find the area of the circle

Answer:

mark each line about 1 in. apart

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A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is

Information from the problem

You have made 160 duct tape wallets to sell

If you sell 3 each day

From the information we can deduce that

assuming amount left is y and the number of days x the  we have

y = 160 - 3x

Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is  y = 160 - 3x

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Answer:

Formula?

Step-by-step explanation:

Triangle = Area = 1/2bh

circle = Area = pi x r^2

Hope it helps

To find the equilibrium volume v for a gas that obeys condition (a) and has an excluded volume, we'll use the given entropy formula s = nkln(v−nb) along with the given value for b. In order to determine the equilibrium volume, we need to find the point where the Gibbs free energy G is minimized. The Gibbs free energy is given by:

G = U + PV - TS
Where U is internal energy, P is pressure, V is volume, T is temperature, and S is entropy. In this case, we are not given values for U, P, or T. Therefore, we cannot explicitly calculate the equilibrium volume v.

However, if more information about the system's temperature and pressure is provided, you could use the equation of state for the gas, along with the given entropy formula, to minimize the Gibbs free energy and find the equilibrium volume v.

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The comparsion of the proportion of metal-tagged penguins that survived to the proportion of electronic-tagged penguins that survived gives us following result:

sample one, x1 =10, n1 =50, p1= x1/n1=0.2

sample two, x2 =18, n2 =50, p2= x2/n2=0.36

finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2)

p^=0.28

q^ Value For Proportion= 1-p^=0.72

null, H : p1 = p2

alternate, H1: p1 ≠ p2

level of significance, α = 0.05

from standard normal table, two tailed z α/2 =1.96

since our test is two-tailed

reject H, if zo < -1.96 OR if zo > 1.96

we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))

z =(0.2-0.36)/\(\sqrt{((0.28*0.72(1/50+1/50))}\)

z =-1.7817

| z | =1.7817

critical value

the value of |z α| at los 0.05% is 1.96

we got |zo| =1.782 & | z α | =1.96

make decision

hence value of |zo | < | z α | and here we fail to reject H

p-value: two tailed ( double the one tail ) - Ha : ( p ≠ -1.7817 ) = 0.0748

hence value of p0.05 < 0.0748,here we fail to reject H .

a) standard normal distribution is approximately

b) null, H : p1 = p2

alternate, H1: p1 ≠ p2

test statistic: -1.7817

critical value: -1.96 , 1.96

decision: fail to reject H

p-value: 0.0748

c) we do not have enough evidence to support the claim that difference of proportions metal-tagged penguins who survive – proportion of electronic-tagged penguins who survive

d) given that,

sample one, x1 =10, n1 =50, p1= x1/n1=0.2

sample two, x2 =18, n2 =50, p2= x2/n2=0.36

standard error = \(\sqrt{( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )\)

where

p1, p2 = proportion of both sample observation

n1, n2 = sample size

standard error = \(\sqrt{( (0.2*0.8/50) +(0.36 * 0.64/50))\)

=0.088

margin of error = Z a/2 * (standard error)

where,

Za/2 = Z-table value

level of significance, α = 0.05

from standard normal table, two tailed z α/2 =1.96

margin of error = 1.96 * 0.088

=0.173

CI = (p1-p2) ± margin of error

confidence interval = [ (0.2-0.36) ±0.173]

= [ -0.333 , 0.013]

e) given that,

sample one, x1 =10, n1 =50, p1= x1/n1=0.2

sample two, x2 =18, n2 =50, p2= x2/n2=0.36

standard error = sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )

where

p1, p2 = proportion of both sample observation

n1, n2 = sample size

standard error = \(\sqrt{( (0.2*0.8/50) +(0.36 * 0.64/50))\)

=0.088

margin of error = Z a/2 * (standard error)

where,

Za/2 = Z-table value

level of significance, α = 0.1

from standard normal table, two tailed z α/2 =1.645

margin of error = 1.645 * 0.088

=0.145

CI = (p1-p2) ± margin of error

confidence interval = [ (0.2-0.36) ± 0.145]

= [ -0.305 , -0.015]

f) Given that,

sample one, x1 =10, n1 =50, p1= x1/n1=0.2

sample two, x2 =18, n2 =50, p2= x2/n2=0.36

finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2)

p^=0.28

q^ Value For Proportion= 1-p^=0.72

null, H : p1 = p2

alternate, H1: p1 ≠ p2

level of significance, α = 0.1

from standard normal table, two tailed z α/2 =1.645

since our test is two-tailed

reject H , if zo < -1.645 OR if zo > 1.645

we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))

zo =(0.2-0.36)/sqrt((0.28*0.72(1/50+1/50))

zo =-1.7817

| zo | =1.7817

critical value

the value of |z α| at los 0.1% is 1.645

we got |zo| =1.782 & | z α | =1.645

make decision

hence value of | zo | > | z α| and here we reject H

p-value: two tailed ( double the one tail ) - Ha : ( p ≠ -1.7817 ) = 0.0748

hence value of p0.1 > 0.0748,here we reject H

g) null, H : p1 = p2

alternate, H1: p1 ≠ p2

test statistic: -1.7817

critical value: -1.645 , 1.645

decision: reject H o

p-value: 0.0748

we have enough evidence to support the claim that difference of proportion between metal-tagged penguins that survived to the proportion of electronic-tagged penguins that survived.

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Answer: The comparison of the proportion of metal-tagged penguins that survived to the proportion of electronic-tagged penguins that survived gives us

Based on Miranda's sample, a good estimate for the total number of quarters in her box is 96, and a good estimate for the total number of dimes is 64.

We have,

Miranda randomly selects 20 coins from the box, and out of those 20 coins, she finds that 8 of them are dimes and 12 are quarters.

To estimate the total number of quarters in her box, we can consider the proportion of quarters in her sample.

Since 12 out of 20 coins in her sample are quarters, we can assume that this proportion holds for the entire box.

Therefore, we estimate the total number of quarters as:

= (12/20) x 160

= 96 quarters.

Similarly, to estimate the total number of dimes, we consider the proportion of dimes in her sample.

Since 8 out of 20 coins in her sample are dimes, we assume that this proportion holds for the entire box.

Thus, we estimate the total number of dimes as (8/20) x 160 = 64 dimes.

Thus,

Based on Miranda's sample, a good estimate for the total number of quarters in her box is 96, and a good estimate for the total number of dimes is 64.

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Answer:

Step-by-step explanation:

The lines are parallel to one another.

A linear system of equations has no solution if the graphs are parallel and the two lines never meet.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

There can be one solution to a system of two linear equations, an infinite number of solutions, or no solutions at all. The number of solutions to a system of equations can be used to categorize it.

A system is deemed consistent if there is at least one solution to the problem. A consistent system is said to be independent if it only has one possible outcome.

Thus, a linear system of equations has no solution if the graphs are parallel and the two lines never meet.

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1/3x*3-4*3≤ 2*3+x*3

x-12≤6+3x

-12-6≤3x-x

-18/2≤2x/2

-9≤x

OR

1÷3x-4≤ 2+x

x-12≤6+3x

-12-6≤3x-x

-18/2≤2x/2

-9≤x

Answer:

[-9 ≤ x] or [x ≥ -9]

Step-by-step explanation:

QUESTION :-

Find the solution set of →  \(\frac{1}{3} x - 4 \leq 2+ x\)

SOLUTION :-

\(=> \frac{x-12}{3} \leq x + 2\)

\(=> \frac{x - 12}{3} \times 3 \leq 3(x + 2)\)

\(=> x - 12 \leq 3x +6\)

\(=> x - 12 - x \leq 3x + 6 -x\)

\(=> -12 \leq 2x + 6\)

\(=> -12 - 6 \leq 2x + 6 - 6\)

\(=> -18 \leq 2x\)

\(=> \frac{-18}{2} \leq \frac{2x}{2}\)

\(=> -9 \leq x\)  or  \(x \geq -9\)

Answer:

12, 2, 6

Step-by-step explanation:

The absolute value of a number is its distance from 0 on the number line.

Answer:

12,2, and 6

Step-by-step explanation:

In absolute value, no value is negative

There is a 0.32 probability that a resident will be too tall to enter the tent without bowing their head.

Based on the empirical rule, approximately 68% of the residents will have heights within one standard deviation (4.2 inches) of the mean (67.8 inches).

Therefore, the probability of a resident being too tall to enter the tent without bowing their head is approximately 32% (100% - 68%).

To express this probability as a decimal to the hundredths place, the answer is 0.32.

In conclusion, there is a 0.32 probability that a resident will be too tall to enter the tent without bowing their head.

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Answer:

children is 48 and adults is 8.25 and children is 90

Step-by-step explanation:

Answer:

x = 2.4

I'm not sure how the answer is 4.5 but I'm pretty sure this is right unless I'm missing something

Step-by-step explanation:

So we need to find how much shorter is the short line compared to the longer one. Basically we need a scale factor, for this we can use the side lengths already given to us, 10 and 15. So u can choose either enlarge the short line or shorten the longer one.

If u want to enlarge the short line then do 15/10 which is 3/2 which u will then multiply the shorter line's equation with it, if u want to shorten the longer line then do 10/15 which is 2/3 and multiply the longer lines equation with it.

I'll be using the 3/2 one cause why not:

3/2(x + 6) = 4x + 3

3/2x + 18/2 = 4x + 3

multiply the entire equation with 2 to make 3/2 no longer a fraction

(3/2x + 18/2 = 4x + 3)2

6/2x + 18 = 8x + 6

3x + 18 = 8x + 6

subtract 18 from both sides

3x = 8x - 12

subtract 8x from both sides

-5x = - 12

divide -5 from both sides

x = 2.4

U can input x into the equation to check:

3/2(2.4 + 6) = 4(2.4) + 3

12.6 = 12.6, it's right

By alternate interior angles theorem ∠3≅∠5, d║e. Therefore, option D is the correct answer.

From the given figure ∠3≅∠5.

The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.

From the given figure, 46° + ∠3 =180°

⇒ ∠3 =134°

∠3 = ∠5 =134° (alternate interior angles)

By alternate interior angles theorem ∠3≅∠5, d║e. Therefore, option D is the correct answer.

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Answer:

\(P(X=2) =0.3906\)

Step-by-step explanation:

Proportion of students using the app, p = 63/100 = 0.63

Proportion of students not using the app, q = 1 - 0.63 = 0.37

Sample size, n = 2

Probability that the two students are using the app.

\(P(X = r) = nCr p^{n} q^{n-r} \\P(X = 2) = 2C2 *0.63^{2} *0.37^{2-2}\\P(X = 2) = 2C2 *0.63^{2} *0.37^{0}\\P(X=2) = 0.63^{2} \\P(X=2) =0.3906\)

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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Answer:

f(x) = −2/5x + 1

Step-by-step explanation:

when putting an equation in function notation first you must make sure the equation is in slope-intercept form and then you must rewrite the equation but instead of putting y you will replace it with f(x), or g(x), whichever one you are given directions to put it as.

Hope This Helps!

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The replacement or substitution approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

This makes it easier to solve by combining two linear equations into one equation with a single variable. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.

By changing the value of another variable in an equation, the variable can be eliminated. Thus, the elimination by substitution method is the name given to this technique.

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The total variance of the portfolio is approximately 0.03756. Among the given options, the closest answer is D) 0.08.

To calculate the total variance of a portfolio with two assets, we can use the formula:

Var(portfolio) = w1^2 * Var(asset A) + w2^2 * Var(asset B) + 2 * w1 * w2 * Cov(asset A, asset B)

Where:

- Var(asset A) is the variance of asset A

- Var(asset B) is the variance of asset B

- Cov(asset A, asset B) is the covariance between asset A and asset B

- w1 and w2 are the weights or proportions of the investments in asset A and asset B, respectively.

Given the information:

Asset A: E(r) = 0.2, σ = 0.5

Asset B: E(r) = 0.4, σ = 0.7

Correlation: -0.8

rf = 0.1

The weights for asset A and asset B are 1:2, respectively.

Plugging the values into the formula, we have:

Var(portfolio) = (1/3)^2 * 0.5^2 + (2/3)^2 * 0.7^2 + 2 * (1/3) * (2/3) * (-0.8) * 0.5 * 0.7

Calculating:

Var(portfolio) ≈ 0.03756

Therefore, the total variance of the portfolio is approximately 0.03756.

Among the given options, the closest answer is D) 0.08.

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Answer:

x = 10, y = 5

Step-by-step explanation:

The sine of 60 is given by the division of the opposite side of 60º by the hypothenuse.

We have that:

sine of 60 is sqrt(3)/2

The oopposite side is 5sqrt(3)

The hypothenuse is x.

So

Then we apply cross multiplication.

The cosine of 60 is the adjacent side divided by the hypothenuse.

The cosine of 60 is 1/2.

The adjacent side is y.

The hypothenuse is x = 10. So

Applying cross multiplication

2y = 10

y = 5

The predicted value of f(3) is 108 using the third-order Taylor series expansion, and the true percent relative error for each approximation is ε₀ = 134.83%, ε₁ = 32.02%, ε₂ = 40.45%, and ε₃ = 39.33%.

The Taylor series expansion of the given function f(x) = 25x³ - 6x² + 7x - 88 about a base point x = 1 is given by:

Taylor series expansion for a function is given as:

f(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + (f'''(a)/3!)(x - a)³ + ... + Rn(a)

Where, a = 1, f(a) = 25(1)³ - 6(1)² + 7(1) - 88 = -62.

The first three derivatives of the function are:

f'(x) = 75x² - 12x + 7

f''(x) = 150x - 12f'''(x) = 150

The zeroth-order approximation is the same as f(1), i.e., -62.

The first-order approximation is given by:  

f₁(x) = f(a) + f'(a)(x - a)f₁(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) = 121

The second-order approximation is given by:

f₂(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)²

f₂(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) + [150(1) / 2!](3 - 1)² = 106

The third-order approximation is given by:

f₃(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + (f'''(a)/3!)(x - a)³

f₃(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) + [150(1) / 2!](3 - 1)² + [150 / 3!](3 - 1)³= 108

The true value of the function f(3) = 25(3)³ - 6(3)² + 7(3) - 88 = 178

The true percent relative error, ε is given by:

ε = |(Approximate value - True value) / True value| × 100

For zeroth-order approximation, ε₀ = |(-62 - 178) / 178| × 100 = 134.83%

For first-order approximation, ε₁ = |(121 - 178) / 178| × 100 = 32.02%

For second-order approximation, ε₂ = |(106 - 178) / 178| × 100 = 40.45%

For third-order approximation, ε₃ = |(108 - 178) / 178| × 100 = 39.33%

Hence, the predicted value of f(3) is 108 using the third-order Taylor series expansion, and the true percent relative error for each approximation is ε₀ = 134.83%, ε₁ = 32.02%, ε₂ = 40.45%, and ε₃ = 39.33%.

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Answer:

1000/10x12= answer

Step-by-step explanation:

Part A:

Divide the number of lightning strikes to the number of seconds to find the average rate.

1000 / 10 = 100 strikes per second

Now, multiply by 12 to find the number of strikes that occurred.

100 * 12 = 1200 strikes in 12 seconds

Part B:

Divide the number of seconds to the number of lightning strikes to find the average rate.

10 / 1000 = 0.1 seconds per strike

Now, multiply by 7250 to find the number of seconds that passed.

0.1 * 7250 = 72.5 seconds in 7250 strikes

Best of Luck!

Answer:

Multiply 1/3 with the numbers in the parenthesis and evaluate

Step-by-step explanation:

The convergent series represented by the equation (3)(5n) has a sum of 2/2, which can be simplified to 1.

The formula for the given series is (3)(5n), where the variable n can take any value from 0 all the way up to infinity. We may apply the formula that is used to get the sum of an infinite geometric series in order to find the sum of this series.

The sum of an infinite geometric series can be calculated using the formula S = a/(1 - r), where "a" represents the first term and "r" represents the common ratio. The first word in this scenario is 3, and the common ratio is 5.

When these numbers are entered into the formula, we get the answer S = 3/(1 - 5). Further simplification leads us to the conclusion that S = 3/(-4).

We may write the total as a fraction by multiplying both the numerator and the denominator by -1, which gives us the expression S = -3/4.

On the other hand, in the context of the problem that has been presented to us, it has been defined that the series converges. This indicates that the total must be an amount that can be counted on one hand. The given series (3)(5n) does not converge because the value -3/4 cannot be considered a finite quantity.

As a consequence of this, the sum of the convergent series (3)(5n) cannot be defined because it does not exist.

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An Agile methodology aims for customer satisfaction through early and continuous delivery of useful software components developed by an iterative process using the bare minimum requirements.

Agile methodology is a software development approach that emphasizes flexibility, collaboration, and iterative development. It focuses on delivering value to customers by prioritizing their satisfaction and adapting to changing requirements throughout the development process. Agile methodologies, such as Scrum or Kanban, promote regular and incremental delivery of working software components.

This allows customers to provide feedback early on, ensuring that the final product meets their needs. By using an iterative approach, Agile methodologies enable teams to continuously refine and improve the software based on customer feedback and changing priorities. The emphasis on delivering useful software components and involving customers throughout the development process sets Agile apart from traditional waterfall methodologies.

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Only one singlet is expected in the 1H NMR spectrum of 2,2,4,4-tetramethylpentane. So, correct option is A.

In the 1H NMR spectrum, the number of singlets corresponds to the number of unique hydrogen environments in the molecule. Each unique hydrogen environment, where the hydrogens are chemically equivalent, will produce a singlet peak.

In 2,2,4,4-tetramethylpentane, all the carbons are identical, and each carbon is bonded to three hydrogen atoms. The four methyl groups (-CH3) are also chemically equivalent to each other. Therefore, all the hydrogens in this molecule are in equivalent environments, and there are no differences between them.

Since all the hydrogens are chemically equivalent, they will produce a single peak in the 1H NMR spectrum. This single peak is called a singlet.

Hence, the correct answer is option a, as only one singlet is expected in the 1H NMR spectrum of 2,2,4,4-tetramethylpentane.

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Answer: Two singlets.

Step-by-step explanation:

The methyl groups are all equivalent with no neighbors, so they all give rise to only 1 peak.

There is a methylene group that gives rise to another peak.

So the total is 2 singlets.

the answer is  34

in order to find answer:

enter tan^-1( 2/3 into calculator

2 is on oppisite side and 3 is on adjacent so we use tan = o/a

Answer:

1 quarter, 2 dimes, 2 nickels, and 1 penny.

Answer:

8 x (x+5) should be the answer I think

Answer:

8x+40

Step-by-step explanation:

Since area is equal to length times width, you can find the expression for area by plugging in the length and width given in the problem.

You know the length is 8 and width is x+5 from the picture, so for the area you need to simplify the expression 8(x+5), which is the same as 8x+40