Reciprocal of 12 1/3

Answer:

B

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Answer: 3 percent of 200 is 6

Step-by-step explanation:

Let "S" represent a container of soup, and "V" represent a cup of vegetables

If for every 10 containers of soup there are 11 cups of vegetables, you can say that:

To determine how many vegetables are in one container of soup, you have to divide both sides of the expression by 10 so that the multiplication on the term "S" gets canceled:

This expression indicates that for every S container of soup there are 11/10 cups of vegetables

Answer:  h^-1(-4)= -2

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The LCM is forty.

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Answer:

40

Step-by-step explanation:

2/5 = 16/40

1/8 = 5/40

The requried, Sara would have completed 18 scarves in 3 days, while Luna would have completed 12 scarves in the same amount of time.

Let's use the following variables to represent the unknowns in the problem:

s: the number of scarves that Sara has completed when Luna catches up

t: the number of days it takes for Luna to catch up to Sara

Using this notation, we can write the following system of equations:

Sara: s = 6 + 6t

Luna: s = nt

where n is the number of scarves that Luna can make per day.

To solve for the unknowns, we can use the fact that they both have to complete the same number of scarves when Luna catches up to Sara. Therefore, we can set the right-hand sides of the equations equal to each other and solve for t:

6 + 6t = nt

6t - nt = -6

t(6 - n) = 6

t = 6 / (6 - n)

Now that we have an expression for t in terms of n, we can substitute it into one of the original equations to solve for s:

s = 6 + 6t

s = 6 + 6(6/(6-n))

s = 6 + 36/(6-n)

To find the values of s and t, we need to know the value of n, which represents the number of scarves that Luna can make per day. Since we don't have that information, we can use some assumptions to explore different scenarios.

For example, if we assume that Luna can make 4 scarves per day, then we can plug in n = 4 to find:

t = 6 / (6 - 4) = 3 days

s = 6 + 36/(6-4) = 18 scarves

Therefore, Sara would have completed 18 scarves in 3 days, while Luna would have completed 12 scarves in the same amount of time. This means that Sara would have completed a total of 24 scarves (6 + 18), while Luna would have completed a total of 12 scarves before they both have to complete the same number of scarves.

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Answer:

-2

Step-by-step explanation:

y = mx + b

y = 3x -  2

y-intercept = b

Answer:

2 < x < 4

Step-by-step explanation:

Answer:

s=47

Step-by-step explanation:

s=\(\frac{611}{13}\)

s=47

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.

When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.

So upstream the speed is:

(14 mi/h - S)

Downstream the speed is:

(14 mi/h + S)

Where S is the rate of current in the stream.

We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:

T = (12 mi)/(14 mi/h + S)

Replacing that in the other equation we will get:

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Also notice that the speeds are in hours, so we can rewrite:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi^2/h - 12mi*S  + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S

- 12mi*S  + 49mi^2/h - 0.25h*S^2 = 12mi*S

-24mi*S -  0.25h*S^2  + 49mi^2/h = 0

This is a quadratic equation, the solutions are:

\(S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)} }{2*-0.25h} \\\\S = \frac{24mi \pm 25 mi }{-0.5h}\)

We only take the positive solution, so we get:

S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h

The rate of current in the stream is 2 mi/h.

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The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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The angle between the floor and the pipe is changing at a rate of approximately 0.68 degrees per minute when the base of the pipe is 2 feet from the wall and being pulled away at a rate of 3 ft/min.

Let's call the distance between the base of the pipe and the wall "x" and the angle between the pipe and the ground "θ".

We want to find dθ/dt (the rate at which θ is changing) when x = 2.

We know that the height of the wall is 4 feet, so using trigonometry, we can say that:

tan(θ) = 4/x

Differentiating both sides with respect to time t, we get:

sec²(θ) × dθ/dt = -4/x² × dx/dt

We want to find dθ/dt when x = 2, so we need to find θ at that point. From the equation above, we have:

tan(θ) = 4/2

= 2

Taking the arctangent of both sides, we get:

θ = tan⁻¹(2)

≈ 63.43°

Now we can substitute x = 2 and θ = 63.43° into the equation we derived earlier, and solve for dθ/dt:

sec²(63.43°) × dθ/dt = -4/2² × 3

dθ/dt = -3/4 × cos²(63.43°)

≈ -0.68 degrees per minute

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Given the Initial principal and interest rate, the time taken for the value of the investment to reach $20,000 is 14.1 Years.

An Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is  number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

A = P(1 + r/n)^(n*t)

We make t the subject of the formula

t = In(A/P) / n[In(1 + r/n)]

t = In(20000/8000) / 365[In( 1 + 0.065/365 )]

t = In(2.5) / 365[In( 1 + 1.78×10⁻⁴ )]

t = In(2.5) / 365[In( 1.000178 )]

t = In(2.5) / 365[In( 1.000178 )]

t = 0.91629 / ( 365 × 0.00017798 )

t = 14.1 years

Given the Initial principal and interest rate, the time taken for the value of the investment to reach $20,000 is 14.1 Years.

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Answer:

Yes, because one of the dogs may be older and not have a good sense of smell. On the other hand if you let the dogs decide on which path to take you will easily know which path to take. If they disagree on which path to take then follow the younger or more trustworthy dog as they will lead you on the correct path.

Step-by-step explanation:

Answer: x=5

x=−5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1=0.788011

2=0.898794

3=0.615661

4=0.292371704722737

Step-by-step explanation:

The cone that has the greatest volume is cone C

The given parameters in the question are

Cone A

Height = 10 cm

Diameter = 4 cm

Cone B

Height = 20 cm

Diameter = 4 cm

Cone C

Height = 10 cm

Diameter = 8 cm

The volume of a cone can be calculated using the following volume equation

Volume of a cone = 1/3π(d/2)²h

Where

h = height of the cone

r = radius of the cone

d = diameter of the cone

Using the above equations, we have the following computations

Volume of a cone A = 1/3π * (4/2)² * 10

Volume of a cone A = 40/3π

Volume of a cone B = 1/3π * (4/2)² * 20

Volume of a cone B = 80/3π

Volume of a cone C = 1/3π * (8/2)² * 10

Volume of a cone C = 160/3π

We can see that 160/3π is greater than 40/3π and 80/3π

Hence, cone C has the highest volume

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(3) The question state that we should explain the relationship between angle ACB and A'C'B' in the given diagram.

From the the diagram in the question, we can see that wa have two different triangle which are ABC and A'B'C'.

The relationship between angle ACB and angle A'C'B' is that they are corresponding angles. because they are on the same side of the line.

Corresponding angles are any pair of angles each of which is on the same side of one of two lines cut by a trasnsversal and on the same side of the transversal.

Therefore, the relationship between angle ACB and angle A'C'B' is that they are corresponding angles.

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer: 4*(x+12)=52.

The visual that can help you in  creating a  3D structure using rectangular prism and others is given in the image attached.

3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.

In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure  will see and work within the real world.

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See text below



1. Start by creating a rectangular prism

as the base of your structure. This will

be the main structure that includes

the walls and interior rooms.

2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.

3. Add another cylindrical tower to the opposite corner of the rectangular

prism. Again, adjust the size and

height to your liking.

4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-

shaped roof to the other cylindrical tower.

5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.

6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.

7. Add a rectangular prism

perpendicular to the main structure,

creating an L-shape. This can be a

separate building or an extension of

the main structure.

8. Add a pyramid-shaped roof to the new

rectangular prism, and a cone-shaped roof to the cylindrical tower on the

opposite side of the main structure. 9. Finally, add spheres as decorative

elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,

pyramids, or cones, as long as you have at least 2 of each of the 5

required shapes.

Answer:

\(\large\boxed{\mathtt{9^{8}}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to simplify the given expression.}\)

\(\textsf{Let's begin by understand an important rule for problems like these.}\)

\(\mathtt{9^{3} \times 9^{5} = 9^{?}}\)

\(\large\underline{\textsf{We should remember that;}}\)

\(\textsf{When exponents multiply, they \underline{add}.}\)

\(\large\underline{\textsf{Why?}}\)

\(\textsf{If not, then the answer will be incorrect. Let's identify why in an example.}\)

\(\large\underline{\textsf{Bad Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2 \times 5 =10}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \neq 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\large\underline{\textsf{Good Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2+5=7}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\textsf{Let's follow the good example!}\)

\({\mathtt{9^{3} \times 9^{5} = 9^{3 + 5=8}}\)

\(\textsf{This means that;}\)

\(\mathtt{9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9.}\)

\(\large\boxed{\mathtt{9^{8}}}\)

\(\huge\text{Hey there!}\)

\(\mathsf{9^3 \times 9^5}\\\mathsf{= 9\times 9 \times 9\ \boxed{\times}\ 9\times 9\times 9 \times 9 \times 9}\\\mathsf{= 81\times 9\ \boxed{\times}\ 81\times81\times9}\\\mathsf{= 729\ \boxed{\times}\ 6,561\times 9}\\\mathsf{= 729\ \boxed{\times}\ 59,049}\\\mathsf{= 43,046,721}\\\mathsf{= 9^3 \times 9^5 \rightarrow 9^{3 + 5}\rightarrow 9^8}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{9^8}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The value each segment length in right triangle ABC are AD = 6 units, BC = 4 units, AB = 4√3 units and BD = 2√3 units

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Since AC = 8 and CD = 2.

Thus, AD = AC - CD = 8 - 2 = 6 units

sin 30° = BC/AC

0.5 = BC/8

BC = 0.5 × 8

BC = 4 units

AB = √(8²-4²)   (Pythagoras theorem)

AB = 4√3 units

BD = √(4²-2²)   (Pythagoras theorem)

BD = 2√3 units

Therefore, drag the value of each segment length in the box accordingly

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Answer:

-7/27

Step-by-step explanation:

-14/54

Hope this helped :)

a = amount invested at 4%.

b = amount invested at 7%.

we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.

how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.

how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.

we also know that the earned interest by those two interest amounts is 1440, so

\(\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}\)

Answer:

5 hours 3 minutes

Step-by-step explanation:

Add all of the times together, but remember that minutes only goes up to 60 minutes. So when you add all the minutes and you get 63, subtract 60 and add an hour, and you are left with 3 minutes.

Answer:

I think u add those numbers up because it's saying figure out the volume below. it must be adding.

Step-by-step explanation:

so just separate the shape into 2 . then you will have one cube 8×8×8 and a rectangle 9×4×8 find the volume of both and then add them together