A water tank discharges at the rate of 80 L/min. How long would it take to
discharge 4800 L?

Answer:

3.3.1

A cylinder has a circular base.

3.3.2

As cylinders have circular bases, the formula for the area of the base of a cylinder should be the same as the formula for the area of a circle:

[tex]\boxed{\mathrm{Area = \pi r^2}}[/tex].

3.3.3

To find the volume of a cylinder, we can imagine stacking multiple circles on top of each other so that the height of the structure increases, and the shape becomes a cylinder.

This means that the volume of a cylinder is simply the area of the base circle multiplied by the height (h) of the cylinder.

∴ [tex]\boxed{\mathrm{Volume = \pi r^2h}}[/tex].

3.3.4

We can use the above formula to calculate the volume of the given cylinder, where:

• r = [tex]\mathrm{\frac{diameter}{2}}[/tex] = [tex]\frac{8}{2}[/tex] = 4 m

• h = 3 m

∴ [tex]\mathrm{Volume = \pi \times (4 \: m)^2 \times 3 \: m}[/tex]

               [tex]= \mathrm{\pi \times 16 \:m^2 \times 3 \: m}[/tex]

               [tex]= \mathrm{48 \pi \: m^3 }[/tex]

               [tex]= \mathrm{\bf150.8 \space\ m^3}[/tex]

Answer:

-2

Step-by-step explanation:

g(x) = -x-4

g(-2) = -(-2)-4

           2 - 4

              -2

Answer:

g(-2) = -2

Step-by-step explanation:

Hello!

To evaluate for -2, we can substitute -2 for x in the equation.

g(-2) is -2.

Answer:

If the length of a tree's shadow is 35.25 meters. The height of the tree to the nearest hundredth of a meter will be : 11.74m

Given:

Denora height=1.35 meters

Length =35.25 meters

Width =31.2 meters

Height of the tree=x

Proportion:

1.35 : 35.25 :: x : 31.2

Now let's determine the height of the tree:

35.25 - 31.2 / 1.35 = 35.25 / x

4.05 / 1.35 = 35.25 / x

Cross multiply

4.05x = 35.25 × 1.35

4.05x = 47.58

Divide both sides

x = 47.58 / 4.05

x = 11.74

In conclusion, if the length of a tree's shadow is 35.25 meters. The height of the tree to the nearest hundredth of a meter will be: 11.74m

The ages of Wilson, Randy and Greg given their total ages is 7, 10 and 15 years respectively.

This means that the total ages of Wilson, Randy and Greg is 7 years, 10 years and 15 years.

Let's represent the information above as follows:

The total ages = Wilson + Randy + Greg

That is, Wilson's age, Randy's age and Greg's ages is given as:

32 = x + (x + 3) + (x + 3) + 5

32 = x + x + 3 + x + 3 + 5

32 = 3x + 11

32 - 11 = 3x

21 = 3x

x = 21/3

x = 7 years

Therefore, from the calculations above,

Wilson's age = x

= 7 years

Randy's age = (x + 3)

= 7 + 3

= 10 years

Greg = (x + 3) + 5

= (10) + 5

= 15 years

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Answer:

1/5 c - 5

Step-by-step explanation:

1/5 c - 5 = (c - 25)/5

Answer:

12.2 km

Step-by-step explanation:

Here is ONE way :

7.6 mi * 5280 ft/mi * 12 in / ft   /   (39.37 in / m * 1000 m / km)  = 12.2 km  

The expression will be 0.01

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do

Rewrite the expression using the negative exponent rule b

b₋ⁿ= 1/b-ⁿ

⁺1/10²

Raise

10

to the power of

2

The result can be shown in multiple forms.

Exact Form:

−

1/100

Decimal Form:

−

0.01

So therefore the expression will be 0.01.

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y=-20, x=-1, c= -5

SOlution :

three-by-three systems:

In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables x,y,z

is called an ordered triple.

To find a solution, we can perform the following operations:

Interchange the order of any two equations.

Multiply both sides of an equation by a nonzero constant.

Add a nonzero multiple of one equation to another equation.

HOW TO: GIVEN A LINEAR SYSTEM OF THREE EQUATIONS, SOLVE FOR THREE UNKNOWNS.

Pick any pair of equations and solve for one variable.

Pick another pair of equations and solve for the same variable.

You have created a system of two equations in two unknowns. Solve the resulting two-by-two system.

Back-substitute known variables into any one of the original equations and solve for the missing variable.

3⁢x+6⁢y−5⁢z=29...(1)

-9⁢x+y+4⁢z=9...(2)

-8⁢x+7⁢y+5⁢z=4...(3)

Solving 1&2

3x+6(9-4z+9x)-5z=29

3x+54-24z+54x-5z=29

57x+54-29-29z=0

57x+25-29z=0

57x-29z=25...(3)

Solving  2& 3

-8x+7(9-4z+9x) +5z=4

-8z+63-28z+63x+5z=4

55x-23z-59=0 ..(4)

Solving 3 & 4

57x-29z=25...(3)

55x-23z-59=0 ..(4)

(55x29-57x23)x=59x23-25x23

-2906x = 2906

x=-1

putting it on equation 4

55x-23z-59=0 ..(4)

55(-1)-23z-59=0 ..(4)

z= - 5

-9⁢(-1)+y+4⁢(5)=9.

9+y+20=9

y=9-20-9

y=-20

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Answer:

(-4, 1, -7)

Step-by-step explanation:

and got it right on edmentum

Answer:

Either, it's 2,800 and that would be 2 zeroes or it is 400,000,000 and that would be 8 zeroes

Step-by-step explanation:

40 x 10 x 7 = 2,800

40 x 10^6 = 400,000,000

Total 8 zeroes are in the product of 40 × 10⁷.

Let's step-by-step dissect the calculation and the total amount of zeros.

We are given the phrase  40 × 10⁷, where 10⁷ is defined as 10 multiplied by 7.

Step 1: Calculate 10⁷

10^7 means 10 raised to the power of 7, which is equal to 10,000,000 (10 million). This is because 10⁷ = 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10,000,000.

Step 2: Calculate the product 40 × 10⁷

Now, we multiply 40 by 10,000,000:

40 × 10,000,000 = 400,000,000

The product 400,000,000 has a total of 9 digits.

Instead of just looking at the overall number of digits, we are more concerned with the amount of zeros in the product.

Counting the zeros:

In the number 400,000,000, there are 8 zeros. These zeros come from the seven factors of 10 in the product 10⁷.

So, the product of 40 × 10⁷ has 8 zeros.

In conclusion, the result of 40 times 10 raised to the power of 7 is 400,000,000, which has eight zeros. This is so because every factor of 10 adds a zero to the final total.

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The lateral surface area of prism is 240cm2, total surface area is 250cm2 of prism , the volume of prism is 100cm2.

What is lateral surface of prism?

The lateral surface area of the right triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h, where a, b and c are the bases of the rectangular faces and h is the common height or the total height of the prism. Also, (a + b + c) is the perimeter of the base (triangle).

What is total surface area of prism?

The total surface area of a right prism is T. S. A. = PH+2A, where P is the base perimeter, A is the base area, and H is the height of the prism.

What is volume of prism?

The formula for the volume of a prism is given by the product of the base and height of the prism. Thus, the volume of a prism can be given as V = B × H where V is the volume, B base area, and H height of the prism.

Given that,

The sides of prism are a=3cm, b= 4cm, c= 5cm

Also given that the height of the prism is h=20cm.

The lateral surface area of prism (LSA) = ah + bh + ch

Lateral surface area of prism = (3)(20)+(4)(20) +(5)(20)

Lateral surface area of prism = 60 + 80 + 100

Lateral surface area of prism = 240 cm2

The Total surface area of prism (TSA) = ph+2a

Total surface area = (LSA) + area of 2 bases

Total surface area = 240 + 2(5)

Total surface area = 250cm2

The volume of prism = base x height

Volume of prism = 5 x 20

Volume of prism = 100cm2.

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The required result of the sliding filament model given below.

The mechanism by which muscles contract is described by the sliding filament model. Actin and myosin myofilaments move over one another as a result of a cycle of repeated occurrences, constricting the sarcomere and creating tension in the muscle.

The A band is the middle, darkly pigmented area of the sarcomere that runs the entire length of the thick filaments. The portion of the thin filaments that cross over the thick filaments is also included. The I band is formed by the remaining thin filaments within the sarcomere but not by any thick filaments. Each A band has a narrow region in the middle called the H zone, which is made up entirely of dense filaments.

Myosin heads pull the thin filaments in the direction of the M line during muscle contraction. Because of this, the thin filaments glide inward, allowing their ends to overlap and connect at the sarcomere's core. The I band and H zone become smaller as a result.

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Answer:

1 cm

Step-by-step explanation:

you multiply 3 by 1/3 and you get 3/3 which is 1

The buffer will probably be destroyed by the addition of HCN.

A weak acid and the conjugate base of the weak acid, or a weak base and the conjugate acid of the weak base, are combined to form the buffer solution, a water-based solvent solution. They withstand being diluted or having modest amounts of acid or alkali added to them without changing their pH.

Given that a 1.0 l buffer solution is 0.15 m in HCN and 0.10 m in NaCN.

We need to find a action which one destroy the buffer solution.

A buffer is a substance made of salt and a weak acid that is beneficial. From the aforementioned chemicals, HCN is a potent acid and NaCN is a salt between HF and NaCN. Therefore, the buffer will probably be destroyed by the addition of HCN.

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Answer:

[tex]=\frac{9}{50}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10}\div \frac{5}{1}[/tex]
[tex]\frac{9}{10}\times \frac{1}{5}[/tex]
[tex]\frac{9\times \:1}{10\times \:5}[/tex]
[tex]=\frac{9}{50}[/tex]

Here is your Answer

step by step explanation

Hit thanks, if it's help full

The length of the diagonal AB of the given square is 8.660

Given that a diagram of a cube having dimensions 5×5×5 and asked to find out the length of diagonal AB(which is a body diagonal of the cube).

To calculate the body diagonal 1st we need to calculate the face diagonal via the Pythagorean theorem

Let's assume the length of the face diagonal is x

By Pythagorean theorem

[tex]x^{2} =5^{2} + 5^{2}[/tex]

[tex]x^{2} =50[/tex]

[tex]x=5\sqrt{2}[/tex]

Therefore, the length of the face diagonal is [tex]5\sqrt{2}[/tex]

Let's assume the body diagonal is y

By Pythagorean theorem

[tex]y^{2} =5^{2} +(5\sqrt{2} )^{2}[/tex]

[tex]y=\sqrt{125}[/tex]

y=[tex]5\sqrt{3}[/tex]=8.660

Therefore, The length of the diagonal AB of the given square is 8.660

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Answer:

LCM = 240

GCF = 8

Step-by-step explanation:

Least common multiple (LCM) is the smallest number that both 40 and 48 go into

Greatest common factor (GCF) is the largest number that can go into 40 and 48.

Answer:

41

Step-by-step explanation:

(3*5*7)((1)/(3) +( 1)/(5) -(1)/(7))
When you simplify this, the answer is 41.

Answer: 41

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

4x180=720 u have to multiply because 4 miled in 180 days is the same as 4x180

The solution to the system of equations is (2.5, -2)

The system of equations is given as:

2x + y = 3

2x - 5y = 15

Subtract the equations to eliminate the variable x

This is represented as

2x - 2x + y - -5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

y + 5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

6y = -12

Divide both sides of the above equation by 6

So, we have

y = -2

Substitute y = -2 in 2x + y = 3

2x - 2 = 3

This gives

2x = 5

Divide by 2

x = 2.5

Hence, the solution to the system of equations is (2.5, -2)

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Answer:

y=2x+5

y=-1.5x+9

3y=-2x+10

Step-by-step explanation:

2x+y=5

y=2x+5

9-y=1.5x

-y=1.5-9

y=-1.5x-9

2x=-3y+10

3y=-2x+10

Answer:

0.2888888889

Step-by-step explanation:

d=m/v

v=15×5×3=225

d=65/225

d=0.2888888889g/cm³

Answer:

0.29 g/cm³

Explanation:

[tex]\sf density \ (g/cm^3) = \dfrac{mass \ (g)}{volume \ (cm^3)}[/tex]

Here given following:

Find density:

[tex]\sf \rightarrow density = \dfrac{65}{225}[/tex]

[tex]\sf \rightarrow density = 0.2888...[/tex]

[tex]\sf \rightarrow density = 0.29[/tex]

Answer: See explanation

Step-by-step explanation:

f=First car seat. s=Second car seat. t=Third car seat

f<=28

15<s<45     ==> Second car seat can hold between 15 and 45 pounds noninclusive.

28<=t<=90   ==> Third car seat can hold between 28 and 90 pounds inclusive.

Answer:

when you =0.8=4/5

4x + 8(4/5)=40

4x=40-32/5

4×=(200-32)/5

x=168/20

Step-by-step explanation:

4x+8y=40, when y=0.8

4x+8(0.8)=40

4x+6.4=40

4x=40-6.4

4x=33.6

x=33.6/4

x=8.4

The equation is  180x+ 100

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used when you do not know the exact number in a calculation.

Given:

cost of tuition = $180

each student pay = $100

let the number times of credit be x hours.

Son the equation is 180x+ 100

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25r(cos^2Ф-sin^2Ф)-6cosФ=0

The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates

The rectangular coordinate system consists of two real number lines that intersect at a right angle

In cylindrical coordinate, x=rcosФ

y=rsinФ

z=z

25(rcosФ)^2=25(rsinФ)^2=6rcosФ

25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ

25r^2(cos^2Ф-sin^2Ф)=6rcosФ

25r(cos^2Ф-sin^2Ф)-6cosФ=0

25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.

Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation

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Given ~

[tex] \: [/tex]

[tex]\tt \: g(x) = - 5x - 5[/tex]

[tex] \: [/tex]

Now , put the value of x.

x = 1

[tex] \tt \: g(1) = - 5(1) - 5[/tex]

[tex] \: [/tex]

[tex]\tt \: g(1) = - 5-5[/tex]

[tex] \: [/tex]

[tex] \underline{\boxed{ \red{\tt \: g(1) = - 10}}}{\green✓}[/tex]

[tex] \: [/tex]

hope helps ~

The value of g(1) in the function g(x) = - 5x - 5 is - 10.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function  g(x) = -5x - 5.

Now to obtain the value of g(1) we'll simply replace x with 1.

∴ g(1) = - 5(1) - 5.

g(1) = - 5 - 5.

g(1) = - 10.

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