A set of data has a normal distribution with a mean of 47 and a standard deviation of 8. Find the percent of data within the following interval.
from 39 to 55

When the pile is 22 feet high, the height of the pile changes to 20/1089π.

Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?

The volume of cone is V = 1/3 * pi * r ^ 2 * h

d=3h

2r = 3h

r = (3h)/2

V = 1/3 * pi * r ^ 2 * h

= 1/3 * pi * ((3h)/2) ^ 2 * h

= 1/3 * pi((9 * H ^ 2 )/4) * h

= (9pi)/12 * h ^ 3

Differentiate w.r.to t

(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)

(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)

(dV)/(dt)=20, h=22 feet

20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)

(dh)/(dt) = 80/ (9pi * (22^ 2))

h^ t = 20/ 1089 *pi   ft / min

Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π

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If the price of the mobile with 13% VAT is Rs 28,476, the discount percent is 10%.

The discount is the difference between the marked price and the selling price.

Discounts are depicted in percentages to show the rates at which the discounts are given.

The selling price of the mobile set with 13% VAT = Rs. 28,476

The selling price of the mobile set without VAT = Rs. 25,200 (Rs. 28,476/1.13)

The difference (discount) between the marked price and the selling price = Rs. 2,800

The marked price = Rs. 28,000 (Rs. 25,200 + Rs. 2,800)

The discount percent given = 10% (Rs. 2,800/Rs. 28,000 x 100)

Thus, we can conclude that the discount percent is 10%.

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The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

\(\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0\)

by substituting the values in the formula of equation of a plane

\(\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0\)

\(\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0\)  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

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Answer:

the answer would be -4

Step-by-step explanation:

Answer:

$4703

Step-by-step explanation:

Given that :

First year :

Net loss = $1250

2nd year:

Net profit = $3475

3rd year :

Net profit = 2478

Net loss or gain over the last 3 years :

Let Net loss be represented as negative and net profit as positive

Net loss + net profit + net profit

(-$1250 + $3475 + $2478)

$4703 net gain over the last 3 years

Answer:

√{9×81×9}=√(9²×9²)=±(9×9)=±81

Answer:

your answer will be 81

Step-by-step explanation:

.......

Answer:

45 sq yd

Step-by-step explanation:

area of square: 8*6= 48

area to triangle: 2*3/2 = 3

48 - 3 = 45

Answer:

m = 200

Step-by-step explanation:

Substitute n = 50 in the equation

         n = 2/5m - 30

       50 = 2/5m - 30

50 + 30 = 2/5m

       80 = 2/5m

         m = 80 ÷ 2/5

         m = 200

Answer:

4

Step-by-step explanation:

(6^2) -5(6) -2 =4

that is the answer

Step-by-step explanation:

6^2 - 5×6 - 2

= 36 - 30 -2

= 4

Answer:

The values of F will be "16.58 i + 11.18 j".

Step-by-step explanation:

The given values are:

Force, F = 20 N

Angle, Ф = 33°

The formula use in the given scenario will be:

⇒  \(x=a \ Cos\theta\)

⇒  \(y=a \ Sin\theta\)

Now,

For Force, \(F=ai+bj\)

⇒  \(a=F \ Cos\theta\)

⇒     \(=20 \ Cos(34^{\circ})\)

⇒     \(=20\times .829\)

⇒     \(=16.58\)

and,

⇒  \(b=F \ Sin\theta\)

⇒     \(=20 \ Sin(34^{\circ})\)

⇒     \(=20\times .55\)

⇒     \(=11.18\)

So that,

⇒  \(F=16.58 \ i+11.18 \ j\)

Answer and Step-by-step explanation:

Hello!

To find the volume of a rectangular prism, you have to multiply the base by the width, the by the height.

The base is 5.5 ft.

The width is 2.5 ft.

The height is 3.5 ft.

So, simply just multiply all three of these numbers together.

5.5 × 2.5 = 13.75

13.75 × 3.5 = 48.125

The volume of the rectangular prism is \(48.125 ft^{3}\).

#teamtrees #PAW (Plant And Water)

Answer:

Exponential Decay is the answer

Answer:

C) P = 12H

Step-by-step explanation:

This is because she makes 12 dollars every hour so it'll be 12 times the number of hours.

Yes, it is possible for a given angle θ to satisfy both cot θ > 0 and tan θ < 0. This is because cot θ = 1/tan θ, which means that for a given angle θ, when tan θ is negative, cot θ will be positive.

To explain further, let's consider an example. Let θ = 270°. The value of cot θ is cot 270° = -1/tan 270° = -1/(0) = 0. Since 0 > 0, cot θ > 0. On the other hand, the value of tan θ is tan 270° = 0. Since 0 < 0, tan θ < 0. Therefore, it is possible for a given angle θ to satisfy both cot θ > 0 and tan θ < 0.

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Answer:

  8 units

Step-by-step explanation:

Points (2, 5) and (10, 5) have the same y-coordinate, so lie on the horizontal line y = 5. The distance between the points is the difference of their x-coordinates:

  10 -2 = 8

The points are 8 units apart.

__

If you plot the points on a graph, you can count the grid squares between them.

Answer:

C

Step-by-step explanation:

I’m pretty sure

The line whose slope will be same as that of the graph given, will be the line parallel to the given line.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a graph of a line.

For a given line to be parallel to the given line, its slope should be same as that of the line plotted. Since the graph is not given, we can make an estimate for the equation of the line parallel to the given line. The four equations given will have their slopes as mentioned -

[A] -   4x + 5y = - 10       [m] = -4/5

[B] -   4x - 5y = 0           [m] = 4/5

[C] -   5x + 4y = 24        [m] = -5/4

[D] -   5x - 4y = -8          [m] = 5/4

Now, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

Therefore, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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Answer:

i tride so hard i dont know but i wish you luck but i think its A

Step-by-step explanation:

Answer:

Its not A thats all i know

Step-by-step explanation:

(C) 31 is the population size, n, when the sum of the squares of the differences between each value and the population mean is 806 and if the population standard deviation is 26.

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured. Whether the data are being treated as a population unto itself or as a sample of a broader population will affect the standard deviation calculation algorithm.

In the event that the data are viewed as a population in and of itself, we divide by the number of data points and If there are less data points in the sample than there are in the total population, we divide by one fewer than the total number of data points.

We require mean to be the point estimate of the unknown population mean in order to build a confidence interval for a single unknown population mean when the population standard deviation is known. The solution can be seen on the attached image.

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Question correction:

The sum of the squares of the differences between each value and the population mean is 806. If the population standard deviation is 26, the population size n is:

Group of answer choices

A. 32

B. 30

C. 31

D. 26

Answer:

Its A :)

Step-by-step explanation:

The equation that describes the graphed function is y = -f(x) - 3

The given (parent) function is f(x) = √x

The given graph shows a real curve that starts from y = -3, when x = 0 and the y-value increases in magnitude in the negative direction as the x-values increases positively from left to right, by the same amount that the parent function increases from left to right

Therefore; The graph is real, therefore, the value of x in √x is x ≥ 0, and y ≠ f(-x) + D

Where, D, is the vertical shift

The graph starts at x = 0, y = -3, compared to the parent function, the vertical shift, D = -3

The y-value of the given curve increases in the opposite direction (negatively) as the y-value of the parent function increases in magnitude in the positive direction.

Therefore, the equation of the given curve comprises of the reflection of the parent function or -f(x)

The graph shows the reflection of the parent function, across the x-axis, and we have, reflection of the parent function, f(x) which is -f(x)

Hence the answer is, the equation that describes the graphed function is y = -f(x) - 3

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The largest open interval on which f is the antiderivative for f is called the indefinite integral of f, and it is denoted by ∫f(x)dx. This interval can be determined by finding all the antiderivatives of f and then taking the union of their domains. Note that the antiderivative of f is not unique, as it can differ by a constant, so the indefinite integral of f is only determined up to an arbitrary constant.
To find the largest open interval on which a function f is the antiderivative for f', we'll first need to know the function f' (the derivative of f). However, you didn't provide the function f' in your question.

To give you a general idea of how to approach this problem, follow these steps:

1. Given the function f'(x), find the critical points by setting f'(x) equal to 0 and solving for x.
2. Determine the intervals based on the critical points.
3. Check the behavior of f'(x) in each interval to see where it's continuous and increasing.
4. The largest open interval on which f is the antiderivative for f' will be the interval in which f'(x) is continuous and increasing.

If you provide the function f'(x), I can help you find the largest open interval for the antiderivative.

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Answer:

second one :D

Step-by-step explanation:

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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The value of x is 128 degrees, given that two lines intersect at 140 degrees and (x+12) degrees and one of the angles formed by the intersection is (x+12) degrees.

If two lines intersect, the angle formed at the point of intersection is 180 degrees. We are given that the intersection of the two lines creates an angle of 140 degrees. Let's call the other angle formed by the two lines "y". Then we have:

140 degrees + y = 180 degrees

y = 180 degrees - 140 degrees

y = 40 degrees

Now, we are also given that one of the angles formed by the two lines is (x+12) degrees. We can set up an equation using this information:

x + 12 + y = 180 degrees

x + 12 + 40 degrees = 180 degrees

x + 52 degrees = 180 degrees

x = 180 degrees - 52 degrees

x = 128 degrees

Therefore, the value of x is 128 degrees.

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The domain of the graph is the set of all real values

The domain is the set of x values of the graph

From the graph, the x values extend in both directions without end

This means that the x values can accommodate all real values

Hence, the domain of the graph is the set of all real values

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Given statement solution:- None of the expressions evaluated are equivalent to 3/16 when x=34.

Let's evaluate each expression to determine if it is equivalent to 3/16 when x=34:

2x+116:

Substituting x=34, we have: 2(34) + 116 = 68 + 116 = 184

184 is not equal to 3/16.

\(x^2\) - 616:

Substituting x=34, we have: \((34)^2\) - 616 = 1156 - 616 = 540

540 is not equal to 3/16.

\((38)^2\)÷ x:

Substituting x=34, we have:\((38)^2\) ÷ 34 = 1444 ÷ 34 = 42.47 (approx.)

42.47 is not equal to 3/16.

x - 14:

Substituting x=34, we have: 34 - 14 = 20

20 is not equal to 3/16.

2x -\(x^2\)- 34:

Substituting x=34, we have: 2(34) - \((34)^2\) - 34 = 68 - 1156 - 34 = -1122

-1122 is not equal to 3/16.

None of the expressions evaluated are equivalent to 3/16 when x=34.

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Answer:

9m^2 - 12mn + 4n^2

Step-by-step explanation:

Answer:

9m²-12mn+ 4n²

Step-by-step explanation:

First you expand it so

(3m-2n)(3m-2n)

9m²-6mn-6mn+4n²

9m²-12mn+ 4n²

And this is the simpliest form , hope this helped:))