Sally can plant 14 plants in 2 hours. How many plants can Sally plant in 6 hours?

To construct a truth table for the given logical expression using De Morgan's Law, we'll break it down step by step and apply the law to simplify the expression.

Let's start with the given expression:

Xyz + X(Y Z)' + X'(Y + Z) + (Xyz)' (X + Y')(X' + Z')(Y' + Z')

Step 1: Apply De Morgan's Law to the term (Xyz)'

(Xyz)' becomes X' + y' + z'

After applying De Morgan's Law, the expression becomes:

Xyz + X(Y Z)' + X'(Y + Z) + (X' + y' + z')(X + Y')(X' + Z')(Y' + Z')

Step 2: Expand the expression by distributing terms:

Xyz + XY'Z' + XYZ' + X'Y + X'Z + X'Y' + X'Z' + y'z' + x'y'z' + x'z'y' + x'z'z' + xy'z' + xyz' + xyz'

Now we have the expanded expression. To construct the truth table, we'll create columns for the variables X, Y, Z, and the corresponding output column based on the expression.

The truth table will have 2^3 = 8 rows to account for all possible combinations of X, Y, and Z.

Here's the complete truth table:

```

| X | Y | Z | Output |

|---|---|---|--------|

| 0 | 0 | 0 |   0    |

| 0 | 0 | 1 |   0    |

| 0 | 1 | 0 |   0    |

| 0 | 1 | 1 |   1    |

| 1 | 0 | 0 |   0    |

| 1 | 0 | 1 |   0    |

| 1 | 1 | 0 |   1    |

| 1 | 1 | 1 |   1    |

```

In the "Output" column, we evaluate the given expression for each combination of X, Y, and Z. For example, when X = 0, Y = 0, and Z = 0, the output is 0. We repeat this process for all possible combinations to fill out the truth table.

Note: The logical operators used in the expression are:

- '+' represents the logical OR operation.

- ' ' represents the logical AND operation.

- ' ' represents the logical NOT operation.

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The value of arc angle EFG is 160⁰.

The value of arc angle EHG is 200⁰.

The length of arc EHG is 200⁰

The value of arc angle FEG is 280⁰.

The value of EFG is calculated as follows;

arc ∠EFG = m∠EDF  + m∠FDG (intersecting chord theorem)

arc ∠EFG = 80⁰  + 80⁰

arc ∠EFG = 160⁰

The value of arc EHG is calculated as follows;

arc EHG = 360 - (160⁰) (sum of angles in a circle)

arc EHG = 200⁰

arc length EHG = 200⁰

The value of arc FEG is calculated as follows;

arc FEG = 360 - 80⁰ (sum of angles in a circle)

arc FEG = 280⁰

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Answer:

4th picture is the correct one :)

Answer:

72cm^3

Step-by-step explanation:

4 *3=12, 12*6=72

Answer:

72 cm.

Step-by-step explanation:

Multiply the length and width (4 x 3)

Multiply the product of that by the height (12 x 6)

And there you have it, 72 cm as your answer!

Answer:

The process capability index for this system is 0.9103

Step-by-step explanation:

Upper specification = 1.649 inches

Lowe Specification = 1.507 inches

Mean = 1.57 inches

Standard Deviation = 0.026 inches

Process Capability Index = PCI

PCI = (Upper specification - lower specification)/6(standard deviation)

So, we get,

PCI = (1.649 - 1.507)/((6)(0.026))

PCI = 0.142/0.156

PCI = 0.9102564

To four decimal places, we get,

PCI = 0.9103

Answer:

Less than

Step-by-step explanation:

1/3 * 7/15 is less than 1/3 because 1/3 * 7/15 is being multiplied by a number that is less than 1.

The Lorentz transformation is the standard tool for the transformation of the position coordinates and time of events in special relativity.

We will use the following set of formulas to derive the answer as follows: x' = γ(x − vt)

y' = y

z' = z

t' = γ(t − vx/c²) where γ = 1/√(1−v²/c²)

The difference between the two events is given by:

Δx' = x'₂ − x'₁ = γ(x₂ − vt₂) − γ(x₁ − vt₁)

= γ(Δx − vΔt)

Δy' = y'₂ − y'₁

= y₂ − y₁

Δz' = z'₂ − z'₁

= z₂ − z₁

Δt' = t'₂ − t'₁

= γ(t₂ − vx₂/c²) − γ(t₁ − vx₁/c²)

= γ(Δt − vΔx/c²)A

The Lorentz transformations are an essential tool in the theory of special relativity. They can be used to calculate the position and time coordinates of events in different inertial frames that are in relative motion. The difference between two events in two different frames can be calculated using the equations derived above. The Lorentz factor γ is an important quantity that determines the relationship between the time and position coordinates in two different frames.

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Answer:

8L - 2 = P

Step-by-step explanation:

Please, just one question per post.  I'll focus on #15

As a reminder, the formula for the perimeter of a rectangle is

P = 2L + 2W, where L is the length and W the width.

Next, we represent the width in terms of the length:  W = 3L - 1.

We want the perimeter of this rectangle in terms of the length, L, with the width, W, not appearing in the final result.

Here P = 2L + 2W = 2L + 2(3L - 1), or

P as a function of L = 2L + 6L - 2 = 8L - 2 = P

Answer:

Use the given functions to set up and simplify .

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Step-by-step explanation:

37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

The area between 550 and 725 on a standardized test of educational achievement is equal to the percentage of students whose scores fall within one standard deviation (or 68%) of the mean score of 600. This can be expressed mathematically as:

Percentage = (725 - 550) / (2 * 50) = 37.5 / 100 = 37.5%

To explain in more detail, a standard deviation is a measure of the spread of a dataset around its mean value. The mean value in this case is 600, and the standard deviation is 50. Therefore, one standard deviation from the mean is calculated by subtracting or adding the standard deviation (50) from the mean (600), giving a range of 550 to 650.

Since the area in question spans across two standard deviations (550 to 725), the area is calculated by subtracting the lower range (550) from the upper range (725) and then dividing it by two standard deviations (100). This gives us the area, which is 37.5%.

To summarize, 37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

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Answer: the car is cheeper 20 miles better

Step-by-step explanation:

Answer:

The number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

Step-by-step explanation:

The possible pathways are as follows:

(0, 0) → (1, 0) → (2, 0) → (3, 0) → (3, 1) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

Thus, the number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

The additional information required to prove  that ΔXYZ and ΔFEG are congruent is  ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE. So option 1 and 5 are correct.

Here in the figure it is given that ∠F and ∠X are congruent. To prove the triangle is congruent we have to prove that either two sides including the angles are congruent or another angle and included side is congruent.

When ∠Z ≅ ∠G and XZ ≅ FG, two angles and included sides are congruent, so triangles are congruent.

∠Z ≅ ∠G and ∠Y ≅ ∠E , we can not apply ASA, since three angles are mentioned

XZ ≅ FG  and ZY ≅ GE , Two sides are given, ASA cannot be applied, we need two angles

XY ≅ EF and ZY ≅ FG, is not possible.

∠Z ≅ ∠G and XY ≅ FE, one corresponding side and two angles are equal, so ΔXYZ ≅ ΔFEG according to ASA.

So, the correct answer is option 1 and option 5.

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The complete question is as follows and image is given below

What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and ∠Y ≅ ∠E

XZ ≅ FG and ZY ≅ GE

XY ≅ EF and ZY ≅ FG

∠Z ≅ ∠G and XY ≅ FE

Answer:

1 and 5 are correct

Step-by-step explanation:

we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)

and tan(A-B)= (tanA-tanB)/(1+tanAtanB)

tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)

tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)

now add the equation (1) and (2) which is LHS of question. So we get:

{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS

Hence proved.

Answer:

68

Step-by-step explanation:

81 +81 is 162

298-162=136

136/2=68

Answer:

y=-3x+4

Step-by-step explanation:

im assuming that you need the equation of the table

to find slope, y2-y1/x2-x1    10-4/-2-0

6/-2=-3   slope=-3  

y=mx+b   just sub in the numbers from a point in the table

10=-3(-2)+b

10=6+b

b=4

y=-3x+b

Answer:

The probability is 9/100

Step-by-step explanation:

First, we know that 70% of the students are with brown eyes. Since we have a total of 20 students, this corresponds to 70/100 * 20 = 14 students

The number of students without brown eyes is thus 20 -14 = 6 students

Now, the probability of selecting a student without brown eyes is 14/20 = 7/10 while the probability of selecting a student with brown eyes is 6/20 = 3/10

Now the probability of selecting two students without brown eyes mean, the first selected is without brown eyes and also the second selected is without brown eyes.

In probability, once we have the work and, we multiply.

So our answer here is 3/10 * 3/10 = 9/100

y = √(x+1)-3

\(Graph {y = sqrt(x+1)-3 [-10, 10, -5, 5]}\)

Graph is a diagram that is used to represent data or information. It is a visual representation of data in the form of points, lines, bars, and other shapes. Graphs can be used to show relationships between different quantities, to compare data, and to show changes over time. Graphs are useful for quickly conveying information in an easy-to-understand visual format. They are especially useful for displaying complex data in an intuitive way.

For example, A bar graph can be used to compare the average monthly temperature of five different cities. The x-axis would show the five cities, while the y-axis would show the temperature. Bars would be drawn to represent the temperature of each city. This would make it easy to visually compare the temperatures of the different cities.

The graph of y = √(x+1)-3 is shown above.

To get three points to graph, let's work through the following examples:

When x = 0, y = √(0+1)-3 = 0-3 = -3

When x = 4, y = √(4+1)-3 = 2-3 = -1

When x = 8, y = √(8+1)-3 = 3-3 = 0

Therefore, the three points to graph are (0,-3), (4,-1), and (8, 0).

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The correct code to swap elements 0 and 1 in the given array {7, 8, 10, 11, 4, 3} would be: int save = array[0];array[0] = array[1];array[1] = save;

The code above uses a temporary variable "save" to store the value of the first element of the array, then assigns the value of the second element to the first element, and finally assigns the value of "save" (which holds the original value of the first element) to the second element.

The other lines of code following this swap code would perform additional operations on the array, but they do not correctly swap the first two elements of the array.

For example, the line array[0] = array[1]; in the given code only assigns the value of the second element to the first element, effectively overwriting the original value of the first element before it can be saved. Similarly, the line array[1] = array[0]; then assigns the overwritten value of the first element to the second element, resulting in no swap at all.

Therefore, the correct code to swap the first two elements of the array is the code I mentioned at the beginning of this answer.

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Which of the following swaps elements 0 and 1 in array?

Answer:

for level 1: x=36

because you just need to do 180-144

for level 2: x = 127

you can just so 180-15-38

for level 3: x = 36

because you start by setting an equation like this:

92 + (2x+16) = 180

subtract 92 from both sides, then subtract 16 from both sides, and finally divide both sides by 2 to get 36

A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. The probability of an up movement is approximately 0.4704, which corresponds to answer choice A.

The probability of an up movement in a binomial tree is given by the formula:

\(p = (e^{r - q} * u - d) / (u - d)\)

where r is the interest rate, q is the dividend yield, u and d are the up and down factors, respectively.

In this case, r = 0.03/12 = 0.0025 (monthly interest rate),

q = 0.01/12 = 0.000833 (monthly dividend yield), \(u = e^{\sigma * \sqrt{1/12}} = e^{0.16 * \sqrt{1/12}}\) ≈ 1.0403, and

d = 1/u ≈ 0.9614.

Substituting these values into the formula, we get:

\(p = (e^{0.0025 - 0.000833} * 1.0403 - 0.9614) / (1.0403 - 0.9614)\) ≈ 0.4704

Hence, the correct option is A) 0.4704.

The complete question is:

A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?

0.4704

0.5065

0.5592

0.5833

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Answer:

y = -1x + 2

Step-by-step explanation:

We need to find y = mx + b

Use the following equation

\(\frac{y_2-y_1}{x_2-x_1}\)

Plug in the values

\(\frac{-1-0}{3-2}\)  = \(\frac{-1}{1} = -1\)

We have found the slope(m) which is -1

We have to find y-int b

Plug in any given x,y into the slope formula

-1 = -1(3) + b

-1 = -3 + b

2 = b

At last the formula is

y = -1x + 2

Rate by which change in the area of the circle when radius is 2 inches with the given given rate of change of circumference is equal to 8 inches per second.

As given in the question,

Let 'r' be the radius of the circle

And 'A' be the area of the circle

Circumference of a circle 'C' = 2πr

Rate of change of circumference dC/dr = 4 inches per second

C = 2πr

⇒dC/dr = 2π(dr/dt)

⇒4 = 2π(dr/dt)

⇒(dr/dt) = 2 / π

Area of the circle 'A' = πr²

⇒dA/dt = 2πr (dr/dt)

When r = 2inches and dr/dt = 2/π

⇒dA/dt = 2π × 2 × ( 2 / π )

⇒dA/dt = 8 inches per second

Therefore, the rate of change of area of the circle when radius is 2 inches is equal to 8 inches per second.

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Answer: m = 5

Step-by-step explanation:

subtract -5 - 5 =10

Add 10 on both sides

simplify

Add 3 on both sides

simplify again

Den divide 5 on both sides

Answer: m = 5

HOPE DIS HELPS YU AND IS RII

Answer:

t = 7

I hope it's helps you

Answer:

Part A)

5th and 6th Choices

Part B)

\(\displaystyle y=\frac{1}{4}x^2-x-4\)

Step-by-step explanation:

We are given a parabola with focus at (2, -4) and the directrix given by y = -6.

Part A)

Since our directrix is an equation of y, the distance from any point (x, y) on the parabola to the directrix will simply be the absolute value of the difference of the y-values. Hence:

\(d_1=|y-(-6)|=|y+6|\)

Again, we will use the distance formula. Let the point (x, y) be (x₂, y₂) and our focus (2, -4) be (x₁, y₁). Then by the distance formula:

\(d_2=\sqrt{(x-2)^2+(y-(-4))^2}=\sqrt{(x-2)^2+(y+4)^2\)

Hence, our answers are the 5th and 6th choices.

Part B)

By definition, any point (x, y) on the parabola is equidistant to the focus and the directrix. Hence:

\(\sqrt{(x-2)^2+(y+4)^2}=|y+6|\)

Square both sides. We may remove the absolute value as anything squared yields a positive. Hence:

\((x-2)^2+(y+4)^2=(y+6)^2\)

Square:

\((x^2-4x+4)+(y^2+8y+16)=(y^2+12y+36)\)

Rearrange:

\((x^2-4x+20)-(36)=(y^2-y^2)+(12y-8y)\)

Combine like terms:

\(x^2-4x-16=4y\)

Divide both sides by 4. Hence, our equation is:

\(\displaystyle y=\frac{1}{4}x^2-x-4\)