Write a summary of how to get the area of a parallelogram.

The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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The given information suggests that the shape could be a rectangle with sides a and c equal and sides b and d equal.

The given information is not sufficient to determine the solid that will form when it is folded. However, we can make a few observations based on the given information.Let's look at the given statements one by one:Sides a and c are equal.This implies that the shape could be a rectangle or a square, depending on whether the length of sides b and d is equal or not. However, we cannot say anything about the net of the solid that will form when it is folded.The length of side a equals the length of side c.Similarly, this statement tells us that the shape could be a rectangle or a square. Again, we cannot say anything about the net of the solid that will form when it is folded.None of the labeled sides are 5 cm long.This statement rules out a square since all sides of a square are equal. It could still be a rectangle.The length of side b equals the length of side d.This means that the opposite sides of the rectangle (assuming it is a rectangle) are equal.None of the labeled sides are 4 cm long.This statement does not give us any additional information.

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Given:

We're given the data for the number of students and the Score for each student.

To find:

The mean points scored

Step-by-step solution:

We know that:

The relation to calculate the mean of any data:

The Total score of Row 1 = 90 × 8 = 720

The Total score of Row 2 = 80 × 19 = 1520

The Total score of Row 3 = 70 × 11 = 770

Thus, putting the values in the formula:

Thus we can say that the mean points scored is 79.2

The probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw is 2/9.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Since there are 5 blue marbles and 10 total, the probability is 5⁄10, or 1/2.

Now since we no longer have that blue marble, there are 4 blue marbles and 9 total. The chances of drawing a blue marble are 4/9.

Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.

1/2 * 4/9

= 4/18

= 2/9

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Complete question

There are 5 blue marbles, 2 yellow, and 3 red marbles. What is the probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw?

The mathematical term used to designate a trapezoid (or trapezium in the UK) having its two non-parallel sides of equal length is an isosceles trapezoid.

The mathematical term used to designate a trapezoid having its two non-parallel sides of equal length is called an isosceles trapezoid or isosceles trapezium in the UK.

This shape is also sometimes referred to as a regular trapezoid, but the term "isosceles trapezoid" is more commonly used.

A trapezoid is a four-sided polygon that has two parallel sides and two non-parallel sides. The parallel sides of a trapezoid are called the bases, and the non-parallel sides are called the legs. The distance between the bases is called the height of the trapezoid.

The area of a trapezoid is given by:

Area = ((base1 + base2) x height) / 2

where base1 and base2 are the lengths of the two parallel sides, and height is the distance between the parallel sides.

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Fοr an equilateral triangle, sketch is drawn fοr side length = 5 cm.

Triangles are a particular sοrt οf pοlygοn in geοmetry that have three sides and three vertices. Three straight sides make up the twο-dimensiοnal figure shοwn here. An example οf a 3-sided pοlygοn is a triangle. The tοtal οf a triangle's three angles equals 180 degrees. One plane cοmpletely enclοses the triangle.

An equilateral triangle in geοmetry is a triangle with equal-length sides οn all three sides.

In the well-knοwn Euclidean geοmetry, an equilateral triangle is alsο equiangular, meaning that each οf its three internal angles is 60 degrees and cοngruent with the οthers.

The given triangle has a side length οf 5 cm.

Sο, each sire measures the same.

Therefοre, the sketch is drawn fοr the same.

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The work done from (2,2,2) to (2π,31,1) by evaluating ∫CF.dr

where F=⟨yzcos(xyz),xzcos(xyz),xycos(xyz)⟩ is -1 + cos 8.

The correct option is B. -1+cos8.

Given a conservative field F=⟨yzcos(xyz),xzcos(xyz),xycos(xyz)⟩ and two points, P1(2,2,2) and P2(2π​,31​,1), the work done by evaluating ∫C​F⋅dr is as follows:

The line segment from P1 to P2 is given as r(t) = ⟨2tπ​,2t+1,2−t⟩ , 0 ≤ t ≤ 1.

The integral can be written as ∫C​F⋅dr= ∫\(0^1\)F(r(t)) . r′(t)dt

Let's calculate the derivatives of r(t) :

r′(t) = ⟨2π​,2,−1⟩F(r(t)) = ⟨yzcos(xyz),xzcos(xyz),xycos(xyz)⟩= ⟨8cos8t,4tπcos8t,4t2πcos8t⟩

The integral can now be written as

∫C​F⋅dr=∫\(0^1\)8cos8t(2π​,2,−1) + 4tπcos8t(2π​,2,−1) + 4t2πcos8t(2π​,2,−1)dt

= ∫0^18cos8t2π​ + 4tπcos8t2π​ + 4t2πcos8t2π​dt

= [2sin8tπ​+cos8tπ​+sin8tπ​]08

= 2sin8+cos8−sin0

= -1 + cos 8

Thus, the work done from (2,2,2) to (2π,31,1) by evaluating ∫CF.dr is -1 + cos 8.

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:\(\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\]\) Multiplying the equation by the least common multiple of the denominators, we get:\(\[16 + 8 = 2x\]\) Simplifying, we get:\(\[2x = 24\]\)Dividing both sides by 2, we get:\(\[x = 12\]\)Therefore, it takes Cindy 12 hours to rake the yard alone.

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The evidence is not sufficient to support the claim since the p-value is 0.1833 higher than 0.05, so e) none of the preceding.

α = significance level = 0.05

n = sample size

df = degree of freedom = n - 1 = 10 - 1 = 9

Before we find the p-value, we use t test formula. But, before that we calculate mean and standard deviation for two population with excel.

In excel we get,

\(\bar x_1\) = 231.8

\(\bar x_2\) = 214.8

\(\sigma_1\) = 41.95

\(\sigma_2\) = 37.90

Next, we can calculate t test. So,

t = \(\frac{\bar x_1 -\bar x_2}{\sqrt{\frac{\sigma^2_1+\sigma^2_2}{n}}}\)

= \(\frac{231.8-214.8}{\sqrt{\frac{41.95^2+37.9^2}{10}}}\)

= \(\frac{17}{\sqrt\frac{3,196.2125}{10}}\)

= 0.9509

Using t score to p-value calculator for 0.9509, we get p-value = 0.1833.

Thus, the p-value is 0.1833 is higher than significance level 0.05 so there is no sufficient evidence to support the claim.

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

The  answer  is  36 x⁴ y⁴

Step-by-step explanation:

Answer:

6.2

Step-by-step explanation:

15+16=31

31/5=6.2

Step-by-step explanation:

\(15 + 16 \div 5 \\ calculate \: the \: sum \: of \: 15 \: and \: 16 \\ 31 \div 5 = 6 \frac{1}{5} \\ or \: 6.2\)

The new radius of the dilated circle is 3.4 centimetres.

The circle has a radius of 17 centimetres and is being dilated by a scale factor of 5. Therefore, the length of the radius after dilation can be calculated as follows:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

The circle was dilated by a scale factor of 5.

Hence,

New length of the radius  = 17 / 5

New length of the radius  = 3.4 centimetres

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The correct option is C. Interacts with diet(low-sodium; standard).

Diet is the total amount of food that a human or other creature consumes. The term "diet" frequently connotes the utilization of a certain nutritional intake for medical or weight-management purposes.

An experiment included a response variable (resting pulse rate) and an explanatory variable (diet: low-sodium and standard). It was found that resting pulse rates were identical for both groups in subjects under the age of thirty. However, for those over thirty, the study found that resting pulse rates were lower for people on the low-sodium diet. It follows that age interacts with diet. In other words, the impact of diet on resting pulse rate varies depending on age. Hence, C. interacts with diet (low-sodium; standard) is the right option.  

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I would say it would be "True friends stay together through good times and bad" because it gives a moral of a story.

Answer:

True friends stay together through good times and bad.

Step-by-step explanation:

The probability vector Vx>0 for any x∈ E. This is true because every state can be reached from any other state since the Markov chain is irreducible.

Given a finite set E and a Markov chain, which is irreducible. To prove that the invariant probability vector v is unique, we need to consider the following details;

Definition of an Irreducible Markov Chain A Markov chain is said to be irreducible if there is only one class and any state can be reached from any other state. It follows that in an irreducible chain, all states are aperiodic. A state i is aperiodic if there is no integer k≥1 such that Definition of Invariant Probability Vector An invariant probability vector v is a non-negative vector that satisfies vP =v, where P is the transition matrix of the Markov chain. Possible Steps to Prove the Theorem The possible steps that we can use to prove the theorem are

Introduce the theorem and explain the concepts involved such as the invariant probability vector, finite set E, and irreducible Markov chain. Prove that the invariant probability vector v is unique by using the Perron-Frobenius theorem. This theorem states that if P is a non-negative matrix with a primitive property, then there exists a positive eigenvalue λmax of P such that every other eigenvalue of P has a modulus that is less than or equal to λmax. λmax is unique up to the choice of eigenvectors with non-negative entries. Since the transition matrix P of the irreducible Markov chain is a non-negative matrix with a primitive property, there exists a unique λmax and hence a unique invariant probability vector v. Prove that the probability vector Vx>0 for any x∈ E. This is true because every state can be reached from any other state since the Markov chain is irreducible.

There is a positive probability of reaching any state from any other state.

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Answer: La Conferencia de las Naciones Unidas sobre el Desarrollo Sostenible (Río+20) representa una gran oportunidad para que el mundo reconozca y aproveche los vínculos inextricables que existen entre la salud humana y el desarrollo sostenible.

Step-by-step explanation:

Answer:

D.

Hope this helps

Answer:

Yes

Step-by-step explanation:

An expression of equality of ratios is called a proportion.

Answer:

C

Step-by-step explanation:

As we can see, there are perfect squares in the first two expressions

thus, we have it that;

√(25x) = 5√x

√(4x) = 2√x

so we have the expression as;

5 √x - 2 √(x + 2 √x

= 5√x

The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

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(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial. A degree three polynomial might be referred to as a cubic polynomial.

A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a ≠0.

here

Let p(x)=\(x^{3}\)−7x+6

From figure, we have p(1)=0

Thus, (x−1) is a factor of p(x)

The other factor is \(x^{2}\)+x−6

=(x+3)(x−2)

Therefore, \(x^{3}\)−7x+6 =(x−1)(x+3)(x−2)

(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial.

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Answer:

18c - 30d + 36

Step-by-step explanation:

To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.

6(3c - 5d + 6)

(6 · 3c) + (6 · -5d) + (6 · 6)

18c + -30d + 36

As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.

Answer:

a)  $498

b) $1052

c) $554

Step-by-step explanation:

to find the median of lower half of data:  find median of all the data, then find middle value from the minimum value to the median (not including median)

to find the median of upper half of data:  find median of all the data, then find middle value from the median to the maximum value (not including median)

interquartile range (IQR) is the difference of the two

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Since 3x > 24, we can find the solution by dividing both sides of the inequality by 3, which gives x > 8.

On the number line, we can represent this solution as a shaded region to the right of 8, since any value of x greater than 8 would satisfy the inequality. The number 8 itself is not included in the solution because the inequality is strict (i.e., "greater than" rather than "greater than or equal to").

The number line would look like:

<----[=======o------------------------)---->

8 infinity

The open circle at 8 indicates that 8 is not included in the solution, while the shaded region to the right of 8 indicates all values of x that satisfy the inequality. The symbol "infinity" indicates that the solution continues indefinitely to the right.

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The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.

We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= 0.94 * 0.08 + 0.09 * 0.92

= 0.0976

where P(not A) = 1 - P(A) = 0.92.

Substituting the values we have:

P(A|B) = 0.94 * 0.08 / 0.0976

= 0.763

Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

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Step-by-step explanation:

probability of not getting six=5/6

is your answer

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The true statement about qualitative design is "qualitative researchers regularly prepare a complicated array of records from a variety of sources."

Qualitative research usually includes accumulating records from multiple sources, along with interviews, observations, and files, among others. Researchers analyze those records in-depth to identify themes, styles, and relationships amongst them, frequently the use of an iterative technique to refine their expertise.

at the same time as qualitative research can offer valuable insights into complex phenomena, it isn't commonly designed to permit causal inferences, as it frequently involves small samples and is centered on exploring the reviews and views of contributors in place of testing hypotheses or making predictions.

Qualitative research may additionally contain some level of assessment, however that is commonly not pre-planned and can be extra exploratory in nature. in addition, reaching constancy of conditions in terms of research settings isn't always normally a number one goal of qualitative studies.

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