In your job as a cashier, a customer gives you a $20 bill to pay for a can of coffee that costs $3. 84. How much change should you give back?.

The interval of convergence is [-2/7,2/7).

To find the interval of convergence of the power series \(2^n / (2n)!\)we use the ratio test:

\(|2^(n+1) / (2(n+1))!| / |2^n / (2n)!| = |2| / (2n+2)(2n+1)\)

Taking the limit as n approaches infinity, we get:

lim |2| / (2n+2)(2n+1) = 0

Therefore, the series converges for all values of x, and its interval of convergence is (-∞,∞).

To find the radius and interval of convergence of the power series \(∑n=1^∞ n^2 (7x-5)^n\), we use the ratio test:

\(|n^2 (7x-5)^n+1| / |n^2 (7x-5)^n| = |7x-5|\)

Taking the limit as n approaches infinity, we get:

lim |7x-5| = |7x-5|

Therefore, the series converges when |7x-5| < 1, which gives the radius of convergence as 1/7. To find the interval of convergence, we need to consider the endpoints x = 2/7 and x = -2/7 separately. For x = 2/7, the series becomes:

\(∑n=1^∞ n^2 (7(2/7)-5)^n = ∑n=1^∞ n^2 2^n\)

which diverges by the divergence test. For x = -2/7, the series becomes:

\(∑n=1^∞ n^2 (7(-2/7)-5)^n = ∑n=1^∞ (-1)^n n^2 2^n\)

which converges by the alternating series test. Therefore, the interval of convergence is [-2/7,2/7).

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Problem 1

Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.

The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.

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Problem 2

horizontal/vertical = horizontal/vertical

24/x = 6/5

24*5 = 6x

120 = 6x

x = 120/6

x = 20

Answer: The flagpole is 20 ft high (about 2 stories tall)

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Problem 3

The formula to use is \(z = \sqrt{x*y}\)

z = geometric mean of x and y

We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.

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Problem 4

For each figure, the y is the altitude and can be determined using the geometric mean formula.

The decimal values are approximate.

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Problem 5

For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.

For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).

Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.

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

For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.

Double the short leg to get the hypotenuse.

2x = 36

x = 36/2

x = 18

This is for the first triangle in the bottom row.

For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.

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

Answer:

x > 4

Step-by-step explanation:

Answer:

x  >  4

Step-by-step explanation:

Answer:

$1.30 per jar of jelly

Step-by-step explanation:

$2.79 x 2 = $5.58

$3.19 x 2 = $6.38

$14.56 - $5.58 - $6.38 = $2.60 ( Two jars of jelly )

$2.60 / 2 = $1.30

Answer:

A is correct.

\(g = \frac{p}{6} - 15\)

Step-by-step explanation:

\(p = 6g + 90\)

\(6g = p - 90\)

\(g = \frac{p}{6} - 15\)

So A is correct.

Answer:

surface area = 6a^2 = 6

hence are = 6 unit.sq

The given events are not mutually exclusive events. Hence, the correct answer is "not mutually exclusive."

In order to determine whether the given events are mutually exclusive or not, it is essential to understand what mutually exclusive events are.

So, the term mutually exclusive events refer to those events that cannot occur together or simultaneously. In other words, if one event occurs, the other event will not occur at the same time.

Now, let's consider the given events:

Select a book:

Get a hardback book and Get a romance book

Here, we can select a hardback book or we can select a romance book. We can select both the books simultaneously as well. Therefore, the given events are not mutually exclusive events. Hence, the correct answer is "not mutually exclusive."

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The hike between the pictures will be 22.32 miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that along a hike, Jon takes 6 pictures. He takes 1 picture at equal distances along the 3.72-mile trail.

The hike will be calculated as:-

Hike = 6 x 3.72

Hike = 22.32 miles

Hence, the hike will be 22.32 miles between the pictures.

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Answer:

13

Step-by-step explanation:

To solve this, lets first find the number of footballs he still needs:

75-24 = 51

Now to find the number of packages, divide by 4, since there are 4 balls per package:

51/4 = 12 Remainder 3

Since there is a remainder, and the Coach MUST have at least 75, then we need to add a package to include the remainder:

12 + 1 = 13 Packages

Answer:

Step-by-step explanation:

To determine what the area of the shaded region is, simply find the area of the large rectangle and subtract the product from the smaller one.

Since they are polynomials. Multiply one binomial to the other and first obtain the product, before subtracting the product of the smaller rectangle.

(5x + 2)(3x - 1) - (x)(x + 7)

15x^2 - 5x + 6x - 2 - x^2 - 7

14x^2 + x - 9.

I believe this would be the solution in standard form.

Therefore , light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.

In a mathematical formula, the equal symbol (=) is used to denote that the statements are equivalent. It is demonstrated that many quantitative variables are comparable using mathematical equations, which are statements of reality. The equal sign, for instance, separates the numbers 12 and b + 6 into 2 halves within the equation y + 6 = 12. It is possible to calculate how many expression words each edge of a symbol represents. The meaning of a symbol usually contradicts itself.

Here,

It is important to understand that the function Corey wrote is:

=>y = (x + 8)(x - 2) (x - 2)

=> y = x² - 2x + 8x - 16

=> y = x² + 6x - 16

Kimberly spelled out y = x + 6x - 16

Joshua spelled out (x + 3)² - 25.

=>  (x + 3)(x + 3) - 25

=>  x² + 3x + 3x + 9 - 25

=>  x² + 6x - 16

In light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.

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Answer:

one value of x would be x=5/2 and x=3/2

Step-by-step explanation:

Answer

Distance = 4.1 km

Explanation

Let the distance between Jane's house from school be x

The distance can be calculated using pythagora's theorem

Therefore, the distance between Jane's house from school is 4.1 km

Based on these observations, we can select the following statements that are true: Function 2 has smaller residuals than Function 1, Function 2 is a better fit for the data than Function 1.

From the given scatter plot and residual plots, we can make the following observations:

- Both functions appear to have a general linear trend that fits the data reasonably well.

- Function 2 appears to have smaller residuals than Function 1 for most of the data points.

- Function 2 appears to best fit the data than Function 1, as it follows the general trend of the data more closely.

- There does not appear to be an outlier at z = 7 for either function.

Based on these observations, we can select the following statements that are true:

- Function 2 has smaller residuals than Function 1.

- Function 2 is a better fit to the data than Function 1.

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The five guiding principles of the learning model are

1. Inquiry-based learning
Inquiry based learning is the process of asking questions and seeking answers. Inquiry based learning encourages students to explore,investigateand draw their own concusions. This type od learning encourges students to think critically and become more engaged in thier learning.

2.Student-centered learning
student-centered learning puts the emphasis on the student and what they need to learn. The focus is on students individual learning styles and thier interest.The teacher is more of a facilitator than a lecturer.

3.Collaborative learning
Collaborative learning is when students work together in groups to complete tasks or projects. This type of learing encourages students to share thier ideas and insights and lear from each other.

4.Experiental learning
Experiental learning is when students lear by doing.This type of learning emphasizes hand-on activities and encourages students to apply thier learning in real world situations.

5.Reflective learning
Reflective learning encourages students to think deeply about their learning and to reflect on their experiences.this type of learning allows students to think critically and gain insight into their own learning process.

These five principles provide a framework for designing effective learning experiences that are tailored to the individual needs and interests of each student.

They focus on engaging students in the learning process and helping them to become more independent learners. By incorporating these principles into the learning model, teachers can create an environment that encourages students to explore, ask questions, and collaborate with their peers.

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The five guiding principles of the learning models that are commonly emphasized are:

Active Engagement, Relevance, Feedback, Collaboration, Reflection

Active Engagement: Learning is more effective when learners are actively engaged in the process, rather than being passive recipients of information. This can include activities such as problem-solving, discussion, and hands-on experimentation.

Relevance: Learning is more effective when it is relevant to the learner's interests, goals, and prior knowledge. Making connections between new information and existing knowledge can help learners remember and apply what they have learned.

Feedback: Learning is more effective when learners receive timely and specific feedback on their progress. This can help learners identify areas where they need to improve and adjust their learning strategies accordingly.

Collaboration: Learning is often enhanced by collaboration with others. Working with peers can provide opportunities for discussion, feedback, and the sharing of knowledge and ideas.

Reflection: Learning is more effective when learners take the time to reflect on what they have learned and how it applies to their own lives and goals. Reflection can help learners solidify their understanding and make connections between different concepts.

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The number of tickets are 42 Adult,  18 Children and  24 Senior tickets

From the question, we have the following parameters that can be used in our computation:

Adult: Child = 7 : 3

Adult : Senior = 7 : 4

When combined, we have

Adult: Child : Senior = 7 : 3 : 4

The number of tickets is 84

i.e. Tickets = 84

So, we have

Adult = 7/14 * 84 = 42

Child = 3/14 * 84 = 18

Senior = 4/14 * 84 = 24

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The number of possible outcomes for each game is 3 (win, lose, or tie). Since there are 2 games left, the total number of possible outcomes is 3 x 3 = 9. Therefore, none of the given answers (a, b, or c) is correct. The correct answer is d.

To determine the number of possible outcomes for your favorite football team's remaining 2 games, we'll consider each game independently. Each game can have 3 possible outcomes: win, lose, or tie. For 2 games, you can use the multiplication principle:

Number of possible outcomes = Outcomes for Game 1 × Outcomes for Game 2

So, the number of possible outcomes is:

3 (win, lose, or tie in Game 1) × 3 (win, lose, or tie in Game 2) = 9

Since 9 is not among the given options, the correct answer is:

d. None of the other answers is correct.

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Given data:

The given deck of card.

The probability of even number card or face card is,

Thus, the probability of even number card or face card is 4/13.

The probability of numbered card or heart is,

Thus, the probability of numbered card or heart is 10/13.

The probability that a flight takes more than 140 minutes is approximately 0.333. (Option d: P(x > 140) = 0.333)

To find the probability that a flight takes more than 140 minutes, we need to calculate the proportion of the total distribution that lies beyond 140 minutes.

Given that the time to fly is uniformly distributed between 120 and 150 minutes, we can determine the length of the entire distribution as:

Length of distribution = maximum time - minimum time = 150 - 120 = 30 minutes.

The proportion of the distribution that lies beyond 140 minutes can be calculated as:

Proportion = (Length of distribution - Length up to 140 minutes) / Length of distribution

          = (30 - (140 - 120)) / 30

          = (30 - 20) / 30

          = 10 / 30

          = 1/3

          ≈ 0.333

Therefore, the probability that a flight takes more than 140 minutes is approximately 0.333.

Hence, the correct option is:

d) P(x > 140) = 0.333

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Complete Question:

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.

What is the probability that a flight takes time more than 140 minutes? *

a-P(x> 140)=0.14

b-P(x> 140)=1.4

c-P(x> 140)=0

d-P(x> 140) = 0.333

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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parthenogenesis: continues reproduction despite  single-gender dominance

pollination: obtains genetically different  varieties of plants

herding: protects calves from predators

broadcast spawning: allows large-scale production of  offspring

Explanation:

hope it's right

Answer:

A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x

The value of angle 7x+6

we know that ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.

so,

\(7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10\)

so ,the measure of green angle would be

\(7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76\)

To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)

so,

\(7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified\)

Solution:

Note that:

Simplify the equation to find x.

Substitute the value of x into the measure of the green angle.

The measure of the green angle is 76°.

An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.

we have that

5 miles -------> 10 minutes (direction of the wind)

5 miles ------> 1 hour (against the same wind)

therefore

10 miles ------> ? (without any wind)

so

Let

x -----> speed of the wind

y -----> speed of the airship

direction of the wind

speed=d/t ------> 5/10=0.5 miles per min

against the same wind

speed=5/60=1/12 miles per min

so

x+y=0.5 ------> x=0.5-y -----> equation 1

y-x=1/12 -----> equation 2

solve the system

substitute equation 1 in equation 2

y-(0.5-y)=1/12

2y=(1/12)+1/2

2y=7/12

y=7/24=0.2917 miles per min

Find the value of x

x=(1/2)-7/24

x=5/24=0.2083 miles per min

therefore

10 miles without any wind

speed=d/t ------> t=d/speed

t=10/(7/24)

Answer:

The y-intercept is (0,-3)

Step-by-step explanation:

The y-intercept is where x=0 and it intersects with the y-axis.  

The measure of angles are

The length of the hypotenuse of the right triangle = 11 inches

The length of the one leg = 10 inches

Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square

Then the equation will be

The length of the other leg = \(\sqrt{11^2-10^2}\)

= \(\sqrt{121-100}\)

= 4.58 inches

Therefore AC = 11 inches

AB = 10 inches

BC = 4.58 inches

The angle B = 90 degrees

Consider the angle A

cos θ = Adjacent side / hypotenuse

cos θ = 10 /11

θ = 24.61 degrees

Consider the angle C

cos θ = Adjacent side / Hypotenuse

cos θ = 4.58 / 11

θ = 65.39 degrees

Hence, the measure of angles are

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Ken left $ 39.36 in balance amount.

We have,

Last balance amount in Ken account = $539.36

Amount that Ken withdraw = $500

So, after withdrawing the amount left

= 539.36 - 500

= $ 39.36

Thus, Ken left $ 39.36 in balance amount.

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Answer:

33/4=8.25

So the best way to do it is 33 divided by 4. That equals 8.25.