Determine the domain of the following graph

The probability that a student chosen randomly from the class plays both basketball and baseball is 2/13.

What are outcomes?

An outcome is a potential outcome of an experiment or trial in probability theory. Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment).

Given that the total number of students in the class is 26. 6 of them play basketball and 15 of them play baseball. There are 9 students who play neither sport.

The number of students who play at least one sport is (26 - 9) = 17.

Assume that n(A) = 6

n(B) = 15.

n(A∪ B) = 17

n(A∪ B) = n(A) + n(B) - n(A∩B)

17 = 15 + 6 - n(A∩B)

n(A∩B) = 21 - 17

n(A∩B) = 4

Therefore 4 students plays both basketball and baseball.

The number of outcomes of favorable event is 4.

The number of total outcomes is 26.

Probability = The number of favorable outcomes/ Total number of outcomes

The probability is 4/26 = 2/13

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The ratio of the final surface charge density (ηf) to the initial surface charge density (ηi) is given by 3.68 * \(Q_i / (A_i \times A_i).\)

To understand the concept and solve this problem, we need to consider the relationship between surface charge density, area, and charge. Surface charge density (σ) is defined as the charge (Q) per unit area (A). Mathematically, we can express this relationship as σ = Q/A.

Let's assume the initial area of the irregular shape is \(A_i\), and the final area after each dimension is reduced is \(A_f\). Since each dimension (x and y) is reduced by a factor of 3.68, we can write the relationship between the initial and final areas as:

\(A_f = (1/3.68) \times A_i\)

Now, let's consider the relationship between charge and area. Since the charge remains constant for a given area, we can express it as \(Q_i = Q_f\), where \(Q_i\) is the initial charge and \(Q_f\) is the final charge.

Since the charge remains constant, the ratio of the surface charge densities can be expressed as:

ηf/ηi = \(\sigma _f/\sigma _i = Q_f/A_f / Q_i/A_i\)

Substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_f/A_f / Q_i/A_i = Q_f / (A_f * Q_i) * (A_i / Q_i)\)

Canceling out the \(Q_i\) terms, we get:

ηf/ηi = \(Q_f / (A_f * Q_i) * (A_i / Q_i) = Q_f / (A_f * A_i)\)

Since \(Q_i = Q_f\), we can simplify further:

ηf/ηi = \(Q_f / (A_f * A_i) = Q_i / (A_f * A_i)\)

Now, substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_i / (A_f * A_i) = Q_i / ((1/3.68) * A_i * A_i)\)

Simplifying, we find:

ηf/ηi = 3.68 x \(Q_i / (A_i \times A_i).\)

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Complete Question:

The irregularly shaped area of charge in the figure has surface charge density ηi. Each dimension (x and y) of the area is reduced by a factor of 3.68.

What is the ratio ηf/ηi where ηf is the final surface charge density?

Answer:

Is that your answer ☺️☺️☺️

The area of the circle formula is useful for measuring the space occupied by a circular field or a plot. A circle is a closed plane geometric shape. The area of the circle with diameter 20 in is 100 π inches².

The area of the circle is defined as the region occupied by the circle in a two dimensional plane. The diameter of the circle is the line which divides the circle into two equal parts and radius is half of the diameter.

The unit of area of a circle is m², cm², etc. The equation used to calculate the area of the circle is:

Area of a circle = π × r²

Here radius = 10 inches

Then the area of circle is given as:

Area = π × 10 × 10 = 100 π inches²

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Answer:

-18

Step-by-step explanation:

If you're looking for the y-intercept for this equation this means that x = 0.

So substitute x as 0 in the equation and you'll get the following.

y + 3 = 5 (0 - 3)

y + 3 = -15

y = -18

Answer:

891.75 sq.ft is the area of the polygon

Step-by-step explanation:

9.2^2 + 10^2= 184.64

√184.64= 13.59 feet

area of regular octagon=A=2(1+√ 2)a^2

A= 2(1+√2)13.59^2

A=891.75 sq.ft(approx)

Answer:

She will touch ground in 30 seconds

Step-by-step explanation:

Answer:

So I Don't Know What The Question Is? But Captain Marvel Will Hit The Ground In 30 Seconds

Step-by-step explanation:

300 Divided By 10 Is 30 :)

a) Age of students in schools: quantitative and continuous. b) Types of cars in KSA: qualitative and discrete. c) Lifetime of car tires: quantitative and continuous. d) Colors of the spectrum of rainbow: qualitative and discrete.

a) Quantitative discrete variable: The number of siblings a person has.

b) Quantitative continuous variable: The height of individuals measured in centimeters.

c) Qualitative discrete variable: The type of pet owned by individuals (e.g., dog, cat, bird).

d) Qualitative continuous variable: The level of satisfaction reported by customers on a scale of 1 to 10.

In the first part, we classify the variables based on their nature. Age is a continuous variable as it can take any value within a range, and it is quantitative since it represents a numerical measurement.

Types of cars are qualitative as they represent categories, and the variable is discrete since it only takes specific values. Lifetime of car tires is a continuous quantitative variable as it can take any value within a range.

Colors of the rainbow are qualitative and discrete since they represent distinct categories.

In the second part, we provide examples for each category. Quantitative discrete variables involve countable values, such as the number of siblings.

Quantitative continuous variables involve measurable quantities, like height. Qualitative discrete variables involve distinct categories, such as types of pets.

Qualitative continuous variables involve non-numeric qualities, such as satisfaction levels.

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This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

The area under the probability distribution is a measure of the probability of all the possible outcomes. Since the sum of all the probabilities of all the possible outcomes must be 1, the total area under the probability distribution must also be 1. This is because the probability of an event happening is the area under the curve of the probability distribution at that event. Thus, the total area under the probability distribution must always equal 1.

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Answer: this was a rotation.

Answer:

a = ± \(\sqrt{\frac{2d-2c}{b} }\)

Step-by-step explanation:

c + \(\frac{1}{2}\) a²b = d ( multiply through by 2 to clear the fraction )

2c + a²b = 2d ( subtract 2c from both sides )

a²b = 2d - 2c ( divide both sides by b )

a² = \(\frac{2d-2c}{b}\) ( take square root of both sides )

a = ± \(\sqrt{\frac{2d-2c}{b} }\)

2/3  is the probability that the product of the two spinners' numbers is even.

How does probability explain work?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                       Statistics is the study of events that follow a probability distribution. There are four primary categories of probability: axiomatic, classical, empirical, and subjective.

An even number comes from multiplying an even and even, even and odd, or odd and even. Since an odd number only comes from multiplying an odd and odd, there are less cases and it would be easier to find the probability of spinning two odd numbers from 1.

            =  1 - 2/4 . 2/3

             =  1 - 1/3

            =  2/3

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Option C is the correct choice as it accurately describes the chi-square test for independence. The chi-square test for independence is used to determine if there is a relationship between two categorical variables. It is similar to neither a single-sample t test nor a correlation because it involves categorical variables, not continuous ones.

Option C accurately describes the chi-square test for independence. It states that the test is similar to an independent-measures t test because it compares separate samples to evaluate the difference between separate populations.

The chi-square test for independence involves creating a contingency table that displays the observed frequencies of the two categorical variables. Then, it calculates the expected frequencies under the assumption of independence. The test compares the observed and expected frequencies using the chi-square statistic. If the observed frequencies significantly differ from the expected frequencies, we reject the null hypothesis and conclude that there is a relationship between the variables.

In contrast, options A, B, and D do not accurately describe the chi-square test for independence. Option A refers to a single-sample t test, which is not applicable to the chi-square test. Option B mentions a correlation, which assesses the relationship between continuous variables, not categorical ones. Option D combines elements of both a correlation and an independent-measures t test, which are not applicable to the chi-square test.

Therefore, option C is the correct choice as it accurately describes the chi-square test for independence.
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In this analysis, a Poisson distribution regression model was fitted to the number of marine bivalve species discovered each year from 2010-2015, where the rate of discovery was modeled as a function of time.

The posterior means of α and β were estimated to be 3.875 and -0.148, respectively, with 95% credible intervals of (2.970, 4.775) and (-0.264, -0.032), respectively.

The negative value of β suggests a decreasing trend in the rate of discovery over time, while the positive value of α indicates an initial high rate of discovery in the first year of observation. The credible intervals suggest a high degree of uncertainty in the estimates of both α and β, which is expected given the small sample size and large variability in the data.

In conclusion, the Poisson distribution regression analysis provides evidence that the rate of discovery of marine bivalve species is changing over time, with a decreasing trend observed from 2010 to 2015. However, caution should be exercised in interpreting the results due to the small sample size and uncertainty in the parameter estimates.

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The Maclaurin series expansion of y = sin²(3x) is

y = (9x²)/2 - (81x⁴)/4 + (243x⁶)/8 - (729x⁸)/16 + ...

To find the Maclaurin series expansion of y = sin²(3x), we can start by using the double angle formula for sine:

sin²(3x) = (1/2)(1 - cos(6x))

Next, we expand cos(6x) using its Maclaurin series expansion:

cos(6x) = 1 - (36x²)/2 + (216x⁴)/24 - (1296x⁶)/720 + ...

Substituting this back into the equation for sin²(3x), we have:

sin²(3x) = (1/2)(1 - (36x²)/2 + (216x⁴)/24 - (1296x⁶)/720 + ...)

Simplifying, we get:

sin²(3x) = (9x²)/2 - (81x⁴)/4 + (243x⁶)/8 - (729x⁸)/16 + ...

This is the Maclaurin series expansion of y = sin²(3x). The series continues with higher powers of x, but the first four terms are shown above.

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the complete question is:

Find the Maclaurin series expansion of y = sin²(3x). Show either a formula in sigma notation or the first four terms of the series.

Answer:

The answer is below

Step-by-step explanation:

Let B represent those that like badminton, F represent those that like football and V represent those that like volleyball. Let x represent the total number of people.

n(B) = (1/3)x, n(F) = (3/4)x, n(V) = (5/6)x

n(B∩F∩V) = 20% of x = 0.2x

n(B∩F) = 17, hence n(B∩F∩V') = 17 - 0.2x

n(V∩F) = 60, hence n(B'∩F∩V) = 60 - 0.2x

n(B∩V) = 65, hence n(B∩F'∩V) = 65 - 0.2x

n(B∪F∪V)' = 8

n(B∩F'∩V') = (1/3)x - 0.2x - (17 - 0.2x) - (65 - 0.2x) = 0.533x - 82

n(B'∩F∩V') = (3/4)x - 0.2x - (17 - 0.2x) - (60 - 0.2x) = 0.95x - 77

n(B'∩F'∩V) = (5/6)x - 0.2x - (60 - 0.2x) - (65 - 0.2x) = 1.033x - 125

Therefore:

x = n(B∩F'∩V') + n(B'∩F∩V') + n(B'∩F'∩V) + n(B∩F∩V) + n(B∩F∩V') + n(B'∩F∩V) + n(B∩F'∩V) + n(B∪F∪V)'

x = (0.533x - 82) + (0.95x - 77) + (1.033x - 125) + (0.2x) + (17 - 0.2x) + (60 - 0.2x) + (65 - 0.2x) + 8

x = 2.1166x - 134

1.1166x = 134

x = 120

Therefore there was 120 students

The value of the piecewise function for f(3) is 4

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

f(x) = 2x if x < 1

f(x) = 1/2x + 5/2 if x >= 1

The function f(3) implies that we make use of the function

f(x) = 1/2x + 5/2

This is because it is valid for x >= 1

substitute the known values in the above equation, so, we have the following representation

f(3) = 1/2 * 3 + 5/2

Evaluate

f(3) = 4

Hence, the piecewise function for f(3) is 4

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Answer:

a loss of 72.47

Step-by-step explanation:

I got this answer right on my test

Answer:

do you like burger or pizza

The probability that 3 of 8 stolen cars will be recovered is 0.296 or approximately 0.30.

The given problem involves a binomial distribution, where the probability of success (recovering a stolen car) is p = 0.78 and the number of trials is n = 8. We need to find the probability of getting exactly 3 successes.

The probability of getting exactly k successes in n trials can be calculated using the binomial probability formula:

P(k successes) = (n choose k) * \(p^k\) * \({1-p}^{n-k}\)

where (n choose k) represents the binomial coefficient, which can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

where n! represents the factorial of n.

Using the above formula with k = 3, n = 8, and p = 0.78, we get:

P(3 successes) = (8 choose 3) * 0.78³ * (1-0.78)⁵

= 56 * 0.78³ * 0.22⁵

= 0.296

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Answer:

A. They have the same domain and range.

Step-by-step explanation:

Edge 2021

Answer:

your answer would be -58

Answer:

\( \sf \: f( - 6) = 78\)

Step-by-step explanation:

Given function,

→ f(x) = 2x² - x

Now we have to,

→ Find the required value of f(-6).

We have to use,

→ x = -6

Then the value of f(-6) will be,

→ f(x) = 2x² - x

→ f(-6) = 2(-6)² - (-6)

→ f(-6) = 2(36) + 6

→ f(-6) = 72 + 6

→ [ f(-6) = 78 ]

Hence, the value of f(-6) is 78.

Hi!

circumference of a circle = \(2\pi r\).

\(2\pi 18\)

\(36\pi\) \(inches\)

(if you use 3.14 as pi, then it would be 113.04 inches)

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Answer:

\(\large\boxed{\tt C = 36 \pi \ in.}\)

Step-by-step explanation:

\(\textsf{We are asked to find the circumference of a circle. There are 2 ways to find the}\)

\(\textsf{Circumference of a circle, including the Radius and the Diameter, either given}\)

\(\textsf{can be used to find the Circumference.}\)

\(\large\underline{\textsf{What is Circumference?}}\)

\(\textsf{Circumference is the area of the perimeter of the circle. Think of the Perimeter}\)

\(\textsf{of shapes, all the sides are added together. The same is with Circles, but it's}\)

\(\textsf{different since Circle's do not have any sides, instead they have arcs. Hence,}\)

\(\textsf{we can say that the Circumference is the sum of all the arcs of a circle.}\)

\(\underline{\textsf{How are we able to find the Circumference?}}\)

\(\textsf{We are able to find the Circumference by using pi, and the radius or diameter.}\)

\(\textsf{The Diameter is multiplied by Pi to equal the exact value of the Circumference.}\)

\(\textsf{It's similar with the Radius, however we have to multiply the Radius by 2 to equal}\)

\(\textsf{the diameter.}\)

\(\underline{\textsf{Formulas;}}\)

\(\tt C = 2 \pi(Radius)\)

\(\tt C = \pi(Diameter)\)

\(\large\underline{\textsf{Finding the Circumference;}}\)

\(\textsf{Since we are given the Radius, let's multiply the Radius by 2.}\)

\(\tt C = 2 \pi (18)\)

\(\tt C = 36 \pi\)

\(\textsf{Now, because the question stated "in terms of pi", this means that we should}\)

\(\textsf{incl\textsf{u}de pi in our answer.}\)

\(\large\underline{\textsf{Hence;}}\)

\(\large\boxed{\tt C = 36 \pi \ in.}\)

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Answer:

Completing the square we get: \((x-2)^2-(2)^2\)

and factoring the term we get: \(x(x-4)\)

Step-by-step explanation:

We need to complete the square for the expression \(x^2-4x\)

For completing the square the expression would be of form \(a^2+2ab+b^2=(a+b)^2\)

For given expression we have to add (2)^2 and subtract to make it complete the square.

\(x^2-2(x)(2)+(2)^2-(2)^2\\(x-2)^2-(2)^2\)

Now, we have to factor the polynomial using formula \((a)^2-(b)^2=(a-b)(a+b)\)

So, \((x-2)^2-(2)^2\\=(x-2-2)(x-2+2)\\=(x-4)(x-0)\\=x(x-4)\)

Completing the square we get: \((x-2)^2-(2)^2\)

and factoring the term we get: \(x(x-4)\)

The correct option is A which is Yixing should clean out the kennels, and Olivia should move the food bags.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

All the parts will be solved below:-

a. Olivia has an absolute advantage as she takes less time for completing both the tasks

b. Olivia's opportunity cost of cleaning a kennel is

= 6 ÷ 6

= 1 bag of food moved.

c. Olivia's opportunity cost of moving one bag of food is

= 6 ÷ 6

= 1 kennel cleaned

d. Yixing's opportunity cost of cleaning a kennel is

= 10 ÷ 12

= 0.83 bags of food moved.

e. Yixing's opportunity cost of moving one bag of food is

= 12 ÷ 10

= 1.2 kennels cleaned

f. From the above calculations, we can see that the opportunity cost of kennel cleaning would be less sin Yixing so here Yixing should have a comparative advantage and Olivia should have moved the food bags

The complete question is given below:-

Olivia and Yixing are volunteering at a cat rescue shelter. The shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. It takes Olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. It takes Yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food.

A. ____has an absolute advantage in completing both tasks.

B. Olivia's opportunity cost of cleaning a kennel:___bags of food moved.

C. Olivia's opportunity cost of moving one bag of food:_____kennels cleaned.

D. Yixing's opportunity cost of cleaning a kennel:____bags of food moved.

E. Yixing's opportunity cost of moving one bag of food:____kennels cleaned.

F. Yixing says it does not matter which task each of them performs because Olivia is faster at both tasks. Is she correct?

A) No, Yixing should clean out the kennels, and Olivia should move the food bags.

B) No, Olivia should clean out the kennels, and Yixing should move the food bags.

C) Yes, Olivia should do both tasks because she is faster at both.

D) No, Yixing should do both tasks so that she can practice and become more efficient.

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Answer:

1.844

Step-by-step explanation:

easyy

Answer:

Step-by-step explanation:

The next term of a Fibonacci sequence is generated by taking the sum of the 2 preceding value of the sequence. Given the the first and third term of a Fibonacci sequence to be x and y

x, _, y...

let the second term be a, fourth term be b and fifth term be c to have the sequence;

x, a, y, b, c...

According to the definition;

x+a = y... 1

a+y = b... 2 and;

y+b = c... 3

From equation 1, a = y-x

Substituting a = y-x into equation 2 to get b we have;

(y-x)+y = b

2y-x = b

b = 2y-x

Substituting b = 2y-x into equation 3 to get 'c'

y +  2y-x = c

3y-x = c

c = 3y-x

The second term of the sequence is y-x

The fourth term of the sequence is 2y-x

The fifth term of the sequence is 3y-x

Answer:

x= -2y/7

Step-by-step explanation:

y=-5x-2x-yif you switch sides you get

-5x-2x-y=y

add similar elements -5x-2x-y=-7x

-7x-y=y

move y to the right side

-7x=2y

decide both sides by -7

-7x/-7 = 2y/-7y

simplify

x = -2y/7