Please Hurry!!!!
Patricia can draw 1/5 a page of his drawing book in 1/3 of an hour. Express this as a unit rate.

The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)

To find a data set with 5 values for which the standard deviation is zero,

⇒ (4, 4, 4, 4, 4)

For the above dataset;

Mean μ = 4

Number of samples n = 5

Standard deviation σ = \(\sqrt{\frac{sumof(xi - x)^2}{n} }\)

                                   = \(\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }\)

                                   = 0

Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).

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Answer:

7

Step-by-step explanation:

Because the parts of the circle are congruent, the segments are as well, we can use that to make an equation then solve it like normal

9x-34=4x+1

-1 on both sides

9x-35=4x

-9x on both sides

-35=-5x

x=7

The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

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Answer:

49 cards would be left from the deck of card.good luck with future questions I hope I am right

Step-by-step explanation:

the answer is in picture

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Given :

P(x 3), Q(7, -1) and PQ= 5 .

To Find :

The possible value of x.​

Solution :

We know, distance between two points in coordinate plane is given by :

\(PQ = \sqrt{(x-7)^2 + ( 3-(-1))^2}\\\\PQ^2 = (x-7)^2 + ( 3-(-1))^2\\\\(x-7)^2 + 4^2 = 5^2\\\\( x- 7)^2 = 3^2 \\\\x - 7 = \pm 3\\\\x = 10 \ and \ x = 4\)

Therefore, the possible value of x are 10 and 4.

Answer: $ 7.20

Step-by-step explanation:

(9x4)/5

36/5

= 7.2

= $7.20

Answer:

5 1/5

step-by-step explanation

After considering all the given data we conclude that the open intervals are as follows
f is increasing on the intervals (2, 4) and (4, ∞).
f is decreasing on the interval (-∞, 2).
The relative maxima of f occur at x = 3.
The relative minima of f occur at x = 4.

To evaluate the open intervals on which \(f(x) = x^3 - 12x^2 + 45x - 13\) is increasing or decreasing, we need to evaluate the first derivative of f(x) and determine its sign.
Then, to calculate the relative maxima and minima, we need to find the critical points and determine their nature using the second derivative test.
To evaluate the intervals on which f(x) is increasing or decreasing, we take the derivative of f(x) and set it equal to zero to evaluate the critical points:
\(f'(x) = 3x^2 - 24x + 45\)
\(3x^2 - 24x + 45 = 0\)
Solving for x, we get:
x = 3, 4
To describe the sign of f'(x) on each interval, we can use a sign chart:
Interval (-∞, 3) (3, 4) (4, ∞)
f'(x) sign + - +
Therefore, f(x) is increasing on the intervals (2, 4) and (4, ∞) and decreasing on the interval (-∞, 2).
To evaluate the relative maxima and minima, we need to use the second derivative test. We take the second derivative of f(x) and evaluate it at each critical point:
f''(x) = 6x - 24
f''(3) = -6 < 0, so f(x) has a relative maximum at x = 3.
f''(4) = 12 > 0, so f(x) has a relative minimum at x = 4.
Therefore, the x-coordinates of the relative maxima and minima of f(x) are 3 and 4, respectively.
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Answer: 10

Step-by-step explanation: When multiplying integers,

if the signs are the same, the product is positive.

So a negative times a negative always equals a positive.

Therefore, -5(-2) is 10.

Answer:

10

Step-by-step explanation:

-5 x -2 = 10

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer:

Step-by-step explanation:I didn't mean to add

Answer:

$27.50 is the amount of money in total she has to pay.

Step-by-step explanation:

$27.50 means the amount of money total she has to pay for admission fee as well as for each nder.

Answer:

H is the hypotenuse (the one in the middle) and the legs are the other two sides of the triangle.

Step-by-step explanation:

By evaluating the function in x = -2, we will get:

f(-2) = -2

To do that, we need to evaluate the given linear equation:

f(x) = -x - 4

We want to find f(-2), so we need to evaluate the linear equation in x = -2, this means that we just need to replace the variable by the corresponding number.

Then we will get:

f(-2) = -(-2) - 4

f(-2) = +2 - 4

f(-2) = -2

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Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer:

I believe it is 2787.6

Step-by-step explanation:

Math

The equation of parabola is \(y=1/4x^{2}+x/2-4\\\\\).

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

Given:

The equation of parabola in vertex form is

\(y=a(x-h)^{2} +k\)

Being vertex here

h=-2

k=-5

According to given question we have

∴

Equation of parabola in vertex form is

\(y=a(x+2)^{2} -5\)

. The parabola passes through point  (4,4)  So the point (4,4)  will satisfy the equation .

\(4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4\)

Hence the equation of parabola is

\(y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\\)

Therefore, the equation of parabola is \(y=1/4x^{2}+x/2-4\\\\\).

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the equation of parabola is missing

The dimensions of a rectangle with the largest area that can be drawn inside a circle with a radius of 5 are L = 5.77 and W = 8.16.

The diameter of the circle is twice the radius, so it is 2 × 5 = 10.

Let's assume that the length of the rectangle is L and the width is W.

Since the diagonal of the rectangle is equal to 10, we can use the Pythagorean theorem to express the relationship between the length, width, and diagonal

L² + W² = 10²

L² + W² = 100

To find the dimensions that maximize the area of the rectangle, we need to maximize the product L × W. One way to do this is to find the maximum value for L² × W².

W² = 100 - L²

Substituting this into the area formula, A = L × W, we have

A = L × (100 - L²)

To find the maximum area, we can take the derivative of A concerning L, set it equal to zero, and solve for L

dA/dL = 100 - 3L² = 0

3L² = 100

L² = 100/3

L = √(100/3)

Substituting this value of L back into the equation for W^2, we have

W² = 100 - (100/3)

W² = 200/3

W = √(200/3)

Therefore, the dimensions of the rectangle with the largest area that can be inscribed inside a circle with a radius of 5 are approximately L = 5.77 and W = 8.16.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

To find the length of \(PD\) in the given rectangle \(ABCD\), we can use the Pythagorean theorem.

The length of \(PD\) is \(\sqrt{} 79\)units.

Given that \(PA = 1\), \(PB = 7\), and \(PC = 8\), we need to find \(PD\).

Since \(P\) is inside the rectangle, we can consider the right-angled triangles \(PAB\), \(PBC\), and \(PCD\).

Using the Pythagorean theorem, we have:

In triangle \(PAB\):

\(PA^2 + AB^2 = PB^2\)

In triangle \(PBC\):

\(PB^2 + BC^2 = PC^2\)

In triangle \(PCD\):

\(PC^2 + CD^2 = PD^2\)

Since the rectangle has equal side lengths, \(AB = BC = CD\), so we can denote them as \(s\).

Now let's substitute the given lengths:

\(1^2 + s^2 = 7^2\)     (Equation 1)

\(7^2 + s^2 = 8^2\)     (Equation 2)

\(8^2 + s^2 = PD^2\)    (Equation 3)

Simplifying Equations 1 and 2, we have:

\(s^2 = 7^2 - 1^2\)      (Equation 4)

\(s^2 = 8^2 - 7^2\)      (Equation 5)

Solving Equations 4 and 5:

\(s^2 = 48\)

\(s^2 = 15\)

From Equation 5, we find that \(s^2 = 15\), so \(s = \sqrt{15}\).

Substituting this value into Equation 3, we can solve for \(PD\):

\(8^2 + (\sqrt{15})^2 = PD^2\)

\(64 + 15 = PD^2\)

\(79 = PD^2\)

Taking the square root of both sides, we find:

\(PD = \sqrt{79}\)

Therefore, the length of \(PD\) is \(\sqrt{79}\) units.

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The expressions x + x + x + x and 4x are equivalent.

We can see this by simplifying the first expression:

x + x + x + x = 4x

So we can see that both expressions represent the same quantity, which is the total of adding x four times.

To explain this using a diagram, we can draw four boxes, each labeled with an "x".

x   x   x   x

Then, we can count the total number of "x" in the diagram, which is 4x.

Alternatively, we can also think of distributing the coefficient 4 to each term in the second expression:

4x = 4 * x

= x + x + x + x

This gives us the same expression as the first one, so they are equivalent.

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The solution of the system is (-3, 22) (option a).

One way to solve this system is to use the method of substitution. In this method, we solve one equation for one of the variables and substitute the expression for that variable into the other equation. Let's solve Equation 1 for y:

y = -8x - 2

Now, we can substitute this expression for y into Equation 2:

-8x - 2 = -6x + 4

We can simplify this equation by combining like terms:

-8x + 6x = 4 + 2

-2x = 6

Dividing both sides by -2, we get:

x = -3

Now, we can substitute this value of x back into either equation to find the value of y. Let's use Equation 1:

y = -8(-3) - 2

y = 24 - 2

y = 22

Therefore, the solution of the system is (x, y) = (-3, 22). This means that the two equations are satisfied simultaneously when x is equal to -3 and y is equal to 22.

Hence the correct option is (a).

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The rate of the plane in still air is 255 km/h and the rate of the wind is 15 km/h.

Let's denote the rate of the plane in still air as x km/h and the rate of the wind as y km/h.

When the plane travels against the wind, its effective speed is reduced. Therefore, the time it takes to travel a certain distance is increased. We can set up the equation:

2130 = (x - y) * 3

When the plane travels with the wind, its effective speed is increased. Therefore, the time it takes to travel the same distance is reduced. We can set up another equation:

2550 = (x + y) * 3

Simplifying both equations, we have:

3x - 3y = 2130 / Equation 1

3x + 3y = 2550 / Equation 2

Adding Equation 1 and Equation 2 eliminates the y term:

6x = 4680

Solving for x, we find that the rate of the plane in still air is x = 780 km/h.

Substituting the value of x into Equation 1 or Equation 2, we can solve for y:

3(780) + 3y = 2550

2340 + 3y = 2550

3y = 210

y = 70

Therefore, the rate of the wind is y = 70 km/h.

In summary, the rate of the plane in still air is 780 km/h and the rate of the wind is 70 km/h.

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Answer:

1

Step-by-step explanation:

Substitute the values for their respective variables.

\(\frac{ac}{b^2+1}\\\\\frac{(2)(5)}{(3)^2+1}\\\\\frac{10}{9+1}\\\\\frac{10}{10}\\\\1\)

Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

Therefore, if the 300th day of year N is a Tuesday, the 100th day of year N-1 will be a Sunday.

To determine the day of the week on the 100th day of year N-1, we need to analyze the given information and make use of the fact that there are 7 days in a week.

Let's break down the given information:

In year N, the 300th day is a Tuesday.

In year N+1, the 200th day is also a Tuesday.

Since there are 7 days in a week, we can conclude that in both years N and N+1, the number of days between the two given Tuesdays is a multiple of 7.

Let's calculate the number of days between the two Tuesdays:

Number of days in year N: 365 (assuming it is not a leap year)

Number of days in year N+1: 365 (assuming it is not a leap year)

Days between the two Tuesdays: 365 - 300 + 200 = 265 days

Since 265 is not a multiple of 7, there is a difference of days that needs to be accounted for. This means that the day of the week for the 100th day of year N-1 will not be the same as the given Tuesdays.

To find the day of the week for the 100th day of year N-1, we need to subtract 100 days from the day of the week on the 300th day of year N. Since 100 is a multiple of 7 (100 = 14 * 7 + 2), the day of the week for the 100th day of year N-1 will be two days before the day of the week on the 300th day of year N.

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Answer:

Step-by-step explanation:

The volume for a right cylinder is

\(V=\pi r^2h\)

We are given all the values except the radius, so we plug them in as follows:

\(18488=\pi r^2(23)\)

Begin by dividing by 23π to get

255.8657603 = r²

and then take the square root of both sides to find that

r = 15.995 or 16 m

To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.

By the using this method. We get, the correct determinant is 68.

Given Determinant:

\(\left|\begin{array}{ccc}1&0&-4\\3&-4&0\\-1&-4&1\end{array}\right|\)

\((-1)\left|\begin{array}{cc}-4&0\\-4&1\end{array}\right] +0\left|\begin{array}{cc}3&0\\-1&1\end{array}\right|+(-4)\left|\begin{array}{cc}3&-4\\-1&-4\\\end{array}\right|\)

= (-1)(-4-0) +0 - 4(-12 -4)

= -1 (-4) + 0 -4(-16)

= 4 + 64

= 68.

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Complete Question:

The expansion of a 3×3 determinant can be remembered by this device. write a second copy of the first two columns to the right of the​ matrix, and compute the determinant by multiplying entries on six diagonals. add the downward diagonal products and subtract the upward products. use this method to compute the following determinant.

\(\left|\begin{array}{ccc}1&0&-4\\3&-4&0\\-1&-4&1\end{array}\right|\)