The wait time for a new roller coaster is at least 90 minutes. State the null and alternative hypothesis for the scenario using math symbols and words.

Abstract Algebra

By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.

Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.

Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.

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In the diagram, the length of minor arc AB is approximately 3.9 inches

From the question, we are to calculate the length of the minor arc AB

To calculate the length of an arc, we can use the formula:

Arc Length = (Central Angle / 360) x (2πr)

Where:

Central Angle is the angle formed by the two radii at the center of the circle

r is the radius of the circle

From the given information,

Central angle = 56°

r = 4 in

Substituting the given values, we get:

Arc Length = (56° / 360) x (2π x 4 in)

Arc Length = 3.9095 in

Arc Length ≈ 3.9 in

Hence, the length of minor arc AB is approximately 3.9 inches

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the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50

The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:

First equation: x + y = 72

Second equation: x - y = 50

To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:

x + y = 72

x - y = 50

--------------

2x = 122

Next, we can solve for x by dividing both sides of the equation by 2:

2x/2 = 122/2

x = 61

Now that we know the value of x, we can plug it back into one of the equations to find the value of y:

61 + y = 72

y = 72 - 61

y = 11

So the solution to the system of equations is x = 61 and y = 11.

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The solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

To solve the quadratic equation (u-3)^(2)-20=0, we will use the following steps:

1. Add 20 to both sides of the equation to isolate the squared term: (u-3)^(2)=20

2. Take the square root of both sides of the equation: u-3=±√20

3. Simplify the radical on the right side of the equation: u-3=±2√5

4. Add 3 to both sides of the equation to isolate the variable: u=3±2√5

5. Write the two solutions separately: u=3+2√5 or u=3-2√5

Therefore, the solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

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The uncertainity for the meter stick and weights in this experiment are σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg), respectively.

This means that the uncertainty in the measurement of the meter stick is 1 × 10⁻³ meters and the uncertainty in the measurement of the weights is 0.05 kg. To calculate the uncertainity of the results, one must use the appropriate formulae, taking into account the uncertainities of each measurement.

For example, if you are measuring the mass of an object, you must use the uncertainty in the measurement of the weight and the uncertainty in the measurement of the meter stick to calculate the uncertainty in the mass.

The uncertainty in the mass is then equal to the square root of the sum of the squares of the uncertainties of the measurements.

By taking into account the uncertainties in each measurement, one can accurately calculate the uncertainty of the results.

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Complete question:

In this experiment you can use  σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg)  as the uncertainity for the meter stick and weights, respec.

Step-by-step explanation:

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Expanding the left-hand side, we have:

(px + 4) (9x + 3) = 9px^2 + 3(4p + 9)x + 12

Comparing this to the right-hand side, we see that we must have:

9p = 18 (to get the x^2 term on the right)

4p + 9 = r (to get the x term on the right)

The first equation gives us p = 2, and substituting into the second equation gives us:

4(2) + 9 = r

r = 17

So one possible value of r is 17. To find the other, we use the fact that p + q = 9. Substituting p = 2, we have:

2 + q = 9

q = 7

Now we can use the same equation as before to find the other value of r:

4(2) + 9 = r

r = 17

So the two possible values of r are 17 and 17.

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Answer:

we have to check the chemical property of the daisy perfume

1) 3/7

2) 9/21

3) 150/350

The series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

To determine the convergence of a series, we can use the Alternating Series Test. This test states that if the absolute value of the terms in the series decrease to zero, then the series is convergent.

First, we need to find the absolute value of the terms in the series:

| (−1)n−13n+4ln(5n+2)​ | = | 3n+4ln(5n+2)​ |

Next, we need to determine if the absolute value of the terms decrease to zero. To do this, we can use the Limit Comparison Test. We will compare the series to the series 1/n:

lim n→∞ | 3n+4ln(5n+2)​ | / (1/n) = lim n→∞ | 3n^2+4nln(5n+2)​ |

Since the limit of the series is infinity, the series is divergent. However, since the series alternates between positive and negative terms, it is conditionally convergent.

Therefore, the series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

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Answer:

11.35

or 11 7/20

Step-by-step explanation:

Answer:

I think question #1 is C

Question #2 is C

and Question #3 is A

To solve this problem, we'll start by finding the polar coordinates r and θ in terms of x1 and x2. We have r^2 = x1^2 + x2^2, tan(θ) = x2/x1.

Taking the derivative of x1 with respect to time t, we have: dx1/dt = dx2/dt - 2x1(dx1^2 + x2^2 - 1) - x1^2(2x1dx1 + 2x2dx2)

Similarly, the derivative of x2 with respect to t is: dx2/dt = -dx1/dt -2x2(dx1^2 +x2^2 -1) - x2^2(2x1dx1 + 2x2dx2) Using the chain rule, we can write: dr/dt = (x1dx1 + x2dx2)/r dθ/dt = (1/r^2)(x2dx1 - x1dx2)

Substituting dx1/dt and dx2/dt in these equations and simplifying, we get: dr/dt = -r(r^2 -1) dθ/dt = -1 Now, to prove that r=1 is a stable limit cycle, we can use the method of linearization.

This involves finding the Jacobian matrix at the equilibrium point r=1, θ=0: Jacobian = [[-3 -1], [-1 -3]] Taking the eigenvalues of this matrix, we get -4 and -2.

Since both eigenvalues are negative, we conclude that the equilibrium point corresponds to a stable limit cycle at r=1, θ=0. In summary, we have shown that the differential equations for dr/dt and dθ/dt are -r(r^2 -1) and -1, respectively. We have also demonstrated that r=1 is a stable limit cycle.

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With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to Gopalkrishna Gandhi, the opposition candidate, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.

According to the given information, M Venkaiah Naidu received 516 votes out of the valid votes cast in the vice-presidential election. The total number of valid votes cast was not explicitly mentioned in the statement, but we can calculate it by adding up the votes received by the two candidates. M Venkaiah Naidu received 516 votes, while his opponent Gopalkrishna Gandhi received 244 votes. Therefore, the total number of valid votes cast was 760 (516 + 244).

To calculate the percentage of valid votes that M Venkaiah Naidu received, we need to divide his number of votes by the total number of valid votes cast and then multiply by 100. Therefore, M Venkaiah Naidu received approximately 68% of the valid votes (516/760 x 100).

It's important to note that this calculation only considers the valid votes cast and not any abstentions or spoiled ballots. Additionally, this percentage reflects the support received by M Venkaiah Naidu among the MPs who voted and does not necessarily reflect the opinions of the broader public or electorate.

Complete question:

According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.

With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.

What is the % of the votes did MRS Naido receive to write the answers to the east wholw%

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The ratio of fiction books to nonfiction books in the library is 5:3.

What are Ratios?

A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.

Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).

Then, the number of nonfiction books in the library is 8x - 5x = 3x.

Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:

5x/3x = 5/3

So, the ratio of fiction books to nonfiction books in the library is 5:3.

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Answer:

277 milliliters

Step-by-step explanation:

945-668= 277

The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).

To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.

For part a:
3/4 = ab⁻²
12 = ab²

Dividing the second equation by the first equation gives us:
16 = b⁴

Taking the fourth root of both sides gives us:
b = 2

Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3

So the formula for the exponential function is:
f(x) = 3(2ˣ)

For part b:
6 = ab⁻³
2 = ab³

Dividing the second equation by the first equation gives us:
1/3 = b⁶

Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)

Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)

So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))

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The equation 5r2 - 5r + 2 = 0 has two real solutions.

The two real solutions of the equation are:
x = (5 + 3i) / 10 and x = (5 - 3i) / 10

To solve this equation, you can use the Quadratic Formula:

x = (-b ± √(b2 - 4ac)) / (2a)

In this case, a = 5, b = -5, c = 2, so:

x = (-(-5) ± √((-5)2 - 4*5*2)) / (2*5)
x = (5 ± √(25 - 40)) / 10
x = (5 ± √(-15)) / 10
x = (5 ± 3i) / 10

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The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The amount of water remaining in the pool after x minutes is given by:

110 - 4x

We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.

110 - 4x < 74

To solve for x, we can first subtract 110 from both sides of the inequality:

-4x < 74 - 110

Simplifying, we get:

-4x < -36

Divide both sides of the inequality by -4,

x > 9

Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

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Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.

Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

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Answer:

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Ms. Twinkle walks a total of 6.6 miles around the park.

What is perimeter ?

Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

To find how far Ms. Twinkle walks, we need to find the perimeter of the rectangle-shaped park, which is the sum of the lengths of all its sides.

The length of the park is 2 miles and the width is 1 3/10 miles. We can write the width as a mixed number of 1 + 3/10 = 13/10 miles.

Therefore, the perimeter of the park is:

Perimeter = 2(length + width)

Perimeter = 2(2 + 13/10)

Perimeter = 2(20/10 + 13/10)

Perimeter = 2(33/10)

Perimeter = 66/10

Perimeter = 6.6 miles

Therefore, Ms. Twinkle walks a total of 6.6 miles around the park.

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The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. A sample space may contain a number of outcomes that depends on the experiment.

For example if a fair die is thrown, the probability of getting an even number. This means that the sample space of even number in a fair die is 3 i.e, 2,4 and 6

Similarly, There are three names with slip, Analise, Benjamin and cora, the sample space to bring 2 slips out with replacement has this results

The slips can be;

1. Benjamin, cora

2. Analise, cora

3. Benjamine, Analise

4. Analise , Benjamin

5. cora, Analise

6. cora, Benjamin

7. cora, cora

8. Benjamin, Benjamin

9. Analise, Analise

The list that shows these result or sample space is list 4

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Answer:

The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)

Step-by-step explanation:

The domain and range for the given functions are: a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞) b) Domain: (-∞, ∞), Range: [9/2, ∞) c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)

The domain of a function is the set of all possible values of x that can be input into the function. The range of a function is the set of all possible values of y that can be output from the function.

a) y = 1/√(x^2 - 4)
The domain of this function is all values of x that make the denominator nonzero and the square root positive. Therefore, x^2 - 4 > 0, which means (x - 2)(x + 2) > 0. The solution to this inequality is x < -2 or x > 2. So the domain is (-∞, -2) ∪ (2, ∞).

The range of this function is all positive values of y, since the square root in the denominator is always positive. So the range is (0, ∞).

b) y = (2x^2) - 2x + 5
The domain of this function is all real numbers, since there are no restrictions on the values of x. So the domain is (-∞, ∞).

The range of this function is all values of y greater than or equal to the vertex of the parabola. The vertex of this parabola is (-b/2a, f(-b/2a)), which is (1/2, 9/2). So the range is [9/2, ∞).

c) y = 1/(1 - 1/(x - 1))
The domain of this function is all values of x that make the denominator nonzero. Therefore, 1 - 1/(x - 1) ≠ 0, which means x ≠ 2. So the domain is (-∞, 2) ∪ (2, ∞).

The range of this function is all values of y except 0, since the denominator can never be zero. So the range is (-∞, 0) ∪ (0, ∞).

In conclusion, the domain and range for the given functions are:
a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞)
b) Domain: (-∞, ∞), Range: [9/2, ∞)
c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)

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The number of child tickets were sold that day are 73.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Cost of child admission= $5.30

Cost of adult admission= $8.70

Now,

Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:

c + a = 163 (equation 1: the total number of tickets sold)

5.30c + 8.70a = 1169.90 (equation 2: the total sales)

We can use equation 1 to solve for "a" in terms of "c":

a = 163 - c

Substituting this expression for "a" into equation 2, we get:

5.30c + 8.70(163 - c) = 1169.90

Simplifying and solving for "c", we get:

5.30c + 1418.10 - 8.70c = 1169.90

-3.4c = -248.20

c = 73

Therefore, by algebra the answer will be 73.

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The quadratic equation f(x) = 3 · x² + 36 · x + 33 shows the quickest choice to determine the y-intercept. The y-intercept is equal to (0, 33).

In this problem we must look up for the quickest way to determine the y-intercept of a quadratic equation, this can be done by evaluating at x = 0 when the expression is of the form, that is, standard form:

f(x) = a · x² + b · x + c

Where a, b, c are real coefficients.

The standard form f(x) = 3 · x² + 36 · x + 33 may help us to determine the y-intercept quickly. The y-intercept is equal to (0, 33).

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Volume is the quantum of space an object occupies. Saddie uses 8 pints of lemon- lime juice rather of orange juice.

This is simply because there are 4 cups of juice in 1 liter. volume is a measure of space possessed by matter.

It is frequently quantified using SI deduced units or colorful US Customary or Imperial units. The description of length refers to volume.

A liter is a measure of commodity liquid, like milk or makeup. A gallon is four liters.

Question:

Sadie is making punch. how numerous further quarts of bomb lime juice will she use than orange juice?

constituents for punch-

8qts Lemon Lime Juice. 4 scoops of vanilla ice cream and 8 mugs of orange juice

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Answer:

Rectangle, yes yes or no rectangle

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the diagonals of a rhombus are perpendicular to each other, then

∠ 1 = 90°

AB and CD are parallel ( opposite sides of a rhombus are parallel )

∠ 2 and 51° are alternate angles and are congruent , then

∠ 2 = 51°

the diagonals bisect the angles , then

∠ 3 = ∠ 2 = 51°

the sum of the 3 angles , in the triangle with ∠ 4 sum to 180°

∠ 1 + ∠ 3 + ∠ 4 = 180°

90° + 51° + ∠ 4 = 180°

141° + ∠ 4 = 180° ( subtract 141° from both sides )

∠ 4 = 39°

then

∠ 1 = 90° , ∠ 2 = 51° , ∠ 3 = 51° , ∠ 4 = 39°

Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.

The Punnett square for this cross would be:

    | F         F

A | A F   A F

A | A F   A F

This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.

Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:

    | F        F

A | A F   A F

A | A F   A F

Hen Rooster

Answer:

1.3 × .85 = 1.105

10.5% greater than original