Find the volume. Round your answer to the nearest tenth.

Answer: 9πcm²

Step-by-step explanation: area of the square= 36cm²

Therefore, the area of one side= √area = √36 = 6cms

Since the circle is touching the sides of the square, the side of the square = the diameter of the circle

Therefore the radius of the circle= side/2 = 3cm

The formula for the ares of the circle is πr²

π*3*3 = 9πcm²

Corrected Question

The solution to an inequality is represented by the number line. How can this same solution be written using set-builder notation? {x | x > }

Answer:

[tex]\{x | x >3 \}[/tex]

Step-by-step explanation:

Given an inequality whose solution is represented by the number line attached below.

We observe the following from the number line

There is an open circle at 3, therefore the solution set does not include 3. (We make use of > or < in cases like that)

The arrow is pointed towards the right. All points to the right of 3 are greater than 3, therefore:

The solution in the number line can be written using set-builder notation as:

[tex]\{x | x >3 \}[/tex]

Answer:

For the first question, there is a 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.

Step-by-step explanation:

100: 224 = 61:x → 61/100 = x/224

100x = 13664

x = 136.64 → 136 groups (You can't round up if you don't have enough people)

Hope this helped!

Answer: 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.

Step-by-step explanation:

:) The other answer is correct too! But just for clarification! :)

Answer:

The correct option is:

x+y = 2

Step-by-step explanation:

Street 1 is given.

If Street 2 is parallel to Street 1, then they will have the same slope.

Find slope of Street 1:

Take any 2 points on Street 1. Consider (-2,3) and (1,0)

Slope is given by:

m = (y₂ - y₁) / (x₂ - x₁)

m = 0-3 / 1-(-2)

m = -3/3

m = -1

For Street 2:

y = mx + c

y = -1x +c

As it passes through (-2,4), substitute the point in the above equation:

4 = -1(-2) + c

c = 2

So substitute m = -1 and c =2 into general form of equation:

y = mx + c

y = -x + 2

or

x+y = 2

Answer:

y= 0.74x

0.74 (1500) = 1,110 euros

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

Since: 1 US dollar = 0.74 Euros

To convert x US dollars to Euros we have to multiply it by 0.74:

y= 0.74x

Where:

y = value in EUROS

x = value in US dollars

For 1500:

y = 0.74 (1500) = 1,110 euros

Feel free to ask for more if needed or if you did not understand something.

Answer:

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Step-by-step explanation:

The given polynomial is 45x² - 20y²

45x² - 20y² = 5 (9x² - 4y²)

45x² - 20y² = 5 [ (3x)² - (2y)² ]

Using difference of two squares,  (3x)² - (2y)² = ( 3x - 2y)(3x + 2y)

45x² - 20y² = 5 ( 3x - 2y) (3x + 2y)

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Answer:

5(3x - 2)(3x + 2)

Step-by-step explanation:

Please indicate exponentiation with " ^ " :  45 x^2 - 20 y^2​.

Identify the GCF and factor it out:  5(9x^2 - 4y^2)

Recognize that (9x^2 - 4y^2) is the difference of two squares, which factors into (3x - 2y)(3x + 2y)

Then   45 x^2 - 20 y^2 = 5(3x - 2)(3x + 2)

Answer:

k = 2

Step-by-step explanation:

Given the equations:

g(x) = 3x² + 8x + k

f(x) = 2x - 1

At the intersection point:

g(x) = f(x)

3x² + 8x + k = 2x - 1

3x² + 6x + (k+1) = 0

If there is only one intersection point, the discriminant must be equal to zero:

b² - 4(a)(c) = 0

6² - 4(3)(k+1) = 0

36 - 12(k+1) = 0

36 - 12k - 12 = 0

24 = 12k

24/12 = k

2 = k

Answer:

-3x^2-15x-30

Step-by-step explanation:

Follow order of operations

Answer:

-3x^2 -15x -30

Step-by-step explanation:

First you would square the parenthesis, and get x^2 +6x+9 inside the parenthesis, then you would multiply it by the -3 and get -3x^2 -18x-27-3+3x then you combine like terms to get the answer.

Answer:

157+364= 521 square mm

Step-by-step explanation:

Area of 1/2 circle = 1/2 pi r-squared = 1/2x10x10x3.14 = 157 square mm

Area of trapezoid = (a+b)/2xh = (20+32)/2 x 14 = 364 square mm

157+364= 521 square mm

Answer: The correct answer is 94 cm.

Step-by-step explanation:

wingspan         length

60 meters        70.5 m

----------------- = ----------------

80 cm                   x

Cross multiply

(60 m)x = (70.5 m)(80 cm)

Solve for x by dividing both sides of equation by 60 m:

x = (70.5 m)(80 cm) / (60 m) = 94 cm

The length of the model is 94 cm.

Answer:

94 cm

Step-by-step explanation:

Write and solve an equation of ratios:

70.5 m       60 m

----------- = -----------

    L           80 cm

Cross multiplying, we get:

(70.5 m)(80 cm) = (60 m)L

                                                                     (70.5 m)(80 cm)

Then the model length, L, should be  L = -------------------------

                                                                              60 m

or

L = 94 cm

Answer:x − 3 y = − 36

Step-by-step explanation:

Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37

Step-by-step explanation:

standard form = ax+by=c so you basically just have to take that and put it into the formula

Hope this helps

Answer:

(2x³ - 3)²

Step-by-step explanation:

4x⁶ - 12x³ + 9

2²x⁶ - 12x³ + 9

2²x²ˣ3 - 2 * 2x³ * 3 + 3²

2² * (x³)² - 2 * 2x³ * 3 + 3²

(2x³)² - 2 * 2x³ * 3 + 3²

(2x³ - 3)²

Hope this helped! :)

Answer:

The perimeter of given figure  = 56.56 ft

Step-by-step explanation:

Step(i):-

From diagram

      The length of the rectangle = 10 ft

     The width of the rectangle = 8 ft

     Perimeter of the rectangle

                      = 2 ( l+w)

                     =  2 ( 10 + 8)

                     = 2 × 18

                     = 36

Step(ii):-

The semi circle is included in the given diagram

Now we will find the perimeter of semicircle

We know that

        perimeter  of the circle

          p = 2πr + d

        perimeter of the semicircle

        [tex]P = \frac{1}{2} 2\pi r + d[/tex]

       P = πr + 2 r    (∵ d = 2 r)

Step(iii):-

From diagram the diameter of semicircle is equal to the width of the rectangle

      d = 8

     d = 2 r = 8

The radius of the circle 'r' = 4  

    perimeter of the semicircle

       P = πr + 2 r  

      P = 3.14 ( 4) + 8

     P= 20.56

Conclusion:-

The perimeter of given figure

                    = perimeter of rectangle + perimeter of semicircle

                    = 36 + 20.56

                   =56.56 ft

Answer:

see below

Step-by-step explanation:

15+2x> 31

Subtract 15 from each side

2x > 16

Divide by 2

2x/2 > 16/2

x > 8

There is an open circle at 8

The line goes to the right

Answer:

Solution,

Finding the value of X,

[tex]11x + 2 = 68[/tex]

( being vertically opposite angles)

[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]

Value of X is 6

Now, finding the value of z

[tex]z + 68 = 180[/tex]

(sum of angle in linear pair)

[tex]z = 180 - 68 \\ z = 112[/tex]

Value of z is 112.

Hope this helps....

Good luck on your assignment...

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

=> [tex]\frac{15}{\sqrt{3} }[/tex]

Multiplying and dividing by [tex]\sqrt{3}[/tex]

=> [tex]\frac{15}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }[/tex]

=> [tex]\frac{15\sqrt{3} }{(\sqrt{3})^2 }[/tex]

=> [tex]\frac{15\sqrt{3} }{3}[/tex]

=> [tex]5\sqrt{3}[/tex]  (A Rationalized denominator!)

Answer:

5√3

Step-by-step explanation:

To rationalize the denominator, all you have to do is multiply both the numerator and the denominator by whatever is in the denominator, if it is only a single term in the denominator. This means you multiply [tex]\frac{15}{\sqrt{3} }[/tex] [tex]* \frac{\sqrt{3}}{\sqrt{3}}[/tex] . Since √3 divided by itself is 1, this doesn't change the value of the expression. Now multiplying this we get (15√3)/3. Now we can divide 15√3 by 3 to get 5√3, which is the final answer.

Answer:

A

Step-by-step explanation:

Edge 2020

Answer:

Step-by-step explanation:

1+2 cos α

[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]

Answer:

x = 25.

Step-by-step explanation:

Since the side of the triangle that is labeled as 60 units bisects the right angle of the largest triangle, we can say that the smallest triangle, medium triangle, and largest triangle are all similar.

Since the smaller length of the middle triangle corresponds to x, and the longer length of the middle triangle (144) corresponds to the longer length of the smaller triangle (60), we can set up a proportion!

[tex]\frac{x}{60} =\frac{60}{144}[/tex]

144 * x = 60 * 60

144x = 3600

2x = 50

x = 25

Hope this helps!

Answer:

A is the correct answer

Step-by-step explanation:

Graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The system of equations

4x + y = 3 and

2x - 3y = 3

In the first line, the slope is -4, and the y-intercept at (0,3)

In  the second line, the slope is 2/3, and the y-intercept at (0,-1)

Thus, graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

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Answer:

36/100

Step-by-step explanation:

this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.

The probability that we get the same number is 9/25.

It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.

Numbers in first bag=10

Numbers in second bag=10

Common numbers=5,6,7,8,9,10

Total common numbers=6

So the probability that we get the same numbers will be

= 6/10* 6/10

=36/100

=18/50

=9/25

Hence the probability that we will get the same numbers is 9/25.

Learn more about probability at https://brainly.com/question/24756209

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Answer:

5/8

Step-by-step explanation:

The value of the expression is 8/15

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)

The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)

We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n

Here, n = 15.

So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30

= 8/15

Hence, The value of the expression is 8/15

For more references on expressions, click;

https://brainly.com/question/14083225

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Answer:

A. 1/8

Step-by-step explanation:

m = rise/run

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

m = (-5- - 4)/(1-9)

m = (-5+4)/(-8)

m = (-1)/(-8)

m = 1/8

Answer:

The answer is A.

Step-by-step explanation:

Given that the formula to find gradient, m, is :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Then, you have to substitute the coordinates into the formula :

[tex]let \: (9, - 4) \: be \: (x1,y1) \\ let \: (1, - 5) \: be \: (x2,y2)[/tex]

[tex]m = \frac{ - 5 - ( - 4)}{1 - 9} [/tex]

[tex]m = \frac{ - 5 + 4}{ - 8} [/tex]

[tex]m = \frac{ - 1}{ - 8} [/tex]

[tex]m = \frac{1}{8} [/tex]

Answer:

$3.55

Step-by-step explanation:

You need to add 29% of $2.75 to $2.75.

That means the price will be 129% of $2.75.

129% of $2.75 =

= 1.29 * $2.75

= $3.55

Answer:

  78π m²

Step-by-step explanation:

The lateral area of the cylinder is ...

  LA = 2πrh

  LA = 2π(3 m)(8 m) = 48π m²

The lateral area of one cone is ...

  LA = πrh . . . . where h is the slant height

  LA = π(3 m)(5 m) = 15π m²

Then the total surface area of the figure is the area of the two cones plus that of the cylinder:

  S = 2(cone area) + cylinder area

  S = 2(15π m²) +(48π m²)

  S = 78π m²

Answer:

(1, 2)

Step-by-step explanation:

The function m(x) has the point (5, 2) on its graph is equivalent to say that m(x) evaluated at x = 5 gives 2 as result, that is, m(5) = 2.

f(kx) transforms point (x, y) into (x/k, y). Therefore: m(5x) transforms point (5, 2) into (5/5, 2) or (1, 2).

Answer:

25

Step-by-step explanation:

The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:

6/15 = 10/?

6*? = 10*15

? = 10*15/6

? = 25

Answer:

The slope of a linear function. The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run

Step-by-step explanation:

:)