What is the perimeter of a regular pentagon inscribed in a circle with radius 1 meter

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer:

Some key features quadratic functions have are:

Step-by-step explanation:

Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''

Answer:

x = 2 and x = 5

Step-by-step explanation:

assuming you require to solve for x

the sum of the 3 angles in a triangle is 180°

the third angle in both diagrams is right , that is 90° as they are the angle in a semicircle.

sum the 3 angles and equate to 180

6

90 + 16x + 40 + 11x - 4 = 180

27x + 126 = 180 ( subtract 126 from both sides )

27x = 54 ( divide both sides by 27 )

x = 2

10

90 + 6x + 18 + 3x + 27 = 180

9x + 135 = 180 ( subtract 135 from both sides )

9x = 45 ( divide both sides by 9 )

x = 5

Reasonable algorithms expand at polynomial rates or less quickly. Unreasonable algorithms expand exponentially. Even for relatively small problem sizes, the time to solve an unreasonable algorithm increases very quickly.

When the algorithm takes an excessively long time, we say that the number of steps is an exponential function of the size of the input (or some other function that is larger than any polynomial). Simply increasing the input size (n) by 1 doubles the number of steps for an algorithm that runs in 2n time.

Depending on the polynomial, polynomial time can be further decomposed. Algorithms with a runtime of approximately n2 operate in quadratic time. (If the input size is doubled, the number of steps is quadrupled.) In practise, polynomial time algorithms that take longer than cubic (n³) time are uncommon.

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The function in the attached graph is nonlinear

The function is negative where x < 0 and where x > 0.

There is an extrema.

The maximum is located at x = 0.

As the x-value decreases the y-value decreases for x < 0

As the x-value increases the y-value decreases for x > 0

The function is not a straight line graph, because of this, it is a non linear function

The extrema refers to points of maximum or minimum values. The function on the graph has a maximum value at (0, 0)

The end behavior of the function is described as

x ⇒ ∞ f(x) ⇒ - ∞

x ⇒ -∞ f(x) ⇒ -∞

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Answer:

x^2-9

Step-by-step explanation:

-3 + 3 = 0 so the x terms cancel out.  This leaves you with only x^2-9

Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.

We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:

15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour

We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:

15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour

To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:

First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons

Second hour: 15 gallons/hour * 1 hour = 15 gallons

Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons

Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours

7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons

So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.

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16 full days will be covered by the 785.7 pounds of food.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

We are able to locate the missing value using the unitary technique.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

According to our question-

1 pound of food will last = 1/48.5 day

Pounds equal 785.7*(1/48.5) = 785.7

= 785.7/48.5

= 16.2

Only full days will be counted, therefore

We'll only count up to 16.

So, the 785.

16 days will pass after 7 days.

The 785.7 pounds of food will therefore be plenty for 16 full days.

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The blank words are 5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

I will prove that quadrilateral KLMN is a square by demonstrating that

all sides are of equal measure,

and adjacent sides are perpendicular.

To prove all sides are equal:

KL = 5 cm

LM = 5 cm

MN = 5 cm

NK = 5 cm

The four sides are of 5 measure.

To prove adjacent sides are perpendicular:

slope of KL = 3/4

slope of LM = -4/3

slope of MN = 3/4

slope of NK = -4/3

The slopes of any pair of adjacent sides are perpendicular.

That being the case, those sides are equal.

Therefore,  5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal are the blank words.

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The weight of the baby after five months is 15 Kg.

Step 1:

Given:

New-born baby weight = 5kg

Monthly average weight gained = 2kg

To find:

The weight of the baby after 5 months.

Average Weight of Baby:

Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).

Step 2:

Represent the unknown.

Let x-the number of months .

Let y-weight of the baby after 5 months.

Step 3:

Formulate the equation.

The mathematical equation is:

5+2x = y

Step 4:

Solve the equation.

5+2x = y

5+2(5) = y

5+10 = y

y = 15

Thus, the baby weight is 15kg after 5 months.

Step 5:

Using the equation 5+2x=y.

5+2x = y

5+2(5) = 15

5+10 = 15

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Answer:

See below

Step-by-step explanation:

When nether of the variable will fall out when adding together.  For example:

2x + 5y = 13

-2x + 7y = 17

When I add these equation together, the variable x will drop out because 2x - 2x = 0 and we would be left with other the y variable which we then can solve for. 12y = 30    

Now another example where the neither the x or y falls out.

x + 5y = 12

2x + 3y= 9

When I add these together, neither variable falls out.

3x + 8y = 21

BUT, if I multiply x + 5y = 12 though by -2 I get

-2x -10y = -24

Now when I add the two equation together the x's will drop out.

-2x -10y = -24

2x + 3y = 9

-7y = --15

Yes the explanation satisfy the questions stated.

From the question, distance is said to be a function of time and the constant rate of change is 64.

y = 64x + 22

The above is in the form of a Linear equation:

y = mx + c

Where y = dependent variable (distance)

x = unrelated variable (time)

m = slope = time/distance

22 for c = constant.

m = constant rate of change = 64

If x (time) = 4

y (distance) = 278 miles

y = 64(4) + 22

y = 256 + 22

y = 256 + 22

y = 278 miles

Therefore the value of y is 278 miles.

The complete question is : Distance is a function of time. The constant rate of change is 64. Write

the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,

Compare your response to the sample response above. Did your explanation

include that distance is a function of time?

include that the constant rate of change, or slope, is 64?

include the equation y = 64x + 22?

say to substitute 4 in for x to get 278 miles?

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As per the given simple interest, the principal amount is $165.35.

The term simple interest in math is defined as  the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.

Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.

Therefore, through the given question we have identified the value of

interest rate = 3.5%

time period = 44

sum amount = 420.

Then the principal amount is calculated by using the formula of simple interest as,

P = A / (1 + rt)

Here first we have to convert R percent to r a decimal, then we get

r = R/100 = 3.5%/100 = 0.035 per year.

Now, we have to apply the values on the equation and then we have to solve our equation, then we get

P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866

P = $165.35

Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.

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The amount of money which the chef spends on steak as calculated from the data given is found to be $412.50.

Now as we know that ,

for a meal of 12 meals the chef uses 3 pounds.

Therefore , for a meal of 250 meals the chef uses x pounds

Now , we will solve this proportion.

x=(250 meals*3 pounds)/12 meals

= 62.5 pounds

Now , cost of steaks = 6.60 dollars.

Therefore cost of 62.5 pounds of steaks will be ,

62.5 pound x $ 6.60/pound

=  $ 412.50

A comparison between two numbers is called a proportion. If two sets of provided numbers increase or decrease in the same ratio, then the ratios are said to be directly proportional to each other.

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Therefore, 25000 people prefer Arab Times, 15000 people prefer Wataniya, and 10000 people prefer other newspapers.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

For the percentage of people who prefer other newspapers are:

100% - 50% - 30% = 20%

So, 20% of the people in Salmiya prefer other newspapers.

Multiply the percentage of people who prefer each type of newspaper by the total number of people in Salmiya (50000):

Arab Times: 50% * 50000 = 25000 people

Wataniya: 30% * 50000 = 15000 people

Other newspapers: 20% * 50000 = 10000 people

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Answer:

x = 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{24}[/tex] = [tex]\sqrt{(2)(2)(2)(3)}[/tex]  We can pull out a pair of 2's

2[tex]\sqrt{(2)(3)\\}[/tex] = 2[tex]\sqrt{6}[/tex]

Using the first index law, the solution provided indicates that this has a value of 1.

X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.

A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.

(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸

= m¹⁸/m¹⁸

= 1

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7 + 3x is not a factor of expression 3x^3 + 7x

Consider given expression  3x^3 + 7x

Let f(x) = 3x^3 + 7x

Assume that  7 + 3x is a factor of 3x^3 + 7x

This means,  7 + 3x = 0 would be the root.

x = -7/3

If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0

We find the value of given polynomial for x = -7/3

f(x) = 3x^3 + 7x

f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)

f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)

f(-7/3) =  [(-343) - 147] / 9

f(-7/3) = -490 / 9

f(-7/3) ≠ 0

Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial  f(x) = 3x^3 + 7x

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As per the power rule of exponents, the solution of 3 to the power of 3 is 27.

The term exponent in math is defined as a number shows how many times the number is multiplied by itself.

Here we have to solve 3 to the power of 3.

Here according to the Power Rule of Exponents then we have the rule as

=> aⁿ = a × a × a... (n times)

Therefore, the given expression is written as

=> 3³

Now, based on the power of exponent rule it can be rewritten as,

=>  3 × 3 × 3

Then we have to multiply the values then we get

=> 27

Therefore, the value of 3 raised to 3rd power is 27.

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Check the picture below.

The required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

What is system of equations?

A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work = t + r

Since she can work up to 25 hours.

Thus  t + r ≤ 25

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning = $25t + 12r

Since she must earn $200.

Then 25t + 12r ≥ 200

Hence, the required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

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The number of blueberry muffins the baker makes on Tuesday is given by the equation A = 24 blueberry muffins

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of blueberry muffins the baker makes be A

Now , the equation will be

The total number of muffins the baker makes on Tuesday = 60 muffins

The percentage of blueberry muffins = 40 %

So ,

The number of blueberry muffins the baker makes A = total number of muffins the baker makes on Tuesday x percentage of blueberry muffins

Substituting the values in the equation , we get

The number of blueberry muffins the baker makes A = 60 x ( 40/100 )

On simplifying the equation , we get

The number of blueberry muffins the baker makes A = 60 x 0.4

The number of blueberry muffins the baker makes A = 24 blueberry muffins

Therefore , the value of A is 24

Hence , the number of muffins is 24

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The function which has greater slope is Function 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Function 1:

y = -2x + 10

and Function 2:

Slope = (5-10)/( 2-0) = -5/2

So, the Equation of line

(y - 10) = -5/2 (x -0)

y - 10 = -5/2x

y = -5/2x + 10

y= -2.5x +10

So, the slope of Function 1 is greater than slope of function 2.

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If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.

We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:

9sqrt(121) = k

Simplifying this expression gives us:

k = 911 = 99

Now that we know the value of the constant, we can use the equation to find g when h = 81:

g*sqrt(81) = 99

Solving for g gives us:

g = 99/sqrt(81) = 99/9 = 11

Therefore, when h = 81, g = 11.

Answer:

13/15

For this question, you could type it into the calculator.

Hence, this question is too trivial, and your question might get deleted as a result. Since this is your first question, I will help you out but subsequently, do use a calculator to solve this kind of questions.

Step-by-step explanation:

4 1/3 can be converted to 13/3 as an improper fraction.

Next, evaluate 13/3 divided by 5

(13/3) / 5 = (13/3) x (1/5)

               = 13/15

Answer:

Step-by-step explanation:

There are a number of ways to do this.  I am going to take a little longer, but I am hoping that it will make sense to you.

4[tex]\frac{1}{3}[/tex] ÷ 5  

Another name for 1 is [tex]\frac{3}{3}[/tex]  I am going to rewrite 4[tex]\frac{1}{3}[/tex] knowing this.

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]

Another way to write 5 is [tex]\frac{5}{1}[/tex].

I want both of my fraction to have the same denominator so I will multiple

[tex]\frac{5}{1}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{3}[/tex]  I am now ready to divide by fractions

[tex]\frac{13}{3}[/tex] ÷ [tex]\frac{15}{3}[/tex]  Divide across

[tex]\frac{\frac{13}{15} }{\frac{3}{3} }[/tex] = [tex]\frac{\frac{13}{15} }{1}[/tex] = [tex]\frac{13}{15}[/tex]

According to the given bar chart options A, B and C are the correct.

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

Given that, the bar chart shows the relative frequencies of students from grades 6 to 12 who participate in the community service activity.

Relative Frequency = Subgroup frequency/ Total frequency.

Relative Frequency = f/ n.

From the given bar chart we can see that

The maximum number of participating students was in grade 9.

The number of participating students in grade 6 was equal to the number of participating students in grade 7.

The relative frequency of all participating students in grades 6 and 7 combined was 0.60.  

Therefore, options A, B and C are the correct answers.

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Complete question is in attachment:

Therefore the expression simplified using only positive exponents is 10h^4v^22.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

A mathematical procedure called multiplication shows how many times a number has been added to itself. The multiplication symbol (x) or (*) are used to denote it. A mathematical process that shows how many equal amounts add up to a given number is called division.

To simplify the expression using only positive exponents, we need to make sure that all the exponents are positive.

We can simplify the expression:

(2h^7v^-3)/(5h^-4v^5)^-5

= (2h^7v^-3)/(1/(5h^-4v^5)^5)

= (2h^7v^-3) * (5h^4v^25)

= 10h^4v^22

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We need to assume the sample was randomly selected because we are making inferences about means. Means refers to the average of a sample of data points, which can be used to estimate the value of an unknown population parameter.

If the sample was not randomly selected, then our estimates of the population parameter could be biased or inaccurate. This is because the sample may not be representative of the population as a whole, which could lead to incorrect estimates of the population parameter.

In order to make valid inferences about a population, it is essential to use random sampling. This is because random sampling ensures that the sample is representative of the population as a whole, meaning that the estimates of the population parameter that you obtain from the sample will be unbiased and accurate. If the sample is not randomly selected, then there is a risk that the sample is not representative of the population, which could lead to incorrect estimates of the population parameter.

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Answer:

y = 2x - 4

Step-by-step explanation:

The equation is y = mx + b

m = The slope

b = y-intercept

To find the slope, we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 2, and the y-intercept is located at (0,-4), so the equation is

y = 2x - 4