What is the surface area of the cylinder with height 8 cm and radius 4 cm? Round
your answer to the nearest thousandth.

Answer :

D - 28 + 14 = 7(4+2)

Answer:

6x+7=13

2/3x+8= 8.66

Step-by-step explanation:

calculator and rule with a compass

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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Answer: 102

Step-by-step explanation:

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

Step-by-step explanation:

Class Interval             Variate         Frequency

16-18                              16                     1

19-21                               0                     0

22-24                               0                    0

25-27                              26,27              2

Answer:

A

Step-by-step explanation:

right on edge 2021

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

To simplify the square root of 252 means to get the simplest radical form of √252.

Step-by-step explanation:

Step 1: List Factors

List the factors of 252 like so:

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Step 2: Find Perfect Squares

Identify the perfect squares* from the list of factors above:

1, 4, 9, 36

Step 3: Divide

Divide 252 by the largest perfect square you found in the previous step:

252 / 36 = 7

Step 4: Calculate

Calculate the square root of the largest perfect square:

√36 = 6

Step 5: Get Answer

Put Steps 3 and 4 together to get the square root of 252 in its simplest form:    

6 √ 7  

Rewrite the function using the change-of-base identity as

\(e^{x^2} \log_{10}(2x) = e^{x^2} \dfrac{\ln(2x)}{\ln(10)}\)

Apply the product rule:

\(\left(e^{x^2} \log_{10}(2x)\right)' = \left(e^{x^2}\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \left(\dfrac{\ln(2x)}{\ln(10)}\right)'\)

Use the chain rule:

\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(x^2\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac{(2x)'}{2\ln(10)x}\)

Compute the remaining derivatives:

\(\left(e^{x^2} \log_{10}(2x)\right)' = 2xe^{x^2} \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac2{2\ln(10)x} = e^{x^2}\left(\dfrac{2x\ln(2x)}{\ln(10)} + \dfrac1{\ln(10)x}\right)\)

If you like, you can convert back to base-10 logarithms:

ln(2x) / ln(10) = log₁₀(2x)

1 / ln(10) = ln(e) / ln(10) = log₁₀(e)

Then

\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(2x\log_{10}(2x)+\frac{\log_{10}(e)}x\right)\)

Answer:

clerk A and clerk B can simultaneously stock a shelf in 180/13 minutes

Step-by-step explanation:

Let the first clerk be A and the second clerk be B

A can stock a shelf in 20 min

B can stock a shelf in 45 min

Consider the complete work to be W

A’s rate of stocking =  per minute

B’s rate of stocking =  per minute

When, A and B work simultaneously, rate of work done =

Total work done simulatenously =  180/13

Therefore, clerk A and clerk B can simultaneously stock a shelf in 180/13  minutes

Answer:

Step-by-step explanation:

The rate of each clerk is 1/25 and 1/45 respectively so together they can stock the shelf

t/25+t/45=1 (the least common multiple of 25 and 45 is 225)

t/25(9/9)+t/45(5/5)=1

(9t+5t)/225=1

9t+5t=225

14t=225

t=225/14 min

t=16 minutes (rounded to nearest minute)

( or 16 minutes and about four seconds :) )

Answer:

4.5

Explanation:

The perimeter of a triangle can be found by adding the lengths of the sides of the triangle together.

So if we're given the perimeter of the triangle to be 63 inches and the length of each side to be (4x + 3), we can find the value of x as shown below;

Answer:

A. (6÷3) + 12

Step-by-step explanation:

Because with the 12 at the end, that's more.

The statement that is a good definition is D. Parallel lines are lines that do not intersect.

A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.

Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.

Therefore, based on the information, the correct option is D

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Using lexicographic ordering of 4-sets, the two correct inequalities are {2,1,4,5}<{1,16,67,4} {1,5,7,8}<{1,6,67,8}

Lexicographic ordering, also known as a dictionary or alphabetical order, is a method of comparing sequences of elements. In this case, we are comparing 4-sets. When comparing two sets, we start by comparing the first elements of each set. If they are equal, we proceed to compare the second element, and so on until we find a pair of elements that are different. The set with the smaller element at that position is considered smaller in lexicographic order.

1. In the first inequality, {2,1,4,5}<{1,16,67,4}, we can see that the first element of the first set (2) is greater than the first element of the second set (1). Therefore, the second set is smaller in lexicographic order, making the inequality correct.

2. In the second inequality, {1,5,7,8}<{1,6,67,8}, the first elements are equal (1). So, we proceed to compare the second elements. The second element of the first set (5) is smaller than the second element of the second set (6), so the first set is smaller in lexicographic order, making the inequality correct.

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Answer:

Explanation: The general form of the equation of the circle is as follows:

(1) is the equation of the circle. since it passes through the point (1,3), therefore substituting the (x,y) values of it in (1) gives the value complete equation (1) as follows:

(2) is the complete equation for the circle, the following graph shows if point B is inside or outside the circle.

Answer:

Step-by-step explanation:

90 miles + 120 miles = 210 total miles

1.5 hours + 3 hours = 4.5 total hours.

Average speed = 210 miles / 4.5 hours = 46 2/3 miles per hour

Answer:

40

Step-by-step explanation:

I know meth

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:c, the answer is c

Step-by-step explanation:

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

The probability that a person who tests positive actually has the disease is 0.012%

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

The probability that a person who tests positive actually has the disease is represented as

Probability = Incidence rate * False positive rate

Substitute the known values in the above equation, so, we have the following representation

Probability = 0.3% * 4%

Evaluate the products

Probability = 0.012%

Hence, the probability is 0.012%

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Answer:

x=120°

Step-by-step explanation:

sum of all angles in a triangle is equal to 180

let the unknown angle be

\( \alpha \)

\(60 + 60 + \alpha = 180 \\ \alpha = 180 - 60 - 60 \\ \alpha = 60 \\ \)

\( \alpha + x = 180 \\ x = 180 - \alpha \\ x = 180 - 60 \\ x = 120\)

The formula that can be used to illustrate consecutive even numbers is a + 2.

It should be noted that the information is incomplete. Therefore, an overview will be given.

It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.

Examples of such numbers include 2, 4, 6,8, 10, etc.

In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.

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Answer:

The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term.

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

In both the short run and the long run, the characteristic of a monopolistically competitive firm is that the market price will be equal to its marginal cost (p = mc).

A monopolistically competitive firm is characterized by several conditions, both in the short run and the long run. In the short run, a monopolistically competitive firm will have a market price that is greater than its marginal cost (p > mc).

In the long run, a monopolistically competitive firm will have a market price that is equal to its marginal cost (p = mc). This is because, in the long run, the firm faces increased competition and has to set its price at the level where its marginal cost equals its price.

In conclusion, in both the short run and the long run, the characteristic of a monopolistically competitive firm is that the market price will be equal to its marginal cost (p = mc). This is because in the short run, the firm has some market power and can charge a higher price, and in the long run, the firm faces increased competition and has to set its price at the level where its marginal cost equals its price.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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For regular nonagon the no, of One int = 40° and the One ext = 140°.

A regular nonagon is a two-dimensional polygon that has nine equal sides and nine equal angles. It is also called an enneagon. The word "regular" means that all the sides and angles of the nonagon are congruent, or equal.

The sum of the interior angles of a regular nonagon is given by the formula:

Sum of interior angles = (n - 2) x 180 degrees, where n is the number of sides

For a regular nonagon, n = 9, so the sum of the interior angles is:

Sum of interior angles = (9 - 2) x 180 degrees = 1260 degrees

Each angle of a regular nonagon can be calculated by dividing the sum of the interior angles by the number of angles. For a regular nonagon, each angle is:

Angle = Sum of interior angles / Number of angles = 1260 degrees / 9 = 140 degrees.

In a regular nonagon each of the 9 exterior angles will be 40° , 360/9 and their sum being 360°.

In the same way,

Each of the 9 interior angles will be 140°, ( 180 -40) , and their sum 1260°

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The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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Answer:

I have no clue what part B is asking because I can't read it, but here is part A!

AB/PQ = 2/3

AC/PR = 2/3

BC/QR = 2/3

Step-by-step explanation:

Since it says that the tiangles are similar, then it means that AB=PQ, AC=PR, BC=QR.

So, AB/PQ = 6/9 = 2/3

And, AC/PR = 8/12 = 2/3

Also,  BC/QR = 10/15 = 2/3

The Direction Angle Of The Given Vector is θ = 59.086

Given :

The Direction Angle Of The Given Vector. V <-3,5) Give Your Answer In Degrees In The Interval [0°, 360°). round to the nearest hundredth (2 decimal places). give just the number without the degree symbol.

what is Direction angle of vector ?

The direction angle of a vector v is the angle from the positive x -axis to v .using the arc tangent of the ratio of the vertical component of the vector and the horizontal component of the vector.

tan θ = b / a

= 5 / -3

= -5 / 3

= 1.67

θ = tan^-1 ( 1.67 )

θ = 59.086

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