Mark bought three pairs of shorts and one pair of shoes. If the shoes cost $25 and he spent
$78.85 before tax, how much do each pair of shorts cost?

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

3

Step-by-step explanation:

Divide: 2 : 2 /3 = 2

1

· 3

2

= 2 · 3

1 · 2

= 6

2

= 2 · 3

2 · 1

= 3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 2 /3  is 3

of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step cancelling by a common factor of 2 gives 3

.

In words - two divided by two thirds = three.

The quotient of 2 and 2/3 is 3

Quotient is expressed as a ratio of two integers. For instance, the ratio of a to be is expressed as a/b

Given the expression 2 ÷ 2/3

This is also expressed as \(2 \times 3/2\)

\(2 \times 3/2 = \frac{6}{2} = 3\)

Hence the quotient of 2 and 2/3 is 3

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a) As per the vector, the minimum polynomial is unique up to associates, meaning that any two minimum polynomials differ only by multiplication by a non-zero scalar.

b) k[α] satisfies all the conditions of being a commutative subring of A.

c) The given statement "k[α] is a field." is false because k[α] may or may not be a field, depending on whether α is algebraic or transcendental over k.

(a) Existence and Uniqueness of the Minimum Polynomial:

The minimum polynomial of α over k is a polynomial of minimal degree in k[x] (the polynomial ring in the variable x with coefficients in k) that annihilates α. In other words, it is the monic polynomial p(x) with coefficients in k of the smallest degree such that p(α) = 0.

To establish the uniqueness of the minimum polynomial, suppose q(x) is another non-zero polynomial in k[x] that annihilates α. We can perform polynomial division on q(x) by p(x), yielding q(x) = p(x) * g(x) + r(x), where g(x) and r(x) are polynomials in k[x] and r(x) has a smaller degree than p(x). Substituting α for x in this equation gives q(α) = p(α) * g(α) + r(α) = 0 * g(α) + r(α) = r(α). Since both q(x) and p(x) annihilate α, r(α) must also be zero. But since r(x) has a smaller degree than p(x), this contradicts the minimality of p(x).

(b) Commutative Subring k[α]:

(i) Subring: A subring of A is a subset that is itself a ring under the same operations. Since A is an algebra over k, it is a ring with respect to addition and multiplication. Since k[α] is a subset of A, it inherits the addition and multiplication operations from A, making it a subring.

(ii) Closure under Addition: Let β, γ be elements of k[α]. By definition, this means that β and γ can be written as polynomials in α with coefficients in k. Let's denote these polynomials as f(x) and g(x) respectively. Then, β = f(α) and γ = g(α). Now, consider the sum β + γ. By performing addition of polynomials, we obtain β + γ = f(α) + g(α). Since addition in A is closed, f(α) + g(α) is an element of A. Therefore, the sum β + γ is also in k[α].

(iii) Closure under Multiplication: Similar to the previous case, let β, γ be elements of k[α], expressed as β = f(α) and γ = g(α), where f(x) and g(x) are polynomials in α with coefficients in k. We can compute the product β * γ as f(α) * g(α). Since A is closed under multiplication, f(α) * g(α) is an element of A. Thus, the product β * γ is also in k[α].

(c) k[α] as a Field:

The statement "k[α] is a field" is generally false. However, there are cases where k[α] can be a field. For k[α] to be a field, it must be both a commutative subring and every nonzero element in k[α] must have an inverse.

In general, for k[α] to be a field, α must be algebraic over k.

If α is algebraic over k, then k[α] is indeed a field. However, if α is transcendental over k (i.e., it does not satisfy any non-zero polynomial equation with coefficients in k), then k[α] is not a field.

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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An equation of the line that passes through the point (12, 9), and has a slope of 5/7 is y = 5x/7 - 3/7.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (12, 9), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - 9 = 5/7(x - 12)

y = 5x/7 - 60/7 + 9

y = 5x/7 - 3/7

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Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

The possible length of the third side of the triangle is x>52 inches.

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.

Given: Sides of two sides of a triangle as 15 and 37 inches.

let the third side of the triangle be x.

then x>15+37

       x>52 inches.

Hence, The possible length of the third side of the triangle is x>52 inches.

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The mean absolute deviation would be higher when comparing the daily high temperature over the course of a year compared to the daily high temperature over the course of a month.

This is because the mean absolute deviation measures the average distance of each data point from the mean, and with more data points in a year, there is likely to be more variability in the daily high temperature. On the other hand, a month has fewer data points, so there may be less variability in the daily high temperature, resulting in a lower mean absolute deviation. Therefore, when comparing the daily high temperature over a year versus a month, we would expect to see a larger mean absolute deviation for the yearly data.

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Answer:

4500

Step-by-step explanation:

4 hours = 3600

8 hours = 4200

10 hours = 4500

The missing length in the given triangles CG is 18.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangles ABC and CFG are similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AC/CG=BC/CF

66/CG=154/42

66×42=154CG

2772=154 CG

Divide both sides by 154

CG=18

Hence, the missing length in the given triangles CG is 18.

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The sample proportion is option(d) i.e, 0.32

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

Given,

Number of successful outcomes  = 16

Total number of outcomes = 50

The sample proportion =

Number of successful outcomes / Total number of outcomes

Sample proportion = 16 / 50

                               = 0.32

Hence, the sample proportion is option(d) i.e, 0.32

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Answer:69 mins

Step-by-step explanation:

Well 1 hour 9 mins and 14 sec

Answer:

435 degrees

Step-by-step explanation:

Using unit circle, you move back 5/12 of the circle and add 360 degrees to it to get 360 + 75 = 435 degrees :)

make me brainliest if i helped

Answer:

\(\sqrt{53}\)

Step-by-step explanation:

Answer:

137 i think

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

\(A^{2}\)+\(B^{2}\)=\(C^{2}\)

7\(6^{2}\) + 5\(7^{2}\)= \(C^{2}\)

3249+5776 = 9025

\(\sqrt[]{9025}\) = 95

Answer:

2(3x - 1)(x - 1)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

e2021

Answer:

The X intercepts would be -1 and 2

Answer:

There are two x-intercepts.

Step-by-step explanation:

They are in the picture attached below.

Answer:

C

Step-by-step explanation:

8x6= 48 (1 hour) 48x2= 96 (2 hours)

Answer: The correct answer is C. 96

[ 8 x 6 = 48 ( 1 hour ) 48 x 2 =96 ( 2 hours ) ]

The distance between the bird and its prey is 19 feet. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry."

We are given that the angle on f depression between a bird and its prey is 70%.

This means that Theta = 70°

Also, the height of the bird from the ground is 18 feet.

Using trigonometry, we get

⇒sin theta = perpendicular side/hypotenuse

⇒sin 70 = 18/hypotenuse

⇒Hypotenuse = 18/sin 70

⇒Hypotenuse = 19.1 ≈ 19 feet

Hence, the distance between the bird and its prey is 19 feet.

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Answer:

\( \frac{1}{3000} \)

Step-by-step explanation:

calculator

The ways that the exercise can be expressed such that for every 6 squares there are 3 circles include:

This question is asked in Spanish on an English site so the answer will be provided in English for better learning by other students.

The ratio of squares to circles is 6:3 or simplified, 2:1. This means for every 2 squares, there is 1 circle.

You could also use a proportional statement such that the number of squares is twice the number of circles. For every 6 squares, there are 3 circles.

There is also equation form where we can say, if S is the number of squares and C is the number of circles, the relationship could be expressed as S = 2C. This means the number of squares is twice the number of circles.

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The translated question is:

How to express this exercise for every 6 squares there are 3 circles.

Answer:

y=-5

Step-by-step explanation:

When the x-value on the graph is equal to -4, the y-value is equal to -5

If the allowable increase for a constraint is 100 units and we add 110 units of the resource, the impact on the objective function value depends on the specific problem and its constraints.

In general, adding more units of a resource beyond the allowable increase can lead to different outcomes:

Feasible Solution: If adding the additional 110 units of the resource still allows the problem to satisfy all constraints and remain feasible, the objective function value may improve or remain the same. This is because the extra resources can be utilized to optimize the objective function further.

Infeasible Solution: If adding the extra 110 units violates any of the problem's constraints, the solution becomes infeasible. In this case, the objective function value may become undefined or have no meaning since the problem cannot be solved within the given constraints.

It's important to note that the specific impact on the objective function value will depend on the nature of the problem, the objective function itself, and the constraints involved. Each problem may have its own unique behavior when additional resources are added beyond the allowable increase.

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It will take approximately 8.84 years for the car's value to be $5000.

We can use the formula for exponential decay to find the time it takes for the car's value to reach $5000:

V = V0 * \(e^{(-rt)\)

where V is the current value, V0 is the initial value, r is the decay rate, and t is the time in years. We can rearrange this formula to solve for t:

t = -ln(V/V0) / r

Plugging in the given values, we get:

t = -ln(5000/17000) / (-0.17) = 8.84 years (rounded to two decimal places)

Therefore, it will take approximately 8.84 years for the car's value to be $5000.

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Probability that he chooses two different types of biscuits is 53.65 %.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

Given

Total biscuits, n = 8

Digestive biscuits = 5

Chocolate biscuits = 3

There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.

∴ The probability of choosing a digestive then a chocolate

= \(\frac{5}{8}\times\frac{3}{7}\)

= \(\frac{15}{56}\)

= 0.267

The probability of choosing chocolate and then a digestive.

= \(\frac{3}{8} \times\frac{5}{7}\)

= \(\frac{15}{56}\)

= 0.267

Hence, The combined probability

= \(\frac{15}{56}+ \frac{15}{56}\)

= \(0.536\)

= 53.6 5 %

Probability that he chooses two different types of biscuits is 53.65 %.

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Regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

This problem can be modeled as a game of incomplete information. The Inspector and Owner are players in the game, and each has two possible strategies: either choose container B, or switch to container C. The payoffs for each player depend on the strategy they choose and which container contains the counterfeit goods.

To solve this game, we can use backward induction. We start by considering the final decision point: whether to switch to container C after seeing that container A does not contain the counterfeit goods. Let's consider the two cases:

If the counterfeit goods are in container B, then the Inspector knows that container C also does not have the counterfeit goods. In this case, the payoff for choosing container B is 100 (if they find the counterfeit goods) or -100 (if they do not).

If the counterfeit goods are in container C, then the Inspector knows that container B does not have the counterfeit goods. In this case, the payoff for switching to container C is 100 (if they find the counterfeit goods) or -100 (if they do not).

Since the Inspector does not know which container has the counterfeit goods, they should choose the strategy with the higher expected payoff. To calculate the expected payoffs, we need to consider the probability that the counterfeit goods are in each container. Since the owner chose one container at random, each container has a 1/3 chance of containing the counterfeit goods.

If the Inspector chooses container B, the expected payoff is:

Expected payoff (choose container B) = (1/3) * 100 + (2/3) * (-100) = -33.33

If the Inspector switches to container C, the expected payoff is:

Expected payoff (switch to container C) = (1/3) * 100 + (2/3) * (-100) = -33.33

Therefore, regardless of what the Inspector chooses, their expected payoff is the same (-33.33). This means that the Inspector does not have a better option than choosing container B, and switching to container C does not improve their chances of finding the counterfeit goods.

For the Owner, if the Inspector chooses container B, then the Owner's expected payoff is:

Expected payoff (Inspector chooses container B) = (1/3) * (-100) + (2/3) * 100 = 33.33

If the Inspector switches to container C, then the Owner's expected payoff is:

Expected payoff (Inspector switches to container C) = (1/3) * (-100) + (2/3) * 100 = 33.33

Therefore, regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

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Answer:

Your answer is 1 more student.

Step-by-step explanation:

For the class to be held it need 16.25 students.

I got that number by multiplying 25 by .65

Because we can't have .25 of a student, and were talking about the minimum requirement. Having less than 16.25 would mean that we wouldn't have the class, so we need 17 students.

The Leaning Tower of Pisa was originally built to be 58.36 meters tall. However, it has since leaned over at a 4 degree angle, which has reduced its vertical height to 55.86 meters. This means that the tower was originally 65 meters tall, to the nearest meter.

The Leaning Tower of Pisa is a bell tower located in the Piazza del Duomo in Pisa, Italy. It was built in the 12th century and began to lean over during construction due to soft ground beneath its foundation. The tower's lean has continued to worsen over time, and it is now one of the most famous tourist attractions in the world.

In 1990, a major restoration project was completed that stabilized the tower and reduced its lean by 44 centimeters. As a result of this project, the tower's vertical height was reduced to 55.86 meters. However, the tower's original height can be calculated by taking into account its current height, its lean angle, and the length of its foundation.

Using these factors, it can be determined that the Leaning Tower of Pisa was originally 65 meters tall, to the nearest meter.

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The Leaning Tower of Pisa was originally built to be 58.36 meters tall. However, it has since leaned over at a 4 degree angle, which has reduced its vertical height to 55.86 meters. This means that the tower was originally 65 meters tall, to the nearest meter.

The Leaning Tower of Pisa is a bell tower located in the Piazza del Duomo in Pisa, Italy. It was built in the 12th century and began to lean over during construction due to soft ground beneath its foundation. The tower's lean has continued to worsen over time, and it is now one of the most famous tourist attractions in the world.

In 1990, a major restoration project was completed that stabilized the tower and reduced its lean by 44 centimeters. As a result of this project, the tower's vertical height was reduced to 55.86 meters. However, the tower's original height can be calculated by taking into account its current height, its lean angle, and the length of its foundation.

Using these factors, it can be determined that the Leaning Tower of Pisa was originally 65 meters tall, to the nearest meter.

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