Find the circumference of the pizza to the nearest tenth.

To find the solution for this system in a graph manner we need to graph both equations and look for the point at which they intercept.

For the first equation we know that the y-intercept is 4. So we will calculate the x-intercept by making y=0.

The first line goes through the points (0,4) and (4/3, 0).

For the second equation we know that the y-intercept is -2. So we will calculate the x-intercept by making y-.

The second line goes through the points (0,-2) and (2/3,0).

To graph each line we can draw a line between the points that belong to it. We have:

Since the solution for the system is the point at which they cross, the ordered pair is (1,1).

The value of Vou = 14, ||V|| = √(106) and ||U|| = √(3).

The cosine of the angle between U and V is (14) / (√(106)√(3)).

To find the following for the vectors V = 9i - 5k and U = i + j + k:

A. Vou and Vol:

Vou is the dot product of vectors V and U, which is given by:

Vou = V · U = (9i - 5k) · (i + j + k)

= (9i - 5k) · i + (9i - 5k) · j + (9i - 5k) · k

= 9i · i - 5k · i + 9i · j - 5k · j + 9i · k - 5k · k

= 9 - 5(0) + 0 - 5(0) + 0 - 5(-1)

= 9 + 0 + 0 + 0 + 0 + 5

= 14

Now, Vol is the dot product of vectors V and U, which is given by:

Vol = V · U = ||V|| ||U|| cos(θ)

Where ||V|| represents the magnitude of vector V, ||U|| represents the magnitude of vector U, and θ is the angle between the two vectors.

B. The cosine of the angle between U and V:

To find the cosine of the angle between U and V, we can use the dot product formula:

cos(θ) = (V · U) / (||V|| ||U||)

||V|| = √((9²) + 0 + (-5²)) = √(81 + 25) = √(106)

||U|| = √((1²) + (1²) + (1²)) = √(3)

Substituting the values into the formula:

cos(θ) = (14) / (√(106) √(3))

Therefore, the cosine of the angle between U and V is (14) / (√(106)√(3)).

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To calculate the cost of each cookie, we can use the formula:

\(\[ \text{Cost per cookie} = \frac{\text{Total amount spent}}{\text{Total number of cookies}} \]\)

Given that Mr. A spent \(\$40\) on cookies and distributed 8 cookies among his four children, we can substitute these values into the formula:

\(\[ \text{Cost per cookie} = \frac{\$40}{8} = \$5 \]\)

Hence, each cookie costs \(\$5\).

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Answer: A. Obstacle

Step-by-step explanation: They have the same meaning.

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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Answer:

24

Step-by-step explanation:

5×5 +3 - 4

25 +3 - 4

28 - 4

24

Answer:

24

Step-by-step explanation:

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Answer:

I think it is b and d .

Step-by-step explanation:

Answer:

Hello again! Both D and B are rectangles.

Step-by-step explanation:

You know that a rectangle has 4 sides like a quadrilateral but it is different. Both of the oppiosite sides are the same length. C would not be one because it is not connected therefore it is not a full shape. Because of  A´s even sides, A is not a rectangle. I hope this helps! :]

Sorry I messed up! :]

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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Answer:

x = 18, y = 6

Step-by-step explanation:

Given the two parallel lines cut through by a transversal, thereby creating perpendicular lines. According to the Perpendicular Transversal Theorem, if a transversal is perpendicular to one of the parallel lines, then it means that the same transversal must also be perpendicular to the other parallel line.

Since perpendicular lines form 90° angles, then it means that each of the angles formed by the intersection of the parallell lines and transversal has a measure of 90°.  

Thus, we can infer that (3x + 6y)° = 90°, and (5x)° = 90°.  

Start by dividing both sides by 5 to solve for x:

5x° = 90°

\(\large\mathsf{\frac{\:5x^{\circ}}{5}\:=\:\frac{\:90^{\circ}}{5}}\)

x = 18°

Substitute the value of x into the (3x + 6y)° to solve for y:

3x° + 6y° = 90°

3(18)° + 6y = 90°

54° + 6y° = 90°

Subtract 54° from both sides:

54° - 54° + 6y° = 90° - 54°

6y° = 36°

Divide both sides by 6 to solve for y:

\(\large\mathsf{\frac{\:6y^{\circ}}{6}\:=\:\frac{\:36^{\circ}}{6}}\)

y = 6°

Therefore, x = 18, and y = 6.

The surface area of the triangular prism is 152 sq, ft.

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

The surface area of the triangular prism is given as:

SA = bh + (b1 + b2 + b3)l

Here, b = 6, h = 4, b1 = b2 = 5, b3 = 6 and l = 8.

Substituting the values we have:

SA = (6)(4) + (5 + 5 + 6) (8)

SA = 24 + (16)(8)

SA = 152 sq. ft.

Hence, the surface area of the triangular prism is 152 sq, ft.

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To find all distinct eigenvalues of A and their corresponding basic eigenvectors, follow these steps. For each eigenvalue λ, solve the equation (A - λI)x = 0, where x is the eigenvector.

Step 1: Find the characteristic equation of matrix A.
Write down the equation |A - λI| = 0, where λ represents the eigenvalues and I is the identity matrix.
Step 2: Solve the characteristic equation.
Find the values of λ that satisfy the equation obtained in Step 1. These values are the eigenvalues of matrix A.
Step 3: Find eigenvectors corresponding to each eigenvalue.
For each eigenvalue λ, solve the equation (A - λI)x = 0, where x is the eigenvector. Find the null space of (A - λI) to determine the basic eigenvectors.
Step 4: State the eigenvalue followed by the basic eigenvectors.
For each eigenvalue, specify the number of basic eigenvectors and list the eigenvectors corresponding to that eigenvalue.
Please note that I cannot provide a specific solution without the matrix A. If you provide the matrix A, I would be happy to walk you through the process with actual calculations.

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5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

An expression is combination of variables, numbers and operators.

Given,

5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

This sentence can be written in the form below

(5⁻² × 5⁶)⁻³

According to laws of indices, we know that;

(a²)³ = a⁶

Thus;

(5⁻² × 5⁶)⁻³=(5⁻² )⁻³×(5⁶)⁻³

⇒ 5⁶ × 5⁻¹⁸

When bases are same then the powers will be added

⇒ 5⁶ × 5⁻¹⁸

⇒ 5⁻¹²

Hence, 5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

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Answer:

1 divided by 5 raised to the twelfth power

Step-by-step explanation:

both of them equal the same thing

Answer: 57.75 m or about 57.8m

Step-by-step explanation:

The z-score that separates the bottom 86% from the top 14% is 1.08 (option B).

Z-score is the number of standard deviations from the mean value of the reference population.

To find the z-score we can use a z-score table or calculator:

Z-score table can be used to calculate the area under a normal bell curve for a binomial normal distribution.

It shows the area to the left of a given z-score, so we can look for the area closest to 0.86 in the table. The z-score that corresponds to this area is 1.08.

Alternatively, we can use a calculator to find the inverse of the standard normal Cumulative Distribution Function (CDF). The CDF gives the area to the left of a given z-score, so we can use the inverse CDF to find the z-score that corresponds to a given area. In this case, we want the z-score that corresponds to an area of 0.86:
z = invNorm(0.86)

  = 1.08

Therefore, the z-score that separates the bottom 86% from the top 14% is 1.08 (option B).

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Answer:

Acceleration: 2.2 m/s^2

Step-by-step explanation:

F=M/A

7.92/ 3.6

2.2.

Using the formula to solve for acceleration you divide force by mass.

Acceleration = 7.92 / 3.6 = 2.2

Answer: 51,000 ; 111,000

Step-by-step explanation:

The formula to calculate the simple interest is: PRT/100

where,

P = principal = 60,000

R = rate = 8.5%

T = time = 10 years

Simple interest =(60000 × 8.5 × 10)/100

= 5100000/100

= 51,000

Total Amount Paid= Principal + Interest

= 60,000 + 51,000

= 111,000

let the pounds be 12

the cost = 12× 6

= 72 dollars

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

112 guests

Step-by-step explanation:

I. If her total cost is 773$

When Total = DJ + Cake + Guest

            773 = 250 + 75 + 4(x)

            773 = 325 + 4(x)

            773 - 325 = 4(x)

            448 = 4x

               x = 448/4

               x = 112

That makes guests are 112

Answer:

\( \frac{8 {x}^{2} y}{6 {x}^{2} {y}^{2} } \\ = \frac{8×3}{6 {y}^{2} } \\ = \frac{24}{6 \times {3}^{2} } \\ = \frac{4}{9} \)

Answer:

5

Step-by-step explanation:

30 divided by 6 = 5

Andrea earns a total of $48 for washing 6 cars at the rate.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.

Using the cross multiplication method, we may determine the answer to a pair of linear equations. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we can write in a proportion to determine the values of unknown variables.

Given that,

$32 = 4 cars

$x = 6 cars

Using the method of cross multiplication:

x = 32(6) / 4

x = $48

Hence, Andrea earns a total of $48 for washing 6 cars at the rate.

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The value of r that indicates a stronger correlation is option (C) r = -0.912 represents a stronger correlation because |-0.912|>|0.721|

The value of the correlation coefficient, denoted by "r", ranges from -1 to 1. A correlation of -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. The absolute value of the correlation coefficient (|r|) represents the strength of the correlation, where the closer |r| is to 1, the stronger the correlation is.

In this case, r = 0.721 indicates a moderate positive correlation, while r = -0.912 indicates a strong negative correlation. The absolute value of -0.912 is greater than the absolute value of 0.721, indicating that the strength of the negative correlation is stronger than the strength of the positive correlation.

Therefore, the correct option is (C) r = -0.912 represents a stronger correlation because |-0.912|>|0.721|

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Answer:

The answer is b = ax- c/x

when i put the / it means fraction

Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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