Problem 2.15. Compute the following sum and justify every step: n?+1 -4k+1 Σ 3(k: + 2)? + + 74k-10 116-7k k=n2

Answer:

W=4, L=5

Step-by-step explanation:

The length is I foot more than the width. Find the Length & width

equation and solve it for a perimeter of 18.

perimeter = 2L + 2W

L=W+1

18=2x(W+1) + 2W

18= 2W +2 +2W =4W +2

4W=18-2=16

W=4 L=W+1 =5

check:

2W + 2L =2X4 +2X5 =8+10 =18

The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)

Answer:

number 1 is $15 if i figure the rest out i will comment

Answer:

thank you

Step-by-step explanation:

Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with unique element of Y, so this is a function.

Table A    

          X               Y

          3                 1

           2                 0

           1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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The radius of the circle is 10 cm.

To find the radius of the circle in which the given central angle intercepts an arc of the given length s, we can use the formula given below:

\(r=\frac{s}{2\sin\frac{\theta}{2}}\)

where r is the radius of the circle,s is the length of the intercepted arc, andθ is the central angle in radians.

For example, if the central angle is 60 degrees and the intercepted arc length is 10 cm, we first need to convert the central angle to radians:

\(\theta = \frac{60}{180}\pi \\= \frac{\pi}{3}\)

Then we can use the formula:

\(r=\frac{s}{2\sin\frac{\theta}{2}}\\=\frac{10}{2\sin\frac{\pi}{6}}\\= \frac{10}{2(\frac{1}{2})}\\=10\\\)

Therefore, the radius of the circle is 10 cm.

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The correct answer is option D which is both Jason’s sample and Yolanda’s sample can be used to make inferences about the population

The complete question is given below:-

Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason’s sample consisted of 0.24% of the population, while Yolanda’s sample consisted of 0.32% of the population. Whose sample can be used to make inferences about the population?

neither Jason’s sample nor Yolanda’s sample

only Jason’s sample

only Yolanda’s sample

both Jason’s sample and Yolanda’s sample

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Since we have given that

Total number of population = 25000

Percent of a sample of Jason = 0.24%

Percent of a sample of Yolanda's = 0.32%

So, the number of the population according to Jason's sample is given by

= ( 0.24 / 100 ) x 25000

= 60

The number of the population according to Yolanda's sample is given by

= ( 0.32 / 100 ) x 25000

= 80

Both the sample can be used to make inferences about the population

Hence, the Last Option is correct.

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Answer: 18 quarts

Step-by-step explanation:

As per given,

Quantity of sparkling juice is proportional to quantity of course with grape juice.

Given: A free cable sparkling juice calls for \(1\dfrac12\) quarters of sparkling water and \(\dfrac34\) course with grape juice .

Let x be the quantity of sparkling water need to mix with 9 quarts of grape juice.

then, by equation of direct proportion , we have

\(\dfrac{1\dfrac12}{\dfrac34}=\dfrac{x}{9}\\\\\Rightarrow\dfrac{\dfrac{3}{2}}{\dfrac{3}{4}}=\dfrac{x}{9}\\\\\Rightarrow\ \dfrac21=\dfrac{x}{9}\\\\\Rightarrow\ x=9\times2\\\\\Rightarrow\ x=18\)

Hence, the quantity of sparkling water need to mix with 9 quarts of grape juice = 18 quarts

Out of the given statistics, the percentage of operations that succeed and are free from infection can be calculated as 84%.

To determine this, we need to subtract the combined occurrence of infection and failure (1%) from the total failure rate (13%). This yields the percentage of operations that fail but do not have an infection, which is 12%. Subtracting this from 100% gives us the percentage of operations that succeed and are free from infection, which is 88%.

However, since the question specifically asks for the percentage of operations that succeed and are free from infection, we need to consider that the 2% infection rate is included in the total failure rate. This means that out of the total failure rate of 13%, 2% accounts for the operations that have both infection and failure. Therefore, we subtract this 2% from the total failure rate of 13%, resulting in a failure rate of 11% without infection.

By subtracting this failure rate without infection from 100%, we obtain the percentage of operations that succeed and are free from infection, which is 89% - 11% = 84%. Thus, approximately 84% of these operations are expected to succeed and be free from infection.

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A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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Answer:

The width is 9 cm

Step-by-step explanation:

Since the formula for the volume of a rectangular prism is,

Volume = (Height)(Length)(Width)

So,

Width = (Volume)/((Height)(Length))

Now, Volume = 2691, Height = 23, Length = 13, so, we get for the width,

Width = (2691)/((23)(13))

Width = 117/13

Width = 9

So the width is 9 cm

Answer:

9 cm

Step-by-step explanation:

Let's use the formula for the volume of a rectangular prism:

Volume = length * width * height

We know that the volume is 2,691 centimeters, the length is 13 centimeters, and the height is 23 centimeters.

We can plug these values into the formula to find the width:

2,691 = 13 * width * 23

2691=299*width

width=2691/299

width = 9 centimeters

Therefore, the width of the rectangular prism is 9 centimeters.

A pizza that is 20 inches in diameter provides sevenfull meals.

Given that a pizza that is 12 inches in diameter provides four full meals, we need to find the number of meals provided by a pizza that is 20 inches in diameter.

To find the number of meals provided by a pizza that is 20 inches in diameter, we can use the following proportion:

12 inches : 4 meals = 20 inches : x meals

where "x" represents the number of meals provided by a pizza that is 20 inches in diameter.

Cross-multiplying, we get:

12 inches × x meals = 20 inches × 4 meals

x = (20 inches × 4 meals) ÷ 12 inches

x = 6.67 meals

Therefore, a pizza that is 20 inches in diameter provides 7 full meals.

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Answer:

-2c^13

hopefully i helped :)

Answer:

The slope is 2/3 and the intercept is ( 0 , 6 )

sorry if I am wrong

While helping a friend in need is understandable, it is important to balance personal relationships with ethical considerations, legal obligations, and the long-term interests of the company and its stakeholders. Opting for the most qualified candidate ensures fairness, enhances company performance, and maintains the trust of employees, customers, and the community.

(a) Strictly legal viewpoint: From a strictly legal standpoint, the decision should be based on merit and qualifications rather than personal relationships. Hiring decisions should follow fair and non-discriminatory practices, adhering to employment laws and regulations. If there are more qualified applicants, it may not be legally justifiable to hire a friend who is less qualified.

(b) Moral and ethical viewpoint: From a moral and ethical perspective, the decision becomes more complex. On one hand, helping a friend in need is a noble gesture and demonstrates loyalty and compassion. However, from an ethical standpoint, it is important to consider fairness and equal opportunity for all applicants. Favouring a friend over more qualified candidates may be seen as unfair and could compromise the integrity of the hiring process.

(c) Long-term best interest of the company: Considering the long-term consequences for the company, it is essential to prioritize the overall success and effectiveness of the organization. Hiring the most qualified candidate ensures that the company benefits from the highest level of competence and expertise. This approach can lead to better performance, productivity, and ultimately, long-term success. Ignoring the qualifications of other candidates in favor of a friend could create resentment among employees, undermine morale, and potentially harm the company's reputation.

Perspective of various groups:

1. Customers: Customers expect to receive quality products or services from a company. Hiring a less qualified friend may result in lower-quality output, potentially disappointing customers and damaging the company's reputation.

2. Stockholders: Stockholders invest in a company with the expectation of financial returns. Hiring the most qualified candidate increases the likelihood of the company's success and profitability, which benefits stockholders in the long run.

3. Employees: Employees seek a fair and equal opportunity to advance within the company. Hiring a less qualified friend over more deserving candidates can create a sense of unfairness and demotivation among employees, leading to decreased morale and potential conflict within the workplace.

4. Government: Government regulations typically require equal opportunity and fair hiring practices. Hiring a friend who is less qualified may violate these regulations and could lead to legal consequences and reputational damage for the company.

5. Community: The community expects businesses to operate ethically and contribute positively to society. Prioritizing merit-based hiring practices promotes fairness and equality, enhancing the company's reputation within the community.

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If the​ P-value for a particular test statistic is 0.31​, she expects results at least as extreme as the test statistic in about 31 of 100 samples provided the null hypothesis is true. As this event is not​ unusual, she will not reject the null hypothesis.

A hypothesis predicts the result of the research. It is an assumption that is based on some evidence. A hypothesis plays a crucial role in testing the significance of differences in experiments and between observations. Null means that have no value i.e. zero. In statistics, the null hypothesis is a type of hypothesis that suggests that no statistical relationship and significance exist in a set of given observations.

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The given differential equation is not linear because it involves the product of x and t. However, it is separable, and we can integrate both sides to find the solution.

The given equation is 9xt(dx/dt) = e^x. To determine whether this equation is separable, linear, or both, we need to rearrange it into a standard form.

Dividing both sides by 9xt, we get:

(dx/dt) = e^x / 9xt

This equation is not linear because it involves the product of x and t in the denominator. However, it is separable because we can separate the variables x and t by writing the equation as:

9xt(dx/dt) = e^x

9x dx = e^x dt/t

Integrating both sides, we get:

4.5x^2 = ln|t| + C

where C is the constant of integration.

Therefore, the given equation is separable but not linear.

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Answer:

11x will be the answer

Step-by-step explanation:

Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.

The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²

f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of  .f(x) =x²-2x+1

Rewrite the given function f(x).

f(x) =  (x-1)²

Now, the graph is stretched vertically by a factor of 2.

= 2(-x-1)²

reflect the graph about the y-axis.

2(x+1)²

move to the left by 3 units.

= 2(x+3+1)²

=2(x+4)²

The function g(x) =2(x+4)²

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The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

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.

The numerical expression is given below.

⇒ 12 × [6.3 + 3 × (1.9)]

Simplify the numerical expression, then we have

⇒ 12 × [6.3 + 3 × (1.9)]

⇒ 12 × [6.3 + 5.7]

⇒ 12 × 12

⇒ 144

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

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Answer:

See below

Step-by-step explanation:

Equation 1:

Step 1:

6 : 9 = x : 54      Ratio

Step 2:

9x = 324     Multiply

Step 3:

36 small dogs       Divide

Equation 2:

Step 1:

6 : 9 = x : 12       Ratio

Step 2:

9x = 72     Multiply

Step 3:

8 small dogs   Divide

First Answer:

36 small dogs

Second Answer:

8 small dogs

Hope This Helps :)

The new trapezoid is parallel to the side PS of the original trapezoid will be AD.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Trapezoid PQRS is rotated counterclockwise 90° about the origin to create trapezoid ABCD.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The new trapezoid is parallel to the side PS of the original trapezoid will be AD.

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Problem:

The point at which a graph hits the x-axis is known as :

Solution:

The zero of the function. This point is characterized by the coordinate

(x, y) = (0, y). Notice that at this point, the coordinate x is always zero.

Answer:

\(\displaystyle 10c - 6a = 110\)

Step-by-step explanation:

We are given the equation:

\(\displaystyle 3x^3 - 25x^2 -50x = 0\)

Where a, b, and c are solutions to the equation and where a < b < c, we want to determine the value of 10c - 6a.

To find the solutions of the equation, we can factor:

\(\displaystyle \begin{aligned} 3x^3 - 25x^2 -50x & = 0 \\ \\ x(3x^2 - 25x -50) & = 0 \\ \\ x(3x+5)(x-10) & = 0 \end{aligned}\)

From the Zero Product Property:

\(\displaystyle x = 0 \text{ or } 3x + 5 = 0 \text{ or } x - 10 = 0\)

Solve for each case:

\(\displaystyle x = 0 \text{ or } x = -\frac{5}{3} \text{ or } x = 10\)

We can see that -5/3 < 0 < 10. Thus, a = -5/3, b = 0, and c = 10.

Therefore:

\(\displaystyle \begin{aligned} 10c - 6a & = 10(10) - 6\left(-\frac{5}{3}\right) \\ \\ &= 100 + 10 \\ \\ & = 110 \end{aligned}\)

Option A is a correct representation of the graph of the function,

g(x) = -1/3f(x).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given the graph of the function,

f(x) is the shape of a parabola so the graph is of a quadratic function.

and given g(x) = -1/3f(x)

graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)

so the function is f(x) = x²

so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)

the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.

and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),

so the graph of Option A only follows the required condition.

Hence option A is correct.

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Answer: -101/18

Step-by-step explanation: I think, I don’t know

Answer:

$9.6

Step-by-step explanation:

The computation of the price of the mixture is shown below:

The price of candy is

= 3 lbs × $1.7 per pound

= $5.1

And for other the price is

= 5 × 0.90

= $4.5

So, the total price of the mixture be

= $5.1 + $4.5

=  $9.6

Answer:

$1.2

Step-by-step explanation:

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