Daniel fish tank holds 24 L of water he uses a 4 L bucket to fill the tank how many buckets of water are needed to fill the tank

For HCF you can list the factors of the numbers and see which is the highest factor that they have in common. For LCM you list put the multiples and find the lowest one they have in common

Answer:

[tex]S_{1893} =5632.98[/tex]

Step-by-step explanation:

The correct form of the question is:

[tex]S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1[/tex]

Required

Solve for Sum of the sequence

The above sequence represents sum of Geometric Sequence and will be solved using:

[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]

But first, we need to get the number of terms in the sequence using:

[tex]T_n = ar^{n-1}[/tex]

Where

[tex]a = First\ Term[/tex]

[tex]a = 1.001^{1892}[/tex]

[tex]r = common\ ratio[/tex]

[tex]r = \frac{1}{1.001}[/tex]

[tex]T_n = Last\ Term[/tex]

[tex]T_n = 1[/tex]

So, we have:

[tex]T_n = ar^{n-1}[/tex]

[tex]1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}[/tex]

Apply law of indices:

[tex]1 = 1.001^{1892} * (1.001^{-1})^{n-1}[/tex]

[tex]1 = 1.001^{1892} * (1.001)^{-n+1}[/tex]

Apply law of indices:

[tex]1 = 1.001^{1892-n+1}[/tex]

[tex]1 = 1.001^{1892+1-n}[/tex]

[tex]1 = 1.001^{1893-n}[/tex]

Represent 1 as [tex]1.001^0[/tex]

[tex]1.001^0 = 1.001^{1893-n}[/tex]

They have the same base:

So, we have

[tex]0 = 1893-n[/tex]

Solve for n

[tex]n = 1893[/tex]

So, there are 1893 terms in the sequence given.

Solving further:

[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]

Where

[tex]a = 1.001^{1892}[/tex]

[tex]r = \frac{1}{1.001}[/tex]

[tex]n = 1893[/tex]

So, we have:

[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }[/tex]

[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }[/tex]

[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }[/tex]

[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }[/tex]

Simplify the numerator

[tex]S_{1893} =\frac{1.001^{1892} -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }[/tex]

[tex]S_{1893} =\frac{1.001^{1892} -1.001^{1892-1893}}{\frac{0.001}{1.001} }[/tex]

[tex]S_{1893} =\frac{1.001^{1892} -1.001^{-1}}{\frac{0.001}{1.001} }[/tex]

[tex]S_{1893} =(1.001^{1892} -1.001^{-1})/({\frac{0.001}{1.001} })[/tex]

[tex]S_{1893} =(1.001^{1892} -1.001^{-1})*{\frac{1.001}{0.001}}[/tex]

[tex]S_{1893} =\frac{(1.001^{1892} -1.001^{-1}) * 1.001}{0.001}[/tex]

Open Bracket

[tex]S_{1893} =\frac{1.001^{1892}* 1.001 -1.001^{-1}* 1.001 }{0.001}[/tex]

[tex]S_{1893} =\frac{1.001^{1892+1} -1.001^{-1+1}}{0.001}[/tex]

[tex]S_{1893} =\frac{1.001^{1893} -1.001^{0}}{0.001}[/tex]

[tex]S_{1893} =\frac{1.001^{1893} -1}{0.001}[/tex]

[tex]S_{1893} =5632.97970294[/tex]

Hence, the sum of the sequence is:

[tex]S_{1893} =5632.98[/tex] ----- approximated

Answer:

3/2 or 1.5 each hour

Step-by-step explanation:

3/4/1/2

=6/4

=3/2

=1.5

or

3/4*2=

1.5

Answer:

D. |w| = 14.2; θ = 107.1°

Step-by-step explanation:

EDGE 2020

Answer:

8 + 18+ 28+ 38+ 48= 140

Step-by-step explanation:

Answer:

Step-by-step explanation:

140

Answer:

b should be the answer

Step-by-step explanation:

Answer:

C is the correct answer

Step-by-step explanation:

I know thus because you go down 5/10 every time and 5/10 as a decimal is 0.5 which means the slope is -0.5

Answer:

wheres the word problem portion of the question

Step-by-step explanation:

tell me and I'll be happy to answer you

Answer: You need to add the question

Step-by-step explanation:

to get the answer I cant see the question that well

Answer:

Pls attach graph

Step-by-step explanation:

Answer:

4.8 hours

Step-by-step explanation:

20% of 24 hours is the product of the decimal form of 20% (which is 0.2) times 24.

The answer is:

0.2 * 24 = 4.8 hours which is the same as 4 hours and 48 minutes.

Answer:

A

Step-by-step explanation:

- to find x we use tan 60 = x/7

- rearrange, tan60*7 = x, x = [tex]7\sqrt{3}[/tex]

- now you have two sides so you can use pythagoras  to find z

y^2 + x^2 = z^2

z = [tex]\sqrt{(7\sqrt{3})^2 + (7)^2 }[/tex]

z = 14

Answer:

I believe the answer would be the last box or the bottom right box

Step-by-step explanation:

Answer:

bottom right one

Step-by-step explanation:

took the unit test

Answer:

The values of b are [tex]\mathbf{b=\pm18}[/tex]

Step-by-step explanation:

We need to find the value of b will cause [tex]27x^2+ bx +3 = 0[/tex] to have one real solution.

If it has one real solution, the discriminant is zero.

The formula of discriminant is: [tex]b^2-4ac[/tex]

In our case: [tex]b^2-4ac=0[/tex]

We have a=27, b=b and c=3

Putting values to find b

[tex]b^2-4ac=0\\b^2-4(27)(3)=0\\b^2-324=0\\b^2=324\\Taking \ square root \ on \ both \ sides\\\sqrt{b^2}=\sqrt{324}\\b=\pm18[/tex]

So, the values of b are [tex]\mathbf{b=\pm18}[/tex]

Answer:

1 question. will be 2.3

2 question. 2.6

3 question. 9.2

Here some answers sry i can't answer all

Answer:

Read the following:

Step-by-step explanation:

1. 2.3

2. 2.6

3. 9.2

4 .6.6

5. 1 and 5/8

6. 24

7. 8/5

hope this helps :)

Answer:

A,C,E.

Step-by-step explanation:

slope=(-12-0)/(4-0)=-3

A.The slope is proportional.

C. Slope is negative.

E. The eq. of line is y=-3x

Answer:

10

Step-by-step explanation:

HCF of 20, 40 & 50:

20: 1, 2, 4, 5, 10, 20

40: 1, 2, 4, 5, 8, 10, 20, 40

50: 1, 2, 5, 10, 25, 50

HCF: 10

Topic: HCF and LCM

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

2

Step-by-step explanation:

Answer:

The answer is 2. Hope this helps you out!

Step-by-step explanation:

Answer: y=1/3x-2

Step-by-step explanation:

To find the equation of the line, we need the slope and y-intercept. To find the slope, we can take any two points on the graph and use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. To find the y-intercept, we find the point that crosses the y-axis. The two points on the graph are (0,-2) and (3,-1).

[tex]m=\frac{-1-(-2)}{3-0} =\frac{1}{3}[/tex]

Now, we know the slope is 1/3.

The graph crosses the y-axis at (0,-2). Therefore the y-intercept is -2. This tells us that the equation is y=1/3x-2.

Answer:

Undefined

Step-by-step explanation:

Answer:

3 adult tickets and 4 child tickets

Step-by-step explanation:

a + k = 7

a = 7 - k

12a + 9k = 72

12a + 9k = 72

12(7 - k) + 9k = 72

84 - 3k = 72

84 - 3k = 72

3k = 12

k = 4

a = 3

The number of adult tickets purchased is 3 and the number of child tickets purchased is 4.

Given that, adult tickets cost $12 and child tickets cost $9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

If they spent $72 total and purchased 7 tickets.

Let the number of adult tickets be x, then the number of children tickets will be 7-x.

Now, 12x+9(7-x)=72

⇒ 12x+63-9x=72

⇒ 3x=72-63

⇒ 3x=9

⇒ x=3

So, 7-x=4

Therefore, the number of adult tickets purchased is 3 and the number of child tickets purchased is 4.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

i thi9nk its the 3rd one or the 1st one im sooooooooooooooo sorry if i gave you the wrong answer hope you pass

Step-by-step explanation:

Answer:

the answer is y=3x+9 if you are looking for it to be in slope intercept form

Answer:

c,

Step-by-step explanation:

have a good day, glad I could help :)

The last one.

........

5 feet = 60 inches

Sarah needs to grow 6 more centimeters.

Answer: So since 5 feet equals 60 inches and 1 inch is about 2.54 centimeters, there are centimeters in 5 feet. Therefore, Sarah needs to grow 6 more centimeters to reach 5 feet. I hoped this helps!! :D

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

Answer:

Step-by-step explanation:

its written as a ratio of two integers, so its a rational number.

Answer:

true

Step-by-step explanation:

Answer:

It's true bro

Step-by-step explanation: