The jug can hold 1500ml. The bucket can hold 2 litres. The barrel can hold 15 litres. Anisa wants to fill the barrel with water. Find 2 ways that Anisa can fill the barrel using the jug and bucket

Answer:

[tex]\large \boxed{\sf \ \ \pi r^2 \ \ }[/tex]

Step-by-step explanation:

Hello,

We will follow the instructions and then we need first to find the area of any regular n-gon.

I attached one graph so that it is easier to understand.

The n-gon can be divided in n similar isosceles triangles.

So we can find the area of one of these triangles and then multiply by n to get the total area, right?

Let's focus on the triangle OAB then. OA = OB = r, right?

The area of this triangle is the (altitude * AB ) / 2

The angle AOB is [tex]\dfrac{2\pi}{n}[/tex] by construction of the regular n-gon.

So half this angle is [tex]\dfrac{\pi}{n}[/tex] and we can use cosine rule to come up with the altitude:

   [tex]\boxed{ altitude = r\cdot cos(\dfrac{\pi}{n}) }[/tex]

Using the sine rule we can write that

   [tex]\boxed{ AB=2r\cdot sin{\dfrac{\pi}{n}} }[/tex]

So, the area of the triangle is

   [tex]\dfrac{1}{2}\cdot r\cdot cos(\dfrac{\pi}{n}) } \cdot 2r\cdot sin(\dfrac{\pi}{n})\\\\=r^2\cdot cos(\dfrac{\pi}{n})\cdot sin(\dfrac{\pi}{n})[/tex]

Ok, but wait, we know how to simplify. We can use that

[tex]sin(2\theta)=2cos(\theta)sin(\theta)[/tex]

So it gives that the area of one triangle is:

   [tex]\dfrac{1}{2}r^2sin(\frac{2\pi}{n})[/tex]

Last step, we need to multiply by n.

[tex]\large \boxed{\sf \ \ A(n)=\dfrac{1}{2}nr^2sin(\dfrac{2\pi}{n}) \ \ }[/tex]

Now, let's use a result from Calculus:

[tex]\displaystyle \lim_{x\rightarrow0} \dfrac{sin(x)}{x}=1[/tex]

How to use it here? Just notice that

[tex]\displaystyle \lim_{n\rightarrow +\infty} \dfrac{sin(\dfrac{2\pi}{n})}{\dfrac{2\pi}{n}}=1\\\\\lim_{n\rightarrow +\infty} \dfrac{n}{2\pi}sin(\dfrac{2\pi}{n})=1\\\\\lim_{n\rightarrow +\infty} nsin(\dfrac{2\pi}{n})=2\pi[/tex]

So, finally

[tex]\Large \boxed{\sf \lim_{n\rightarrow +\infty} A(n)=\dfrac{1}{2}r^22\pi=\pi r^2 }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

The deductible amount will be controlled constantly in which the asset is arranged.

Answer:

Step-by-step explanation:

First one is 200 dollars for insurance which will be the constant and 15 dollars an hour which means the equation will be;

C = 15h +200 (Sinking Rivers)

Second one is $30 an hour and $110 for insurance which is the constant so he equation is;

C = 30h + 110 (Floating Down The Stream)

Answer:

  [tex]\textbf{B. }\ \dfrac{3}{2}\sqrt{2}[/tex]

Step-by-step explanation:

You know the short side of an isosceles right triangle is 1/√2 times the hypotenuse. So, the hypotenuse of the 30°-60°-90° right triangle is ...

  6/√2 = (6√2)/2 = 3√2

You also know the short leg of a 30°-60°-90° right triangle is half the length of its hypotenuse, so ...

  x = (1/2)(3√2)

  x = (3/2)√2

_____

Additional comment

For many trig and geometry problems, it is useful to remember the ratios of side lengths for "special" right triangles:

  isosceles right triangle: 1 : 1 : √2

  30°-60°-90° triangle: 1 : √3 : 2     (shortest to longest)

This knowledge usefully relates to the trig function values for these "special" triangles.

Answer:

3/√2 or 3√2/2

Step-by-step explanation:

Bigger triangle has internal angles 45/45/90, so the legs have equal length and = 6/√2 as hypotenuse = 6

Smaller triangle has hypotenuse of 6/√2 and the angle against leg x is 30°

As we know the leg opposite to 30° angle is half the hypotenuse, so

Answer:

1:15 pm

Step-by-step explanation:

It takes 6 hours to reach London from Minneapolis and she reached Minneapolis at 7:15pm so

7:15 - 6 = 1:15

Answer:

[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]

Step-by-step explanation:

According to the given situation, as we know that the triangle which is ADE and triangle which is ABC are the same

. (as in the diagram)

So, the ratio of their corresponding sides are the same or an equal so that it can be reached at the truth which is here below:

[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]

With the help of a diagram, we can better understand which has been attached.

The ratios  AD : DB  and  AE : EC  are equal.

Answer:

select the first, second, and third option

Step-by-step explanation:

the fourth option is wrong because the lines are intersecting

Answer:

56,735 people

Step-by-step explanation:

We can set up an equation to model this:

The equation for exponential decay is y = C(1 - r)^t, where C is the original amount, r is rate of change, and t is time.

We can plug in the corresponding values and solve:

y = 62500(1 - 0.016)^6

y = 62500(0.984)^6

y = (62500)(0.9077)

y = 56,734.94, which we can round to 56,735 people

Hope you understand :)

Answer:

2 mins 30 secs

Answer:

x = 2

Step-by-step explanation:

x + 1/2 (6x - 4) = 6

Expand the brackets.

x + 3x - 2 = 6

Add like terms.

4x - 2 = 6

Add 2 on both sides.

4x = 6 + 2

4x = 8

Divide 4 into both sides.

x = 8/4

x = 2

Answer:

x=5/4

Step-by-step explanation:

Answer:

x = 6 , − 5

Step-by-step explanation:

Move  x   to the left side of the equation by subtracting it from both sides.  x^ 2 − 30 − x = 0

x2-30-x=0

Use the quadratic formula to find the solutions. − b ± √ b 2 − 4 ( a c )/ 2 a  

-b±b2-4(ac)/2a  

Substitute the values  

a = 1  ,  b = − 1  , and  c = − 30  

into the quadratic formula and solve for  x

x . 1 ± √ ( − 1 ) 2 − 4 ⋅ ( 1 ⋅ − 30 )/ 2 ⋅ 1    

Simplify.

x = 1 ± 11/ 2    

The final answer is the combination of both solutions.

x = 6 , − 5

Answer:

Step-by-step explanation:

2^{60}=8^x

2^{60}=(2^3)^x

2^{60}=2^{3x}

60=3x

x=20

Answer:

8^20 would be the answer

Answer:

[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{4}[/tex]=[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

This sentence isn't always true.

The trick is to use fractional numbers .

let's analyse this example :

1/2=0.5 and 1/4=0.25 but 1/8=0.125

0.125<0.25<0.5

The product of two positive numbers is less than either number i.e. 4 × (1/2) = 2 < 4 which counterexample shows that the conjecture is false.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

We have been that conjecture "The product of two positive numbers is always greater than either number."

As per the given condition,

For example: 4 × (1/2) = 2 < 4

Therefore, the product of two positive numbers is less than either number i.e. 2 < 4.

Hence, the above counterexample shows that the conjecture is false.

Learn more about the number system here:

https://brainly.com/question/21751836

#SPJ2

Answer:

So we must create 4-digit numbers with the 5 odd digits in the image.

First, a number is only divisible by 5 if the last digit is 0 or 5, and we only can use the last digit equal to 5 (because 0 is not in the image).

if each odd number can be used only once, we have:

Now, for the other 3 digits we have 4 options.

So for the first one we have 4 options,

for the second we have 3 options (because one is already taken)

for the last one we have only 2 options

then the number of combinations is:

C = 4*3*2 = 24.

If the numbers can be repeated (for example, 5555 is allowed, then)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third we also have 5 options, then we have a total of:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

V = 960 cm ^3

Step-by-step explanation:

The volume is given by

V = Bh where B is the area of the base

B = 1/2 bh since the base is the triangle

B = 1/2 *12*8 =48

V = 48 * 20

V = 960 cm ^3

Answer:

960 cm^3

Step-by-step explanation:

volume of prism = (area of base) * (height of prism)

This is a triangular prism, so the base is a triangle.

area of base of prism = area of triangle = bh/2

The base of the triangle is 12 cm. The height of the triangle is 8 cm.

The height of the prism is 20 cm.

volume = (12 cm)(8 cm)/2 * 20 cm

volume = 960 cm^3

Answer:

Step-by-step explanation:

10)a) Let the number = x

4x + 8 = 16

Subtract 8 form both sides

4x + 8 - 8 = 16 - 8

4x = 8

Divide both sides by 4

4x/4 = 8/4

x = 2

The number is 2

b) Let the number = x

4x - 8 = 6

Add 8 to both sides

4x - 8 + 8 = 6 + 8

4x = 14

Divide both sides by 4

4x/4 = 14/4

x = 3.5

The number is 3.5

11) a) Increase in cost = 105 - 100 = $ 5

b) Percentage increase = [tex]\frac{5}{100}*100[/tex]

                                       = 5%

12)  Number of girls = 35

Number of girls wearing glasses  = 15

Number of boys = 40

Number of boys wearing glasses  = 10

a) Percentage of boys wearing glasses = [tex]\frac{10}{40}*100\\[/tex]

                                                                 = 25%

b) Percentage of girls wearing glasses = [tex]\frac{15}{35}*100[/tex]

                                                                 = 42.86%

c) Total children = 35 +40 = 75

Total children wearing glasses = 15 + 10 = 25

Percentage of children wearing glasses = [tex]\frac{25}{75}*100[/tex]

                                                                        = 33.33%

Answer:

50 years

Step-by-step explanation:

the answer is 50 years bc 2% of 3000 is 60 and to get to 300 from 60 you would multiply by 50 to get 3000 added to the populationg colorado has now you get 6000.

brainliest pls

Answer:

This is an arithmetic sequence with a common difference d of -9

Step-by-step explanation:

When you find out d, you realize the difference between the numbers to be -9. Since it is d and not common ratio r, it is an arithmetic sequence.

Answer:

Originally there was 324 nuts in the bag.

Phillip took 108, Joy took 54, Brent took 81 and Preston took 10.

Step-by-step explanation:

Let's call the total amount of nuts N, and the number of nuts each child took by the initial of their name (Phillip will be P1 and Preston will be P2).

So we can write the following equations:

P1 = N/3

After removing N/3, the remaining nuts is (N - N/3):

J = (N - N/3)/4 = (2N/3)/4 = N/6

After removing N/6 from (N - N/3), the remaining nuts is (N - N/3 - N/6):

B = (N - N/3 - N/6)/2 = (N/2)/2 = N/4

P2 = 10

In the final there were 71 nuts remaining, so we have that:

N - N/3 - N/6 - N/4 - 10 = 71

N - N/3 - N/6 - N/4 = 81

N/4 = 81

N = 324 nuts

The amount of nuts took by each child is:

P1 = N/3 = 108 nuts

J = N/6 = 54 nuts

B = N/4 = 81 nuts

P2 = 10 nuts

Answer:

Step-by-step explanation:

even #s between (or including) 1 and 12:

2, 4, 6, 8, 10, 12

there are 6

6/12 for the first one

5/11 for the second one (one even # less)

4/10 for the third one

To find the probability of picking three even numbers from 1 to 12 in a row three times:

multiply the probabilities together:

(6/12)*(5/11)*(4/10)=(24/120)*(5/11)=(12/60)*(5/11)=(1/5)*(5/11)=5/55=1/11

Answer:  x=3

Step-by-step explanation:

5x+9 =24   subtract 9 from both sides

    -9    -9

5x = 15    Divide both sides by 5

x = 3

Answer:

[tex]5x = 24 - 9 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]

Answer:

Answer:

They are both correct.

Step-by-step explanation:

As we can see, it does not matter whether you plug in x or y in a system of equatins. One thing somebody might be skeptical about in this equation is that one of the equations does not contain a variable. BUT, if reading closer, one can see that both x and y have to be in one of the equations to make the other true.

Hope this helped!

We will see that both Jared and Nicole are correct.

So we know that Jared found an equation:

y = x + 10, then he substituted y for (x + 10) on the other equation, this would be the substitution method, and Jared is correct so far.

We also know that Nicole found the equation:

x = y - 10

And she replaced x by y - 10 on the other equation, she is also correct.

Each one just substituted a different variable, that is why they have different approaches, but in both cases the substitutions are correct.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

The answer is option B

Step-by-step explanation:

t^12/t^6

Use the rules of indices.

Since they have the same base and they are dividing we subtract the exponents.

That's

t^12 - 6

= t^6

Hope this helps you

Answer:

Option B is the right option.

Solution,

[tex] \frac{ {t}^{12} }{ {t}^{6} } \\ = {t}^{12 - 6} \\ = {t}^{6} [/tex]

Explanation:

To divide expression with same base, we copy the base and subtract the indices.

Hope this helps...

Good luck on your assignment..

Answer:

False

Step-by-step explanation:

A definition produces out of nothing a new mathematical entity. But a theorem utilizes some relation between previously defined mathematical entities.

Usually a theorem must be verified by a proof of its correctness on the basis of generally accepted statements or on the basis of previously established statements which might include other theorems.

Answer:

24p = 72

Step-by-step explanation:

Let the number be p.

The product of p and 24 equals to 72.

p × 24 = 72

24p = 72

Answer:

24p = 72

Step-by-step explanation:

A

Answer:

[tex]-12-10i[/tex]   is the required answer.

Step-by-step explanation:

[tex]\left(-9-8i\right)-\left(3+2i\right)\\\\\mathrm{Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number}\\\\=\left(-9-3\right)+\left(-8-2\right)i\\\\=-12-10i[/tex]

Best Regards!

Answer:

Step-by-step explanation:

   45=5*3^2

    75=5^2*3

1.  LCM=product of the common and uncommon prime factors  at the biggest   power

LCM=3^2*5^2=9*25=225

2. HCF= product of the common prime factors at the lowest power

HCF=3*5=15

3. 10*x-3

4. 6^2-7^2=36-49=-13

5. I. K=4-1=3 drinks

    II. Total=4+3=7 drinks

6. You will draw exact as inthe drawing with dimensions l=8 cm,h=3cm, w=4 cm

Answer:

Step-by-step explanation:

LCM of two numbers is the smallest number that is evenly divisible by the two numbers

1) 45 = 3 * 3 * 5 = 3² * 5

75 =  3 * 5 * 5  = 3 * 5²

LCM = 3² * 5² = 9 *25 = 225

LCM = 225

2) HCF of two numbers is the greatest number which divides each of them exactly.

HCF of 45 and 75  = 3*5 = 15

HCF = 15

3) 10x  - 3

4) m² - n² = 6² - 7²

               = 36 - 49

               = -13

m² - n² = -13

When two numbers are in different sign, subtract and the result will have the sign of the bigger number.

5)a)  Kate prepared  (4-1) 3 drinks

  b) Total volume of drinks = 4 + 3 = 7