The width of a rectangle 4n-9.5 feet and the length is 9.5n+10 feet. Find the perimeter of the rectangle

The range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -

(ax + b) > (cx + d)    

kx < 6

Given is the inequality statement as -

"The area of a circle is more than 2 square units but less than 4 square units".

The area of a circle is -

{A} = πr²

Mathematically, we can write the inequality statement as -

2 < {A} < 4

2 < πr² < 4

(2/π) < r² < (4/π)

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  

Therefore, the range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

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Scientists believe that it is helpful for the periodical cicadas to emerge every 13 to 17 years because this allows them to synchronize their population cycles with those of their predators.

The GCF of the years is 1

The intervals are given as: 13 years and 17 years

Factor both intervals (i.e. 13 and 17)

13 = 1 * 13

17 = 1 * 17

The common factor between both products is 1

So, we have:

GCF = 1

Hence, the GCF of the years is 1

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Answer:

s= 19/-9

s≈-2.111

Step-by-step explanation:

s is being multiplied by -9

so, to get s by itself we divide both sides by -9

s= [tex]\frac{19}{-9}[/tex]

if you need it in decimal form, s≈-2.111

Answer:  Anica is correct

For example,  5-3 can be written as 5 + (-3)

Subtracting a positive is the same as adding a negative.

Answer:

yes

Step-by-step explanation:

It can be written as an addition of a negative

Example     3-5    is the same as    3 + (-5)

For the system of equations to have a unique solution the value of k must not be 6

Now, According to the question:

The given equations are,

kx + 2y = 5

3x + y = 1

The above equations can be written as,

kx + 2y – 5 = 0

3x + y – 1 = 0

We need to find the value of k.

So, we know that if the two equations are [tex]a_1x+b_1y+c_1=0[/tex], [tex]a_2x+b_2y+c_2=0[/tex] Then we will compare the coefficients such that

[tex]\frac{a_1}{a_2},\frac{b_1}{b_2} and \frac{c_1}{c_2}[/tex].

If [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]  then the equations have unique solution, if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]

then the equations have infinitely many solutions and if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

then the equations have no solutions.

Here we can clearly see that,

[tex]a_1=k,b_1=2,c_1=-5\\\\\\a_2=3,b_2=2,c_2=-1[/tex]

So, [tex]\frac{a_1}{a_2},\frac{b_1}{b_2} , \frac{c_1}{c_2}[/tex]

[tex]\frac{a_1}{a_2}=\frac{k}{3}, \frac{b_1}{b_2}=\frac{2}{1} , \frac{c_1}{c_2}=\frac{5}{1}[/tex]

We know that if the system of equation has unique solution then [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]

So, we solve on putting their values and we get,

[tex]\frac{k}{3}\neq \frac{2}{1}[/tex]

[tex]k\neq 6[/tex]

Hence, for the system of equations to have a unique solution the value of k must not be 6.

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The given question is incomplete, complete question is:

Find the value of k for which the following system of equation has the unique solution:-

kx + 2y = 5

3x + y = 1.

The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.

Given it has triangles and three vertices, each triangle qualify as a polygon. It belongs to the primitive geometric. Triangle ABC is the term utilized to refer to a triangle with the points A, B, and C. Once the three components are not collinear, a unique rectangle and square in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the main parts of the triangle merge are called to as the triangle's corners. Three triangle ratios are multiplied to yield 180 degrees.

given

by Side ratio theorem

BD/DA = BE/EC

= x/12 = 8/10

x = 8*12/10

x = 9.6

The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.

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The measure of the angle ∠DBC, m∠DBC, found by writing an equation based on the angle addition postulate is m∠DBC = 30°

An equation consists of two expressions that are specified as being equivalent, by joining them by an equals to '=' sign.

The specified information are;

m∠ABD = (3·x+ 15)° and m∠DBC = (2·x)°, m∠ABC = 90°

The angle addition postulate indicates that we get;

m∠ABC = m∠ABD + m∠DBC

m∠ABC = 90° = (3·x+ 15)°  + (2·x)° (substitution property)

90° = (3·x+ 15)°  + (2·x)°  = (5·x+ 15)°

(5·x + 15)° = 90°

5·x = 90° - 15° = 75°

5·x = 75°

x = 75°/5 = 15°

x = 15°

m∠DBC = 2·x

Therefore, m∠DBC = 2 × 15° = 30°

m∠DBC = 30°

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The value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [tex][1,4][/tex] is -5.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4].

Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.

Using the method of integrating by parts, we have:

∫[tex]x????"(x)????(x) dx= x????(x)[/tex] ×[tex]\frac{x}{2} -[/tex]∫[tex](\frac{x^{2} }{2} )????'(x) dx[/tex]

We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let [tex]u=\frac{x^{2} }{2}[/tex] and [tex]dv=????'(x) dx[/tex]. Then [tex]du=x dx[/tex] and [tex]v=????(x)[/tex].

So we have:

∫[tex]x????"(x)????(x) dx = x????(x)[/tex]× [tex]\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c[/tex]

Where C is an arbitrary constant of integration.

We can use the given values of ????(1) and ????(4) to evaluate the definite integral:

∫[tex]x????"(x)????(x) dx[/tex] = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)

= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.

Therefore, the value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4] is -5.

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Answer: -7

Step-by-step explanation:

Here we will show you step-by-step with detailed explanation how to calculate 98 divided by 14 using long division.

Instead of saying 98 divided by 14 equals 7, you could just use the division symbol, which is a slash, as we did above.

Also note that all answers in our division calculations are rounded to three decimals if necessary.

Here are some other ways to display or communicate that 98 divided by 14 equals 7:

98 ÷ 14 = 7

98 over 14 = 7

98⁄14 = 7

The easiest way we found to answer the question "what 98 divided by 14 means", is to answer the question with a question: How many times does 14 go into 98?

The greatest common factor of 12 and 80 is 12, so we can use the distributive property to factor that out.

Identify the greatest common factor (GCF). In this case, it's 12.

Rewrite the expression so the GCF is outside of the parentheses. 12 + 80 = 12(1 + 80/12).

Simplify the expression inside the parentheses. 1 + 80/12 = 7.

Substitute the simplified expression back into the original equation. 12 + 80 = 12(7).

Simplify the expression. 12 + 80 = 84.

Therefore, 12 + 80 = 84 after applying the distributive property to factor out the greatest common factor of 12.

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The slope of line G is also -5/3, since parallel lines have the same slope.

line g has a slope of -5/3 bc parallel lines have the same slope

hope this helps you

If monthly disability is $1000, the amount of disability per week is $250.

Based on the provided information in the question, the average monthly disability benefit (cash received) per person is $1000. The weekly benefit can be determined using division operation. The weekly benefit will be the average monthly disability benefit divided by number of weeks per month. Assuming that there are 4 weeks per month, the weekly benefit is:

Weekly monthly disability benefit = Monthly benefit/Number of weeks per month =$1000/4 = $250

Hence, if the monthly disability benefit is $1000 per person, then the weekly disability benefits is $250 per week.

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The sampling technique used in the scenario of selecting five auto repair classes from a local technical school and interviewing all of the students from each class is called "Cluster Sampling."

Cluster Sampling is a type of probability sampling method where the units of analysis are organized into groups, called clusters, and a random sample of these clusters is selected.

In this scenario, the auto repair classes are the clusters and the students are the units of analysis.

By selecting five classes, all of the students from each class are included in the sample. This method is often used when it is difficult or impractical to get a complete list of all the units of analysis in a population.

In conclusion, cluster sampling is a useful technique when it is challenging to get a complete list of all the units of analysis in a population, as it reduces the time and resources required while still giving a relatively accurate representation of the population.

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The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.

The equation that can be used to determine the total cost of renting shoes at both locations is:

total cost = fixed cost + variable cost

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

Where

x = number of games played

In order to determine the number of games that would make the cost

equal in both locations, the following steps would be taken:

$5 + $1.1x = $3 + $1.50x

Combine similar terms

$5 - $3 = $1.50x - $1.1x

$2 = $0.40x

Divide both sides of the equation by $0.4

x = 2 / 0.4

x = 5 games

Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50

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The probability that the profit is greater than $400 is 0.0082.

The cumulative distribution function (CDF) of the normal distribution can be used to calculate the likelihood that the profit will be larger than $400.

We may determine the likelihood that a random variable will be less than or equal to a certain value using the CDF of the normal distribution. We can deduct the CDF from 1 to get the likelihood that the random variable is greater than a specific value.

The normal standard variable that correlates to x will be referred to as z. By taking the mean away and dividing it by the standard deviation, we may standardize x:

z = (x - $360) ÷ $50

The CDF of the standard normal distribution can be found using a standard normal table.

Calculating the value of z we get.

z = (400 - $360) ÷ $50 = 2.4

Therefore, the probability that x > $400 is given by:

p(x > $400) = 1 - p(x <= $400) = 1 - φ(2.4)

where φ is the standard normal CDF.

A standard normal table can be used to estimate the value of φ.

Using the standard normal table φ = 0.9918.
Substituting the values we get,

p(x > $400) = 1 - 0.9918 = 0.0082

This means that there is about a 0.82% chance that the store will make a profit greater than $400 on a randomly selected day.

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Answer:

is 2

because it's below for and two is the closest answer to the function variable answer to this question that you have here

By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.

When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.

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The value of the expression is 32^3/5 is 8

An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 4³. 4 is the base and 3 is the index.

Fractional indices are powers of a term that are fractions. Both parts of the fractional power have a meaning. x^ab. The denominator of the fraction (b) is the root of the number or letter. The numerator of the fraction (a) is the power to raise the answer to.

In the expression 32^3/5, 32 is the base and 3/5 is the index.£

fifth root of 32 is 2 i.e 2⁵ = 32

2×2×2×2×2 = 32

and 2³ = 8

therefore 32^ 3/5 = 8

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When 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

Dividend/Divisor is the quotient.

Divide the dividend by the divisor to obtain the quotient.

Here, Dividend = 1/4

Divisor = 3

Divisor/Dividend =(1/4)/3 = 1/12

So, when 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

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Answer:

2347

2347 * 2347 = 5508409

Step-by-step explanation:

Hope it helps! =D

Answer: f = 14h (f is total fee, h is the hour luke worked)

Step-by-step explanation:

Dont worry I gotchu

Answer: 33.7°

You need to include an image or the measurements. No one can give you the answer without those numbers.

The volume of a right-circular cone of base radius 7cm and height 24cm is 1232 cm³.

An object or substance's volume is the amount of space it takes up. The capacity of a container is typically understood to be equal to its volume rather than the amount of space it occupies. The SI unit for volume is the cubic metre (m³).

Given that radius r = 7

height h = 24

The volume formula of a right-circular cone is

V = 1/3hπr²

Putting the values, we get

[tex]$\text V = \frac{1}{3} \times 24 \times \frac{22}{7} \times 7 \times 7[/tex]

V = 1232 cm³

Thus, The volume of a right-circular cone of base radius 7 and height 24 is 1232 cm³.

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Complete question:

Find the volume of a right-circular cone of base radius r and height h, from the figure given below.

Answer:

An obtuse triangle is always an isosceles triangle.

Step-by-step explanation:

The value of b on the given linear equation is: b= 9.

Here we have a linear equation.

Remember that the general linear equation can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the two points (2, 3) and (3, 0), then the slope is:

a = (0 - 3)/(3 - 2) = -3

The line is like:

y = -3*x +b

To find the value of b, we can replace the values of the point (3, 0), then we will get:

0 = -3*3 + b

0 = -9 + b

9 = b

That is the value of b.

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Answer:

Step-by-step explanation:

Part A: Vertical angles are angles that are opposite each other and are formed by two intersecting lines. They are congruent, meaning they have the same measure, and are supplementary, meaning they add up to 180 degrees.

Part B: We are given that m∠1 = (2x — 5)° and m∠3 = (1/3x + 60)°. Since vertical angles are congruent, we can set the two equations equal to each other:

(2x — 5)° = (1/3x + 60)°

Solving for x, we get:

2x — 5 = 1/3x + 60

5/3x = 65

x = 39

So, m∠1 = (2x — 5)° = (2 * 39 — 5)° = 77°.

Part C: We are given that m∠2 = (5y + 7)° and m∠4 = (7y — 33)°. Since vertical angles are congruent, we can set the two equations equal to each other:

(5y + 7)° = (7y — 33)°

Solving for y, we get:

5y + 7 = 7y - 33

-2y = -40

y = 20

So, m∠2 = (5y + 7)° = (5 * 20 + 7)° = 107°.

The equation of the tangent line to the curve 3x3,  3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

A slope graph looks like a line graph, but with an important difference: there are only two data points for each line.

Given that,

The equation of the tangent line to the curve 3x3 ,

3[tex]y^{2}[/tex] - 11 = 4xy - x

3[tex]y^{2}[/tex] - 4xy + x - 11 = 0

Differentiate both side with respect to 'x'

6y [tex]\frac{dy}{dx}[/tex] - 4 ( x  [tex]\frac{dy}{dx}[/tex] + y ) - 1 = 0

For slope at point ( 1 , -1 ) put x = 1 and y = -1

6(1)  [tex]\frac{dy}{dx}[/tex] - 4 ( 1  [tex]\frac{dy}{dx}[/tex] - 1 ) -1 = 0

6  [tex]\frac{dy}{dx}[/tex] - 4 [tex]\frac{dy}{dx}[/tex] + 4 -1 = 0

2  [tex]\frac{dy}{dx}[/tex] + 3 = 0

2  [tex]\frac{dy}{dx}[/tex] = 0 - 3

2  [tex]\frac{dy}{dx}[/tex] = - 3

[tex]\frac{dy}{dx}[/tex] = -3/2

slope = [tex]-\frac{3}{2}[/tex]

Therefore,

The equation of the tangent line to the curve 3x3,  3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].

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The number of unique committees is 240 / 4 = 60. So the answer is d. 60.

What is the combination?

The permutation is to select an object and then arrange it and it cares about the orders while Combination is about only selecting an object without caring about the orders.

To form a committee with 2 women and 2 men, we have 4 choices for the first woman, 3 choices for the second woman, 5 choices for the first man, and 4 choices for the second man.

Therefore, the number of ways to form a committee is 4 * 3 * 5 * 4 = 240. This is the total number of combinations, and to find the number of unique committees,

we need to divide by the number of ways to arrange the members within each committee.

As the members are distinguishable, the number of arrangements is simply 2! * 2! = 4.

Therefore, the number of unique committees is 240 / 4 = 60. So the answer is d. 60.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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