordinates.

Thus, (-2, 8) and (2, -8) are reflections and (4, -3) and (-3, 4) are also reflections.

Let me know if this helps :)

Answer:

14.5

Step-by-step explanation:

You would plug 5 into the equation for m and have w = 1.5 (5) + 7

Then you would multiply 1.5 and 5 and get 7.5 and then add 7 and get 14.5

The weight of the baby in pounds at 5 months of age is 14.5 pounds.

Given,

The weight in pounds of a baby in the first six months of life can be modeled by the function:

w = 1.5m +7, where x is the age of the baby in months.

According to this model, we need to find what is the weight, in pounds, of a baby at 5 months of age.

A function has an input and an output.

Example:

f(x) = x + 1

x = 1, f(1) = 1 + 1 = 2

Here,

x = 1 is the input and 2 is the output.

We have,

Function:

w = 1.5m + 7

We can consider that m = number of months.

This is why the question says this model can be used to find the weight of the baby in the first six months by putting m = 6.

w = 1.5m + 7

Here,

7 = the weight of the baby at birth

1.5m = baby weight increases by 1.5 per month.

Now,

The weight in pounds of the baby at 5 months of age is:

m = 5 months

w = 1.5 m + 7

w = 1.5 x 5 + 7

w = 7.5 + 7

w = 14.5 pounds.

Thus the weight of the baby in pounds at 5 months of age is 14.5 pounds.

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Answer:

5 cm

Step-by-step explanation:

volume equals length x width x height

then exchange the width for 3 and height for 3

3 x 3 = 9

45 divided by 9 = 5

therefore,

the answer is 5 cm

have a good day friend :)

By using the concept of combinations, there are 13,122,848 ways.

For getting the number of ways to distribute 30 people into 4 distinct rooms with the given conditions, we will use the concept of combinations.

In the case of 2 people in room 3 and 26 in room 4, the number of ways to distribute them is:
²⁸C₂ = 28! / (2!(28-2)!) = 378

After calculating the total number of ways, we find that there are 13,122,848 ways to distribute 30 people into the 4 distinct rooms with the given conditions.

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Based on the side-angle-side congruence theorem (SAS),

Missing statement is: ΔHIK ≅ ΔHJK

Missing reason is: SAS

If there are two pairs of congruent sides and a pair of included corresponding congruent angles in two triangles, then based on the side-angle-side congruence theorem (SAS), the two triangles are congruent to each other.

The two triangles have the following:

Two pairs of congruent sides which are: HI ≅ HJ, and HK ≅ HK

One pair of included corresponding congruent angles which is: <IHK ≅ <JHK.

This means that both triangles are congruent triangles based on SAS.

Therefore,

Missing statement is: ΔHIK ≅ ΔHJK

Missing reason is: SAS

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The product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).

The given expression is:

\((1.466*10^{-8} )(5.02*10^5)\)

We can rewrite the given expression as

\((1.466*5.02)(10^{-8} *10^5)\)

If we have two numbers with the same base we can write the product of the numbers as a single base followed by the addition of exponents.

\(a^m*a^n = a^{m+n}\)

\(1.466*5.02=7.35932\)

\(10^{-8} *10^5 = 10^{-3}\)....from exponent addition rule

So, \((1.466*10^{-8} )(5.02*10^5)=7.35932 *10^{-3}\)

Therefore, the product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).

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Answer:

7.3593 and -3

Step-by-step explanation:

Got it right on the assignment.

Step-by-step explanation: To find the cost of one taco, we can use a system of equations. Let x be the cost of one burger and y be the cost of one taco. Then we have:

2x + 4y = 22.50 x + 3y = 14.50

Multiplying the second equation by -2, we get:

-2x - 6y = -29 2x + 4y = 22.50

Adding the two equations, we get:

-2y = -6.50 y = 3.25

So one taco costs $3.25.

Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

Answer: No

Step-by-step explanation:

It should be 2x-4 (2*×=2x and 2*2=4)

No, the simplified expression is not correct.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given expression

2(x - 2) - 2(3)

so 2(x - 2) = 2x - 2(2)

= 2x - 4

and 2(3) = 6

substitute the value

2(x - 2) - 2(3) = 2x - 4 - 6

= 2x - 10

and equation of Marty is  2x - 8

Hence the equation of marty is incorrect.

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Answer:

130

Step-by-step explanation:

18+4(28)

18+112

130

The equation that relates y,x, and z when constant variation is -2: y = -2 *(z²) / x.

An equation is a mathematical statement that shows the equality of two expressions. It usually consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can have one or more unknown variables, and the goal is often to find the values of these variables that make the equation true. Equations are used in many different areas of mathematics and science to describe relationships between quantities, to solve problems, and to model real-world phenomena.

Here,

If y varies directly as the square of z and inversely as x, we can write:

y = k * (z²) / x

where k is the constant of variation. We are told that the constant of variation is -2, so we can substitute this value into the equation:

y = -2 * (z²) / x

This is the equation that relates y, x, and z.

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Approximately 31.7 people signed up for both yoga and aerobics.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let's define the following events:

Event A: a person signed up for yoga.

Event B: a person signed up for aerobics.

P(A) = 92/756

P(B) = 113/756

P(neither A nor B) = 575/756

We can use the following formula:

P(A and B) = P(A) + P(B) - P(A or B)

We can calculate P(A or B) as:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 92/756 + 113/756 - P(A and B)

P(A or B) = 205/756 - P(A and B)

P(neither A nor B) = 1 - P(A or B)

Substituting in the calculated value for P(A or B), we get:

575/756 = 1 - (205/756 - P(A and B))

575/756 = 551/756 + P(A and B)

P(A and B) = 24/756

P(A and B) ≈ 0.0317

Therefore, approximately 31.7 people signed up for both yoga and aerobics.

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Answer:

\(y=\frac{1}{12}x-\frac{26}{3}\)

Step-by-step explanation:

\(y+9=\frac{1}{12}(x+4) \\ \\ y+9=\frac{1}{12}x+\frac{1}{3} \\ \\ y=\frac{1}{12}x-\frac{26}{3}\)

Answer:

8

Step-by-step explanation:

The length of the rectangle is 24 meter.

Here,

The width of a rectangle is 2 m.

The length of the rectangle is 4 times a number increased by 4.

The area of the rectangle is 48.

We have to find the length of a rectangle.

What is Area of rectangle?

The formula for the area of a rectangle is multiply length x width.

Now,

The width of a rectangle = 2 m

Let a number is x.

Then the length of rectangle =(4x + 4) m

Area of rectangle =  length x width.

                           = (4x + 4) * 2

Here, The area of the rectangle is 48.

So,

(4x + 4) * 2 = 48

Divide both side by 2,

4x + 4 = 24

4x = 24 -4

4x = 20

Divide both side by 4,

x = 5

Hence, the length of rectangle,

⇒ 4x + 4 = 4 * 5 + 4 = 20 + 4 = 24 m

So, The length of the rectangle is 24 meter.

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Answer:

What is the question?! I don't understand, sry?!

Step-by-step explanation:

to find the number of plants in the pond at the time t we can use the equation N(t) = 150(3)^t.

        The equation that can be used to find the number of plants in the pond at time t, given that the number of plants is growing exponentially, is:

                      N(t)=ab^t.

         The given values in the table for the function N(t) are:

                      t  N(t)0  1501  450

         We can use these values to determine the values of constants a and b in the equation

                       N(t)=ab^t:

          Substitute t = 0 and N(t) = 150 in the equation

                      N(t)=ab^t.

          Then, 150 = a × b^0 → 150

                            = a × 1 → a

                            = 150

            Substitute t = 1 and N(t) = 450 in the equation N(t)=ab^t.

             Then, 450 = 150 × b^1 → b = 3.

     Now that we have found the values of a and b, we can write the equation that can be used to find the number of plants in the pond at time t as:  N(t) = ab^t = 150(3)^t.

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Answer:

The answer is below

Step-by-step explanation:

Given that:

The radius of the circle (r) = 5 units

The central angle (θ) = 25π

A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:

\(Area\ of\ sector=\frac{\theta}{360} *\pi r^2\)

Substituting the radius of the circle and the central angle:

\(Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}\)

When the function f(x) is divided by 2x − 1, the quotient is 3x^2 − 5x + 8 and the remainder is 3, then the function f(x) = 6x^3 - 13x^2 + 21x - 5

From the question,

Divisor = 2x - 1, Quotient = 3x^2 − 5x + 8, Remainder = 3 and Dividend = f(x).

As we know the formula,

Dividend = Divisor × Quotient + Remainder

Now substitute the values

f(x) = (2x - 1) × (3x^2 − 5x + 8) + 3

We solve using the distributive property

f(x) = 3x^2(2x - 1) − 5x(2x - 1) + 8(2x - 1) + 3

Now simplify again using the distributive property

f(x) = 6x^3 - 3x^2 − 10x^2 + 5x + 16x - 8 + 3

Now simplify by solving the same terms

f(x) = 6x^3 - 13x^2 + 21x - 5

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The complete question is:

When the function f(x) is divided by 2x − 1, the quotient is 3x^2 − 5x + 8 and the remainder is 3. Find the function f(x) and write the result in standard form.

Answer:

2.25 ft

Step-by-step explanation:

Volume = length x height x width

54= 8 x 3 x ?

Combine: 54= 24 x ?

Find ?: 54/24=2.25

Recheck: 24 x 2.25 = 54