m=(3x)/(pi r^(2)h)

solve for "r"

Answer

The answer is Distributive property

SOLUTION

Problem Statement

We are given the mathematical statement below:

We are asked to find the property that justifies the above statement.

Solution

To solve this problem, we need to understand what the distributive property is.

The distributive property states:

If A = 5, B = x and C = -3

Thus, applying the Distributive property on the left-hand side of the mathematical equation given:

This conforms to the Distributive property

Final Answer

The answer is Distributive property

Answer:

\(3^{a}\) = 11

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n , then x = \(b^{n}\) , so

\(log_{3}\) 11 = a ⇒ 11 = \(3^{a}\)

Answer:

no solution

Step-by-step explanation:

If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.

Answer:

\(A.\ \tan(x) \to 2.\ \sin(x) \sec(x)\)

\(B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)\)

\(C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)\)

\(D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)\)

\(E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}\)

Step-by-step explanation:

Given

\(A.\ \tan(x)\)

\(B.\ \cos(x)\)

\(C.\ \sec(x)csc(x)\)

\(D.\ \frac{1 - (cos(x))^2}{cos(x)}\)

\(E.\ 2\sec(x)\)

Required

Match the above with the appropriate identity from

\(1.\ \sin(x) \tan(x)\)

\(2.\ \sin(x) \sec(x)\)

\(3.\ \tan(x) + \cot(x)\)

\(4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}\)

\(5.\ \sec(x) - \sec(x)(\sin(x))^2\)

Solving (A):

\(A.\ \tan(x)\)

In trigonometry,

\(\frac{sin(x)}{\cos(x)} = \tan(x)\)

So, we have:

\(\tan(x) = \frac{\sin(x)}{\cos(x)}\)

Split

\(\tan(x) = \sin(x) * \frac{1}{\cos(x)}\)

In trigonometry

\(\frac{1}{\cos(x)} =sec(x)\)

So, we have:

\(\tan(x) = \sin(x) * \sec(x)\)

\(\tan(x) = \sin(x) \sec(x)\) --- proved

Solving (b):

\(B.\ \cos(x)\)

Multiply by \(\frac{\cos(x)}{\cos(x)}\) --- an equivalent of 1

So, we have:

\(\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}\)

\(\cos(x) = \frac{\cos^2(x)}{\cos(x)}\)

In trigonometry:

\(\cos^2(x) = 1 - \sin^2(x)\)

So, we have:

\(\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}\)

Split

\(\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}\)

Rewrite as:

\(\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)\)

Express \(\frac{1}{\cos(x)}\ as\ \sec(x)\)

\(\cos(x) = \sec(x) - \sec(x) * \sin^2(x)\)

\(\cos(x) = \sec(x) - \sec(x)\sin^2(x)\) --- proved

Solving (C):

\(C.\ \sec(x)csc(x)\)

In trigonometry

\(\sec(x)= \frac{1}{\cos(x)}\)

and

\(\csc(x)= \frac{1}{\sin(x)}\)

So, we have:

\(\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}\)

Multiply by \(\frac{\cos(x)}{\cos(x)}\) --- an equivalent of 1

\(\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}\)

\(\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}\)

Express \(\frac{1}{\cos^2(x)}\ as\ \sec^2(x)\) and \(\frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}\)

\(\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}\)

\(\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}\)

In trigonometry:

\(tan^2(x) + 1 =\sec^2(x)\)

So, we have:

\(\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}\)

Split

\(\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}\)

Simplify

\(\sec(x)csc(x) = \tan(x) + \cot(x)\)  proved

Solving (D)

\(D.\ \frac{1 - (cos(x))^2}{cos(x)}\)

Open bracket

\(\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}\)

\(1 - \cos^2(x) = \sin^2(x)\)

So, we have:

\(\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}\)

Split

\(\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}\)

\(\frac{sin(x)}{\cos(x)} = \tan(x)\)

So, we have:

\(\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)\)

\(\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x)\) --- proved

Solving (E):

\(E.\ 2\sec(x)\)

In trigonometry

\(\sec(x)= \frac{1}{\cos(x)}\)

So, we have:

\(2\sec(x) = 2 * \frac{1}{\cos(x)}\)

\(2\sec(x) = \frac{2}{\cos(x)}\)

Multiply by \(\frac{1 - \sin(x)}{1 - \sin(x)}\) --- an equivalent of 1

\(2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}\)

\(2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}\)

Open bracket

\(2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}\)

Express 2 as 1 + 1

\(2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}\)

Express 1 as \(\sin^2(x) + \cos^2(x)\)

\(2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}\)

Rewrite as:

\(2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}\)

Expand

\(2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}\)

Factorize

\(2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}\)

Factor out 1 - sin(x)

\(2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}\)

Express as squares

\(2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}\)

Split

\(2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}\)

Cancel out like factors

\(2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}\) --- proved

1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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Answer:

number of Lola hats = h

number of Polly hats = 3h

number of Darla hats = 3h - 8

Step-by-step explanation:

Lola has h number of hats . Polly has triple as many as Lola . Then Darla has eight number of hat less than Polly. The expression for how many hat each person has in terms of h can be express below.

Let

number of Lola hats = h

number of Polly hats = 3h (recall Polly has triple as many as Lola)

number of Darla hats = 3h - 8(Note Darla has 8 number less of hats than Polly who already have 3h number of hats)

The simplest way to explain this is that Lola has h number of hats. This means she has h number of hats .Polly has triple of Lola hats, this implies that 3 times h of Lola hats is Polly hats.  Then finally Darla hats is 8 less than Polly hats. This simply means if you subtract 8 from Polly's hats you have gotten Darla's hats.

The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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Answer:

Step-by-step explanation:

Use the cosine identity:

cos(x) = adj/hyp.

Here, adj = 2 and and x = 50° and hyp is unknown and what we are solving for.

adj/cos(x) = hyp, 2/cos(50) = hyp.

hyp = 3.11

Answer:

The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.

The daily balances are as follows:

* July 7: $216.71

* July 14: $268.75

* July 17: $284.37

* July 21: $116.71

* July 24: $260.74

The average daily balance is therefore $226.81.

The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.

The finance charge is therefore $7.43.

The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.

Here is the solution in mathematical form:

* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81

* Finance charge = 226.81 * 0.0125 * 31 = 7.43

* New balance = 216.71 + 7.43 = 224.14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: Hornell

Step-by-step explanation:

Answer:

5 is the correct answer ....

Answer:

lol I rlly thought hahhahaha

Answer: 4

Step-by-step explanation:

The standard equation of a circle is (x−h)^2 + (y−k)^2 = r^2, with (h,k) being the center and r being the radius. In the equation you provided, r = 4.

Answer:

Step-by-step explanation:

(x-h)²+(y-k)²=r²

radius=r

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

2/3

Step-by-step explanation:

There are 4 red balls and 8 yellow balls.

Therefore, there are total 12 balls in the bag.

n(S) = 12

Let A be the event when the ball drawn is not a red ball.

The balls which are not red will be yellow balls and there are 8 yellow balls so,

n(A) = 8

Probability that the ball drawn randomly from the bag is not a red ball,

p(A) = n(A) / n(S)

= 8/12

= 2/3

Therefore, the probability of the ball drawn randomly is not a red ball is 2/3.

Answer:

4.75 megabytes per second

Step-by-step explanation:

500-25 = 475

475 / 100 = 4.75

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

$2792.39

Step-by-step explanation:

→ Work out interest rate

( 100 + 5 ) ÷ 100 = 1.05

→ Multiply the amount by the interest rate to the power of 9

1800 × ( 1.05 )⁹ = 2792.39

Answer:

Angle NKO and Angle OKL are adjacent and complementary

Step-by-step explanation:

Adjacent - yes - they have the common vertex K and the common side KO.

Vertical - no - vertical angles are created by two intersecting lines, and angles NKO and OKL are not.

Complementary - yes - since it's given to us that JL and MN are perpendicular, that means that they intersect at 90 degree angles. This means that angles NKO and OKL add up to 90 degrees, and because complementary angles are angles that add up to 90 degrees, NKO and OKL are complementary.

Supplementary - no - supplementary angles are angles that add up to 180 degrees, and since NKO and OKL add up to 90 degrees, they can't be supplementary.

Linear Pair - no - a linear pair is a pair of angles that are adjacent and supplementary. Angles NKO and OKL are adjacent, but since they're not supplementary they can't be a linear pair.

Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

First one is 436: 75*5+61=436

Second one is 48x^2-12: Just substitute 4x for x. 3*16x^2-12=48x^2-12

The probability that a person will purchase no more than one costume is given as follows:

93%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

187 + 228 + 29 = 444.

Only 29 people purchased more than one costume, hence the probability of at most one costume is calculated as follows:

(444 - 29)/444 = 0.93 = 93%.

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Answer:

75%

Step-by-step explanation:

\(Percentage_{successful} = \frac{36}{48} * 100\\\\Percentage_{successful} = \frac{3}{4} * 100\\\\\\Percentage_{successful} = 0.75 * 100 = 75\)

75%

-Chetan K

Answer: 75%

Step-by-step explanation:

Conversion to a percentage = number who completed/number overall × 100

36/48 = 0.75

0.75 × 100 = 75 Q.E.D 75%

It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

Answer:

Solve for the Unknown

You are suppost to solve for x,...

Chow,...!

Answer:

linear Regression

Step-by-step explanation:

Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.

Answer:

D. \sqrt(384)

Step-by-step explanation:

All you have to do is to expand the root the way I have done. I hope you understand and rate this answer well.

Don't forget 8 is the same as root(8) * root(8) which will give root(64) and the square root of 64 is 8.

Answer:

1042.5

Step-by-step explanation:

Given :-

Using Unitary Method :-

→ Cost of 1 m is P 69.95

→ Cost of 15m is P ( 69.5 * 15 ) = P 1042.5

Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.