cylinder:
diameter = 6 mm
height = 18 mm

The probability of randomly choosing a number either divisible by 5 or divisible by 3 is 1/2.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of randomly choosing a number either divisible by 5 or divisible by 3 = (numbers divisible by 3 / total number) + (numbers divisible by 5 / total number)

10/32 + 6/32 = 16/32=  1/2

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Answer:

7/16

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Volume = 2714.34

Step-by-step explanation:

This is answer because the formula to finding cylinder volume is: [tex]\pi[/tex][tex]r^{2}[/tex]h

Radius = [tex]\frac{Diameter or Base}{2}[/tex]

Radius = 12

12 squared = 144

144*6 = 864

864[tex]\pi[/tex] = 2714.34 (rounded)

The surface area of the right triangular prism is : 20,568 [tex]in^{2}[/tex]  

using this formula ;SA = bh + (s1 + s2 + s3)*l

A traingular prisms is a prism that has triangles as its base. It has two triangles which are called the bases and three rectangles called the lateral faces.

Given data:

where; SA means the surface area

Therefore:

SA = 24*12 + ( 13 * 13 * 24 ) * 5

SA = 288 + ( 4056) * 5

SA = 288 + 20280

SA = 20,568 [tex]in^{2}[/tex]

In conclusion, the surface area of the right triangular prisms is 20,568 [tex]in^{2}[/tex]

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Answer:

20,568..............................

Answer:

Option B, [tex]396\ units^2[/tex]

Step-by-step explanation:

Step 1:  Determine the area of the bottom

[tex]A = l * w[/tex]

[tex]A = 12\ units * 8\ units[/tex]

[tex]A = 96\ units^2[/tex]

Step 2:  Determine the area of the back

[tex]A = l * w[/tex]

[tex]A = 9\ units * 8\ units[/tex]

[tex]A = 72\ units^2[/tex]

Step 3:  Determine the hypotenuse

Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]

[tex]12^2 + 9^2 = c^2\\[/tex]

[tex]144 + 81 = c^2[/tex]

[tex]225 = c^2[/tex]

[tex]\sqrt{225} = \sqrt{c^2}[/tex]

[tex]15 = c[/tex]

Step 4:  Determine the area of the top

[tex]A = l * w[/tex]

[tex]A = 15\ units * 8\ units[/tex]

[tex]A = 120\ units^2[/tex]

Step 5:  Determine the area of the triangles

[tex]A = \frac{h\ *\ b}{2}[/tex]

[tex]A = \frac{9\ units\ *\ 12\ units}{2}[/tex]

[tex]A = \frac{108\ units^2}{2}[/tex]

[tex]A = 54\ units^2[/tex]

Step 6:  Determine the surface area

[tex]96\ units^2 + 72\ units^2 + 120\ units^2 + 2(54\ units^2)[/tex]

[tex]396\ units^2[/tex]

Answer: Option B, [tex]396\ units^2[/tex]

Answer:

Step-by-step explanation:

Remark

The figure inside the circle is a quadralateral. The 4 angles touch the circumference of the circle. The figure is further defined as a cyclic quadrilateral.

One of the properties of such a figure, is that the opposite angles are supplementary. That is they add to 180.

Equation and solution

? + 100 = 180             Subtract 100 from both sides

? + 100 - 100 = 180 - 100

? = 80 degrees

Answer

? = 80

Answer:

Step-by-step explanation:

In the question it is given that the volume of a sphere is 4,500π cubic yards. And we have to find the radius.

We know that,

Now, Substituting the values in the fomulae :

⇒ 4/3πr³ = 4500π

Cancelling π from both sides :

⇒ 4/3r³ = 4500

⇒ 4r³ = 4500 × 3

⇒ 4r³ = 13500

⇒ r³ = 13500/4

⇒ r³ = 3375

Taking cube root on both sides we get :

⇒ r = 15

Therefore,

Answer:

Step-by-step explanation:

In this question we have provided volume of sphere that is 4500π cubic yards . And we are asked to find the radius of the sphere .

We know that ,

[tex] \qquad \: \frak{Volume_{(Sphere)} = \dfrac{4}{3}\pi r {}^{3} } \quad \bigstar[/tex]

Where ,

Solution : -

As in the question it is given that volume of sphere is 4500π . So equation it with volume formula :

[tex] \dashrightarrow \: \qquad \: \dfrac{4}{3} \pi r {}^{3} = 4500\pi[/tex]

Step 1 : Cancelling π as they are present on both sides :

[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} \cancel{\pi }r {}^{3} = 4500 \cancel{\pi}[/tex]

We get ,

[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} r {}^{3} = 4500[/tex]

Step 2 : Multiplying with 3/4 on both sides :

[tex]\dashrightarrow \: \qquad \: \dfrac{ \cancel{4}}{ \cancel{ 3}} r {}^{ 3} \times \dfrac{ \cancel{3}}{ \cancel{4}} = \cancel{ 4500} \times \dfrac{3}{ \cancel{4} }[/tex]

On further calculations, We get :

[tex]\dashrightarrow \: \qquad \: r {}^{3} = 1125 \times 3[/tex]

[tex]\dashrightarrow \: \qquad \:r {}^{3} = 3375[/tex]

Step 3 : Applying cube root on both sides :

[tex]\dashrightarrow \: \qquad \: \sqrt[3]{r {}^{3} } = \sqrt[3]{3375} [/tex]

We get :

[tex]\dashrightarrow \: \qquad \: \purple{\underline{\boxed{\frak{r = 15 \: yards}}}}[/tex]

Answer:

I just did for your previous posting.

Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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Answer:

Side length: z + 4

Perimeter: 64

Step-by-step explanation:

Hello!

Since the area of a square is the square of the sde length,

using the special binomial product formula: (a+b)² = a² + 2ab + b²:

The side length of the square is (z+4)².

The perimeter is 4(z + 4), where z is 12:

The side length is z + 4, the perimeter is 64

3/4 inch

3 miles

the length of the map

Based on the given conditions, write:

x= 34/ 4 · 25/ 3

Write as a single fraction:

x= 3 × 25/ 4/ 3

Divide a fraction by multiplying its reciprocal:

x= 3 x 25/ 4 × 1/ 3

Write as a single fraction:

x= 3 x 25/ 4 × 3

Reduce fraction to the lowest term by canceling 25 the greatest common factor:

x= 25/4

therefore,the length of the map is 25/ 4.

Answer:

4u-15 is your answer

Step-by-step explanation:

20(1/5u-3/4)

20/5u-60/4

4u-15

Lets solve:

⇒20(1/5u-3/4)

Divide by 20 on each side

⇒20/5u-60/4

Solve the problems

---------------------------------------

⇒4u-15

Final answer: 4u-15

hope this helps :)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{42}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{42}-\stackrel{y1}{21}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{21}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{21}=\stackrel{m}{\cfrac{21}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-21=\cfrac{21}{2}x-21\implies y=\cfrac{21}{2}x[/tex]

Answer:

3/1 is the slope.

Step-by-step explanation:

Slope formula: y2 - y1/x2 - 1

Plugging in the given values, we get:

-9 - (-6)/3-4

-3/-1

Two negatives cancel each other out, so:

3/1 is the slope.

Answer:

Exact form: [tex]\frac{16}{81}[/tex]

Decimal form: 0.1975308

Answer:

Answers are in bold (in order)

Step-by-step explanation:

For the table, the question is asking us to take our x value and put it into the equation. for example:

y = 8x +1 . if x = 0, we can write this as this

y = 8(0) + 1 -> (the brackets mean times)

8 x0 = 0. 0+1 = 1.

if we follow this rule, the values are: 1, 9, 17, 25, 33.

For the function machine, if x = 1, then we can write 1 where the x is. The function machine is telling us that 1 x3 and then -2 = y, y being a random number we don't know. 1 x 3 = 3. That means 3-2 = y . 3-2 = y. So, y = 1 when x = 1.

When x =-9 we can rewrite x as -9. That means that -9 x 3, then -2 = y.

-9 x 3 = -27.

That means that -27 -2 = y

-27 -2 = -29, so when x = -9, y = -29.

For the third part we need to work out the gradient and the equation of the table. The gradient (how much our values go up by) The gradient can be worked out by diving the change in y (our y value) by the change in x (our x value). So, if we take the first two y values, we have -2 and 8. The difference/chance between these two is 10. (-2+10=8). And for the x values, the first two x values are 0 and 1. The difference/change between these two is 1. (1-0=1.) So, all we need to do is divide these values 10/1 = 10. So our gradient is 10. That means that the first box on the function machine will be “x10” to work out the second, we simply do the first box and go from there. If our x = 1, then 1 x 10 = 10. Our table says that when x = 1, y = 8. So to we need to work out the change between these is, to get our answer. To get from 10 to 8, we minus two. So the final box on the function machine must be “-2”

For the last part of the question, we are just substituting in the values of x.

If t = 1, then 4(t-3) is basically 4(1-3)

1-3 = -2. 4(-2) = -8.

so when t =1, s = -8. If you do this for the next two questions, you should get the answers:

s = -28 when t = -4

s = -12 when t = 0

Answer:

x = 9, y = 3

Step-by-step explanation:

-2x-2y=-24 (EQ 1)

-3x-2y=-33 (EQ 2)

Combining terms we means we either add or subtract the equations in order to eliminate a x or y terms. Simply choose a equation and change it to it's opposite (ex. -3 becomes 3.)

Let's try swapping EQ 1

2x + 2y = 24

(Simply add similar variables and numbers like you would a addition problem.)

-3x-2y=-33

-x = -9

x = 9

Now plug that into one of your equations to get y.

-2(9) -2y = -24

-18 -2y = -24

(Add 18 to both sides.)

-2y = -6

y = 3

Answer:

you have to multiple 5x5x5

Answer:

68.3 cm^2

Step-by-step explanation:

Assuming slant height is 5 cm :  ( the Q does not say)

The base area will be   5 x 5 = 25 cm^2

then you have 4 equilateral triangles of side length 5 cm

  total area = 43.3 cm^2

SUM = 68.3 cm^2

The number of bags of flour would be 40.

And, the number of bags of sugar would be 120.

Given that,

You must buy three times as many bags of sugar as there are bags of flour.

And, you are on a budget of $720. Flour costs $6 per bag and sugar costs $4 per bag.

Let us assume that,

The number of bags of flour = x

And, the number of bags of sugar = y

Hence, we get;

y = 3x  .. (i)

And, 6x + 4y = 720  .. (ii)

Substitute x = 3y in (ii);

6x + 4 (3x) = 720

6x + 12x = 720

18x = 720

x = 720/18

x = 40

From (i);

y = 3 × 40

y = 120

Thus, The number of bags of flour = 40

And, the number of bags of sugar = 120

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Answer:

175

Step-by-step explanation:

35 times 5 is 175

Hope This Helped

Answer:

  Future amount = 48(1 + 0.316074)^12

Step-by-step explanation:

You want the exponential equation that can be used to find the number of bacteria in a colony after 12 days if it starts with 48 bacteria and triples in 4 days.

The exponential function can be written in the form ...

  future amount = a·b^(t/p)

where 'a' is the initial amount, 'b' is the growth factor in period p.

The problem statement tells you the initial amount is 48, and the factor by which the amount grows is a factor of 3 in 4 days. This lets you write the function as ...

  future amount = 48·3^(t/4) . . . . . where t is in days.

This equation can be rearranged so the only exponent is t:

  future amount = 48·(3^(1/4))^t = 48·1.316074^t

  future amount = 48·(1 +0.316074)^t

Then the amount in 12 days is ...

  future amount = 48·(1 +0.316074)^12

The numbers that go in the boxes are 0.316074 and 12.

__

Additional comment

Working from our original equation, we would compute the number after 12 days to be ...

  future value = 48·(3)^(12/4)

Putting the growth factor in "1 +" form, this could be ...

  future value = 48·(1 +2)^3

and your box numbers would be 2 and 3. We doubt your answer checker will accept this version of the equation.

Either way, the number of bacteria after 12 days is 1296.

If you use 3^(1/4) -1 as the growth rate in the first box, you need to report it to at least 5 significant digits in order for the future value to come out right. We have shown the value with 6 significant figures.

<95141404393>

Answer:

Step-by-step explanation:

The expression (2m^4)^3is an algebraic expression, and the simplified value is 8m^12

The expression is given as:

(2m^4)^3

Expand the bracket

(2m^4)^3 = 2^3 * m^(4 * 3)

Evaluate the exponents

(2m^4)^3 = 8 * m^12

Evaluate the product

(2m^4)^3 = 8m^12

Hence, the simplified value is 8m^12

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Answer:

Step-by-step explanation:

7*.01= .7

2*100=200

3*1000=3000

4*1=4

5*.01=.05

.7+200+3000+4+.05=3204.75

Answer:

yes because 1/2= .5

and 6/12= .5 so they are equivalent

yes

In order to determine whether or not 6/12 is equivalent to 1/2, we need to reduce the first fraction.

Reduce by dividing the top & bottom by 6 ↓

[tex]^6/_{12}=^1/_2[/tex]

hope helpful ~

Answer:

y = 9/13

Step-by-step explanation:

x = -4 + y

5(-4 + y) + 4y = 7

-20 + 9y = 7

9y = -13

Answer:

5x + 4y = 7 × -2

-2x - 2y = 8 × 5

-10x - 8y = -14

-10x - 10y = 40

Step-by-step explanation:

2y = -54 ÷2

y = -27

Now substitute the value of y into equation (1)

5x + 4y = 7

5x + 4(-27) = 7

5x = 7 + 108

5x = 115

X = 23

Answer:

The value of x = 6

Step-by-step explanation:

=> 4(x + 2) = 32

=> 4x + 8 = 32

=> 4x = 32 - 8

=> 4x = 24

=> x = 24/4

=> x = 6

Answer:

6441.46 (2d.p.)

Step-by-step explanation:

47×89= 4183÷(845)=0.571×879000=502434.319÷78= 6441.46