What will be the whole number or fraction

The equation of the parabola formed by the plane that is parallel to a generating line of a double napped cone is y = (A/B)x^2 + (6/B)x + (9/B + K/B).

The equation of a double napped cone is given by:

\(Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Jz + K = 0\)

Where A, B, C, D, E, F, G, H, J and K are constants.

A plane that is parallel to a generating line of a double napped cone will intersect the cone at a single point, forming a parabola. The equation of a parabola can be written as:

y = ax^2 + bx + c

Where a, b, and c are constants.

We can find a, b and c by substituting the equation of the plane into the equation of the double napped cone.

For example, if the equation of the plane is x + y – z = 3 then we can substitute this into the equation of the double napped cone and solve for the coefficients a, b and c.

Substituting x + y – z = 3 into the equation of the double napped cone:

\(Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Jz + K = 0\)

We get:

\(Ax^2 + B(x + 3)^2 + C(-x - 3)^2 + K = 0\)

Expanding, we get:

\(Ax^2 + Bx^2 + 6Bx + 9B + Cx^2 - 6Cx - 9C + K = 0\)

Grouping terms and solving for a, b and c, we get:

a = A/B

b = 6/B

c = 9/B + K/B

Therefore, the equation of the parabola formed by the plane that is parallel to a generating line of a double napped cone is y = (A/B)x^2 + (6/B)x + (9/B + K/B).

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Answer:

-5 ≤ x≤ 3

Step-by-step explanation:

The domain is the values for x

x starts and -5 and includes -5 since the circle is closed

and goes to 3 and  includes 3 since the circle is closed

-5 ≤ x≤ 3

Answer:

first option

Step-by-step explanation:

The domain are the values from the x- axis that can be input into the function.

The closed circles at the ends of the graph indicate that x can equal these values.

left side value of x = - 5 and right hand value of x = 3, thus

domain is - 5 ≤ x ≤ 3

The largest area the rectangle can have is -1024 square units.

To solve the given problem, follow the steps given below:

Step 1: Sketch the given graph on a coordinate plane as shown below:

Step 2: Let's assume that the base of the rectangle is x units and its height is y units.

Step 3: As the base of the rectangle is on x-axis, we have the length of the base as the x-coordinate of the upper two vertices of the rectangle.

Now, the x-coordinate of the upper two vertices of the rectangle lie on the given semicircle whose equation is y = V1 - 32.

So, we can write:

y = V1 - 32x^2 = (y + 32)^2 ⇒ x^2 = y^2 + 64y + 1024

Step 4: Now, we can write the area of the rectangle as: A = base × height= x × y

Using the value of x from equation (1), we get: A = (y^2 + 64y + 1024)1/2 y

So, we have an equation for area in terms of y. Let's differentiate it with respect to y to find the maximum value of A. dA/dy = (y^2 + 64y + 1024)-1/2 (2y + 64)

By equating dA/dy = 0, we get: 2y + 64 = 0y = -32

Substituting the value of y in equation (2), we get:x^2 = 1024 ⇒ x = ±32

The given rectangle lies in the first quadrant.

Hence, the length of the base of the rectangle is x = 32 units.

So, we have the dimensions of the rectangle as length = 32 units and breadth = height = y = -32 units.

However, as the length and breadth of the rectangle cannot be negative, we cannot consider the negative value of y.

Therefore, the maximum area of the rectangle is: A = base × height= 32 × (-32)= -1024 sq. units

Hence, the largest area the rectangle can have is -1024 square units.

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Answer:

Step-by-step explanation:

Let x be the variable.

One fourth times the difference of ten and x is 2/3

1/4 (10 - x) = 2/3

10 - x = 3/2

-x = 3/2 - 10

x = -3/2 + 10

x = 13/2

The answer is:

\(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\)

Work/explanation:

First, the variable is d

Then, the difference of 10 and d is 10 - d.

One-fourth is 1/4.

The equation is : \(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\).

Answer: Square and rectangle

Step-by-step explanation:

The integral ∫₀₇ f(x) dx, where f(x) is defined as 5 for x < 5 and x for x ≥ 5, can be split into two separate integrals over different intervals: ∫₀₅ f(x) dx and ∫₅₇ f(x) dx.

In the first interval, from 0 to 5, f(x) is a constant function equal to 5. Thus, the integral becomes ∫₀₅ 5 dx, which simply evaluates to 5x evaluated from 0 to 5. This results in 5(5) - 5(0) = 25.

In the second interval, from 5 to 7, f(x) is the identity function, which means f(x) = x. Therefore, the integral becomes ∫₅₇ x dx, which evaluates to \((1/2)x^2\)evaluated from 5 to 7. This gives us\((1/2)(7)^2 - (1/2)(5)^2 = 49/2 - 25/2 = 24/2 = 12\).

Combining the results of the two intervals, we have ∫₀₇ f(x) dx = ∫₀₅ f(x) dx + ∫₅₇ f(x) dx = 25 + 12 = 37.

In summary, the value of the integral ∫₀₇ f(x) dx, where f(x) is defined as 5 for x < 5 and x for x ≥ 5, is equal to 37. This is obtained by evaluating the integral over the intervals 0 to 5 and 5 to 7 separately, resulting in a sum of 25 and 12, respectively.

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Answer:

x > -1/4

Step-by-step explanation:

-3/5x + 1/5 > 7/20

Subtract 1/5 from each side, you'll have to change 1/5 to 4/20 so they have the same denominator. 7/20 - 4/20 + 3/20

-3/5x > 3/20

Divide each side by -3/5

To divide fractions, you flip the second fraction and then multiply so you would have 3/20 times -5/3.

-3 * 5 = -15

20 * 3 = 60

Answer is -15/60 which simplifies to -1/4

x > -1/4

The time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

The time taken to reach 14200 with interest compounded semi-annually can be calculated by

\(A = P (1 +\frac{R}{100n})^{nT}\)

where A is the total amount at the end of the period

          P is the principal amount

          R is the rate of interest

          n is the no. of interest compounded per year

          T is the time period

We know that A = 14200

                       P = 9000

                       R = 4.25%

                       n = 2

By substituting these values, we get

                    14200 = 9000 [1 + (4.25 /200\(]^{2T}\)

                    14200/9000 =  \((1+0.02125)^{2T}\)

                              1.5778 =  \((1+0.02125)^{2T}\)

                          1.5778 =  \((1+0.02125)^{2T}\)

                           1.5778  =\((1 +0.02125)^{2T}\)

Taking logs on both sides,

                    log (1.5778) = log \((1+0.02125)^{2T}\)

                    log (1.5778) = 2T log(1 +0.02125)

                              0.198 = 2T log(1.02125)

                             0.198 = 2T (0.00913)

                             0.918 = 0.01826 T

                                    T = 0.918 / 0.01826

                                    T = 50.27 yrs

                                    T ≅ 50 years

Therefore, the time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

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Answer:

Answer:

this and that, I ain't even gonna cap I don't know the answer  

Step-by-step explanation:

The value of a₄ is,

⇒ a₄ = 108

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The value is,

⇒ a₁ = - 4

And, \(a_{n} = - 3a_{n - 1}\)

Now, We can put n = 2;

⇒ a₂ = - 3 a₁

⇒ a₂ = - 3 x - 4

⇒ a₂ = 12

Put n = 3;

⇒ a₃ = - 3 a₂

⇒ a₃ = - 3 x 12

⇒ a₃ = - 36

Put n = 4;

⇒ a₄ = - 3 a₃

⇒ a₄ = - 3 x - 36

⇒ a₄ = 108

Thus, The value of a₄ is,

⇒ a₄ = 108

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Value of a₄ in sequence is -108.

In mathematics, geometric sequence, also known as a a geometric progression, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given,

a₁ = 4 and aₙ = -3aₙ₋₁

a₂ = -3a₂₋₁

a₂ = -3a₁

a₂ = -3(4)

a₂ = -12

a₃ =  -3(-12)

a₃ = 36

a₄ = -3a₄₋₁

a₄ = -3a₃

a₄ = -3(36)

a₄ = -108

Hence, -108 is value of a₄ of the sequence.

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Answer:

74 km/hr

Step-by-step explanation:

185 km  / 2.5 hr = 74 km/hr

Answer:

\(0.0166\)

Step-by-step explanation:

Let the sample proportion be \(\hat{p}=0.14\) and the sample size be \(n=439\):

\(\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166\)

The relationship between the variables x, y and z is an illustration of similar triangles

The values of x, y and z are 6, \(\sqrt{117}\) and \(\sqrt{52\)

Right triangles are triangles with an angle measure of 90 degrees, and we have the following equivalent ratio from the triangle

\(x : 9 = 4 : x\)

Express as fraction

\(\frac x9 = \frac 4x\)

Cross multiply

\(x^2 = 36\)

Take the square root of both sides

\(x = 6\)

The value of y is then calculated using the following Pythagoras theorem

\(y = \sqrt{9^2 + x^2\)

This gives

\(y = \sqrt{9^2 + 6^2\)

\(y = \sqrt{117\)

The value of z is then calculated using the following Pythagoras theorem

\(z = \sqrt{4^2 + x^2\)

This gives

\(z = \sqrt{4^2 + 6^2\)

\(z = \sqrt{52\)

Hence, the values of x, y and z are 6, \(\sqrt{117}\) and \(\sqrt{52\)

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Answer:

p=32

Step-by-step explanation:

4+12=16

16×2=32

p=32

After substituting W = 12, h = 4, in the equation P = 2(w + h), P = 32

"An element greater than or equal to all the elements in a given set."

"It is an expression which contains an equal symbol."

For given question,

Given equation: P = 2(w + h)

W = 12, h = 4

After substituting these values in given equation,

⇒ P = 2 × (12 + 4)

⇒ P = 2 × 16

⇒ P = 32

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To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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Answer:

4. Buy at a local store where the item’s regular price is $58 and it is on sale for 10% off

Step-by-step explanation:

For the sake of someone needing help present time this is how you do it;

1st- 50 + (.89 x 11) = 59.79

2nd- 57 + (.49 x 11) = 62.39

3rd- 60 - 5 = 55

4th- 58 - 10% or 58 x .10 = 52.2: Lowest Answer

Answer:

74.9

Step-by-step explanation:

Number of students interested in only cloud computing: A - 215

Number of students interested in only machine learning: B - 177

Number of students interested in only home/city automation: C - 201

Number of students interested in none of these topics: 368 - (A + B + C - 234)

To determine the number of students interested in only cloud computing, machine learning, home/city automation, and none of these topics, we can use the principle of inclusion-exclusion.

Let's denote:

A = Number of students interested in cloud computing

B = Number of students interested in machine learning

C = Number of students interested in home/city automation

We are given the following information:

A ∩ B = 133 (interested in both cloud computing and machine learning)

A ∩ C = 157 (interested in both cloud computing and home/city automation)

B ∩ C = 119 (interested in both machine learning and home/city automation)

A ∩ B ∩ C = 75 (interested in all three topics)

We can calculate the number of students interested in only cloud computing using the formula:

(A - (A ∩ B) - (A ∩ C) + (A ∩ B ∩ C))

Substituting the given values:

(A - 133 - 157 + 75) = A - 215

Similarly, we can calculate the number of students interested in only machine learning and only home/city automation:

(B - 133 - 119 + 75) = B - 177

(C - 157 - 119 + 75) = C - 201

Finally, to find the number of students interested in none of these topics, we subtract the total number of students interested in any of the topics from the total number of students who responded to the poll:

Total students - (A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C))

Substituting the given values:

368 - (A + B + C - 133 - 157 - 119 + 75) = 368 - (A + B + C - 234)

Now, let's calculate the values:

Number of students interested in only cloud computing: A - 215

Number of students interested in only machine learning: B - 177

Number of students interested in only home/city automation: C - 201

Number of students interested in none of these topics: 368 - (A + B + C - 234)

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Answer:

Yes

Step-by-step explanation:

There are obviously six possible rolls   1  2  3  4   5  6

   picking any two of them ( rolling a 2 or three) would be

           2 out of 6 =   2/6 = 1/ 3 = 33.333%

Answer:

\(\sqrt[]{1}= 1\\\sqrt[]{169}= 13\\\sqrt{400}=20\)

Step-by-step explanation:

If you have to show work i am sorry but i got the answers all on a calculator

The required answer to this question is \(\frac{2}{243}\).

What is probability?

Use the notation ABCDEFGH for this cube, with A as the origin.

The bug cannot go back to any vertex since it must visit the other vertices in 7  movements.

The probability that the bug will find a viable route from vertex A to vertex B, called the "next vertex," is \(\frac{3}{3}\), starting at vertex A.

The chance of the bug then reaching a new vertex is \(\frac{2}{3}\). Give this a C. On the same plane at all times are A, B, and C.

We now divide the cases.

Case 1: With a chance of \(\frac{1}{3}\), the bug travels to the vertex E on the space diagonal across from A.

Since there is no path in or out of D, the bug must then visit D on the plane of ABC last.

As a result, there is only a 1 route out of 81 to D last.

Case 1: With a chance of \(\frac{1}{243} \cdot \frac{6}{9} = \frac{6}{2187}\) chance of discovering a suitable path.

Case 2: The bug has a \(\frac{1}{3}\) chance of going to vertex D on plane ABC.

The bug then has a \(\frac{1}{3}\) probability because there is only a 1 path between it and a point E on the opposite face.

The bug is then given an option between two vertices on the face across from ABCD.

As a result, there is a \(\frac{2}{3}\) chance of discovering a direct route to F.

After then, there is only a 1 way out of 9 movements to visit the remaining two vertices on that face.

The probability in this situation can be multiplied to obtain the value \(\frac{2}{243} \cdot \frac{6}{9} = \frac{12}{2187}\)

The probability for these two scenarios are added to provide \(\frac{18}{2187} = {\textbf{(C) }\frac{2}{243}}\).

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The resulting function -f(x) · g(x) is -x³ + x² + 4x - 4, and its domain is all real numbers.

To perform the function operation -f(x) · g(x), we first need to evaluate each function separately and then multiply the results.

Given:

f(x) = x - 2

g(x) = x² - 3x + 2

First, let's find -f(x):

-f(x) = -(x - 2)

= -x + 2.

Next, let's find g(x):

g(x) = x² - 3x + 2

Now, we can multiply -f(x) by g(x):

(-f(x)) · g(x) = (-x + 2) · (x² - 3x + 2)

= -x³ + 3x² - 2x - 2x² + 6x - 4

= -x³ + x² + 4x - 4

To find the domain of the resulting function, we need to consider the restrictions on x that would make the function undefined.

In this case, there are no explicit restrictions or division by zero, so the domain is all real numbers, which means the function is defined for any value of x.

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Answer:

5/2

Step-by-step explanation:

5/2= 2 1/2

while 16/9=1 7/9

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

1/4

Step-by-step explanation:

2^7/2^9 = 1/2^2

Answer:

By the amount of time it took you guys to get there

Step-by-step explanation:

For example, if I start walking at 8:55 and arrive by 9:10, then it took me about 15 minutes to get there.

If you start walking at 9:10 and arrive by 9:20, it took you 10 minutes to get there meaning you walked faster.

Hope I helped.

When continuous data points such as age or GPA are divided into groups, they have been reduced to discrete data.

This process of dividing continuous data into discrete categories is called "discretization" or "binning". Discretization can be useful in some cases, such as when we want to simplify data analysis or make data more understandable to non-experts. However, it can also lead to information loss, as we are losing some of the detailed information contained in the original continuous data.

Continuous data is a type of data that can take on any value within a given range. For example, age can be any value between 0 and infinity, and GPA can be any value between 0 and 4.0 (or higher, in some cases). These types of data are typically measured using numerical scales, such as inches, centimeters, or percentages.

However, when we divide continuous data points into groups, we are creating categories that can only take on certain values. For example, if we divide ages into groups of 10 years (e.g., 0-9, 10-19, 20-29, etc.), we are reducing the continuous data to a set of discrete categories. Similarly, if we divide GPAs into categories (e.g., 0-1.0, 1.1-2.0, 2.1-3.0, etc.), we are also reducing the continuous data to a set of discrete categories.

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