7y- (5y - 12) = 20 + 2y +4

The variable h, as the subject of the given formula is h = 3 / (G.V + 1)

From the question, we are to make h the subject in the given formula

The given equation is

(3 - h) / V = G . h

Multiply both sides of the equation by V

V × (3 - h) / V = G . h × V

3 - h = G . h . V

Add h to both sides

3 - h + h = GhV + h

3 = GhV + h

Factorize h

3 = h(G.V + 1)

Now,

Divide both sides of the equation by (G.V + 1)

That is,

3 / (G.V + 1) = h

∴ h = 3 / (G.V + 1)

Hence, the value of h is 3 / (G.V + 1)

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Answer:

(-2,3)

Step-by-step explanation:

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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The greatest common divisor (GCD) of 735 and 504 is 21. Using the Euclidean algorithm, we find that the GCD can be expressed as 735x + 504y, where x = 11 and y = -5.

(a) To compute the GCD using the Euclidean algorithm, we start by dividing the larger number (735) by the smaller number (504):  \(735 = 504 * 1 + 231\)

Next, we divide the previous divisor (504) by the remainder (231):

\(504 = 231 * 2 + 42\)

We continue dividing the previous divisor by the remainder until we reach a remainder of 0:

\(231 = 42 * 5 + 21\\42 = 21 * 2 + 0\)

The last non-zero remainder is 21, which is the GCD of 735 and 504.

(b) To find integers x and y such that the GCD of 735 and 504 can be written in form 735x + 504y, we can use the extended Euclidean algorithm.

Starting with the last two equations from part (a):

\(21 = 231 - 42 * 5\\21 = 231 - (504 - 231 * 2) * 5\)

To simplifying, we have:

\(21 = 11 * 231 - 5 * 504\)

Therefore, we can write the GCD of 735 and 504 as:

\(21 = 11 * 735 - 5 * 504\)

So, x = 11 and y = -5 satisfy the equation 735x + 504y = 21, with x and y being integers.

In conclusion, the GCD of 735 and 504 is 21, and it can be expressed as 735x + 504y, where x = 11 and y = -5.

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The probability of the flight being overbooked is 0.38742 or 38.7%.

To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:

\(P(x) = ^nC_x * p^x * q^{(n-x)}\)

Where:

P(x) is the probability of x number of events occurring.

n is the total number of trials.

p is the probability of success.

q is the probability of failure.

nCx is the number of ways to choose x items from a set of n items.

Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."

In our case:

n = 10 (total number of passengers)

p = 0.9 (probability of a passenger showing up)

q = 0.1 (probability of a passenger not showing up)

We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:

P(9 or 10) = P(9) + P(10)

P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰

P(9 or 10) = 0.38742 or 38.7%

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Complete Question:

Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.

A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?

Answer:

3 is the smallest prime factor.

Step-by-step explanation:

ionk how to explain it but trust me its right.

So the final expression is: (change in y/y) = n (change in a/a).

We can start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(aⁿ)

Using the rule that ln(aⁿ) = n ln(a), we can simplify this to:

ln(y) = n ln(a)

Next, we can take the derivative of both sides with respect to a:

d/d(a) ln(y) = d/d(a) (n ln(a))

Using the chain rule, we can simplify the right-hand side to:

d/d(a) ln(y) = n (1/a)

Now, we can multiply both sides by a/y:

a/y * d/d(a) y = n(a/y) * (1/a)

Simplifying, we get:

dy/y = n da/a

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Answer:

x ∈ { ( 6 + \(\sqrt{23}\) * i) , { ( 6 - \(\sqrt{23}\) * i) }

Step-by-step explanation:

Given: \(x^2-12x+59=0\)

First, collect like terms. \(x^2\) and -12x, 59 and 0:

\(x^2-12x=0-59\)

+59 is changed to -59 when transferred. Then subtract:

( x - 12 ) x = -59

Finally divide both sides by -59:

x ∈ { ( 6 + \(\sqrt{23}\) * i) , { ( 6 - \(\sqrt{23}\) * i) }

Answer: (a) The English system of units used in surveying:

Length: The basic unit of length is the foot (ft).

Area: The basic unit of area is the square foot (ft²).

Volume: The basic unit of volume is the cubic foot (ft³).

Angles: The basic unit of angles is degrees (°).

(b) The SI (International System of Units) system of units used in surveying:

Length: The basic unit of length is the meter (m).

Area: The basic unit of area is the square meter (m²).

Volume: The basic unit of volume is the cubic meter (m³).

Angles: The basic unit of angles is the degree (°) or the radian (rad).

It's worth noting that while the English system is still used in some countries, the SI system is the globally recognized and widely adopted system of measurement.

Step-by-step explanation:

In the given word problem, Nevaeh's age is 7.

Given that,

Nevaeh is older than Kareem.

Their ages are consecutive integers.

The sum of the square of Nevaeh's age and twice Kareem's age is 61.

Assume Nevaeh's age as x.

Since Nevaeh is older than Kareem, Kareem's age would be x-1.

According to the problem,

The sum of the square of Nevaeh's age and twice Kareem's age is 61.

So, we can write the equation as:

x² + 2(x-1) = 61.

Expanding the equation, we get:

x² + 2x - 2 = 61.

Rearranging the terms, we have:

x² + 2x - 63 = 0.

x² + 9x - 7x - 63 = 0

x(x + 9) - 7(x + 9) = 0

(x - 7)(x+9) = 0

x = 7 or x = - 9

Since age is a positive quantity, therefore, proceed x = 7

Therefore, Nevaeh's age is 7.

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Answer:

Linear

Step-by-step explanation:

The rule is that linear equations must have exponents of 1 (a sloped line) or 0 A verticle or horizontal line). This function can be simplified to

y = 3x - 12 + 5 = 3x - 7 which is the standard form of a linear equation

y - mx + b where m is the slope and m is the y intercept.

4 radians is equivalent to approximately 229 degrees after rounding off.

The radian, represented by the symbol rad, is the standard unit of angular measurement used in many branches of mathematics. It is a unit of angle in the International System of Units (SI). The unit was once a supplementary SI unit (before that category was abolished in 1995). According to the SI, a radian is a dimensionless unit with a value of 1 rad. Thus, it is frequently written without a sign, particularly in mathematical writing.

Geometric angle measurements are often measured in radians, which are then converted to degrees. There are two distinct measurement techniques for angles. Radians and degrees are the two units used to quantify an angle.

To convert radians to degrees, you can use the formula:

Degrees = Radians x (180/π)

Substituting 4 for radians in the formula, we get:

Degrees = 4 x (180/π) = 229 degrees (rounded to the nearest degree)

Therefore, 4 radians is equivalent to approximately 229 degrees.

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All pairs of parallel segments are given below.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Given,

a) Line segment = AC and FD

Parallel = AC ║FD

b) Line segment = AE and BD

Parallel = AE ║BD

c) Line segment = EC and FB

Parallel = EC ║FB

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The given information is:

- They surveied 164 pet owners

- 61 own a dog

- 66 own a cat

- 11 own both a dog and a cat

We have to find how many owned neither a cat nor a dog.

We can represent this survey in the following diagram:

To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:

The people who own neither a dog nor a cat are 26.

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Option A, "Yes, because every x-value corresponds to exactly one y-value," accurately describes the situation presented in the table. Option A is the proper response, so.

The table represents a function.

A mathematical relationship known as a function is one in which every input (x-value) has exactly one corresponding output (y-value). In the given table:

xy

3 1

4 3

5 2

6 5

6 6

Every x-value in the table corresponds to exactly one y-value. There are no repeated x-values, and for each x-value, there is only one corresponding y-value. The definition of a function is met by this.

The answer given in Option A, "Yes, because every x-value corresponds to exactly one y-value," appropriately sums up the situation shown in the table. Option A is the proper response, so.

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Since the point B is between points A and C, the length BC is 22.25 units

From the question, we have the following parameters that can be used in our computation:

Length AB = 6x - 9

Length BC = 3x + 17

Length AC = 5x + 16

The above implies that the point B is between points A and C

So, we have the following equation

AC = AB + BC

Substitute the known values in the above equation

So, we have the following equation

5x + 16 = 6x - 9 + 3x + 17

Collect the like terms

So, we have the following equation

5x - 6x - 3x = -9 + 18 - 16

Evaluate the like terms

So, we have the following equation

-4x = -7

Divide by -4

x = 7/4

Substitute x = 7/4 in the equation BC = 3x + 17

So, we have the following equation

BC = 3 x 7/4 + 17

Evaluate

BC = 22.25

Hence, the numerical length of BC is 22.25 units

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Answer:

  x ≈ 7.68

Step-by-step explanation:

You want to find the length x of the tangent segment in the given figure.

Drawing an altitude of the triangle to the upper point of tangency, we have the figure shown in the first attachment. All of these right triangles are similar, so ∠CAB ≅ ∠CDA = 52°.

The tangent of the angle 52° is given by ...

  Tan = Opposite/Adjacent

  tan(52°) = BC/BA

The tangents to the circle from point C are the same length, so BC = x and ...

  tan(52°) = x/6

  x = 6·tan(52°) ≈ 7.68 . . . . cm

The value of x cm is about 7.68 cm.

<95141404393>

Answer:

\(x \approx 7.68 \text{ cm}\)

Step-by-step explanation:

We can solve for the length of segment x in this circle diagram by using the principles of tangency and the altitude of a right triangle.

First, we can assume that the hypotenuse of the diagrammed right triangle is tangent to, or parallel with, the circumference of the circle at its point of intersection it. This means that it is perpendicular, or at a right angle, to the radius at the point of intersection with the circumference.

Second, we can see that the altitude of the diagrammed right triangle is the radius of the circle which intersects with the circumference at the hypotenuse's point of tangency (see the attached image).

We can use our knowledge of a right triangle's altitude to make the assertion that the three triangles formed by drawing the altitude are all similar. This means that their angles are the congruent.

We can solve for the length of the horizontal segment \(h\) (the hypotenuse of one of the triangles formed by drawing the altitude) by using the trigonometric ratio cosine.

\(\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\)

↓ plugging in the known values

\(\cos(52\°) = \dfrac{6}{h}\)

↓ dividing both sides by 6

\(\dfrac{\cos(52\°)}{6} = \dfrac{1}h\)

↓ taking the reciprocal of both sides

\(h = \dfrac{6}{\cos(52\°)}\)

Finally, we can solve for x by constructing another right triangle, assuming that the segment of length x is tangent to the circle's circumference. We know that the sides of the right triangle are: the radius, \(h\), and x. We already know two of these values (the radius and \(h\)), so we can solve for x using the Pythagorean Theorem.

\(a^2 + b^2 = c^2\)

↓ plugging in the known values

\(x^2 + 6^2 = \left(\dfrac{6}{\cos(52\°)}\right)^2\)

↓ subtracting 6² from both sides

\(x^2 = \left(\dfrac{6}{\cos(52\°)}\right)^2 - 6^2\)

↓ taking the square root of both sides

\(x = \sqrt{\left(\dfrac{6}{\cos(52\°)}\right)^2 - 6^2}\)

↓ evaluating using a calculator

\(\boxed{x \approx 7.68\text{ cm}}\)

Dominque's mistake in calculating the percent change is that she misidentified the amount of change and the initial amount.

Hence the correct percent change is given as follows:

39.66%

The percent change is obtained as the change divided by the initial amount and then multiplied by 100%.

The parameters for this problem are given as follows:

Hence the percent change is given as follows:

P = (2558/6450) x 100%

P = 39.66%.

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Answer:

Hollerith tabulating machine

Step-by-step explanation:

The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.

Answer:

23÷8=2.875

Step-by-step explanation:

You take twenty three divide by eight .That will give you the answer

y = -t is  parametric equation of the line passing through a and parallel to b

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

  and parallel to a vector <a, b, c> is given by :

  x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    

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Given the following equation:

You can solve for the variable "y" in terms of "x" by following the steps shown bellow:

1. You can rewrite the fraction as a decimal number, by dividing the numerator by the denominator:

2. Apply the Distributive property, which states that:

Then:

3. Apply the Division property of equality by dividing both sides of the equation by 0.75:

Therefore, the equation solved for "y" in terms of "x", is:

Answer:

\(Surface\ Area = 179.25cm^2\)

Step-by-step explanation:

Given

See attachment for figure

Required

Determine the surface area

To do this, we calculate the surface area of each individual shape.

For the semicircle.

\(Area = \frac{1}{2}\pi r^2\)

Here, the diameter (D) is given

\(D = 10cm\)

The radius is:

\(r = \frac{1}{2}D\)

\(r = \frac{1}{2}*10cm\)

\(r= 5cm\)

So, the area is:

\(Area = \frac{1}{2} * 3.14 * (5cm)^2\)

\(Area = \frac{1}{2} * 3.14 * 25cm^2\)

\(Area = 39.25cm^2\)

For the triangle, the area is:

\(Area = \frac{1}{2}bh\)

\(Area = \frac{1}{2} * 10cm * 8cm\)

\(Area = 40cm^2\)

For the rectangle

\(Area = Length * Width\)

\(Area = 20cm * 5cm\)

\(Area = 100cm^2\)

So, the surface area is:

\(Surface\ Area = 39.25cm^2 + 40cm^2 + 100cm^2\)

\(Surface\ Area = 179.25cm^2\)

the required sample size is approximately 178. Answer (c) is correct.To determine the required sample size, we can use the formula:

n = (z * σ / E)^2

where:
- n is the sample size
- z is the z-score for the desired level of confidence (99% corresponds to z = 2.58)
- σ is the standard deviation of the population
- E is the maximum error we want to allow in our estimate of the population mean

Plugging in the values given in the problem, we get:

n = (2.58 * 14 / 4)^2 ≈ 178

Therefore, the required sample size is approximately 178. Answer (c) is correct.

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Answer:

No it isnt

12 divided by 6 is 2, that means 14 need to be divided by 6 as well. but 14 divided by 6 is not 3

Answer:

No

Step-by-step explanation:

3 is not a multiple of 14 so you see not.

Answer:

29 ft

Step-by-step explanation: