A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?​

Answer:

To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:

students/adults = 9/7

You can then cross-multiply to find the value of "students":

7 * students = 9 * adults

7 * students = 9 * (832/(9+7))

7 * students = 832

students = 832 / 7

students = approximately 118.85714285714 students

To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:

Copy code

students/adults = 9/7

You can then cross-multiply to find the value of "students":

Copy code

7 * students = 9 * adults

7 * students = 9 * (832/(9+7))

7 * students = 832

students = 832 / 7

students = approximately 118.85714285714 students

Since the number of students must be an integer, the number of students at the open house is approximately 118 students.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the last part of the problem, you have to follow PEMDAS.

Instead of you added before dividing. After the step of 36÷3+9x2 you have to divide.

Answer:

The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.

Step-by-step explanation:

Ok so basically you have to do

Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

Answer:

Step-by-step explanation:

Heavy metal (or simply metal) is a genre of rock music that developed in the late 1960s and early 1970s, largely in the United Kingdom and the United States.

Answer:

His savings were of $4,200.

Step-by-step explanation:

Mr. Hughes gave 5/14 of his savings to his son, 2/3 of the remainder to his daughter, and the rest to his wife:

This means that the son and daughter amount is:

[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14})[/tex]

As [tex]\frac{9}{14}[/tex] is the remained that his son did not get. So

[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14}) = \frac{15}{42} + \frac{18}{42} = \frac{33}{42}[/tex]

Fraction his wife got:

[tex]1 - \frac{33}{42} = \frac{42}{42} - \frac{33}{42} = \frac{9}{42}[/tex]

If his wife got $900, what were his savings?

Total savings are x, wife got [tex]\frac{9}{42}[/tex] of x. So

[tex]\frac{9x}{42} = 900[/tex]

[tex]9x = 900*42[/tex]

[tex]x = \frac{900*42}{9}[/tex]

[tex]x = 100*42[/tex]

[tex]x = 4200[/tex]

His savings were of $4,200.

Answer:

x = -11, 2/3

Step-by-step explanation:

-3x^2-11x+2=0

-(3x^2+11x-2) = 0

3x^2 + 11x - 2 = 0

3x^2 + 33x - 22x - 2 = 0  ==> 33-22=11 and 33/11=3 and -22/11=-2

3x(x + 11) - 2(x + 11) = 0  ==> factor

(3x - 2)(x + 11) = 0

3x - 2 = 0                x + 11 = 0

3x = 2                x + 11 - 11 = 0 - 11

{ x = 2/3                         x = -11 } ==> x = -11, 2/3

Answer:

(1,9), (2,11), (3,13) (4,15)

Step-by-step explanation:

When u plug in those numbers for your x values, you get those numbers for the y values.

Answer:

3 watermelons

Step-by-step explanation:

So this is a basic unit rate problem, so you're going to divide:

6 ÷ 2 = 3

So DeShawn can buy 3 watermelons with $6

hope this helps:)

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Use similar triangles,

BAC and DAB are similar

therefore

CA/AB = BA/AD

CA/20 = 20/10

cross multiply

AC = CA = 20*20/10 = 40

Or use metric relations

CA*AD = BA^2

CA = BA^2/AD = 20^2/10 = 40

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

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Answer:

1/2

Step-by-step explanation:

Slope(m)

= (y2 - y1)/(x2 - x1)

= (8 - 1)/(7+7)

= 7/14

= 1/2

Answer:

60,000 liters

Step-by-step explanation:

30% of 60000 = 18000

60000 - 18000 = 42000

Answer:

A. There are no y-intercepts

Step-by-step explanation:

I calculated it logically

Answer:

c is incorrect

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

(a) As of the Cartesian vector approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

(b) Using a scalar approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

here,
[tex]\vec F = 4 \hat i + 12\hat j -3 \hat k\\ \vec B = 4 \hat i + 3\hat j - 2 \hat k\\[/tex]

Scalar approach,
moment about the x-axis is given by,
[tex]M_x = B_yF_z - ZF_y\\M_x = 3(-3)-(-2)(12)\\M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb,[/tex] and [tex]M_z = 36\ Ft-lb[/tex]

Vector approach,
Moment about the x-axis is given by,
[tex]M_x = U_x \times[ {\vec B \times \vec F]}\\M_x = \left[\begin{array}{ccc}1&0&0\\4&3&-2\\4&12&-3\end{array}\right][/tex]

The above expression given is of determinate, when solving the above determinate,
[tex]M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex],

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The value of the common length BD would be 8 units, approximately.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The AD line is perpendicular to the line AC.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

So, We know that

  Sin A = BD / AB

  Sin A = BD / c

c Sin A = BD

Substitute angle A = 53.13 and c = 10.

BD = (10) Sin (53.13)

BD = 10 (0.79)

BD = 7.99

BD ≈ 8

The question was incomplete, but the complete question is given below.

Considering line BD as a side of ABD, express its length in terms of variables representing side lengths and angle measures in ABD. Show your work.

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Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:

5(y + 9) = 3

Next, we can distribute the 5 to obtain:

5y + 45 = 3

Finally, we can subtract 45 from both sides to solve for y:

5y = -42

y = -42/5

y = -8.4

Therefore, the equation that represents the given sentence is y = -8.4.

Step-by-step explanation:

Answer:

C = π (4yd)

C = 12.6yd

Step-by-step explanation:

Answer:

A. 36  ÷ a

B. 55 - b

C. 18 + c

D. 49 · d

E. e ÷ 62

F. f - 71

Using the formula for the midpoint of the line with given points  A and B as the end points of the line, the coordinates of the point B is (6,-8).

To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.

What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.

Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line,  and using the midpoint formula for a line AB,

Midpoint(M) = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B

so , (7,-7) = [tex](\frac{8+x2}{2} , \frac{-6+y2}{2})[/tex]

equating the corresponding points,

7 =(8+x2)/2

therefore, x2 = 6

and , -7 = (-6+y2)/2

therefore , y2 = -8

Hence the coordinates of B is , (x2,y2 ) = (6,-8)

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Answer:

The solution you are looking for is D.)

Step-by-step explanation:

To determine this, we need to find the amount of miles left they need to travel (243 - 157 = 86). Then we can divide that by the amount of miles per gallon (86 / 21.5 = 4). Because a possible solution to the answer is 4, we know that the dot needs to be solid (filled in), and because the solution can be greater than four, the arrow would be directed to the right / positive side of the line.

The equation of the trend line will be : Y = (1/4)x - 1.

Given is a scatter plot a shown in the image.

The general equation of a straight line is -

y = mx + c

{m} - slope

{c} - intercept along the y - axis

We can find the slope as follows. The line passes through the points -

(4, 0) and (0, - 1). We can write -

m = (- 1 - 0)/(0 - 4)

m = - 1/-4

m = 1/4

and

[c] = - 1

So the equation of the trend line will be -

Y = (1/4)x - 1

Therefore, the equation of the trend line will be : Y = (1/4)x - 1.

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Answer:

The appropriate solution is:

(a) 0.1056

(b) 0

(c) 0.9544

Step-by-step explanation:

The given values are:

Mean,

[tex]\mu = 75[/tex]

Standard deviation,

[tex]\sigma = 4[/tex]

(a)

⇒  [tex]P(x>80)=1-(x<80)[/tex]

                     [tex]=1-P[\frac{x-\mu}{\sigma} <\frac{80-75}{4} ][/tex]

                     [tex]=1-P[\frac{x-\mu}{\sigma} <\frac{5}{4} ][/tex]

                     [tex]=1-P(z<1.25)[/tex]

By using the table, we get

                     [tex]=1-0.8944[/tex]

                     [tex]=0.1056[/tex]

(b)

According to the question, the values are:

[tex]n[/tex] = 64

[tex]\mu_\bar{x}[/tex] = 75

Now,

⇒  [tex]\sigma_\bar{x}[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

         = [tex]\frac{4}{\sqrt{64} }[/tex]

         = [tex]\frac{4}{8}[/tex]

         = [tex]0.5[/tex]

⇒  [tex]P(\bar {x} >80 ) = 1 - P(\bar x <80 )[/tex]

                      [tex]=1 - P[\frac{(\bar x-\mu_\bar x)}{\sigma \bar x} < \frac{80-75}{0.5} ][/tex]

                      [tex]=1-P(z<10)[/tex]

By using the table, we get

                      [tex]=1-1[/tex]

                      [tex]=0[/tex]

(c)

As we know,

⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

        = [tex]\frac{4}{\sqrt{64} }[/tex]

        = [tex]\frac{4}{8}[/tex]

        = [tex]0.5[/tex]

then,

= [tex]P(74< \bar x <76)[/tex]

= [tex]P[\frac{74-75}{0.5} < \frac{\bar x-\mu \bar x}{\sigma \bar x} < \frac{76-75}{0.5} ][/tex]

= [tex]P(-2<z<2)[/tex]

= [tex]P(z<2)-P(z<-2)[/tex]

By using the table, we get

= [tex]0.9772-0.0228[/tex]

= [tex]0.9544[/tex]