a 12 inch thin‑crust cheese pizza is cut equally into eight slices. assuming a uniform distribution of sauce and toppings,

The Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

What is Boolean expression?

A Boolean expression is an expression or equation that evaluates to true or false. It includes the use of logical operators such as AND, OR, and NOT, as well as comparison operators such as equal to (=), greater than (>), less than (<), and more.

The Boolean expression that is not equivalent to the expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

Let's break down each option and evaluate its equivalence to the given expression:

A. (num < 0) AND (num * -1 = 10)

This expression checks if "num" is negative and if the absolute value of "num" is equal to 10. It does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

B. (num < -10) OR (num = -10)

This expression checks if "num" is less than -10 or if "num" is exactly equal to -10. It also does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

C. (num * -1 > 10) OR (num = -10)

This expression checks if the negative value of "num" is greater than 10 or if "num" is exactly equal to -10. Although it involves the negative value of "num," it represents the condition "num * -1 > 10" when "num" is positive. Therefore, it is equivalent to the given expression.

D. NOT num * -1 < 10

This expression checks if the negative value of "num" is not less than 10. While it involves the negative value of "num," it does not directly represent the condition "num * -1 ≥ 10." Additionally, the use of "NOT" operator flips the condition, which makes it different from the original expression. Hence, it is not equivalent.

Therefore, the Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

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Answer:

C is  not true.

Step-by-step explanation:

√9/√4

= 3/2 which is rational.

Answer:

C.

\({ \sf{ \frac{ \sqrt{9} }{ \sqrt{4} } \: is \: an \: irrational \: number}}\)

Step-by-step explanation:

(√9)/(√4) is rational, because

\( \frac{ \sqrt{9} }{ \sqrt{4} } = \frac{3}{2} \)

Answer:

60

Step-by-step explanation:

Answer: f(t) = -16(t - 1)2 + 24

Step-by-step explanation:        

Here f(t) represents the path of the T-shirt in t seconds.

Since, It is given,

Initially, t = 0 and f(t) = 8

And, For t = 1, f(t) = 24

Thus, (0,8) and (1,24) are the points of given parabola.

⇒These points must satisfy the equation of the parabola.

When we put x = 0 and y = 8 in all the equations one by one,

We found, Equations  f(t) = -16(t - 1)2 - 24, f(t) = -16(t + 1)2 - 24 are not satisfying.

Therefore, they can not be the equation of the given parabola.

Again by putting x = 1 and y = 24,

f(t) = -16(t + 1)2 + 24 is not satisfying.

Therefore f(t) = -16(t + 1)2 + 24 also can not be the equation of the given parabola.

Thus, Only equation f(t) = -16(t - 1)2 + 24 is satisfied by the points (0.8) and (1,24).

⇒ f(t) = -16(t - 1)2 + 24 can be the equation of the given path of T-shirt.

Step-by-step explanation:

Answer:

Step-by-step explanation:

max 24 is at 1 sec

now, consider the equation:

f(t)=-16(t-h)^2+k,

since (h,k) is vertex, where h is the x value (time in this case), and k is y value (height in this case),

we put in 1 for h and 24 for k

now we have  f(t)=-16(t-1)^2+24

The quilter wants to make a design using the Golden Ratio, specifically focusing on the ratio of triangle heights. To find the height ratio, we can use the properties of the Golden Ratio.

The Golden Ratio is a mathematical concept where two quantities are in proportion if their ratio is equal to the ratio of their sum to the larger of the two quantities. Mathematically, it can be represented as (a + b) / a = a / b, where a is the larger quantity and b is the smaller quantity.

In this case, the quilter wants to find the ratio of triangle heights. Let's assume the height of the larger triangle is a and the height of the smaller triangle is b. According to the Golden Ratio, we have (a + b) / a = a / b.

To solve for the height ratio, we can cross-multiply and simplify the equation. We get a^2 + ab = a^2, which simplifies to ab = a^2 - a^2, or ab = 0.

Since ab = 0, we can conclude that the height ratio of the triangles is 0. This means that the height of the smaller triangle is 0, while the height of the larger triangle can be any positive value.

In summary, when using the Golden Ratio to determine the ratio of triangle heights, the ratio is 0.

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Line segment BD is 12 units

Using the pythagorean theorem a^2 + b^2 = c^2

Answer:

Step-by-step explanation:

45 47

Concluimos que hay 8 libros de aritmética.

Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.

Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.

Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:

N = 10 + X

Y usando la relación de arriba, podemos escribir:

X = (4/9)*N = (4/9)*(10 + X)

Ahora podemos resolver esto para X.

X*(9/4) = 10 + X

X*(9/4) - X = 10

X*(5/4) = 10

X = (4/5)*10 = 8

Concluimos que hay 8 libros de aritmética.

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Therefore, x = -1, 1 + √2, and 1 - √2 are the answers to the equation f(x) = g(x). The answer is not any of the above because none of these methods correspond to any of the possible answers. (E).

A formula that expresses the connection between two phrases on each side of a symbol. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2. In the provided example, the variable x exists.

First, we need to set up the equation f(x) = g(x):

x² - 3x - 4 = |x + 3| - 2

We can split this equation into two cases: one where x + 3 is non-negative, and one where x + 3 is negative.

Case 1: x + 3 ≥ 0

In this case, the absolute value bars are unnecessary, and we can rewrite the equation as:

x² - 3x - 4 = x + 1

Simplifying this equation, we get:

x² - 4x - 5 = 0

Factoring the left-hand side, we get:

(x - 5)(x + 1) = 0

So the solutions for this case are x = 5 or x = -1.

Case 2: x + 3 < 0

In this case, we need to negate the expression inside the absolute value bars, giving us:

x² - 3x - 4 = -(x + 3) - 2

Simplifying this equation, we get:

x² - 2x - 1 = 0

Using the quadratic formula, we find that the solutions for this case are:

x = 1 ± √2

Therefore, the solutions to f(x) = g(x) are x = -1, 1 + √2, and 1 - √2. None of these solutions match any of the answer choices, so the answer is none of the above (E).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given possible roots have the form that we'd get by using the quadratic formula, so let's start with that.  Here the coefficients are {2, -6, 3}, and so the discriminant (b^2 - 4ac) is (-6)^2 - 4(2)(3), or 36 - 24 = 12.

Because the discriminant is positive we know immediately that there are two different real roots.

      -(-6) ± √12         6 ± √12

x = ------------------ = ----------------     These are equivalent to Answers E and F.

            2(2)                    4

The possible coordinates of point l are (7,3),(7,-13),(-5,3),(-5,-13),(9,1),(9,-11),(-7,1), and (-7,-11).

Given that:-

Coordinates of k = (1,-5)

Distance between point k and point l = 10 units.

We have to find the coordinates of point l.

Let the coordinates of point l be (x,y).

By using distance formula, we can write:-

\(\sqrt{(x-1)^2+(y+5)^2} =10\)

Squaring on both sides, we get:-

\((x-1)^2+(y+5)^2=100\)

For, integer coordinates, the possibilities are 36+ 64 or 64+36.

Hence, we can write,

\((x-1)^2+(y+5)^2 = 36 + 64 \\or\\(x-1)^2+(y+5)^2 = 64 + 36\)

Hence,

\((x-1)^2 = 36\)

x - 1 = 6 or x -1 = -6

x = 7 , -5

\((y+5)^2 =64\)

y + 5 = 8 or y + 5 = -8

y = 3,-13

or

\((x-1)^2=64\)

x - 1 = 8 or x - 1 = -8

x = 9,-7

\((y+5)^2\)

y + 5 = 6 or y + 5 = -6

y = 1,-11

Hence, the possible values of coordinates of point l are (7,3),(7,-13),(-5,3),(-5,-13),(9,1),(9,-11),(-7,1), and (-7,-11).

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If a tree casts a shadow 21 feet long and a yardstick (which is 3 feet tall) casts a shadow 2 feet long, then the tree is 31.5 feet tall.

Let h be the height of the tree. Then we have the proportion:

\(h/21=3/2\)

Simplifying this proportion, we have:

\(h=21*3/2 = 31.5\)

Therefore, the height of the tree is 31.5 feet.

To see why this proportion works, imagine that the tree and the yardstick are placed next to each other in the sun, with the yardstick closer to the observer. At the same time, the shadows of the tree and the yardstick are projected onto the ground. We know the length of the yardstick's shadow is 2 feet, and we can measure the height of the yardstick as 3 feet. We also know the length of the tree's shadow is 21 feet. By setting up the proportion as above, we are essentially saying that the ratios of the heights of the tree and yardstick to their respective shadow lengths must be equal. Solving for the height of the tree gives us the answer above.

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The key features of the quadratic equation y = - x² - 2x + 1 is  line of symmetry is x = -1; vertex = (h, k) = (-1, 2); y-intercept is (0, 1);  

the domain = -∞ ≤ x ≤ ∞ and the range = 2 ≥ y ≥ -∞.

What are the key features of a quadratic function?

Three properties that are universal to all quadratic functions:

1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior);

2) The domain of a quadratic function is all real numbers; and

3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

According to the given question:

The given equation is y = - x² - 2x + 1

The general vertex form is y = a·(x - h)² + k

h = -b/(2·a) = 2/(-2) = -1

k = f(h) = -(-1)² - 2×(-1) + 1 = 2

Therefore;

1) The line of symmetry goes through the vertex and the line of symmetry is x = -1

2) The vertex = (h, k) = (-1, 2)

3) The y-intercept is the coordinate of the point where x = 0 which is  

   (0, 1)

4) The domain are the possible x-values, therefore,

    the domain = -∞ ≤ x ≤ ∞

5) The range is the possible values y-values.

    On plotting the graph, we have the range = 2 ≥ y ≥ -∞

Complete question:

Identify the key features of the Quadratic Function y = - x² - 2x + 1

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Answer:

Step-by-step explanation:Typical breakdown is 66-75% of a show is content (22 minutes of total content for a half hour; 42-45 minutes for an hour). In a typical 30 minute show on network TV, you'll usually get 3 breaks of about 2-3 minutes each. The numbers that have been mentioned are not for televised sports, which have more commercials.

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer: I

Step-by-step explanation:

For various levels of output, businesses in a competitive market have the following production costs. Right now, the price on the market is $4. Total Cost Quantity 0 1 10 2 13 3 18 4 25 34. Therefore,

1. Each firm maximizes profit by supplying 2 units where MR = MC.

2. At $4 market price, market not in long-run equilibrium as ATC ($6.5) > price.

3. Market reaches long-run equilibrium at $6, the minimum point of ATC curve.

To determine the units each firm will supply to maximize profit and calculate the profit, we need to examine the cost and revenue associated with each quantity of output.

Quantity                    Total Cost

0                                       1

1                                       10

2                                      13

3                                      18

4                                     25

1. To find the quantity that maximizes profit for each firm, we need to compare the marginal cost (MC) and marginal revenue (MR) at each quantity level.

Quantity   Total Cost   MC       MR

0                  1                   -       -

1                  10                 9       4

2                  13                 3       4

3                  18                 5       4

4                  25                 7       4

To maximize profit, a firm will produce where MR equals MC. Looking at the table, we can see that at a quantity of 2, the MR and MC are equal. Therefore, each firm will supply 2 units to maximize profit.

2. To determine if the market is in long-run equilibrium at a market price of $4, we need to compare the market price with the average total cost (ATC) for each firm. If the market price is equal to or greater than the ATC, the market is in long-run equilibrium.

Let's calculate the ATC for each firm at a quantity of 2:

\(ATC = \frac{Total Cost}{Quantity}\)

\(ATC = \frac{13}{2}\)

ATC = 6.5

The ATC for each firm is $6.5, which is greater than the market price of $4. Therefore, the market is not in long-run equilibrium because firms are not covering their costs and would not continue to operate in the long run.

3. To determine the price at which the market will be in long-run equilibrium, we need to find the minimum point of the average total cost (ATC) curve. This point represents the price at which firms can cover their costs and earn a normal profit in the long run.

Looking at the table, we can observe that the minimum ATC occurs at a quantity of 3. Let's calculate the ATC at this quantity:

\(ATC = \frac{Total Cost}{Quantity}\)

\(ATC = \frac{18}{3} = 6\)

Therefore, the market will be in long-run equilibrium at a price of $6, which corresponds to the minimum point of the ATC curve.

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Answer:

Minimum Price: $230,700

Maximum Price: $261,900

Explanation:

To find the minimum and maximum prices, we need to find the z-score of the middle 70%

70% = 0.7

1 - 0.7 = 0.3

0.3/2 = 0.15

Then the inverse normal of 0.15 is -1.04

Therefore,

and

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.

This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.

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Answer: C

Step-by-step explanation:

13-3=10

Answer:

9.34

Step-by-step explanation:

add 6 then mulitiply 11-1 xC=9.34

Answer:

Find the cost of supplies charged by the instructor for each student.

The coordinate of the vertices of the triangle are

A triangle is a polygon with three sides.

The vertices of a triangle are the points where the sides of the triangle intersect.

Let

Since the midpoints of the sides of the triangle are

We know that the coordinates of the midpoint of a line with coordinates

x = (x' + x")/2 and y = (y' + y")/2

So, using these, we have that the midpoints of the sides are

For coordinates (2,4) we have that

(x₁ + x₂) = 4 (1) and

(y₁ + y₂) = 8  (2)

For coordinates (1/2,7/2) we have that

(x₁ + x₃) = 1 (3) and

(y₁ + y₃) = 7 (4)

For coordinates (5/9,9/2) we have that

(x₂ + x₃) = 10/9 (5)and

(y₂ + y₃) = 9 (6)

From equation (1) x₁ = 4 - x₂ (7)

From equation (2) y₁ = 8 - y₂ (8)

Substituting equations (7) and (8) into (3) and (4), we have

(x₁ + x₃) = 1 (3) and

(y₁ + y₃) = 7 (4)

4 - x₂  + x₃ = 1  and

8 - y₂ + y₃ = 7

- x₂  + x₃ = 1 - 4 and

- y₂ + y₃ = 7 - 8

- x₂  + x₃ =  - 3 (9) and

- y₂ + y₃ =  - 1 (10)

Now, adding equations (5) and (9), we have

x₂ + x₃ = 10/9 (5)

- x₂  + x₃ =  - 3 (9)

2x₃ = 10/9 - 3

2x₃ = (10 - 9)/9

2x₃ = 1/9

Dividing through by 2, we have

x₃ = 1/9 ÷ 2

x₃ = 1/18

Substituting this into equation (9), we have

- x₂  + x₃ =  - 3

- x₂  + 1/18 =  - 3

- x₂  = - 3 - 1/18

- x₂  = (- 54 - 1)/18

- x₂  = - 55/18

Dividing through by -1, we have

x₂  = 55/18

Substituting this into equation (1), we have

(x₁ + x₂) = 4 (1)

x₁ + 55/18 = 4

x₁ = 4 - 55/18

x₁ = (72 - 55)/18

x₁ = 17/18

Also, adding equations (6) and (10), we have

y₂ + y₃ = 9 (6)

+

- y₂ + y₃ =  - 1 (10)

2y₃ = 9 - 1

2y₃ =  8

y₃ =  8/2

y₃ =  4

Substituting this into equation (10), we have

- y₂ + y₃ =  - 1 (10)

- y₂ + 4 =  - 1

- y₂ =  - 1 - 4

- y₂ =  - 5

Dividing through by -1, we have

y₂ = 5

Substituting this into equation (2), we have

(y₁ + y₂) = 8  (2)

y₁ + 5 = 8

y₁ = 8 - 5

y₁ = 3

So, the coordinate of the vertices are

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Step-by-step explanation:

a diagram is necessary. please provide a diagram.

If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is \(\frac{dP}{dt}=200\)

The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.

dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable

According to the question,

Size of population at t time = P(t)

Also given ,The differential equations have a linear growth in the size of the population.

So, The degree of the variable must be one. And the equation of the population will be quadratic.

Therefore , dP/dt = 200 tells us the rate change of population with respect to time.

A derivative of linear function is constant .

Hence , option B is correct.

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The angle of depression should be 26.57 degrees so the security camera should be directed downwards from the wall.

To find the angle of depression, we can use the tangent function. Let's call the angle of depression "θ". The tangent of an angle is equal to the opposite side (the difference in height between the camera and the spot) divided by the adjacent side (the horizontal distance between the camera and the spot). So, in this case:

tan(θ) = 6/12 = 1/2

Now that we have the tangent value, we can use the inverse tangent function (arctan) to find the actual angle:

θ = arctan(1/2)

Using a calculator, we can find that the angle of depression is approximately 26.57 degrees. So the security camera should be directed downward at an angle of 26.57 degrees to be directed at the spot 6 feet above the floor and 12 feet from the wall.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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